UNIT I

BASICS OF WEATHER AND CLIMATE

Shallow film of Air– stratified & disturbed atmosphere – law – atmosphere Engine.
Observation of parameters: Temperature – Humidity – Wind - Pressure – precipitation-
surface – networks. Constitution of atmosphere: well stirred atmosphere – process around
turbo pause – in dry air – ozone – carbon Dioxide – Sulphur Dioxide– Aerosol - water.
Evolution of Atmosphere. State of atmosphere: Air temperature – pressure – hydrostatic –
Chemistry – Distribution – circulation
1 BASICS OF WEATHER AND CLIMATE
WEATHER
Weather is the short-term atmospheric conditions of any particular place, day and time
CLIMATE
It describes larger areas- like countries, or any cities. It is the average of weather conditions
over a long time and space
Difference between weather and climate
• Weather is day-to-day information of the changes in the atmospheric conditions in
any location for a particular time
• Climate is statistical weather information, that provides information about the
average weather condition of a particular location over a long period of time – 30
years
• Weather is affected by temperature, pressure, humidity, cloudiness, wind,
precipitation, rain, flooding, ice storms, etc
• climate is the long term observations of the atmospheric conditions at any location
like humidity, temperature, sunshine, wind, solar radiation, etc.
• The weather may affect the day-to-day occupation, it may hamper transportation
services, agriculture, etc
• Climate affects agriculture, industries
• Changes is observed weather condition very frequently
• climate take a longer time to observe.
• Weather forecasting -observed by the Meteorological Department of any particular
place
• Climate is predicted by the Climate Prediction Centre

1.1 SHALLOW FILM OF AIR

 an especially striking sunset, or a particularly massive and ominous cloud overhead,
to rekindle interest
 size of the human frame, and its usually surface-based viewpoint, can produce very
misleading impressions of the scale of atmosphere at the bottom of which we spend
almost all of our lives
 the Earth's atmosphere has two very different scales.
 Horizontally the atmosphere is enormously larger than we can perceive from a point
on the Earth's surface, just as the earth itself is larger

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  The order of magnitude of the maximum horizontal scale of the atmosphere is of
course that
 of the Earth itself, which is tens of thousands of kilometres, written - 10 000 km
 the vertical scale of the atmosphere is very much smaller than the
 radius of the Earth
 the atmosphere has no definite upper surface. For example its
 density falls continuously with increasing height, from values close to 1 kg m-3 at
 the surface, to values more than ten thousand million (1010) times
 the vertical extent of the
 atmosphere can be usefully quantified by a so-called scale height

 the lowest 100 km of the Earth's atmosphere the decadal scale height for pressure
 Thus pressure a mean sea level (MSL) and at 16, 32 and 48 km above MSL, are about
1000, 100, 10 and 1 mbar respectively
1.2 THE STRATIFIED ATMOSPHERE
 the atmosphere is squeezed into such a shallow layer overlying the surface, the
distributions of temperature, humidity and indeed of almost every observable property
are strongly anisotropic
 vertical structure being usually much more closely packed and vertical gradients
correspondingly larger
 For example, away from the complicating close proximity of the surface,
 temperature decreases with height at a typical rate of about 6°C km - 1 up to heights
of between 10 and 15 km above MSL, whereas the strongest extensive horizontal
temperature gradients – isopleths (lines or surfaces of equal quantity, such as isobars
and isotherms)
 this marked stratification of the structure of the atmosphere, there is an equally
marked stratification of its behaviour
 the Earth's surface is a region dominated by turbulent interaction with the surface
the planetary boundary layer.

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 Its depth varies greatly with time and location, and even with the particular
atmospheric property under discussion, but is often -500 m
 the rest of the atmosphere (about 95% of the total mass) is much less directly
influenced by the surface and is accordingly termed the free atmosphere
 The planetary boundary layer together with the first 10-15 km of the free atmosphere
comprises the troposphere
 The active and cloudy troposphere is separated from the relatively quiet and cloud
free stratosphere above by the nearly horizontal and often very sharply defined
tropopause
 The thin atmospheric layer on the horizon is visible because of light scattered from
air molecules, dust and some cloud. Molecular scattering produced a blue cost in the
original colour photograph
 it is so flattened by gravity and compressibility, and disturbances are much more
isotropic

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1.3 DISTURBED ATMOSPHERE
 Cumulus clouds as big as the mountains they resemble erupt and dissolve in periods
of tens of minutes
 In middle latitudes vortices of continental scale (Fig. 1.1) grow and decay in periods
of a few days
 They are streaked with great bands of cloud which produce rain, snow and locally
hail, and are associated with large areas of depressed atmospheric pressure at the
surface such depressions is extratropical cyclones
 The technical name for such depressions is extratropical cyclones
 Each of these weather systems contains and interact with activity on relatively smaller
scales: all types of cyclone contain cumulus, and
 cumulus contain large turbulent elements
 meteorology - should be the study of everything above the Earth's surface, but in
practice it has come to mean the study of the physical rather than the chemical
nature of the lower atmosphere, especially the troposphere
 to focus on the dynamic, changeable aspects of this nature, leaving the term
climatology to cover the typical and average aspects

• low latitudes centred on longitude 140°E Among the substantial areas of cloud
• there are two which hove the dense
• swirl appearance typical of severe tropical storms:
• Typhoon Dot lies east of the Philippines and Typhoon Cecil lies over Vietnam.

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 • cumulus showing flat bases,
• knobbly sides and tops, and
• the mountainous bulk typical of rapidly growing convective clouds

1.3 PHYSICAL LAWS

 the observed structure and behaviour of the atmosphere can be related to the operation
of physical and chemical laws, and the forecasting directs attention to the former in
particular
 the lower atmosphere appears at least in the laws of statics and dynamics, matter, heat
and radiation
 However, it is emphasized repeatedly specific feature of the atmosphere, no single
law suffices
 for example, the forces acting on a small volume of air, curiously but conventionally
entitled an air parcel.
 In the lower atmosphere there are three such forces, arising respectively from pressure
gradients, gravity and friction.
 At a given time and place there is a resultant F of these forces which is related to the
acceleration a of an air parcel of mass M by a form of Newton's second law of
motion

 the planetary boundary layer there are quite large frictional forces associated with the
relatively intense turbulence

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1.4 CAUSE AND EFFECT
 It is difficult to avoid considering F and a probably because in homes, factories and
laboratories
 Arrange forces to achieve desired effects; but it is important to realize that the natural
laws which man has identified
 For example - a certain pressure gradient force caused air to accelerate, the
terminology would be misleading since the resulting redistribution of air to cause a
change in the pressure gradient force
 to identify cause and effect is strong because it satisfies our innate desire for order -
weather-giving activity
 the planetary boundary layer the dominant types of disturbance are in the cumulus and
larger scales
 examples rest uneasily between statistical uniformity and individual uniqueness.
 In their combination of individuality, regularity and transience, cumulus,
thunderstorms, depressions, hurricanes etc.
 a statement such as “the weakening of the anticyclone over the British Isles is
allowing a belt of rain to move into north-west Ireland'

1.5 THE SUN AND THE ATMOSPHERIC ENGINE

 Solar energy it in the form of visible sunlight, pours continually onto the Earth,
affecting both the surface and the overlying air
 In fact the role of the Sun in determining the condition and behaviour of the Earth's
atmosphere is even greater than our experience of its warmth, or observation of the
growth of cumulus clouds on sunny mornings
 The atmosphere is quite literally solar-powered, and the Sun can be considered as the
prime mover of all atmospheric activity
 Napier Shaw, a distinguished pioneer of modern meteorology, wrote in the early years
of the twentieth century that 'the weather is a series of incidents in the
working of a vast natural engine'
 As in man-made heat engines, heat is taken in at a heat source, and exhausted at a
heat sink and mechanical energy is generated, i.e. massive bodies are made to move
 The source is provided by the absorption of solar energy, mainly at the Earth's
surface, and the sink by the emission of infra-red terrestrial radiation to space
 the atmospheric engine is not constrained by a rigidly pre-ordained structure of
turbines, gear trains etc
 It also controls its intake of solar energy by producing cloud masses which reflect a
very significant proportion of sunlight to space
 these two effects act like a governor which keeps the activity of the engine close to its
normal level
 the behaviour of an engine which continually regenerates and regulates itself is much
more complex and subtle than that of man-made engines, but there is no difference in
underlying principle
 for the moment it is enough to accept that the sun is its furnace

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1.6 TEMPERATURE MEASUREMENT
 Feel hot or cold depending on whether our bodies are having to waste or conserve
heat to maintain their internal temperatures
 At about 37˚ c and these is happening at any moment depends on exposure to
sunlight, terrestrial radiation, wind humidity, health and the time, size and
temperature
 The mercury in glass thermometer was perfected Fahrenheit in the early eighteenth
century to measure air temperature, over a century elapsed before the need for careful
exposure was generally recognized
 Human-body the thermometer is sensitive to solar and terrestrial radiation from which
it must be shielded to isolate the effect of air temperature
 Stevenson screen (Fig. 2.1) is a simple, robust and reasonably satisfactory
compromise solution.
 The white surfaces absorb little sunlight, and the thick wooden walls insulate the
interior from the warming effect of residual solar absorption, and from the warming
and cooling effects of terrestrial radiation
 Walls and floor allow natural ventilation of the interior by available wind.
 The access door is placed on the poleward side of the screen so that direct sunlight
does not enter when readings are taken
 Stevenson screen with open door for thermometer reading, showing the normal dry
and wet-bulb thermometers inside
 The horizontal thermometers are maximum and minimum dry-bulb thermometer
 Two disadvantage:
o It cannot be used at very low temperature. since mercury freezes at about 40˚ c
o It cannot give a continuous record of temperature automatically
 Continuously recording thermometers (thermographs) contain a
bimetallic strip which moves a pen over a clockwork-powered chart drum
 in recent years a wide range of thermometers has been developed making use of the
temperature sensitivity of electrical resistance to produce continuous records.

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1.7 HUMIDITY MEASUREMENT:
 The amount of water vapour in the air is measured by hygrometers
 When evaporation or condensation is the main interest, the most relevant measure is
the relative humidity, which is the ratio of the actual vapour density to the value
which would produce saturation at the same temperature
 Since the saturation vapour density depends only on temperature - a dependence well-
known from laboratory measurement
 Animal tissues, such as hair or skin, respond directly to relative humidity, and this
response is the basis for several simple hygrometers
 Example: HAIR HYGROMETER, a hair is kept under slight tension so that the
decrease in its length with increasing relative humidity is easily registered.
 The length variation is sufficiently regular and repeatable to allow any particular hair
or bunch of hairs to be calibrated in different known relative humidities to produce a
quantitative instrument
 Hair and skin hygrometers have lags - 10 seconds at room temperature, but are much
more sluggish at lower temperature.
 Their simplicity and ability to produce a continuous record (hygrograph) make them
very popular for semi-quantitative purposes
 Some hygrometers measure relative humidity through its effect on the electrical
resistance of a hygroscopic surface, and can be made somewhat more reliable than the
hair and skin types
 Psychrometers measure the humidity of the air from the cooling effect of water
evaporating into it, and their simplicity and reliability make them
 wet-bulb depression is very large (- 10 °C}, whereas it is zero in saturated air, for
example in fog
 Given the wet and dry bulb temperatures
 When the Stevenson screen is inadequately ventilated, the actual humidity of the air
outside

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  the screen is overestimated somewhat, since the air inside the screen is significantly
moistened by evaporation from the wet bulb
 measure of the humidity of the air is the dew-point temperature, or simply dew point,
which is defined to be the temperature of a chilled surface just cold enough to collect
dew from the adjacent moist air
 In a dew-point meter a polished metal surface is chilled progressively below the
temperature of the ambient air
 the dew-point depression below the ambient air temperature is twice the wet-bulb
depression, ranging from tens of degrees in arid air to zero in saturated air

1.8 WIND MEASUREMENT:

 Horizontal wind direction is indicated by vanes which are in principle the same as
those exposed on church steeples and old buildings
 An electromechanical device can be used to give a remote and recordable readout of
the vane direction
 The meteorological convention is to describe the direction of a horizontal wind by the
direction from which it is blowing, as in everyday speech.
 Thus a north-westerly wind blows from the north-west, or equivalently from an angle
of 315°
 The branches of physical science, where the direction of any motion is considered to
be the direction towards which the body of air is moving, but arises naturally from the
age-old practice of sailors and farmers of looking upwind to see impending weather
 Wind speed is measured by various types of anemometer, but because these are
surprisingly difficult to make usefully accurate and reliable
 This famous Beaufort scale was soon extended to include the effects of wind over
land and is still used
 Subsequent measurement by anemometer has associated a range of wind speeds with
each Beaufort number
 The common cup anemometer is insensitive to the horizontal wind direction or
azimuth, unlike the propel/or type which has to be kept pointed into the wind by a
steering vane
 The cups of the former type whirl continually because the drag of the wind is greater
when blowing into the mouth rather than into the back of each cup
 Design the rate of cup rotation can be made almost directly proportional to wind
speed over a usefully wide range of speeds.
 The observations the run of wind is found by converting the number of cup axle
revolutions in a certain time period into a length of wind.
 Divided by the time period used, which ranges from ten minutes to a day depending
on the type of observation, the run of wind yields the average wind speed in this
period
 The only anemometer not requiring prior calibration in a wind tunnel is the pitot tube
type, which measures the excess pressure developed in air
 as it rams into the mouth of a small tube steered into the wind by a vane
 Since the rammed air is more or less completely halted in the process, the air loses all
its kinetic energy, with the result that the excess pressure is proportional to the square
of the wind speed (by Bernoulli's equation) and the instrument is insensitive to low
wind speeds

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  the horizontal component of wind is the only one of interest
 This is largely true because the flattened shape of the atmosphere ensures that the
horizontal wind speeds are usually more than 100 times larger than vertical ones, and
almost always more than 10 times larger
 When the vertical component is to be included, additional vanes and anemometers are
used
 Small-scale turbulence in particular has an important vertical component which is
comparable with the horizontal ones because the turbulence is essentially isotropic
 It is measured from aircraft traversing through them by using routine and specialized
aircraft instrumentations

1.9 PRESSURE MEASUREMENT:

Man is insensitive to naturally occurring pressure variations below the audible
range (say 20 Hz), with the result that the existence of substantial but much slower
variations in atmospheric pressure was quite unsuspected before the development
 of the barometer in the mid seventeenth century
 the barometer has occupied an important place among meteorological instruments
 The basic absolute instrument is still the mercury-in-glass barometer, working on the
same principle as the ones first made by Torricelli in 1644
 Atmospheric pressure acts on an exposed surface of mercury to maintain a column of
mercury in a vertical glass tube whose top end is sealed and evacuated.
 The vertical height h of the top of the mercury column above the exposed surface is
related to the atmospheric pressure p by the barometric equation
p=gph
 where g is the gravitational acceleration and p is the density of mercury
 Marine barometers are mounted in gimbals so that they remain nearly vertical despite
the movement of the ship.
 The reading procedure imposes an effective lag of - 10 s on the mercury barometer
 atmospheric pressure associated with weather systems occur over much longer time
periods
 robust precision aneroid barometer has largely replaced the mercury-in-glass type in
the meteorological network
 A partly evacuated (aneroid) flexible metal capsule expands as the ambient air
pressure decreases
 the capsule movement is displayed by mechanical linkages whose friction
 Barograph the movement of the aneroid capsule is communicated mechanically to a
pen writing on a graph fixed to a drum rotating by clockwork

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  At the moment electromechanical linkages are beginning to be produced which
should give much better accuracy, and instruments using the pressure sensitivity of
electrical properties of crystals

 A Fortin-type mercury barometer

1.10 PRECIPITATION MEASUREMENT:

 Most precipitation reaches the surface as rain, but strictly the term includes all the
forms in which water and ice fall to the surface, which include the various types of
snow and hail, as well as rain and drizzle
 Rainfall measurements are of great interest to hydrologists concerned with the
management of rivers and reservoirs, as well as to meteorologists
 The quantity of rainfall in an observation period is specified by the depth of water
collected on a horizontal area, but because this may be as little as 0.1 mm in a typical
collecting period
 Rain gauges always use funnels to concentrate the precipitation after collection
 The commonest standard gauge has a circular mouth about 130 mm in diameter, and a
much narrower glass measuring cylinder with graduations adjusted to allow for the
concentrating effect of the funnel
 Automatic gauges with wider mouths operate by registering electrically the times
taken to fill small cups beneath the spout of the collecting funnel
 For example - the tipping bucket gauge
 manual gauges are read once or twice per day, which is adequate for many purposes
but obliterates all the interesting variations occurring in the intervals between
successive readings.
 These are revealed by automatic gauges, many of which register the collection of 0.05
mm of rain
 The time charts of rainfall revealed by automatic gauges

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  Rain gauges set inside a turf wall and in a pit, to minimize interference by airflow
over the gauges

 The bucket see-saw tilts into the dashed position when the filling bucket is full

 Rate of rainfall recorded on a Jardi-type gauge

1.10.1 TYPES OF GUAGES:

 X mm of rainfall at gauge A in a certain storm, but what would have been collected
by identical gauges nearby if they had been in operation
 Gauge exposure
 Topographical influence
 Inherent rainfall patterns
 GAUGE EXPOSURE
o The efficiency of collection and therefore the accuracy of a gauge is quite
sensitive to the way in which the collecting mouth is exposed
o Gauge mouths were always raised above the surrounding surface to avoid
flooding or splash-in
o Placing the gauge mouth about 30 cm above the surface has been found to be
an adequate compromise over land
 PROBLEMS OF EXPOSURE
o ship-borne gauges, where spray and the effects of the ship's large bulk and
motion are effectively unavoidable
 TOPOGRAPHICAL INFLUENCE
o Rainfall can be very strongly enhanced over the windward side of high ground
and reduced in its lee
o Important effect on agriculture and water supply
o for example – represented by any feasible gauge network
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  INHERENT RAINFALL PATTERNS
o Showers in particular are difficult to allow for since they often contribute
significantly to local totals, but yet are so small that they tend to slip between
the inevitably sizeable gaps in the gauge network.
1.11 SURFACE OBSERVATIONS
 to be good indicators of the current state of the atmosphere from the point of view of
forecasting, and are complex in ways which make them difficult to instrument.
 For example, the amounts, types and heights of clouds are judged by eye, using
 internationally agreed categories of cloud which have been perfected over the last ISO
years and are now enshrined in the International Cloud Atlas
 The current or present weather is described by selecting one from a series of 99 types
arranged in order of increasing forecasting significance,
 For example, all types of fog are less significant than rain, light rain is less significant
than moderate rain, and the most significant weather type of all is a heavy hail shower
with thunder

1.12 OBSERVATION NETWORKS

 weather in middle latitudes was organized in moving patterns with horizontal scales
of 1000 km or more
 The development of the electric telegraph by Morse in 1844 transformed the situation.
 A network of meteorological observing stations connected by telegraph to a centre for
analysis and forecasting was established in France in 1863, and the USA, Britain
 WWW is geared to record the present state of the atmosphere with just enough detail
and accuracy to permit useful forecasting

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  The complete observing, communicating, and analyzing and forecasting system is
now entitled World Weather Watch (WWW)
 all sea and air transport, and land transport in hazardous conditions, as well as
agriculture and industry, and the public at large
 the networks of surface and upper air stations making synoptic observations have
evolved to fit this role, to the extent that this scale of weather phenomena is now
called synoptic scale
1.13 SURFACE NETWORK
 In regions where such regularity cannot be relied on, efforts are made to ensure that
the observations at 0000, 0600, 1200 and 1800 Z are made and reported
 The treatment of precipitation totals is rather different, since manual gauges are
traditionally read at 0900 and 2100 local time to reveal the systematic differences
between night and day which are so conspicuous over land
 The correction p is calculated from a form of equation, where h is the height of the
station above MSL and p is the fictional air density, which is equal to or closely
related to the air density at the station
 Wind speed increases with height above the ground surface, as well as with distance
from upwind obstructions

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1.14 UPPER AIR NETWORK:
 Observations of wind, temperature, relative humidity and pressure are made by
radiosondes - free-flying balloons released from the upper air stations of the
synoptic network
 The sonde’s are released at 0000 and 1200 Z daily, and climb at about 5 m s _, until
they burst between 20 and 30 km above
 MSL, whereupon the instrument package returns to the surface by parachute for
possible re-use.
 While in flight the temperature, humidity and pressure data are sent by radio to the
ground station, and the sonde's position is monitored by automatically tracking radar.

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  Humidity data are usually ignored above the 10 km level because sensors are unreliable
in the very low temperatures prevailing at these and higher levels
 The alternation of these wind sondes with the radiosondes at six-hourly intervals
provides sufficient resolution in time to define the structure of the troposphere and low
stratosphere associated with synoptic-scale weather and northern hemisphere systems
 Upper air data from sea areas are obtained only from the few weather ships remaining
in the North Atlantic and North Pacific after increasing cost enforced a sharp decline in
numbers in the last twenty years
1.15 SATELLITE NETWORK:
 The first meteorological satellite was launched in 1960 and immediately provided
extremely interesting and useful data
 First, the huge panoramic views of the atmosphere directly revealed and confirmed the
structures of large cloudy weather systems
 Types of satellite orbits
 Sun synchronous
 Geo synchronous
 Meteorological satellites have multiplied and developed considerably since 1960
 a permanent network of satellites is probably now established, although details may
continue changing for years to come
 meteorological satellites are platforms for electromagnetic scanning of the atmosphere
from above - top-side observation
 The data are sent in sequence to a receiving station on Earth for reconstitution of the
whole picture.
 The width of a scan line on the Earth's surface fixes the ultimate limit of resolution
since details less than a few lines across are unresolved

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 The satellite orbits about 860 km (i.e. one seventh of an Earth radius) above the surface,
passing near the poles but making an angle to the meridians which is just enough to
allow the orbit to remain effectively fixed relative to the sun
 The satellite takes about 102 minutes between successive passes near one pole, while
its radiometers scan the swath of planet passing continually below it
 the satellite orbits about 36 000 km above the equator, moving in the same direction as
the rotating Earth.
 Since the orbital period at this distance is exactly one sidereal day, the satellite hangs
vertically above a fixed point on the equator

1.16 CONSTITUTION OF ATMOSPHERE

 The well-stirred atmosphere
 Dry air
 Ozone
 Carbon dioxide
 Sulphur dioxide
 Aerosol
 Water
 Evolution of atmosphere
1.16.1 THE WELL-STIRRED ATMOSPHERE
 It is found that up to about 100 km above sea level the atmosphere consists largely
 of a mixture of gases in remarkably uniform proportions
 with a small and variable quantity of water vapour concentrated almost entirely in the
troposphere
 the uniform mixture dry air to distinguish it from moist air which includes water
vapour as well

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  In addition to these gases there are small quantities of water and ice in the form of
clouds and precipitation, and a population of even tinier particles known as aerosol
particles, all heavily concentrated in the troposphere
 it represents the vertical distributions
 Over 99.90Jo of the mass of dry air in the atmosphere consists of a mixture of
molecular nitrogen, oxygen and argon in the proportions
 the absolute amount of any constituent (in kilograms per cubic metre for example)

DIFFUSIVE AND CONVECTIVE EQUILIBRIA

 The atmosphere is not a static fluid whose properties are to be explained in terms of
some dynamic origin long since past
 including the uniform distributions now in question, must arise from a balance
between continuing competing processes
 Distinguish between processes promoting uniformity and those promoting variability
 It is fairly obvious that mixing tends to promote uniformity
 For example, an uneven distribution of ink in a beaker of water is replaced by a
uniform distribution almost as soon as stirring begins, whether by a stirring rod or
convection from a heated base
 if there were no stirring, but the equilibrium state would take months rather than
seconds to achieve, because molecular diffusion is so very much slower than bulk
stirring
 In domestic circumstance, diffusion in gases is much faster than diffusion in liquids,
because of the much freer molecular motion, but it is still easily swamped by stirring
if the dimensions of the gas volume exceed a few millimetres
 It is incessantly dynamic and active, and yet continually maintaining a nearly steady
state
 Promoting uniformity
 promoting variability
 the lower atmosphere; at great heights the air is so tenuous that molecules can move
considerable distances between consecutive collisions, and since they move at about the
speed of sound, the speed of diffusion can be very high indeed
 In a room-sized volume of air, mixing by either stirring or diffusion tends to even
out all distributions, just as in the case of ink in water
 if the volume of air is at least 1 km tall, gravity will produce a significant lapse of air
density from bottom to top

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 the two types of mixing tend to produce different vertical distributions
 tall air column - each molecular species settles into an
 equilibrium distribution in which the downward drift of its molecules
 Heavier molecules diffuse toward an equilibrium with a steeper lapse of number
density than do lighter molecules
 Diffusive equilibrium under gravity. The specific masses of the heavier molecular
species are greater at low altitudes
 The lighter molecular species are greater at high altitudes
 convective equilibrium The combination of conservative motion and sharing-through-
mixing, endlessly repeated

 the great bulk of the atmosphere is in convective rather than diffusive equilibrium.
 The region in which this dominance prevails is known as the turbosphere, and it
extends from the Earth's surface to an ill-defined turbopause at about the 100 km level,
above which diffusive equilibrium prevails
 the same balance between gravitational separation and turbulent mixing tends to apply to
dust particles etc. whose fall speeds through still air are much smaller than typical
vertical speeds of parcels in the stirring air

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1.16.2 TURBOPAUSE:
 Above about 100 km, diffusive equilibrium produces marked stratification of
constituent gases according to molecular weight
 with the heaviest components concentrating at the lowest levels
 As height increases there is increasing photo dissociation of molecules into their
constituent atoms
 It affects the composition of air above about the 80 km level.
 For example, above about 120 km the reaction
O2 + photon (solar UV) --> 2O
 maintains more than half of the population of oxygen atoms and molecules in the form
of atomic oxygen (0)
 Absorbs solar ultraviolet with wavelengths between 0.1 and 0.2 micrometres warming
which maintains the thermosphere
 the atomic oxygen acts like a gas with half the molecular weight and therefore half the
density of molecular oxygen (02)
 Reduces the density of air at these levels
 Photoionization also increases with altitude. For example, the reaction
O + photon (solar UV) --> Q+ + electron
 maintains a population of ionized oxygen atoms and free electrons, absorbs solar
 photoionization in the upper half of the turbosphere to justify its description as the
lowest part of the ionosphere

1.16.3 DRY AIR:

 air density with increasing height only one millionth of the mass of the atmosphere
nitrogen (N2), molecular oxygen (O2) and Argon (40Ar)
 Argon is chemically inert and is therefore the simplest of the major gases in its
chemical behaviour
 the uniformity of its specific mass throughout the turbosphere, despite its having the
heaviest molecules of the major atmospheric gases
 the isotope 40Ar, which has accumulated throughout Earth's history by radioactive
decay of potassium (40K)
 the solid bulk of the planet and subsequent gradual diffusion to the surface
 40Ar is so slow in comparison with the rate of its dispersion throughout the
turbosphere by mixing
 The half-life for radioactive decay of 40K is 1.3 x 10⁹ years - nearly one third of the
age of the Earth
 Nitrogen in its molecular form accounts for nearly three quarters of the mass of the
atmosphere
 Atmospheric N 2 is fixed and removed from the atmosphere in three main ways whose
magnitudes have been estimated
 fixation by biological micro-organisms, mainly on land
 fixation by lightning and other ionizing processes in the atmosphere
 industrial fixation, mainly to make artificial fertilizers

20
 A particular N2 molecule must spend about 42 million years in the atmosphere
between one denitrification and the next fixation
 The residence time for nitrogen in the atmospheric branch of the nitrogen cycle,
found by dividing the mass of the reservoir
 Any particular molecule may move through the atmosphere very much more quickly
or slowly
 Fixation and denitrification rates are very impressive when expressed in tonnes per
annum
 The residence time for atmospheric N2 is so long that stirring of N2 throughout the
turbosphere
 Oxygen is chemically the most reactive of the major atmospheric gases
 All inorganic terrestrial materials are already fully oxidized
 O2 is consumed by many types of respiration through which living organisms
produce energy by highly regulated oxidation of food, and by decay
 the annual consumption is about 200 units, where a unit is about one millionth (10-6)
of the mass of O2 in the atmosphere
 photosynthesis in the presence of sunlight by green plants on land
C02 + H20 + photon (Solar visible) --+ CH20 + 02
 where CH20 represents the sugars which are the basic foods for the photosynthesizing
organisms

21
1.16.4 OZONE
 A minute fraction of total atmospheric oxygen is maintained in the form of ozone (03)
by photochemical reactions involving solar ultraviolet
o O2 + photon (solar UV) .... 2O
o O2 + O + M --> O3 + M
o O3 + photon (solar UV) .... O2 + O
o O + O3 .... 2O2
 In first reaction maintains a proportion of oxygen in the form of atomic oxygen
 It maintains a proportion of oxygen in the form of atomic oxygen which is very small
in the upper stratosphere and almost zero at lower levels
 In the second reaction atomic and molecular oxygen combine to form ozone
 The third body M of the triple collision can be any other gas molecule
 the ozone is a powerful absorber of soft solar ultraviolet
 This series of reactions maintains a maximum number density of ozone molecules
between the 20 and 30 km levels
 The maximum specific masses - 10 km higher
 the first and fourth reactions balance to maintain a small but not negligible proportion
of oxygen in the form of odd oxygen as distinct from molecular oxygen
 Antarctica have shown a sharp temporary fall in the amount of stratospheric ozone in
late winter and spring
 this ozone 'hole' is being produced by domestic and industrial CFCs
chlorofluorocarbons used in refrigerators and some aerosol

22
1.16.5 CARBON DIOXIDE:
 Carbon dioxide (CO2) interacts with the biosphere in ways which complement the O2
reactions, being produced by combustion and respiration
 the ratio of their molecular weights (44/32)
 the mass of CO2 in the atmosphere is so much smaller than the mass of O2
 the residence time of CO2 in the atmosphere between successive involvements with
the biosphere is only about five years
 Continual exchange with the relatively very large reservoir of c02 dissolved in the
oceans
 CO2 levels in the immediate vicinity may fall 20% below average values
 The burst of photosynthesis by land plants in middle latitudes in spring and early
summer consumes more C02 than is released by respiration
 The weak oscillation observed in Antarctica with a six-month phase shift gives a clue
to the speed of mixing of C02 across the globe in the low troposphere
 The speed is sufficient to carry
 The southern hemisphere oscillation from its source in middle southern latitudes to
the biological desert of Antarctica
 The troposphere, which extends to a little over 10 km in the middle and high latitudes
depicted
 The increase in C02 is much slower than its speed of mixing through the atmosphere,

23
1.16.6 SULPHUR DIOXIDE:
 If sources are too strong or inadequately ventilated, local concentrations
 By natural oxidation of reduced sulphur compounds such as hydrogen sulphide (H2S)
and dimethyl sulphide ((CH3) 2S)
 Irritation and damage to plant and animal tissues are caused
 concentrations of about I ppm are still recorded in some modern cities with the result
that anthropogenic
 S02 is one of the biggest causes of serious lung damage after cigarette smoking
 oxidation of S02 tends to produce S03 which is hydrated to H2S04 in cloud droplets
 Producing acidity far in excess of the natural pH limit of about 5.6 maintained by
solution of atmospheric carbon dioxide
 when there is a stable 'lid' only a few hundred metres above the surface source region
 This century in the industrial heartlands of Europe, North, America and Japan
 Now maintain zones of seriously acidified rain and snow in broad, persistent,
downwind swathes,
 With consequent biological damage to soils, vegetation, rivers and lakes, over areas
which can approach continental scale
 That oxides of nitrogen and other substances and factors are involved

 Norway spruce in Bavaria showing 'classic' crown thinning attributed to acid rain and
associated air pollution.

24
1.16.7 AEROSOL
 An aerosol is a suspension in air of solid and liquid particles
 the very large numbers of solid and liquid particles which are found in the lower
atmosphere
 they range in size from aggregates of only a few hundred molecules to particles about
ten thousand times larger
 Particles with radii less than 0.1 m are called Aitken nuclei because they make up the
great majority of particles
 enter the atmosphere at or near land surfaces, their concentrations are particularly
high in continental air, often exceeding 10⁶ per litre.
 The fall speeds of such tiny particles are - 10 cm per day at most which is slower than
the random Brownian motion
 the Aitken population reduces quite rapidly by Brownian collision and coagulation of
adjacent Aitken nuclei to form larger particles
 Aitken nuclei are also removed by being dragged by water vapour diffusing onto the
surfaces of growing cloud droplets
 Particles with radii between 0.1 and 1.0 um are called large nuclei
 at least ten times less numerous than the Aitken nuclei but comprise nearly half of the
total particulate mass
1.16.8 WATER
 the atmospheric water substance to provide water in all its states and forms vapour,
cloud and precipitation
 For example, the overall specific humidity
 the atmosphere is only about 0.30%, whereas the specific humidity of the warmest
parts of the troposphere often exceeds 3%
 About 97% of the hydrosphere is currently in the oceans
 cover the Earth's surface to a depth of about 2.8 km if evenly distributed
 The hydrosphere is believed to have been formed by outgassing of steam from
volcanoes during the early life of the Earth
 the vapour condensing on the cool exterior to form the oceans

25
  within the hydrosphere, a much more rapid exchange takes place continually as the
water substance moves through the hydrologic cycle
 the vapour content of moist air, condensing to form cloud, and being precipitated back
to the surface
 after movement through groundwater, rivers and lakes
 The flux of water through the hydrologic cycle is very rapid indeed
 the total mass of the hydrosphere is fixed on meteorological timescales
 This precipitation must be balanced on average by evaporation
 the residence time of water substance in the oceans is about 2800 years, but that it is
only II days in the atmosphere.
 This conversion to vapour is maintained by solar heating,
 Either directly as when moist land surfaces are dried quickly in strong sunlight
 Water vapour moves rapidly on the winds and up draughts and downdraughts
 the rapid cooling and cloud formation which take place in rising air
 precipitation which returns water and ice to the surface from all but the smallest
clouds
CLOUD AND PRECIPITATION
 the sharp temperature falls with increasing height imposed by nearly adiabatic cooling
of rising air and warming of sinking air
 As moist air rises from the surface layers in convection and other up draughts
 To saturation as the air expands and cools
 Deep frontal clouds and shower clouds quite quickly return a very considerable
fraction of their cloud water and ice to the surface
 A large fraction of the vapour entering the atmosphere rises little more than a
kilometre or two before condensing to form the clouds
 Noctilucent clouds are occasionally observed well after dusk at altitudes of about 80
km, but their constitution is not well established
 Residence times of the atmospheric water substance in the form of cloud
 Precipitation are very much shorter than the eleven days found for water vapour

 time and date the nearest daylight at sea level is over 10° of latitude further north

26
1.16.9 THE EVOLUTION OF ATMOSPHERE
ORIGINS
 solar system emerged by gravitational agglomeration of gas and dust about
4.6 Gy BP (4600 million years ago)
 The current amount of 36Ar is about 10⁶ times less than the value for the solar
system
 Earth's interior as it warmed by self-compression and radioactive decay
 Initial fast outgassing of water vapour, hydrogen, carbon monoxide and dioxide,
hydrogen chloride and molecular nitrogen (N2) was largely complete
 The water vapour probably condensed quite quickly to form deep Archaean oceans
 the very light hydrogen molecules escaped from the Earth's gravitational field, leaving
the atmosphere dominated by C02 and N2
 Sun's heat output being about 300% below current values
 paleo atmosphere was very different from today's
 carbon dioxide is reduced to a trace
 molecular oxygen (02) is the most abundant gas after N2

EVOLUTION:
 There is no fossil evidence of life
 Absence of photosynthetic production
 Atmospheric 02 levels must have been limited to 10⁻⁹ present values
 Maintained by photolysis of H20 and C02 by solar UV
 The subsequent increase in atmospheric 02 is closely related to the evolution of life on
Earth
 When atmospheric 02 reached about 1% of present values, a new and much more
efficient type of aerobic photosynthesizing organism developed
 Raising oxygen levels
 here is fossil evidence of such organisms from about 1.2 Gy BP, distinguished by the
appearance of a nucleus in each single cell
 Required dissolved oxygen in equilibrium with atmospheric 0 2 levels of at least
100% of present values
 Temporary depletion of C02 which reduced the greenhouse effect and encouraged
 The great Permian ice ages (280 My BP) 40K was decaying radioactively to 40Ar
which slowly diffused
 Present atmosphere has evolved from its paleo atmospheric origins; how a variable
greenhouse effect has maintained
 surface temperatures in the narrow range needed to allow the accelerating evolution of
life

27
1.17 STATE OF ATMOSPHERE
 The vertical profile of temperature
 The vertical profile of Pressure
 Hydrostatic equilibrium
 Chemistry
 Distribution
 Circulation
1.17.1 THE EQUATION OF STATE
 A minute fraction of the mass of the atmosphere consists of the mixture of gases
called air
 how the condition or state of an air parcel depends on its temperature and pressure

 A gas has neither rigidity nor shape the only remaining simple property is its volume
 Relationship between temperature, pressure and volume
 For one mole of ideal gas the equation of state is
p V = R. T

28
  where p, V and T are respectively the pressure, volume and absolute temperature of
the gas, and R is the universal gas constant
 To find an equivalent equation involving the density of the air rather than its volume
V
 This is the meteorological form of the equation of state
p = pR T
 where R is the specific gas constant for the gas
 The densities of ideal gases at the same pressures and temperatures are inversely
proportional to their molecular weights
 A mixture of gases, each with molecular weight M; and specific mass X; behaves as a
single ideal gas with specific gas constant R given by
R = Σᵢ xᵢ R ᵢ
 The equivalent molecular weight of the mixture is M = 1 / Σᵢ xᵢ Mᵢ

1.17.2 THE VERTICAL PROFILE OF TEMPERATURE

 Only the upper turbo sphere in middle and high latitudes in winter
 The first 10-15 km above sea level stand out as being a region in which temperature
 falls sharply and fairly consistently with increasing height
 Temperature lapse rate is closely related to the widespread occurrence of convection
there, both cloudy and cloudless
 For example, the value on the occasion of the radiosonde flight displayed was 6.5 ˚C
km⁻ⁱ
 The cooling occurs as air molecules in the expanding parcel collide with their
retreating neighbours
 Molecular kinetic energy in the process
 When there are no complicating gains or losses of heat
 Exchange between the parcel and its near or distant environment, the process is said
to be adiabatic
 There is a convective equilibrium distribution of specific masses of the constituents of
dry air
 In cloudless air there is a single well-defined temperature lapse rate of very nearly 10
˚C km⁻¹
 In cloudy air the lapse rate ranges continuously from around 5 ˚C km⁻¹ in high
temperatures to the cloudless limit at the lowest temperatures
TROPOPAUSE AND LOW STRATOSPHERE
 there may or may not be a temperature inversion
 below the deep, nearly isothermal layer which makes up most of the low stratosphere
 the non-adiabatic effects of solar and terrestrial radiation on the temperature profile to
be more pronounced
 to maintain the steep lapse rate associated with cloud-free convection
 The upper stratosphere is even more obviously dominated by the diabetic effects of
radiation
 The Earth's surface about 50 km below, is maintained by the absorption of soft
ultraviolet radiation by ozone

29
  temperatures are maintained by a combination of diabetic heating and cooling, and
weak vertical and horizontal movements of air from hotter and cooler regions
 For example: In middle and high latitudes,
 Temperatures throughout the stratosphere fall sharply in winter
 As solar warming is reduced Cooling by net infra-red emission continues
 Northern hemisphere winters, there is a dramatic sudden warming of the low
stratosphere as air moves and sinks rapidly
 In high latitudes the average temperature of the high stratosphere varies from about
+20 ˚C in summer to -40˚C in winter

1.17.2 THE VERTICAL PROFILE OF PRESSURE

 Decreasing by a factor of about a million between the surface and the turbo pause
 This huge variation in pressure is very regularly distributed in the vertical
 The height interval in which pressure drops to one tenth of any initial value
approximate 16km
 Smoothness: There are no signs of any fine structure in the vertical pressure profile
corresponding to those in the associated temperature profile
 Horizontal pressure variations are very much smaller
 A toy balloon is blown up and burst
 A water manometer will show that the excess pressure inside the balloon just before
bursting is a few tens of millibars
 Low troposphere this is equivalent to the pressure
 over several hundreds of metres of altitude
 over hundreds of kilometres in the horizontal
 over a day or more at a fixed position
 On bursting, the rubber is almost instantaneously removed, leaving a large, localized
pressure excess in the air

30
  A fraction of a second it is distributed over a volume five or six orders of magnitude
larger than that of the balloon

REGULARITY
 The foregoing does not argue that atmospheric pressure should be uniform
 the pressure distribution to be expected when the air is fully adjusted to the prevailing
force
 the equilibrium of air at rest under its own weight, looking for an explanation for the
marked regularity of vertical distribution apparent
 In a static atmosphere the upward and downward forces on any air parcel must
balance
 Gravitational attraction between the parcel and the Earth produces a downward force
 under gravity and raising the pressure at lower altitudes to the point
1.17.3 HYDROSTATIC EQUILIBRIUM
 the difference in atmospheric pressure between two heights to the weight of the
intervening layer of air
 the pressure difference is simply equal to the weight M g of the air column (mass M)
P₁- P₂ = Mg
 where P₁ is the pressure at height z ₁ and P₂ is the smaller pressure at the greater
height Z₂
 the gravitational acceleration g as a separate factor implies that it has the same value
at all heights
 the variation in g can be accommodated by replacing actual height by the very slightly
different geopotential height
 the atmospheric pressure at any level is proportional to the total mass of the
atmosphere in a vertical column
 For example, value of atmospheric pressure at sea level is 1010 mbar
 To find that about 10.3 tonnes of atmosphere rest on each horizontal square metre of
the sea surface

31
  the pressure about 5.5 km above sea level is only 500 mbar, it follows that only about
half of the atmospheric mass lies above this height
∂p = -g p
∂z
 The term ∂p/∂z is the instantaneous vertical gradient of pressure,
 p is the atmospheric density at the same location
 hydrostatic equilibrium of any fluid, whether liquid or gas
 Incompressible and homogeneous liquid like the sea
 By replacing air density using the equation of state
∂p = -p / He
∂z
 where He = RT/g and is termed the exponential scale height
 This integration becomes very simple when the air temperature T does not vary with
height, giving an exponential relationship between pressure and height
p₁ = p₂ exp {- (z₂-z₁) / Hẹ}
1.17.3 THE VERTICAL PROFILE OF DISTRIBUTION
 The vertical distribution of air density in the atmosphere follows from the
distributions of pressure and temperature
 Density with increasing height and a decadal scale height which is never very far from
16 km throughout the turbo sphere
 Only 10 km above sea level the air density is usually a little less than one third of sea -
level values
 The peak of Mount Everest is at about this level
 Air breathing aircraft engines, such as the common turbojet
 Advantage of the reduced airflow drag on the airframe
 For example, high-altitude research balloons floating at an altitude of 50 km above
sea level become extremely cold at night
PRESSURE:
 Horizontal and vertical distributions of meteorological variables and their relationship
with the state and behaviour of the atmosphere

32
  The largest and most persistent horizontal gradients are those in meridional directions
 First the meridional distributions of monthly mean pressure at the base and in the
middle of the troposphere
 the distribution of pressure at the base of the troposphere is represented by the heights
of the 1000 mbar isobar above mean sea level (MSL).
 On average this is between 100 and 200m, which corresponds to MSL pressures of
between 1008 and 1016 mbar
 After allowing for the lapse of about 1.2 mbar per 10 m

TEMPERATURE
 The distribution of the tropopause indicates that in low latitudes
 The troposphere is deepest in low latitudes
 Strong solar heating
 In summer, when the low stratosphere in middle and high latitudes is relatively warm
because of the long hours of daylight,
 The poleward temperature lapse reverses above the 200 mbar level, and the
equatorward lapse exceeds 30˚C at 100 mbar
 Recalling the connection between thickness and layer mean temperature
 The poleward downslope of isobaric surfaces
 The 500 mbar surface must persist and increase up to somewhere between the 300 and
200 mbar levels

33
1.17.4 THE GENERAL CIRCULATION
 the incessant variations of direction associated with weather systems do not cancel out
on averaging, but leave a bias towards some particular directions
 For example, surface winds in middle latitudes show a pronounced westerly bias, in
that winds with azimuths lying between 181 and 359° are more common and stronger
than winds with a component from the east
WESTERLY COMPONENTS
 the troposphere in middle and high latitudes westerly components predominate
strongly over easterly components.
 Surface winds are westerly in middle latitudes extensive and intense westerlies are
found in the upper troposphere
 maximum wind speeds occurring between the 200 and 300 mbar levels

 In winter there is a single very strong maximum in the high troposphere

 averaged wind speeds exceed 40 m s –I
 In summer, the maximum is considerably weaker and lies substantially further
poleward
 each hemisphere a vast belt of the troposphere is moving from west to east at speeds
which even after seasonal and zonal
 Each belt is entitled a circumpolar vortex
EASTERLY COMPONENTS
 Easterly components are apparent at low latitudes in both the low and high
troposphere, and at high latitudes in the low troposphere
 The surface and low troposphere easterlies of low latitudes are the zonal components
of the trade winds
 The summer easterlies in the high troposphere in low latitudes are a downward
extension of the easterlies of the summer stratosphere
 cold winter and the warm summer hemispheres at these altitudes
MERIDIONAL COMPONENTS
 The general circulation flows are the horizontal branches of an enormous pair of
meridional circulations
 Each Hadley cell is completed by a rising branch in the rainy equatorial zone, and a
descending branch in the arid subtropical zones
 The descent and divergence are associated with the zones of elevated sea-level
pressure often called the subtropical high-pressure zones

34
ZONAL AND MERIDIONAL COMPONENTS
 The association of westerlies with poleward motion and easterlies with equatorward
motion is quite
 the movement of air across its spherical shape
 Air at low latitudes at rest on a weather map is actually moving very quickly eastward
because of the Earth's rotation - at over 460 m s- 1 on the equator
 At higher latitudes the eastward motion is smaller because points on or near the
Earth's surface are closer to its axis of rotation.
 For example, the eastward speed at latitude 30° is only 402 m s – 1
 the angular momentum air starting at rest on the equator will arrive at latitude 30° as a
westerly wind - the weather with speed 134m s-¹

35
 UNIT II

ATMOSPHERIC DYNAMICS
Atmosphere dynamics: law – isobaric heating and cooling – adiabatic lapse rates –
equation of motion - solving and forecasting. Forces – Relative and absolute acceleration –
Earth's rotation Coriolis on sphere – full equation of motion – Geostrophy;- Thermal
winds –departures – small-scale motion. Radiation, convection and advections: sun &
solar radiation – energy balance – terrestrial radiation and the atmosphere – Greenhouse
effect- Global warming - Global budget – radiative fluxes - heat transport. Atmosphere
and ocean systems convecting & advecting heat. Surface and boundary layer – smaller
scale weather system – larger scale weather system

2.1 ATMOSPHERIC DYNAMICS

 Heat enters and leaves the atmosphere in many different ways, and the air is usually
warmed or cooled as a result
 For example: solar radiation warms the atmosphere, and cooling is usually the net
result of the absorption and emission of terrestrial radiation
 Large amounts of heat are evolved or absorbed within air parcels as their contained
water substance changes state
 For example: heat is evolved during cloud formation
 Heat of vaporization being released and shared with the air between the swelling
droplets
2.2 THE FIRST LAW OF THERMODYNAMICS
 To allow for its response to the injection and removal of heat, as well as to its
expansion and compression
 Relationship between exchanges of heat and changes of temperature and volume
 the behaviour of unit mass of an ideal gas:

 where dQ is a very small heat input

 dT is a very small rise in temperature, and
 d Vol is a very small increase in the parcel volume Vol
 The first term on the right-hand side of equation represents the amount of heat
input

 the constant of proportionality Cv - the specific heat capacity of the air at constant
volume, where d Vol is zero
 The value of Cv for dry air throughout the turbo sphere is close to 7I7 J K⁻¹ kḡ⁻¹

36
  The second term on the right-hand side of eqn (1) represents the amount of the heat
input which is used in doing work against the surrounding air as the parcel expands
 It is proportional to the expansion and to the internal pressure p of the parcel
 the heat input to the air parcel is shared between the two processes in question:
 warming
 Expansion
 Example: principle of conservation of energy, which is believed to hold under all
circumstances
 the resulting density variations dp are replaced using the equation

 the little pressure change dp is zero shows

 CP is the specific heat capacity of the air at constant pressure

 It follows from the values of the terms on the right-hand side that the value of
 C P for dry air in the turbo sphere is about 1004 J K⁻¹ kg ⁻¹
 the different heat capacity of water vapour makes the CP value for moist air differ
slightly from the value for dry air
2.3 ISOBARIC HEATING AND COOLING
 Much heating and cooling of the atmosphere occurs while air pressure is steady or
nearly so
 For example, the warming of the planetary boundary layer by day
 Its cooling by night occur at pressures determined by the weight of the overlying
atmosphere
 the atmosphere the heating or cooling does not in itself change the air Pressure
 isobaric processes when the term involving dp is zero
 The first term on the right-hand side (CP dT) then completely determines the
relationship between heat exchange and temperature change
 to estimate temperature changes from known gains or losses of heat, or vice versa:

 the isobaric warming or cooling of a mass M of air, rather than unit mass

 On a sunny morning overland, it is often observed that the air temperature near the
ground rises by a couple of degrees per hour for several hours in response to solar
heating
 Observation in depth shows that the warming layer is often about 300m deep
 Assuming the density of air to be 1.2 kg m⁻ᶾ
 the warming of a column resting on one horizontal square metre of ground, the mass
of a 300 m column is 360 kg

37
 Example:
 the sun-warmed ground surface: warm, buoyant parcels rise up, while cool ones sink
down, and the continual mixing distributes the net heat input throughout the
convecting layer.
 Such heat is called sensible heat because it can be sensed directly by thermometers as
the warm and cool air parcels pass by

2.3 THE DRY ADIABATIC LAPSE RATES

 to find the equivalent relation between temperature and height for the dry adiabatic
process
 when an air parcel of density p moves dry adiabatically and vertically through
ambient air
 hydrostatic equilibrium and has local air density p
 small changes in parcel temperature dT and
 height dz are related by

 the density ratio p' I p is equal to the inverse ratio of the absolute air temperature T I
T'

 the lower atmosphere since g variations are - 0.50%

 CP is essentially uniform thanks to very efficient mixing
 When values for g and CP are inserted

38
  The magnitude of the vertical temperature gradient is almost exactly 0.0098˚ c m -I,
or 9.8˚c km – 1. This is known as the dry adiabatic lapse rate

 to rise dry adiabatically through the full depth of the troposphere, it would cool by
about 100° in the shallow
 troposphere of high latitudes, and by about 150° in the deep tropical troposphere
2.4 THE EQUATION OF MOTION
 When a force Facts on a body of mass M, then according to Newton's second law of
motion

 where Vis the velocity of the body and MV is called its momentum
 rate of change can arise because of changing mass or changing velocity or both
 constant mass:

 where a(=dV/dt) is by definition the acceleration of the body

 Newton's second law of motion apparent in eqn (2) is used so widely in meteorology
that it is known simply as the equation of motion
 The vector notation of eqn (2) allows for the fact that both acceleration and force have
magnitude as well as direction
 their directions are the same: acceleration takes place in the direction of the acting
force
 The convention in meteorology is to use the axes with origin 0 at a convenient point
on the Earth's surface
 x, y and z axes pointing horizontally eastward and northward and vertically upward
respectively

39
  The wind speeds in these respective directions are written as u, v and w by the same
convention
For example:

 The vertical component of the equation of motion is as follows, regardless of the

horizontal components

 where Fz is the vertical component of the net force or forces acting on the parcel, and
dw / dt is the parcel's vertical acceleration
2.5 FORCES
 If the gradient of air pressure at a given location is steepest along a certain axis
 there is subjected to a force along that axis toward low pressure, because the pressure
on the up-gradient side of the parcel is greater than on the opposite side
 the force per unit mass of air parcel is
 -(1/p) /∂p /∂n
 where ∂p /∂n is the instantaneous pressure gradient in the direction
 of increasing n (distance along axis)
 p is the density of the air in the parcel
 The minus sign indicates that the force acts in the direction of decreasing p
 with four independent variables - x, y, z and t
 For example, ∂p/ ∂x represents the eastward gradient of pressure at fixed y, z and t
 represents the rate of variation of pressure with time at fixed position (x, y and z)
 the pressure tendency as measured from a fixed barograph

 The pressure gradients along the x, y and z axes are found in the case of any particular
axis n
 the angle between then and z axes is a, then the vertical pressure gradient ∂p/ ∂z is
given by

40
2.4.1GRAVITATIONAL FORCE
 Gravitational attraction between an air parcel and the Earth produces the downward
force on the parcel
 the Earth's surface show that the weight of any body of mass M is given by Mg, where
g has an average value of 9.81 m s⁻² , and varies slightly with latitude and altitude z
 The factor g is known as the gravitational acceleration because it is equal to the
downward acceleration which the body would undergo in the absence of any other
force

2.4.2 FRICTION FORCE

 Friction arises when bodies in contact move with different velocities friction occurs in
all normal fluids
 Such differences appear in the form of shears of air flow
 A strong concentration of vertical shear of horizontal wind is almost universal in the
planetary boundary layer, particularly in its lowest levels
 Assuming the shear to be two-dimensional - both wind speed and direction vary with
height

 Momentum is transferred across wind shears because air itself is transferred

 This occurs in two very different ways in the atmosphere random thermal motion,
and the resulting diffusion of momentum is called viscosity
 Rapid diffusion of momentum is often ascribed for convenience to eddy viscosity
 If γzx is the viscous drag per unit area in the x direction experienced by the horizontal
upper surface of an air parcel because of the relative motion of the air to increase the
momentum of the air parcel in the x direction at just this rate
 If γzx is the viscous drag per unit area in the x direction experienced by the horizontal
upper surface of an air parcel because of the relative motion of the air

41
  According to Newton's empirical law of viscosity, the shearing stress and shear
are directly proportional, the constant of proportionality being the dynamic coefficient
of viscosity p

 the net viscous force per unit mass eastward on a thin horizontal slab of air embedded
in the shear ∂u / ∂z is given by

 Combine eqn 1 and eqn 2

 where v is the kinematic coefficient of viscosity (u / p) of the air.

 The value of v depends mainly on temperature in typical atmospheric conditions and
is about 14 x I0⁻⁶ m2 s⁻¹ in the low troposphere

 the coefficient of eddy viscosity K defined by equation is not related in any simply
predictable way to the thermodynamic state of the air
 Values of K derived from field measurements and equation range across many orders
of magnitude
2.5 RELATIVE AND ABSOLUTE ACCELERATIONS
 Newton's second law of motion (eqn (1) relates resultant force and acceleration as
measured from an unaccelerated observation platform
F = d /dt (MV)
 Acceleration relative to the lift is zero if he is standing steadily

42
 It does not follow that the downward force exerted on his feet by the scales
 It will be equal to his weight
 The lift is accelerating upward the scales will register more than his true weight
 if it is accelerating downward they will register less than his weight
 Now atmospheric motions, including accelerations, are measured from a reference
frame fixed to the Earth
 The meteorological reference frame is rotating and therefore accelerating continually,
 This acceleration must be allowed for when using the equation of motion,
 Otherwise mysterious forces will seem to invalidate Newton's second law of motion
and any predictions based on it
 It represents a model train T running at speed V
 around a circular track of radius R on a turntable which is rotating with angular
velocity Ώ about the centre of the track 0.
 the basic kinematic rule that a body whirling at speed v round a circle of radius r
experiences a continual centripetal acceleration v²/r toward the centre of the circle
 It follows that the centripetal acceleration of the train toward 0 is
 V² I R as measured by an observer rotating with the track and turntable
 (V + ΏR)2/ R as measured by a non-rotating observer
Example:
 one sitting beside the turntable, where ῼR = Vt is the tangential speed of any part of
the track on account of its rotation
 The difference between expressions (2) and (1) represents the centripetal acceleration
which is ignored
 When observations are made from the turntable other than a non-rotating frame an
outward (centrifugal) force acting on the train
 Example - the toy train would tip outward off its rails if the turntable rotation and
train speed
 Multiplying out the bracket of the absolute centripetal acceleration (2) and
 subtracting the relative centripetal acceleration (1)
 find that the difference comprises the two terms

43
2.6 THE EARTH'S ROTATION AND APPARENT G
 If the Earth were a perfect sphere with concentric distribution of mass
 if the gravitational force is measured relative to a fixed point on the rotating Earth's
surface
 A 'mysterious' centrifugal force at all latitudes except the poles
 the centrifugal force: it is a consequence of ignoring the centripetal acceleration of the
Earth-bound reference frame
 to measure g from a frame moving over the Earth's surface
 Consider the consequences of having an equatorward horizontal component of
apparent g
 The atmosphere and oceans would move toward the equator and accumulate
 Adding to the equatorial girth of the fluid planet by denuding the polar regions
 If the oceans were frozen and unable to move accumulation of air in low latitudes
produced a poleward pressure-gradient force everywhere exactly balancing the
equatorward apparent g force
 the equilibrium distribution in which there is no longer any component of apparent g
parallel to the Earth's surface
 the Earth's equatorial radius exceeds its polar radius by about 21 km the strength of
apparent g varies with latitudes

44
2.7 THE CORIOLIS EFFECT
 The largest effects of the Earth's rotation, and leaves the resting atmosphere ocean
effectively dynamically unaffected by that rotation provided
 fluids begin to move relative to the spinning Earth the smaller
 Coriolis effect comes into play, producing terms which are proportional to the wind
and current speeds
 There are temporary accommodations which change as the atmosphere and oceans
ceaselessly shift and vary
 The Coriolis effect to apply to the many different situations in meteorology
 Consider the model train again, but this time moving steadily along a straight track
placed at random on the same rotating turntable
 The train is forced to accelerate laterally
 The train may be moving straight towards
 The turntable axis, or away from it, or along any intermediate line
 The Coriolis acceleration is perpendicular to the track to the left or right depending on
the direction of turntable rotation

 looking at P down the z and y axes separately, with the sense of rotation as for the
northern hemisphere
 the Coriolis acceleration in the directions of the conventional x, y and z coordinates
axes

45
  the only Coriolis component is a horizontal acceleration toward the east (i.e. in the x
direction).
 Westerly winds and up draughts are each associated with two Coriolis components,
and a wind with significant components in all three directions is associated with a
similarly three-dimensional Coriolis acceleration

2.8 THE EQUATIONS OF MOTION

 A balance between accelerations (A terms) and forces (F terms), each of which is a
vector quantity
RA + FA = PGF + GF + FF
 The relative acceleration RA is what is observed from the meteorological reference
frame
 For example, on the large scale, air on a chart of the upper troposphere may be seen
accelerating into the core of a jet stream
 moving in a horizontal circular path around a centre of low pressure, which implies a
centripetal acceleration toward the centre of the circle
 The frame acceleration FA contains only the Coriolis acceleration CA because
the large fixed component of centripetal acceleration
 The frame acceleration FA contains only the Coriolis acceleration CA because the
large fixed component of centripetal acceleration has been accommodated
 the rotating Earth and the use of apparent g instead of true g
 the apparent Coriolis force CF is equal and opposite to the Coriolis acceleration CA
RA = CF+ PGF+ GF+ FF
 The remaining terms on the right-hand side are the pressure gradient force PGF, the
gravitational force GF
 The equation of motion is broken into its x , y and z components
 These equations form an elaborate set whose complete solution

46
2.9 GEOSTROPHIC FLOW
 The scale analysis of the last section therefore suggests that horizontal flow is
determined by the following equations:

 where f = 20 sin is called the Coria/is parameter

 Represents the Coriolis effect arising from the component of the Earth's rotation about
the local vertical
 The relative accelerations du/dt and dv/dt may be an order of magnitude smaller than
the Coriolis and pressure gradient terms
 the relative accelerations and Coriolis terms by setting up the ratio

 Rossby number (Ro), after the Swedish meteorologist who pioneered ways of dealing
with the meteorological implications of the Earth's rotation

 When Ro << 1 the Coriolis terms predominate over the relative acceleration terms,
observations of real and model atmospheres show types of flow characterized by
large, flat vortices about the local vertical
 the Rossby number were zero. Equation 1 would then simplify to

 The approximation is not nearly so good as the hydrostatic approximation which

dominates the vertical component of the equation of motion, but it is good enough to
be extremely useful purely westerly wind (i.e. positive u and zero v) eqns (2) simplify
to

47
 the pressure gradient must be parallel to the y axis, with pressure increasing in the
negative y direction
 it follows that the isobars in this case must lie east-west, which is parallel to the
assumed westerly air flow
 the pressure gradient is directly proportional to wind speed means that isobar spacing
must increase with decreasing wind speed

 the horizontal wind speed v and the horizontal pressure gradient ∂p/ ∂n are connected
in magnitude by

 19th century Buys-Ballot -- as 'low pressure in the northern hemisphere is on the left
hand when facing downwind
 observations of surface winds blowing round extratropical and tropical cyclones
 It is customary to rearrange eqn 3 in the form

 Geostrophic flow can be regarded as equilibrium between pressure-gradient force and

Coriolis force
 the horizontal is always quite small in the lower atmosphere no significant confusion
of vertical and horizontal gradients arises from this practice
 It follows that the contours of an isobaric surface are almost exactly parallel to the
isobars on a closely adjacent horizontal surface
 Buys-Ballot's law holds when lower contours are substituted for lower pressures
 The replacement of ∂p!∂n and ∂Zp/∂n very conveniently removes the variable p from
eqn (4), giving

48
  It shows isobaric contours and actual winds in the vicinity of a polar-front jet stream
over the British Isles.
 The data are taken from synoptic radiosonde ascents on the occasion
 the contours sketched by interpolation between the point measurements of the height
of the 300 mbar surface.
 The wind vectors, measured from the horizontal drift of the radiosondes as they rose
through the 300 mbar surface
 They are parallel to the isobaric contours to within 20° everywhere and 10° over most
of the area.

2.10 THERMAL WINDS

 Geostrophic wind speed is proportional to isobaric contour slope
 Geostrophic wind direction is parallel to isobaric contours on a horizontal plan
 It follows that if the contour slope varies consistently with altitude, so must the
geostrophic wind
 The situation is two dimensional, there is no change of the direction of contour slope
and wind with height slope
 Wind direction with height
 The isobaric slopes at pressures PI and p2
 The geostrophic wind speed directly by subtracting the equations for the two surfaces

49
 The right-hand side of eqn (1) contains the thickness gradient

 The horizontal gradient of the vertical separation of the PI and p2 isobaric surfaces
 The thickness of the layer between the 1000 and 300 mbar surfaces increases sharply
to the right
 The thickness of a layer bounded by any two isobaric surfaces is proportional to the
mean temperature of the layer
 Geostrophic wind speed across such a layer is proportional to the horizontal gradient
of the layer mean temperature
 The thermal wind relation is therefore a relation between geostrophic wind shear and
baroclinity
 Buys-Ballot's law connects the directions of vertical shear and nearly horizontal
temperature gradient:
 In the northern hemisphere low mean temperature is on the left when standing with
back to the geostrophic wind shear

 hydrostatic equilibrium that the connection between layer thickness and layer mean
temperature

 which is the finite difference form of the thermal wind equation

 a very thin layer of air

 Hydrostatic equilibrium holds so very accurately on the synoptic scale

50
2.10.1 THERMAL WINDS-APPLICATIONS
 The circumpolar vortex of westerly winds which dominates the troposphere in middle
and high latitudes
 The thermal-wind relationship appears in the conjunction of the increase of westerly
 winds with height and the meridional temperature gradient imposed by the sun's
unequal input
 Buys-Ballot's law, just as the easterly shear is associated with an equatorward
temperature lapse

 the horizontal temperature gradient is perpendicular to the vector difference between

the low- and high-level winds
 can be applied in finite-difference form to a simple model of a sloping frontal zone
with horizontal width ∆n

 Rearranged to give an expression for the frontal slope ∆z/ ∆n

 frontal slope to be 1:60 in middle latitudes, tending to zero at the Equator, where as
usual geostrophic balance is impossible

51
2.11 GEOSTROPHIC DEPARTURES
 Observations of winds in the entrance region of the core of polar-front jet streams
show that there is a systematic tendency for winds to be Super geostrophic
 The opposite tendency appears in jet exit regions; such tendencies appear in other
cases where synoptic-scale flow - linear acceleration
 To provide for the linear acceleration towards the jet maximum
 The Coriolis force must exceed the pressure gradient force and be angled forward
 the speed which will exactly balance the contour gradient through geostrophic
equilibrium
 Lateral accelerations - accelerations effectively perpendicular to the wind direction
such as those associated with cyclonic and anti-cyclonic rotation of air
 It contains a dynamic sketch of cyclonic flow of air round a horizontal circular path of
radius R in the northern hemisphere
 the wind must have speed V such that the pressure gradient force exceeds the Coriolis
force by V 2 /R
 Examination of the balance of radial forces and acceleration shows

52
 Since the pressure gradient can always be replaced by the Coriolis term involving
 the equivalent geostrophic wind

 Confirming that the balancing wind speed is sub geostrophic.

 Winds satisfying this equilibrium are called gradient winds.
 Expressed as a fraction of the gradient wind
 Speed this geostrophic departure is

 which is a Ross by number for the laterally accelerating flow

 Observations suggest that deficits of actual winds below geostrophic winds often
exceed 20% in vigorous extratropical cyclones
 The streamlines of flow- analysis of observed winds on weather maps may be quite
misleading in this respect for at least two important reasons
• fairly unsteady, so that streamlines are incessantly wriggling
• A succession of streamline segments from a series of maps at consecutive
observation times

• The Coriolis parameter f is zero

• Synoptic-scale flow is therefore analysed by drawing streamlines through the
observed winds
• the pressure gradients apparent on weather maps in those regions are much weaker
than at higher latitudes
• with a laboratory-scale analogue of the atmosphere rather incongruously called the
dish-pan

53
2.12 SMALL-SCALE MOTION
2.12.1 SCALE ANALYSIS
 Consider air flowing in the vicinity of a moderate-sized hill or shower cloud
 The horizontal scale L is - 10 km, which is effectively the same as the vertical scale
set by the depth of the troposphere
 Horizontal wind speeds are by and large set by the synoptic-scale situation
 Vertical wind speeds are about an order of magnitude smaller, so that there is some
asymmetry but very much less than on larger scales
 A list of basic and secondary scales is as follows, others being the same as in the list
for synoptic scales

 The turbulent friction is difficult to scale even roughly

 The magnitudes of terms in the components of the equation of motion

2.12.2 HORIZONTAL MOTION

 In the horizontal, the balance is mainly between acceleration and pressure gradient
larger value of the Rossby number

54
  two orders of magnitude too large for quasi-geostrophic balance
 The time period for air parcels in the influence of such small systems is so short
that the Earth's rotation is largely irrelevant
 Air undergoing a linear acceleration tends to experience falling pressure, and
decelerating air experiences rising pressure
For example
 the bluff side of a hill and decelerates into a stagnation zone on the upwind side of the
hill its pressure rises even if it moves absolutely horizontally, with the result that the
pressure of the whole zone is raised slightly

 Pressure is also raised a little in the lee of the hill

 there are local accelerations which are perpendicular to the local wind, as air flows
round tightly curved trajectories
 The equation for cyclostrophic balance in air moving at tangential speed V around a
circular path of radius R is simply

 Air near the funnel of a tornado often blows at speeds well in excess of 50 m s⁻¹
around paths with radii of curvature of about IOO m, which indicate very large
centripetal accelerations
2.12.3 VERTICAL MOTION
 Vertical motion on the small scale is still dominated by hydrostatic balance between
the vertical pressure gradient and gravity
 vertical accelerations are known to occur at the bottoms and tops of vigorous
cumulonimbus
 for example: the length and timescales of accelerating and decelerating air are locally
each an order of magnitude smaller than the listed values
 For example, cold air pours downwards in shafts of heavy precipitation in
cumulonimbus
 The ambient vertical pressure gradient is therefore related to the ambient air density
by

55
 The upward pressure gradient force and the downward gravitational force on the
convecting parcel can be put together to produce the net upward force

 This deviation from hydrostatic balance is more familiarly known as the buoyant
force
 the direction and magnitude of the associated acceleration depends on what other
forces are acting in addition
 vertical acceleration with net buoyant force by examining the dimensionless ratio
known as the Froude number Fr:

 this is the internal Froude number, to distinguish it from the original number used by
the pioneer fluid dynamicist Froude in modelling ship wakes and waves.
 to rank with the Reynolds and Rossby numbers, and describes the relative importance
of gravity in the dynamical balance
 When Fr is much less than unity in the present context, the buoyancy is much larger
than the vertical acceleration
 Values for B in cumulus are surprisingly small ( 1 /300 ) on account of the very small
temperature excesses in rising air
 It follows from such values and observed strengths and dimensions of updraughts
that Fr values in atmospheric convection cover a considerable range centred on
about 0.2
 Reynolds and Rossby numbers, and describes the relative importance of gravity in the
dynamical balance
 Newton's second law of motion equation, whose vertical component can be written as

 where NFz represents the resultant of all vertical components of force on the parcel.
 The left-hand side of eqn (7 .2) can be expanded to make explicit the effects of
variations in parcel mass M:

 The first term is the familiar product of mass and acceleration.

 The second term represents the rate of increase of momentum which is accounted for
in the rate of increase of the parcel mass rather than acceleration.
 Example - strength of the net force NFz

56
2.13 RADIATION, CONVECTION AND ADVECTIONS

2.13.1 SUN & SOLAR RADIATION

 The Sun is a powerful emitter of electromagnetic radiation in wavelengths ranging
from the ultraviolet to the infra-red
 all solar radiation comes from the photosphere, a relatively shallow shell of
incandescent gases in the outer parts of the sun
 The photosphere has an outer radius of nearly 700 000 km consists mainly of
hydrogen helium at temperatures of nearly 6000 K
 The visible spectrum is centred on wavelengths of about 0.5 µm
 wavelength of maximum solar emission per unit wavelength range
 when the sun is viewed through a spectroscope, the dark Fraunhofer lines produced by
selective absorption of certain wavelengths by relatively cool solar gases outside the
photosphere
 The Earth's cloudless atmosphere modifies the solar spectrum quite significantly
by selective absorption and scattering
 Clouds are much less wavelength-selective reduce the total transmitted power very
considerably when thick enough radiators are known as blackbodies because perfectly
efficient absorbers, they reflect no electromagnetic radiation
 To estimate the power radiated from each square metre of the photosphere to be about
70 MW m⁻²
 Solar radiation floods outward through the solar system, its irradiance falling with
increasing distance from the Sun

 the total is absorbed by the planets and interplanetary dust and gas, the same
total radiant flux must pass through any spherical surface concentric with the Sun
 Simple geometry then shows that the irradiance I at any distance R from the sun is
related to the photospheric emittance I, by
I = Is (Rs / R)²
 where Rs is the radius of the photosphere

57
2.13.2 THE EARTH’S ENERGY BALANCE
 The Earth's composite system of atmosphere, ocean and land surface undergoes
irregular vacillations between warm and glacial epochs on timescales ranging from
10⁴ to 10⁸ years
 The planet Earth are very much smaller than the constituent influxes and effluxes
 The atmosphere, ocean and land surfaces are in a nearly steady thermal state when
viewed over one or more full years
 The next largest is the geothermal flux from the Earth's hot interior
 Four orders of magnitude smaller than the solar constant, being about 0.05 W m⁻²
 When averaged over the whole Earth's surface
 Starlight and the gravitational connections with the Moon and Sun through the Earth's
ocean tides contribute even less
 the Earth emits terrestrial radiation as a uniform spherical black body whose size and
surface temperature completely determine the total power output in the form of
terrestrial radiation
 Since the Earth and Sun subtend small angles when viewed from each other, the
 Earth intercepts solar radiation almost exactly as a disc with radius equal to the
Earth's radius Re
 The rate of interception must therefore be
R²E S,
where S is the solar constant

 not all intercepted radiation is absorbed

 significant amounts are scattered back to space and play no part in the Earth's energy
balance.
 The fraction lost in this way is called the planetary albedo and is denoted by the
symbol a
 The rate of absorption of solar energy is
(l-a) R²E S
 As a spherical blackbody of radius R and absolute temperature TE
 Stefan's law requires the total radiant power output to be 4 R²E S σ T⁴ S
 After rearrangement to isolate TE TE = [ (1-a) S ] ¼
4σ

58
2.14 TERRESTRIAL RADIATION AND THE ATMOSPHERE
 Terrestrial radiation is electromagnetic radiation emitted by a blackbody with
temperature 255 K
 The power spectrum of radiation emitted by a blackbody at this temperature
 Emission spread across wavelengths ranging from about 4 to 100 µm
 with maximum emission per unit wavelength centred around 12 µm, which is
consistent with Wien's law

 the terrestrial radiation spectrum is very much flatter and more spread out in
wavelength
than the spectrum of solar irradiance
 according to Kirchhoff's law, the minor components carbon dioxide and water vapour
absorb it so strongly that the atmosphere is almost completely opaque in substantial
parts of the spectrum of terrestrial radiation
There are two main features
 there is strong absorption by water vapour between wavelengths 5 and 8 µm, and
again beyond 14 µm by water vapour and carbon dioxide; and secondly there is
near transparency in a window centred at about I0 µm

59
  The wavelengths strongly absorbed by water vapour and carbon dioxide
 A layer of air deep enough to contain 300 g of water vapour in a vertical column
resting on a square metre of horizontal surface
 Completely absorbs wavelengths between about 5 and 7 µm estimation shows that the
same layer
 It contains enough carbon dioxide and water vapour to absorb all terrestrial radiation
with wavelengths greater than 14 µm
 Consider a package of radiant energy emitted from the Earth's surface in these heavily
absorbed wavelengths
 By Kirchhoff's law, water vapour and carbon dioxide must emit these same
wavelengths with the same efficiency as they absorb
2.15 THE GREENHOUSE EFFECT
 the difference of over 30°C between the average surface temperature of the Earth and
the effective blackbody temperature of the planet as a whole
 the planet does not act as a blackbody with a single emitting surface situated at the
land and sea surfaces
 the terrestrial radiation emitted to space comes mainly from the atmosphere and
 only in small part from the solid and liquid surfaces
 About 90% of the terrestrial radiation emitted to space comes from the atmosphere
 The highest opaque layer is in the upper troposphere
 The temperature is usually 40° or more below the temperature of the underlying
surface
 to raise the temperatures of land and sea surfaces well above those which would
prevail in the absence of the atmosphere
 This elevation of surface temperatures is called the greenhouse effect because the
 glass of a greenhouse is similarly transparent to solar and opaque to terrestrial
Radiation
 the name is quite misleading because the interior of a greenhouse stays warm
primarily because the glass inhibits convective heat loss to the surrounding air
o quartz greenhouse
o polythene greenhouse
2.15.1 VENUS:
 The planet Venus has an atmosphere about 100 times the mass of the Earth's,
consisting almost entirely of C02 and a thick shroud of sulphuric acid cloud
 An effective blackbody temperature of only 245 Compared with the Earth's 255 K
with less than half the solar constant
 Total amounts of carbon in the surface layers (atmosphere, ocean and crust) of Earth

60
2.15.2 RADIATIVE FORCING
 Response to wholesale injection of carbon dioxide into the atmosphere by artificial
combustion
 To calculate the radiative forcing of the terrestrial energy balance - the resulting
increase in the trapping of outgoing terrestrial radiation
 Two overlapping periods, each starting from the dawn of the industrial revolution, and
the second projecting into the middle of the twenty-first century
 The atmospheric C02 level is expected to have doubled
 Increases in C02 and a number of other greenhouse gases, differing sharply in
efficiency per molecule
Global warming

2.16 GLOBAL WARMING

 Radiative forcing is the reduction in net upward flux of terrestrial radiation at
tropopause levels produced by increasing absorption by greenhouse gases
 This flux to be about 240 W m - 2 initially - equivalent to an effective terrestrial
blackbody temperature of 255 K
 By excess of solar input over reduced terrestrial output, until the flux had been
restored to its original value
 A forcing of 8 W m - 2 requires a rise of just over 2 K at around 255 K
 Greenhouse gas of all (water vapour) because it is not directly anthropogenic
 Average surface warming range from about 2 to 5 oc for a doubling of atmospheric
carbon dioxide
2.16 AVERAGE RADIANT – ENERGY BUDGET
• THE ENERGY BUDGET OF THE EARTH'S SURFACE
• THE ATMOSPHERIC ENERGY BUDGET
• THE SURFACE AND TROPOSPHERE TOGETHER

61
2.16.1 AVERAGE RADIANT – ENERGY BUDGET
• In the last 50 years, people have developed ways of dealing with the complex fine
structure of lines and bands underlying the gross absorption spectrum sketched
• with the result that interactions between the real atmosphere
• The radiation streams to use observed distributions of all the radiatively active
materials to calculate all significant items
• In budgets of radiant energy for the Earth's atmosphere and surface
• averaged distributions of temperature, pressure, water vapour, carbon dioxide, ozone,
cloud and surface albedo
• Early 1960s, data from meteorological satellites have been used to improve some of
the data and to check some of the predicted fluxes

• the radiant energy budget on the global scale was made by London in 1957
• For the global picture, the data were averaged further to produce what is in effect an
annual global average of the budget of radiant energy
• all horizontal variations have been removed by averaging, the picture represents the
vertical distribution of radiant fluxes
• the annual global average rate of input of solar energy per unit horizontal area at the
top of the atmosphere

2.16.2 THE ENERGY BUDGET OF THE EARTH SURFACE

 After traversing the atmosphere, solar radiation reaches the surface as both direct
and diffuse radiation
 The major diffuser is cloud, though air molecules and haze
 The scattering of light by air molecules was first described theoretically in the
nineteenth century by Rayleigh,

62
  Who showed that shorter wavelengths are much more efficiently scattered than longer
wavelengths
 When the scattering bodies are much smaller than the scattered wavelengths
 the preferred scattering of the blue out of the line of sight leaves the direct sunlight
reddened.
 The reddening is particularly noticeable when the sun is near the horizon because the
long path length through
 the atmosphere enhances the blue-biased molecular scattering, and the unbiased
scattering by much larger droplets and particles
 By contrast clouds, mists and most hazes do not alter the colour of sunlight scattered
by their droplets and particles
 Clouds therefore appear nearly white in normal sunlight, and are red near dawn and
dusk only
 The chromatically uniform scattering of all available wavelengths is called diffuse
Reflection
 this accounts for 21 out of 47.5 units of solar radiation reaching the surface, compared
with 7 units scattered by air molecules and dust
 terrestrial radiation consists of large and opposing fluxes which have a relatively
small upward resultant
 The upward flux is equivalent to the output from a blackbody with temperature 288 K
 Cloud, carbon dioxide and water vapour radiate strongly downwards, but do not quite
match the upward radiation from the surface because of the absence of any downward
flux in the window when there is no cloud
2.16.3 THE ATMOSPHERIC ENERGY BUDGET
 Consider the stratosphere first. Three units of solar input are absorbed, mainly in
the form of selective absorption of soft ultraviolet between altitudes of 25 and 45 km
 the input was not balanced by the small net output of terrestrial radiation from the
carbon dioxide and ozone
 This does not mean that there are no convective heat fluxes either within the
stratosphere or between stratosphere and troposphere
 Of the 97 units of solar radiation entering the top of the troposphere,
16 units are absorbed by aerosol particles and water vapour, 30.5 units are
scattered back out to space, mainly by cloud, 3 units are absorbed by cloud, and
47.5units pass through to the surface either directly or after the scattering
 the distributions of temperature, water vapour, carbon dioxide and cloud, the output of
terrestrial radiation from the troposphere to space is 59 units, much of it from the high
troposphere
 This large loss is only partly offset by the net gain of 10 units by terrestrial exchange
with the surface, so that the troposphere suffers a net loss of 49 units by terrestrial
radiation
 Including both solar and terrestrial radiation, it is apparent that the troposphere
suffers a net loss of 30 units of radiant energy, which is equivalent to 100 W m⁻²,
and is exactly equal to the net radiative gain by the surface

63
2.16.4 THE SURFACE AND TROPOSPHERE TOGETHER

 Radiative equilibrium overall, like the stratosphere and like the Earth as a whole
 A large radiant energy imbalance between its two components, amounting to 100 W
m⁻² on a global annual average
 There is no appreciable warming of the surface, or cooling of the troposphere, from
year to year
 A non-radiant heat flux of 100 W m - 2 from the surface to the troposphere

2.17 RADIATIVE FLUXES

 MERIDIONAL DISTRIBUTION OF RADIATIVE FLUXES

 SEASONAL VARIATIONS OF RADIATIVE FLUXES
 DIURNAL VARIATIONS OF RADIATIVE FLUXES
2.17.1 MERIDIONAL DISTRIBUTION OF RADIATIVE FLUXES
 The global energy budget a calculation of the distribution of radiative fluxes with
latitude
 The latitude scale has been deliberately chosen so that equal lengths represent zonal
rings of equal surface area, and it follows that equal areas under the curves
 It represents equal energy flows to or from the Earth
 the meridional distribution of absorbed solar input S to the surface and atmosphere
and the terrestrial output T to space
 The solar input is concentrated in low latitudes because the sun passes near the zenith
there each day, whereas at higher latitudes it misses the zenith by an angle which
increases with latitude, and is equal to the angle of latitude at the equinoxes

 the direct solar beam by scattering and diffuse reflection, and increase the relative
proportion of solar energy which is absorbed
 by the atmosphere rather than the surface
 In annual averages, the resulting concentration of solar input Sin low latitudes

64
  If it were not for the 23.5° angle between the earth's solar orbital and equatorial planes
 The slight bias of S away from the Antarctic is due to the presence of the permanent
ice cap there, which scatters more sunlight to space than does the seasonally broken
sea ice of the Arctic ocean
 The solar and terrestrial fluxes in Fig. 8.7(a) are regrouped in Fig. 8.7(b) to show
the meridional profiles of flux densities of net radiative input to the planet, to
the surface, and to the atmosphere
 poleward fluxes must consist of an exchange of warm and cool air, called advection
 the meridional variation of the emission of terrestrial radiation T is very much smaller
 Since continuing convection keeps most parts of the upper troposphere close to
saturation
 the vapour density there is effectively determined by air temperature alone

2.17.2 SEASONAL VARIATIONS OF RADIATIVE FLUXES

 In middle latitudes the seasonal rhythm of solar input - western margins of continents
 the difference between the winter and summer values of the solar input to the Earth's
surface and atmosphere exceeds 100 W m⁻² poleward of about latitude 25°, and is
about 150 W m⁻²
 A variation of 100% at the lower-latitude limit and much more at higher latitudes, and
is a direct consequence of the march of the Sun into first one hemisphere and then the
other
 The net radiative balance between summer and winter, the latitude zone of maximum
net input shifting from about 15 °N in the northern hemisphere summer to 25 os six
months later

65
  the latitudinal position and magnitude of the maximum of net radiative input
 the extensive meridional gradient of net radiative input stretching from the maximum
in the summer hemisphere to the minimum at or near the winter pole
 the positive maximum and the strongly negative minimum is nearly 500 W m - 2, and
the steep and extensive gradient between them

2.17.3 DIURNAL VARIATIONS OF RADIATIVE FLUXES

 The average surface budget conceals large diurnal variations
 The solar input, averaging 45 units overall, is obviously zero at night
 average 90 units in daylight, assuming a 12-hour day and no variation with latitude
 assuming a semi-sinusoidal profile of solar influx from dawn to dusk
 the noon maximum is 141 units (486 W m - 2) consistent with values estimated from
solar elevation and atmospheric Transmissivity
 Maximum noon values can reach about 320 units (1100 W m ⁻²)
 on average the Earth's surface loses 15 units by net output of terrestrial radiation.
Since five of these are lost direct to space through
 the atmospheric window, which is closed about 500% of the time by cloudy overcast,
 the net loss by the surface in cloudless conditions must be about 10 units
 It follows from all these values that there can be very large diurnal variations
about the average value of 100 W m⁻²
 the net solar and terrestrial radiative input to the Earth's surface.
 On cloudless days at low latitudes a maximum net input of about 1000 W m⁻² at noon
may give way to a net output of about 70 W m-2 during the ensuing cloudless nights
 At higher latitudes the effect of the reduction in noon solar input is modulated by the
increasing seasonal variability of day length and net losses of about 70 W m⁻²
continue throughout the polar nights

66
2.18 CONVECTIVE HEAT FLUXES
 Convection carries the excess heat from the Earth's surface and distributes it through
the depth of the troposphere
 On a global annual average, the convective flux must be 100 W m - 2 at the Earth's
surface and zero
 Such a decrease is consistent with observations of the cumulus family of clouds
 If the Earth were arid, all this convective flux would have to be borne as sensible
heat, warmer air parcels rising and cooler ones sinking to effect a net upward
transport of heat
 presence of water, ice or moist ground at the surface means that the air
 all this convective flux would have to be borne as sensible heat, warmer air parcels
rising and cooler
 An extraction of heat by evaporative cooling at the location of the evaporation and a
delivery of this heat to the location where the vapour condenses to form cloud

 convert a vapour mass flux into its associated flux of latent heat simply by
multiplying by the coefficient of latent heat L
 the convective heat flux between sensible and latent forms has long
 the ratio of sensible to latent heat fluxes is known as the Bowen ratio
 In arid zones such as the subtropical deserts, values are much larger than unity while
in warm, humid zones they are much smaller than unity
 the global hydrologic cycle is nearly steady over time periods of a couple of months
or more
 the total convective flux is defined by the radiant energy budget; the sensible heat flux
is found by deficit to be 37 W m⁻² or 11 budget units

67
2.19 ADVECTIVE HEAT FLUXES
 the annual average fluxes of solar and terrestrial radiation produce a net heat gain for
the planet between latitudes about 32 °N and 38 °S requires a balancing advection of
heat from low to high latitudes
 the thermal expansion of air allows energy to be stored and transported in the form of
the gravitational potential energy of vertically expanded air columns
 the flows of latent heat implicit in net fluxes of vapour, are needed
 the lengths of the local latitude circles to produce average fluxes per unit length of
latitude circle

 'average' is the operative word: at any particular time and place the instantaneous
 advection between the goal-posts might be poleward or equatorward depending on the
local air flow
 fluxes per unit length of latitude circle is to displace the maxima poleward from the
latitudes of reversing radiant balance
For example:
 the middle latitudes of summer hemispheres would seem to require no poleward heat
advection
2.20 WEATHER AND OCEAN SYSTEMS CONVECTING AND ADVECTING HEAT
 there are two main types of weather system at work in the troposphere:
 vertical cumuliform convection associated with the whole
 cumulus family smallest fair-weather cumulus to the largest cumulonimbus
 Largescale systems, such as equatorward flows associated with extratropical cyclones
and the intertropical convergence zone of the Hadley circulation
 Horizontal areas ranging from - 10² m² to - 10 km²
 Temperature excesses in up draughts are usually quite small, seldom exceeding 0.5°C
in small cumulus, and exceeding 5°C only in large cumulonimbus
 The large areas of subsiding, cloud-free air in anticyclones and ridges of high pressure
 The two types often cooperate: cumuli form convection is often quite vigorous in cold
fronts and in the extensive equatorward flows of air which follow them

68
 Areas small cumuliform convection pumps heat into the lower troposphere
 Preparing the air there for subsequent slope convection to the high troposphere in a
front
 For example, the severe tropical cyclone (hurricane, typhoon or cyclone) depending
on geographical zone
 Vertical transport of heat in the oceans is effected by wind-induced stirring of the
surface layers

 The sinking warm water and the cold water continually filling the deeps from high
latitudes maintain
 A dynamic equilibrium in a region of strong vertical temperature gradient, known as
the permanent thermocline
 Advection of heat occurs in both the atmosphere and the surface layers of the oceans
 Regarded as heat engines, the oceans are relatively inactive because both their low-
latitude heat sources and their high-latitude heat sinks are concentrated at the same
level, the sea surface

69
  In middle and high latitudes, the poleward advection of heat in the troposphere is
effected largely by extratropical cyclones and anticyclones
 In low latitudes the meridional advection of heat is directly related to the Hadley
circulation
 Air warmed in the great cumulonimbus populations of the ITCZ drifts poleward in the
high troposphere
 The potential temperature of this air is very high indeed
 As it flows equatorward again at low levels in the trade winds, it has a much lower
potential temperature than it had when flowing poleward in the high troposphere
 heat advection from low to middle latitudes occurs when weather systems develop in
gaps in the chain of subtropical high-pressure systems girdling the hemispheres, and
 the seasonal disruptions associated with the monsoons of the northern hemisphere
land masses in particular

2.21 SURFACE AND BOUNDARY LAYER

2.21.1 INTRODUCTION
• The lower boundary of the atmosphere is the solid or liquid surface of the Earth
• natural and artificial fluid flows, it is observed that there is one or more zone, adjacent
to the boundary
• to the extent that the affected zones are called boundary layers
• Within a few millimetres of any surface, no matter how irregular, air motion is so
strongly restrained by friction with the surface
• Momentum, heat and matter such as water vapour are transported mainly by
• molecular diffusion. This is the laminar boundary layer

 A minute fraction of the total volume of the troposphere, the laminar boundary
 Layer significantly affects large-scale exchanges between the surface and the bulk of
the troposphere
 The turbulent or surface boundary layer extends upwards from the laminar boundary
layer for a highly variable and rather poorly defined distance
 The region strongly influenced by the surface through molecular diffusion,
 The region which the surface influences strongly by eddy diffusion
 the turbulent transport of momentum, heat and matter through it is poorly understood
in detail

70
2.21.2 SURFACE SHAPE AND RADIATION
 The surface of the Earth can be regarded as a horizontal plane with projections and
indentations ranging in size from the microscopic to the mountainous
 the effects of surface shape on direct solar input
 Solar radiation is concentrated on the sun-facing side at the expense of the other the
concentration is total if the other side is in shadow
 In middle latitudes the typical slopes of steep hills and mountains are such that
sunlight often falls nearly normally on sun-facing slopes
 Surface irradiance is proportional to the sine of the angle between the plane of the
illuminated surface and the line of the incident sunbeam

 the ratio of sloping surface irradiance to horizontal irradiance is given by sin (a +

E)/sinE,
 where a is the angle of slope and E is the angle of solar elevation
 the sun at low angles of elevation
Advantage
 distribution of cumulus convection over hilly country
 such convection is driven by very small temperature excesses
 it can be concentrated similarly over sun-facing slopes,

71
 It is producing lines or streets of cumulus drifting downwind from the nursery slopes

 projections such as buildings or vegetation, the concentrations of input are too

localized to have any significant effects on larger scales
 the sunlit face concentrates insolation which would have been distributed over a much
larger area
 The leaves playing the same role as the absorbing and reflecting material in the water
 Example- surface shape blurs the normally sharp interface between atmosphere and
surface, the radiatively active layer being concentrated in this case in the upper parts
of the surface projections
 In many regions, more than half of all surface irradiance
 is diffuse, having been scattered from the incident direct beam by cloud, haze and air
molecules
 diffuse sunlight is very much less directional than direct sunlight
 There is no equivalent of the direct solar beam and the ways in which it is shaded

72
2.21.3 SURFACE HEAT INPUT AND OUTPUT
 the radiative and convective processes injecting and removing heat from
representative parts of the Earth's surface
 Consider first the absorption of solar radiation
 The albedos of terrestrial surfaces range very widely from a few % for damp, dark
soils to over 90% for fresh Snow
 Snow values are localized in high altitudes and latitudes
 the globe values are dominated and held low by the presence of water and vegetation
Over land albedos are mostly between 5 and 20% values for solar input

 consider a horizontal surface with 15% albedo irradiated by the sun from an angle of
elevation of 50° through a relatively clear sky which is transmitting 70% of the solar
beam
 surfaces have emissivity values of between 0.9 and 0.98
 only deserts have emissivities less than 0.9
 the presence of quartz sand which is partly transparent in terrestrial wavelengths
 the value corresponding to the global annual mean surface temperature
2.21.4 SURFACE THERMAL RESPONSE
 There are daily and annual rhythms of heat gain and loss by any part of the Earth's
surface and have estimated their orders of magnitude
o WATER
o LAND
2.21.4.1 WATER
 water is fairly transparent to solar wavelengths, especially in the visible range
 sunlight is attenuated progressively as it travels downwards below the surface
 A small fraction of the incident energy usually reaching depths of tens of metres
 Ocean surface layers increases the depth of water effectively influenced by sunlight,
enhancing their effective heat capacity
 Daily gains and losses of 5 MJ m⁻² would produce temperature rises and falls of 0.125 °C
 Seasonal gains and losses of 500 MJ m⁻² would produce temperature changes of .2.5° C

73
LAND
 Vegetated land surface to surface heating and cooling is very difficult to analyse
 Homogeneous layer of rock or soil as it responds to a regular cycle of warming and
cooling at the surface
 The rate of rise of temperature after the onset of surface heating will increase with the
thermal conductivity k of the intervening layer and decrease with its heat capacity
 The net effect is determined by the thermal diffusivity
K = k/p C
 where p and C are respectively the density and specific heat capacity of the layer material

• The larger the value of K, the more freely is a change in surface temperature
conducted downwards
• the surface heating and cooling cycle has period P, then there is an important depth
parameter D which is known as the damping depth and is given by
D = (k P/)½
2.21.5 SURFACE THERMAL RESPONSE
 annual temperature wave affects a soil layer to a depth of no more than a few metres
 Even in a responsive wet soil, a worm living at a depth of about 6 m would experience
only 10% of the annual temperature range experienced by its cousin living at the
surface
 the effective heat capacity of typical ground layers

74
2.21.6 PARTITIONING BETWEEN SURFACE AND AIR
 the situation at the surface because it ignores the finite effective heat capacity of the
air
 the total heat input H during the warming phase of the surface temperature cycle

 heat transfer in the atmospheric boundary layer is by convection rather than by

conduction, and in the surface layers of the seas
 the amplitude of the surface temperature wave to the heat input H by

2.21.7 THE LAMINAR BOUNDARY LAYER

 Air molecules in contact with a liquid or solid surface are so effectively stuck to it by
molecular attraction that there is no relative motion
 a very little distance from the surface, molecules can move, but only very smoothly
and sluggishly on account of viscous friction
 distance ∂ from the surface, such unsteadiness overcomes the smoothing and damping
effects of viscosity, and the air flow ceases to be laminar

75
  the diffusion of momentum, heat and water vapour through the laminar boundary
layer increases with its thickness
 velocity parameter in the turbulent air beyond the laminar boundary layer which is
called the shear velocity or friction velocity u
u = (r/p)½
 its depth o corresponds to a critical value 10 for the Reynolds number

 Values of r can be measured directly by attaching delicate strain gauges tangentially

to horizontal plates
 the laminar boundary layer covers all exposed surfaces
 For example, sensible heat diffusing from the surface obeys the equation for heat
conduction

2.21.8 TURBULENCE
 the gustiness of all but the lightest winds
 the unsteady dispersion of smoke plumes
Properties
 Turbulent flow is irregular in both space and time
 For example, the wind speed varies continually and widely but shows no trace of
regular oscillations such as might be associated with waves
 The unsteadiness and irregularity typical of turbulent flow represents a large
amplitude, highly chaotic response to inherent instability


 involve statistics ranging from the simple arithmetic mean and root mean square
deviation to the sophisticated power Spectrum
 Turbulence is intrinsically three-dimensional and cannot be adequately described in
fewer dimensions

76
  This handicaps pictorial description and mental conception
 range of atmospheric turbulence is isotropic
 Turbulence is hierarchical
 Inherent instability produces large eddies which in turn produce smaller eddies

2.21.8 THE ORIGINS AND ROLE OF TURBULENCE

• Turbulence persists because air flow is continually disturbed on scales which are
• much too large to be smoothed away by viscosity
• If disturbances of scale 100 m are being introduced into an air flow of average speed 1
m s⁻¹
• Air parcels embedded in the wind shear tend to roll forward about a lateral horizontal
• axis, temporarily becoming the rotating parcel
• a parcel begins to roll about a lateral axis, it tends to generate by friction
• opposing rolls about longitudinal axes on either side
• All rolling parcels have descending air on one side and ascending air on the other
• the magnitude of the dimensionless number - Richardson number

• surface cooling is sufficiently strong to raise the value of ∂ to the point where Ri
exceeds the critical value

• Thermally-driven convection also generates turbulence, provided heating from

• beneath exceeds the ability of the air to transfer heat by molecular conduction
• In a layer of air of depth ∆z and potential temperature lapse ∆, this balance
• is described by the dimensionless Rayleigh number (Ra)

77
• In all terrestrial conditions in which a relatively warm surface maintains a lapse
• turbulence transports momentum, heat and material such as water vapour and aerosol
• this transport occurs whenever air parcels moving in different directions
• the downward transport by turbulence of V momentum through horizontal unit area

• the average value of the vertical mass flux is zero near a horizontal surface
• the momentum flux can have quite substantial values when variations in w and V are
negatively correlated
• The equation simplifies to

• where V' is the instantaneous deviation of V from its average value

• Combining

• which stresses the interpretation of u as a velocity related to the gustiness of winds.

• air flow in terms of average rather than instantaneous values
• It allows for correlations between variations occurring within the averaging period
• The vertical turbulent flux of sensible heat H is given by

• where wT' is the covariance of updraught and temperature

78
2.21.9 THE SURFACE BOUNDARY LAYER
• the distributions and vertical transports of momentum, heat and matter such as water
vapour and carbon dioxide throughout most of the atmospheric boundary layer

• where n is a horizontal axis pointing upwind

• Ignoring vertical variations of air density p, the change ∆r in r to be expected in a
vertical depth ∆z is given by a simple form of eqn

• the constant flux layer because of the vertical uniformity of the vertical fluxes of heat
• consistent expression for the shear ∂V / ∂Z is of the form

• where A is a pure number and U is a velocity characteristic of air flow in the layer
• A great deal of experimental evidence in the atmosphere, and in wind tunnels and
water flows, confirms that this simple relationship actually holds in the form

• where u is the friction velocity

• k is an apparently universal constant with value close to 0.4 named after von Karm

79
2.21.10 AIRFLOW OVER UNEVEN SURFACES
• A number of different processes give rise to patterns of atmospheric behaviour near
the surface which have horizontal scales ranging from - 10 m to as much as 100 km
• SLOPE WINDS
• SEA BREEZES
• HILL AND MOUNTAIN WAVES
• CLOUD AND PRECIPITATION
SLOPE WINDS
• When a sun-facing slope is warmed, a proportion of the buoyant forces generated
• can cooperate on the scale of the sloping surface itself to produce an overall upslope
wind
• Violent katabatic winds can sweep down snow-covered coastal slopes, triggered no
doubt by some shift in the larger-scale air flow
• for example - threaten small boats coasting round Greenland and Iceland
• the climatology of the coastal fringe of Antarctica is dominated by the katabatic gales

SEA BREEZES
• When coastal land is warmed by the morning sun
• the adjacent cooler and denser air over the sea, in a weak but persistent large-scale
buoyancy effect
• The rising air is replaced by the cool, moist air which is drawn inland over the coast
as a sea breeze
• In temperature, humidity and haziness being ascribed to the presence of a sea breeze
front

80
HILL AND MOUNTAIN WAVES
 When an airflow impinges on a hill or mountain, air is diverted horizontally and
vertically by the obstruction
 the forcible elevation of air passing over a hill
 higher layers of air, sets up vertical oscillations of the air about its undisturbed level
 high winds are induced by congestion of air flow near the crest of the hill
 with lower wind speeds where air flow is reduced by stagnation
 a valley which is nearly parallel to the prevailing wind has a channelling effect which
raises wind speeds

81
2.21.11 CLOUD AND PRECIPITATION
• Consider the flow of moist air over a hill or mountain
• A layer which is well stirred by mechanical or thermal convection from the surface up
to cloud base and beyond
• The level of cloud base over the surrounding low ground should be maintained over
the hill
• It is normal to see low cloud blanketing the upwind slopes of hills at levels far below
the base of the nimbostratus producing the general rain
• Air in the lower parts of what is the sub cloud layer over the low ground is
significantly moistened by evaporation from the wet surface and the falling
precipitation
• At higher levels, moist air may be raised to condensation giving humps of cloud
outlining the distorted airflow
• there is a deep layer of nimbostratus, then it is deepened and its rate of precipitation
enhanced over and slightly upwind of the hill
• reduction in cloud on the downwind side of the hill, and a reduction in precipitation
which may produce a climatological rain shadow

2.21.12 SURFACE MICROCLIMATE - VEGETATION

• Conditions near the ground surface are strongly influenced by the presence of
vegetation
• Short grass establishes the value of the aerodynamic roughness length z0
• The binding of the soil by grass roots prevents the production of dust storms
• for example: it is the upper parts of the vegetation which are warmed during the day
and cooled at night
• These gains and losses of heat are only subsequently communicated downwards by
• turbulence, radiation and even by the falling of rainwater from wetted leaves
• The effect on daytime and night time temperature profiles in a stand of vegetation
• the elevation of the radiatively active layer above the ground surface
• to make the microclimate of the layer of the region between the active layer and the
ground much less extreme
• depressing daytime maxima to produce a much smaller diurnal variation

82
2.21.13 SURFACE MICROCLIMATE – FOG
• Fog forms when air close to a surface becomes slightly supersaturated and a layer of
cloud in contact with the surface
Radiation fog
• Radiation fog forms in shallow layers, usually only a few metres deep
• When radiative cooling of a ground surface cools the overlying air below its dew
point
• the air in the first few metres above the surface is almost still, and the fog when it
forms
Advection fog
• Advection fog occurs when relatively warm air is chilled to saturation by overrunning
a sufficiently cool surface

RADIATION FOG REDIATIVE COOLING

83
 • In autumn and winter particularly, the land is usually much cooler than the sea, so that
the invading air is cooled quite sharply
• radiative cooling under clear night skies often completes the production of saturation
and fog
• The top surface of a substantial fog layer replaces the shrouded underlying surface as
the new radiatively effective surface
• The old local name for them is pea soupers, which nicely describes the greeny-brown
obscurity in which they enveloped buildings and people
• Advection fog also forms over the sea

2.22 SMALLER-SCALE WEATHER SYSTEMS

10.1 Introduction
10.2 Cumulus
10.3 Cumulus development
10.4 Cumulonimbus
10.5 Clouds and their environment
10.6 Severe local storms
10.7 Convective systems
10.8 Atmospheric waves
2.22.1 INTRODUCTION
• the structure of the atmosphere both controls and is maintained by atmospheric
behaviour
Types of surface weather:
• cumulus clouds blossom briefly and fade, showering the surface with precipitation
• depressions develop and trail their attendant fronts across thousands of kilometers of
middle latitude warm oceans and drive westward
• At one or two adjacent stations on any particular map. Such systems are called sub-
synoptic in scale
• Meso-scale usually refers to systems or patterns of systems intermediate in scale

2.22.2 CUMULUS
• small cumulus
• clear skies over land in mid-morning, after the stable layer left by the previous night's
cooling has been eliminated by solar heating
• fair-weather cumulus because it is typical of fine summer weather,
• The clouds subsequently develop enough to give a showery afternoon
• The individual cumulus has a very characteristic shape, and is usually just a few tens
of metres
• The lifting condensation level of the well-mixed sub-cloud layer when observations
are available

84
 • Closet inspection (Fig) usually reveals a raggedness of cloud base on a scale of
metres, and a slight but consistent upward tilt in the ambient downwind Direction the
maximum
• updraught speed inside the cloud, because the rising mass of air continually tends to
turn itself inside out like a rising smoke ring
• Two factors may affect the shape of the cloud:
• only a few tens of metres below the base of a convectively stable layer
• the cumulus will be vertically stunted by the loss of buoyancy in air rising into the
• base of the stable layer flattened cumulus in anticyclones often maintains large areas
of stratocumulus

2.22.3 CUMULUS DEVELOPMENT

• some small cumulus seem to avoid the dissolution
• the process of development of such cumulus congestus from small cumulus
• The buoyancy is weak because the temperature excess in a thermal is usually less than
1 °C
• the temperature excess is small because of the weakness of solar warming of the
terrestrial surface
• the loss of buoyancy associated with the evaporative cooling which occurs all over the
upper surfaces of a cumulus
• the formation and persistence of cumulus: because the temperature stratification is
neutral or even
• the ambient air above cloud-base level is sufficiently moist to minimize evaporative
cooling

85
2.22.3 CUMULONIMBUS
• a few spots of rain may reach the surface from a small cumulus congestus, and low
stratocumulus
• the dark bases of such tall clouds, shadowed by efficient backscatter of sunlight by
the thick Cloud
• if a shallow cloud managed to avoid dissolution, fall speed and updraught
• cloud base is reasonably high and the shower is viewed against a pale background
sky, in cool equatorward airflows in middle latitudes.
• The visible thinning of the precipitation arises as the smaller precipitation droplets
• rainfall on any part of the strip is inversely proportional to the total length of the strip
and is greatest when the shower is stationary
• Rainfalls from showers of normal intensity are observed by standard rain gauges to
range from about I to 10 mm correspond to short bursts of moderate to heavy rain,
with rates of rainfall - 30 mm h-I,

• a cumulus congestus, having taken 20 min point of becoming a cumulonimbus by

building slowly up to a vertical extent of several kilometres, begins to grow
• the under surface of the anvil near the tower may hang down in smooth breast-like
shapes known as mammatus
• Initial growth as cumulus congestus is followed by the transition to cumulonimbus

86
 • Precipitation falls in intensive shafts through the interior of the cloud body and into
the clear air beneath cloud base
• The main trunk of cloud dissolves into a temporary veil of precipitation hail is
produced by the relatively rapid accretion of ice and super cooled water onto a falling
frozen embryo
• Hailstones more than a few millimetres across remain unmelted even after falling
through a kilometre or more of warm air
• The air is warm and humid, both factors contributing to the convective potential of the
situation
• trees begin to move a few seconds before the squall of downdraught reaches the
observer

2.22.4 CLOUDS AND THEIR ENVIRONMENT

• between cloudy and cloud-free air as if they were as separate as they appear
• the ambient air around thermals below cloud base, and around the cloudy thermals
• If the individual thermals are scarce and weakly interactive with their surroundings,
the ambient air may wait so long between successive interactions
• the temperature excesses inside clouds are usually so small, less than 1 K in cumulus
humilis and usually less than 5 K
• The vertical scale has been made roughly proportional to the logarithm of height to
enlarge the details of structure in the lower troposphere
• Conditions inside a cloud of the cumulus family are always very close to saturation

87
• The cloudy updraughts are only one part of an unsteady convective cycle which
• must include downdraughts as well
• These up-and-down motions must maintain a close balance of mass flux
• hot towers, on account of their role in piping latent and sensible heat from the warm
• surface to the vicinity of the equatorial tropopause about 15 km above
• In fact such hot towers collectively represent the ascending branch of the Hadley
circulation

88
2.22.5 SEVERE LOCAL STORMS
• When intensity is judged by rates of precipitation, maximum size of hail, squally wind
• speeds, and electrical activity
• Such storms also quite often produce one or more tornadoes intense localized vortices
extending from cloud base to surface
• they produce damaging winds
• number of forecasting and research meteorologists
• severe local storms occur in many regions scattered throughout the world, including
the British Isles, Europe and European Russia, north India, north Indochina and
China,

• there are two features which are usually present when such storms occur accumulating
and then fairly suddenly releasing substantial convective instability
• wind shear distributed through a considerable depth of the troposphere
• two different types of storm - the multicell and the supercell storms
• Different geographical regions, and usually depends on quite
• specific local distribution of sea, land and topography, though the release of
conditional Instability
• the air in the low troposphere well ahead of the advancing cold front is flowing
northwards from the Gulf of Mexico
• In the multicell storm, the wind shear between lower and middle levels
• In the supercell storm the prevailing deep layer of wind shear allows a single
powerful convective cell to become organized into an essentially steady, though
highly dynamic, state

2.22.6 CONVECTIVE SYSTEMS

• individual cumuliform elements can combine and cooperate to produce more
extensive and persistent systems
• Convective cooperation which produce distinctive systems of cumuliform elements
on scales ranging from - 100 m (small scale) to more than 1000 km (synoptic scale)
• cumulus often appear in remarkably straight, parallel lines called streets separation of
adjacent lines is about 1 km
• cumulus streets are a symptom of a larger-scale dynamic structure in the convecting
layer which has the effect of encouraging convection along long parallel lines produce
a very marked degree of alignment
• Satellite pictures of showery air streams over oceans in middle latitudes

89
  Each cell seems to consist of an extensive cloudless area surrounded by a roughly
hexagonal ring of well-developed cumulus
 Cells range in diameter from about 20 to 200 km, depending on larger-scale
meteorological conditions
 cellular structure is observed on the western margins of the great maritime subtropical
anticyclones air flows polewards and eastwards
 All such cells are termed open on account of their open centres
 Oceanic areas covered by extensive stratocumulus are observed to be patterned by
closed cells
 smaller horizontal scale and a much smaller vertical scale than open cells

2.22.7 ATMOSPHERIC WAVES

 atmospheric waves on the small and meso-scales which are at least superficially
similar to waves on the ocean surface
 gravity waves, in which vertical displacement from equilibrium is restored by
gravity, with subsequent under- and overshooting of the equilibrium level giving rise
to a series or train of waves internal
 water waves which are observed under water on horizontal boundaries between
water of slightly different densities
 A vertically diffused layer in which density lapses with increasing height is simply a
convectively stable layer

• Brunt-Vaisala frequency N / 2

• ∂ / ∂Z is the vertical gradient of ambient potential temperature

• the frequency of oscillation increases with stability, just as the rate of vibration of a
spring-mounted mass increases with the stiffness of the spring
• Kelvin-Helmholtz instability of a strongly sheared layer
• Such shearing instability is responsible for the flapping of a flag
• the atmospheric case the sheared layers are horizontal and the restraining force is

90
• the convective stability of the sheared layer
• the Richardson number Ri

• Lenticular clouds - trains of lee waves are the norm in the vigorous cloudy airstreams
associated with extratropical cyclones
• at least some of the strong patterns of rain and snowfall long observed in hilly terrain
• the denser cloud on the upwind side is able to grow much more rapidly by collision
and coalescence
• ice crystals falling through air suddenly forced toward
• water saturation by uplift grow rapidly by the Bergeron-Findeisen mechanism

• Mechanisms such as these are believed to be involved in the enhancement

of rainfall on the upwind flanks of hills and mountains, and its depletion on
the near downwind side
• When first encountered by high-flying aircraft, these were judged most surprising
in cloudless air, where there was no obvious convective source of turbulence, and
became known as clear-air turbulence
• Turbulence of small scale and amplitude is wide- spread in the high troposphere
• Shear waves occasionally produce clouds which pick out the crests of the turbulent
wavelets arranged across the shear are called billow clouds

91
2.23 LARGE-SCALE WEATHER SYSTEMS IN MIDDLE LATITUDES
11.1 Historical
11.2 Extratropical cyclones
11.3 The mature depression
11.4 Three-dimensional airflow
11. 5 Anticyclones
11.6 Waves in the westerlies
11.7 Polar lows and heat lows
11.8 Middle-latitude climates
2.23.1 HISTORICAL
• The middle latitudes must be very large
• It is much larger than can be appreciated from any single viewpoint on the Earth's
surface
• rotation anticlockwise in the northern hemisphere and clockwise in the southern,
which is the observed sense of rotation around low pressure centres.
• The opposite rotation, observed round high-pressure centres, is called anti cyclonic
• in the middle of the nineteenth century, there was no point in trying to organize
networks of people to observe and possibly forecast the movement of storms over
extensive areas, because many storms moved and changed at least as quickly as the
fastest available means of communication - the galloping horse

2.23.2 EXTRATROPICAL CYCLONES

ORIGINS:
• The weather map in the northern Atlantic:
• a front is strung out from west to east across several thousand miles of ocean
• fact since each moves eastwards along the extended front during its life cycle, the
sequence from west to east
• The front which links these depressions is called the polar front in the Norwegian
terminology
• sharp temperature contrast separating the warm air of low latitudes from the cold air
of high latitudes
• For example, in the north Atlantic in winter
• there is a particularly sharp contrast between the cold polar continental air in the
interior of North America
• the warm tropical maritime air over the west
• Atlantic warmed by the powerful poleward flow of very warm water in the Gulf
Stream
• The north-western Atlantic breeds depressions which drive across the Atlantic to
arrive in a mature state in the western approaches to Europe, and the north-western
Pacific and the northern Mediterranean

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LIFE CYCLE AND STRUCTURE
• the warm air pole wards to the east of the centre and the cold air equator wards to the
west and sharpening the horizontal temperature gradients there
• time large areas of continuous precipitation have appeared close to the deforming
front
• cirrostratus fanning north-eastward over the crest of the frontal wave
• the regions of strongest horizontal temperature gradient slope upwards at such very
small angles

• Temperature gradients 5 °C per 100 km are observed where the cold polar air
• undercuts the warm tropical air at the cold front
• a very sharp thermal boundary between the warm sector and the cold air to the north-
west.
• The warm front acts as a weaker eastern boundary

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 • the frontal wave and falling of the pressure minimum at its crest
• as showing the beginning of the mature stage of the life cycle
• The minimum surface pressure may now be tens of millibars below the
undisturbed value, and surface winds
• Pole wards and eastwards ahead of the warm front, enlarging the 'spume‘polar
front jet stream in the high troposphere
2.23.3 FAMILIES OF DEPRESSIONS
• The eastward and poleward motion of the depression from birth to occlusion is not
well represented
• Move and develop rapidly in the prevailing westerly flow, testing the skill of
forecasters
• This residual front still contains considerable contrast between polar air flowing
equator wards down the western side of the depression and the tropical air at lower
latitudes

94
2.23.4 THE MATURE DEPRESSION
• PRESSURE AND WIND
• CLOUD AND PRECIPITATION
• THE JET STREAM
• WARM SECTOR AND COLD FRONT
• DIVERSITY OF WEATHER
• SEA WAVES AND STORM SURGES

PRESSURE AND WIND

• The low-pressure centre lies close to the apex of the surface fronts, and the isobars
form a large pattern with many closed isobars
• The isobars curve round fairly smoothly in the cold air but run almost straight across
the warm sector
• Weather usually moves parallel to the warm sector isobars- a useful rule of thumb in
forecasting
• These sharp kinks are hydrostatically consistent with a boundary between cold dense
air and warm less dense air which slopes up from the position of the surface front
• Moving horizontally from the surface front into the cold air, the increasingly deep
• layer of denser air produces a relatively sharp increase of surface pressure
• This sharp pressure gradient appears as a sharp clockwise turn of the isobars
• The warm sector into the cold surface air across the surface cold front
• Clockwise rotation of wind direction is known as veering
• Anticlockwise rotation is termed backing

95
CLOUD AND PRECIPITATION
• the depression while their individual movement along the overall pattern reveals
• the relative flow of the air in the high troposphere
• This air should move so that cooler air is on the left looking downwind in the northern
hemisphere
• The cloud layer now consists of cirrostratus and altro stratus

• hexagonal ice crystals can produce by refraction a faint but striking halo around the
sun, whose angular radius is 22°c
• Nearer the surface position of the front most of the lower troposphere too is filled
with cloud
• The precipitation consists of large ice crystals sifting down through the very gentle
uplift of air in the front
• If the air in the low troposphere is cold enough, no more than a degree or so above
freezing rain falling into cold air
• the surface at the narrow end of the wedge of cold air near the surface front will
saturate the cold air to produce frontal fog
THE JET STREAM
• The Norwegians originally had little upper-air data, and had to rely on visual
• observations from the surface
• the radiosonde network has changed all that, and the polar-front jet stream
• the jet cores lie in the warm air (although at these levels there is nothing like the
thermal contrast typical of the low troposphere) roughly vertically above the positions
of the frontal zones in the middle troposphere
• Core speeds of as much as 75 m s -I are quite typical in vigorous cold fronts
• The hooked cirrus ahead of the warm front is moving on the eastern flank
• of the jet core there: hence the visible equatorward motion noted earlier.
• the fronts which begins and maintains the production of cloud and precipitation.
• the cold front the air is climbing as it travels pole wards

96
WARM SECTOR AND COLD FRONT
• At least clear of the poleward extremity where stratus and even fog may form as the
humid air is carried pole wards over colder and colder surfaces
• In summer the warmth may become positively balmy when the sun adds to the
intrinsic warmth of the air by heating the underlying land surface
• The dew-point temperature is a much more secure indicator of air-mass differences
• The dew point is highest in the warm sector, indicating its origin in the humid warmth
of lower latitudes
• The cold front may arrive with great vigour, with heavy bursts of precipitation, winds
and thunder
• the frontal cloud mass can be correspondingly much more rapid than its counterpart
• Nimbostratus edge stretching from horizon to horizon as it retreats from the observer
• Facing the retreating edge, small-scale structure such as aircraft condensation trails,
etc
• the upper part of the edge moves quickly from right to left with the jet stream there

DIVERSITY OF WEATHER
• The observer is now about to repeat the sequence of observation and experience
recounted above as another system moves across
• No two systems are the same - in intensity, path, speed, and maturity at time of
passage
• the fronts make quite large angles with their direction of propagation
• the adjacent surface is unaffected by cloud and precipitation

97
 • An unlucky stretch passes under almost the entire length of both the warm and cold
Fronts
• If the location is to the east of the centre of the old low, the winds are persistently
southerly
• Regular inspection of weather maps shows that a huge variety of conditions and
sequences of conditions can arise depending on the orientation of the depression track
• to apply to the southern hemisphere, bearing in mind that the direction of map rotation
about the local vertical, and all related phenomena, reverses there
• a depression and its fronts in southern hemisphere mid-latitudes.

SEA WAVES AND STORM SURGES

• Trees, buildings and crops are liable to damage in the more vigorous storms
• the damage increasing rapidly as the average winds rise above gale force
• The sea surface too becomes increasingly disturbed, with waves increasing in height,
wavelength and celerity as the winds strengthen
• The strong winds raised mountainous seas in the narrow North Channel between
Scotland and Northern Ireland just as the car ferry Princess Victoria was making her
way westwards
• these difficulties also arise from an interaction between wind and water which is
much less obvious, but even more potentially damaging, than the great wind-driven
waves of a storm. This is the so-called storm surge
• depression moves across a body of water, the sea over a considerable area may
respond in ways which produce substantial alterations to the water level
• two types of response
• a static one in which the sea surface behaves like an inverted water barometer
• a dynamic one in which shallow water in confined zones is set in vast oscillation by
the moving and changing tangential wind stress

98
2.23.5 THREE-DIMENSIONAL AIRFLOW
• air moving in the low troposphere around the equatorial side of a mature depression
• two points - air approaching a front near the surface obviously cannot pass through it
as isobaric motion
• wind speed and direction vary so strongly
• Large-scale vertical motion would indeed be insignificant if the atmosphere had
comparable vertical and horizontal scales
• For example - estimated below to be about 10 cm s - 1

99
 • airflow in a mature depression, as revealed by isentropic analysis of many systems in
North America and the north Atlantic
• flow of air upwards and pole wards in and ahead of the advancing cold front, rising
from the low troposphere in the warm air deep in the warm sector
• warm conveyor belt because the air seems to be rising along an invisible ramp fixed in
the moving system

2.23.6ANTICYCLONES
• high surface pressure occurs in the middle of anticyclonically rotating air masses and
the name anticyclone began to be used
• the slowly subsiding air which fills its broad core, and the subsidence inversion which
separates this from the local convecting boundary layer
• Ridges - high pressure which separate members of a family of depressions
• Blocks - the normal eastward procession of depressions in middle latitudes
• Continental highs - anticyclonic circulation in the low troposphere
• Anticyclones develop regularly in winter over continental interiors,the Siberian High
which extends over Siberia and northern asiatic Russia, and influence a considerable
portion of the Asian continent in winter

2.23.7 WAVES IN THE WESTERLIES

• Mid-latitude weather systems look like flat waves on weather maps
• Kelvin-Helmholtz instability which makes a flag flap in response to a difference in
wind speed on either side of its fabric
• for example : weather maps show that the wave-like disturbances of the great mid
latitude weather systems usually move at different speeds at different altitudes
• Cyclone waves
• Long waves
• Topographical locking
• Index cycle

100
CYCLONE WAVES
• when isobaric contours are plotted in the middle and upper troposphere,
• A sequence of such pictures of a developing depression creates an irresistible
impression of an amplifying travelling wave
• when isobaric contours are plotted in the middle and upper troposphere
• A sequence of such pictures of a developing depression creates an irresistible
impression of an amplifying travelling wave

• a shear is associated geostrophically with a layer-deep temperature gradient across the

flow with the north-south baroclinity of the zonal flow
• a shear of the critical value is associated with a horizontal temperature gradient of
about 1°c per 400 km in middle latitudes, or about 5°c across the middle 20° of
latitude
• the crest of the thermal wave lags behind the crest of the wave in the mid-tropospheric
isobaric contours by one quarter of a wavelength

LONG WAVES
• The identification of weather systems with individual waves is the simultaneous
presence of several identifiable wavelengths in any particular observed situation
• Long waves do not depend on the presence of baroclinity
• They do depend crucially on the tendency of absolute vorticity to be conserved in
very large-scale flow in the middle troposphere
• The air will move to higher and higher latitudes, where is larger and larger
• The wave speed relative to the Earth's surface is given by

101
TOPOGRAPHICAL LOCKING
• Positions for long waves in relation to large-scale dispositions of land masses and
topography
• When the air passes over the crest of the mountain ridges, the falling topography
enforces large-scale horizontal convergence which in turn produces cyclonic
curvature
• The air moves polewards, losing cyclonic curvature as it moves to regions with larger
f
• all long waves seem to exert a controlling
• influence over the faster-moving baroclinic
• waves both by steering and amplitude control

INDEX CYCLE
• the long-wave pattern round the whole hemisphere seems to vacillate between
two extremes:
• maximum meridional amplitude of waviness
• Minimum amplitude
• zonal index which is defined to be the zonally averaged pressure difference across
an agreed meridional segment of middle latitudes at some particular level
• for example between latitudes 35° and 55° at the 500 mbar level

102
2.23.8 POLAR LOWS AND HEAT LOWS
• Norwegian cyclone model - one quite dynamic type, the polar low of the eastern
Atlantic, and the relatively static and ephemeral heat low
Polar lows:
• Weak surface lows form in the vicinity of Iceland and move south-eastwards with the
air in the low troposphere
• there are snow showers from cumulonimbus in the wake of the system, just as there
are showers in the wake of a normal depression
• the lower half of the troposphere, limited to little more than 500 km in horizontal
extent
• the shallow but strongly baroclinic zone between the cold airflow off the Greenland
ice cap and the much warmer air
• The two lows apparent produced substantial snow falls in the British Isles, including
some exceeding 250 mm in average depth
• Fresh snow lies to an average depth which is at least ten times the equivalent depth of
rainfall

103
HEAT LOWS
• In warm summer weather in middle latitudes low pressure developing daily over
islands and peninsulas in the absence of any strong synoptic-scale pressure gradients
• These lows are a meso -scale, even synoptic-scale, response to the rapid development
of strong temperature contrasts between land and adjacent sea
• The land surface may soon be 20 °C or more warmer than the sea, and the
temperature difference in the overlying layer of air may be half as large
• For example, if a layer of air 300 m deep warms isobarically by 10°c in roughly 300
K, its density must fall by about 300 k according to the equation of state for a perfect
gas

• the movement is complete when the isobars at the top of the heated layer become
horizontal again
• air equivalent in mass to a 10 m layer of the low troposphere has been removed,
which corresponds to a loss of pressure of a little more than 1 mbar at the surface
• the upward movement of the top of the warming layer is slow

104
 • If the warming is not fully offset by the subsequent nocturnal cooling, because of
a change in the sypnotic situation
• if the sea breeze persists for more than a few hours, it suffers Coriolis deflection

2.23.9 MIDDLE-LATITUDE CLIMATES

• the middle-latitude troposphere is a chronically active zone:
• opposing radiative imbalances at lower and higher latitudes maintain a strong
meridionally baro clinic zone whose deep westerly flow
• The climatic potential in the seasonal and meridional variations of solar elevation
• is very great: at latitude 65° the noon solar elevation - ranges from only 1.5° in
midwinter to 48.5 ° in midsummer, and at latitude40° the range is from 26.5 to 73.5
• Western margins
• Continental interiors

• generating long waves and cyclone waves

• the seasonal march of the sun produces large seasonal variations in solar and
terrestrial radiative fluxes
• seasonal rhythms of mean temperature and diurnal temperature range
• which are especially significant overland (Fig), an account of the small
• effective heat capacities there

105
2.24 LARGE-SCALE WEATHER SYSTEMS IN LOW LATITUDES
• 12.1 Subtropical anticyclones
• 12.2 Monsoons
• 12.3 Tropical weather systems
• 12.4 Tropical cyclones
• 12.5 Low-latitude climates
2.24.1 SUBTROPICAL ANTICYCLONES
• anticyclones nearly girdle the Earth in the tropics and maintain the subtropical high-
pressure zones
• They are very large, persistent, zonally elongated areas of high sea-level pressure, and
are particularly well-developed over the oceans, especially in winter
• skies are not clear, clouds are generally reported to be low, with stratocumulus
• the potential temperature increases sharply with height
• The warmer air has very low relative humidities, often lower than 20%, so that cloud
formation or maintenance
• This contrasts sharply with the air in the low troposphere, below the temperature
inversion

106
 • Observations from mountains or aircraft often show a very sharp haze top which
coincides with the base of the inversion
• SUBSIDENCE
• CLOUD AND SMOG
• AIRFLOW
SUBSIDENCE
•The potential warmth and the low humidity of air in the middle troposphere of an
anticyclone are both consequences
• As air sinks down from high levels it warms, and because there is virtually no cloud
present
• cloud or precipitation to evaporate in the warming air, the specific humidity in the air
is conserved
• The stable layer in the low troposphere of an anticyclone is called the subsidence
inversion because it is maintained by the subsidence of the warm,
• dry air which makes up the bulk of the air in the system
CLOUD AND SMOG
• If the air in the convective boundary layer is normally humid, the lifting condensation
Level will be a few hundred metres
• convection is persistent, a layer of stratocumulus forms, which may be thick enough
to reduce the sunlight
• If the air in the convecting boundary layer is dry enough, then the lifting condensation
level
• convecting air will still be unsaturated when its upward motion is stopped
• the solar warming of the surface may become intense in the middle of the day,
warming the convective boundary layer
• industrial pollution of the confined layer may produce significant enhancement of
concentrations - Los Angeles smog

107
AIRFLOW
• The anticyclonic circulation which is so pronounced in the lower troposphere
• air is persistently subsiding in the middle troposphere it must be persistently
converging in the high troposphere and diverging in the low troposphere
• Near the surface, turbulent friction encourages divergence by enabling air to
• flow with a substantial component of motion outward across the isobars toward
lower pressure
• the subtropical highs such diverging flow feeds air into the warm sectors of the mid-
latitude depressions as they sweep eastward, maintaining their warmth and supplying
air to the warm conveyor belts

2.24.2 MONSOONS
• The word monsoon means season in Arabic, and dramatic seasonal change is a
• common thread which links a wide variety of climatic events occurring annually in
• low latitudes
• the largest meridional shifts occur in the vicinity of the Indian subcontinent
• In January the nearest convergence zone lies about 10° south of the equator
• Mechanisms
• Rainy seasons

108
2.24.3 THE INDIAN MONSOON
• air picks up further large quantities of water vapour from the Arabian Sea and reaches
the west coast of India as the south-west monsoon
• Slow-moving synoptic-scale low-pressure systems, such as subtropical cyclones
• monsoon depressions flows and can produce large areas of rain and quite strong
winds even though surface pressures are depressed by only a few millibars
• the tropical easterly jet stream is a semi-permanent feature of that region in the
summer months at latitudes
• About 15 °N

2.24.4 TROPICAL WEATHER SYSTEMS

• Solar heating of surface and troposphere reaches a broad maximum between the
tropics, and terrestrial radiation
• an amount which leaves a radiative excess varying little with latitude
• Horizontal temperature gradients at any level are usually very small, and differences
of more than - 5°c

109
2.24.5 TROPICAL CYCLONES
• there are several closed isobars on surface charts and strong cyclonic circulation,
cloud and rain over a substantial area
• When winds exceed gale force (19m s- 1 at 10m) they are called tropical storms
• Tropical cyclones form only over oceans where surface temperatures exceed
about 26.5° cover a substantial area at latitudes of at least 5°
• Structure
• Winds
• Warm core
• Pressure and central zone

STRUCTURE
• The dense white ring extending a couple of hundred kilometres out from the centre is
the shield of cirrus fanning out in the high troposphere
• the centre and a thin dull ring mark the inner and outer limits of this dense shield

• The inner zone contains a dense mass of cumulonimbus and sheets of cloud spreading
from them at all levels, circling faster and
• faster as the centre is approached
• the fastest flow is reached in the vicinity of a nearly solid ring of giant cumulonimbus
• Completely encircles the eye

110
WINDS
• Highest winds occur to the right of the centre,
• facing in the direction of the storm's overall motion, where the speeds of rotation and
translation are Added
• Sustained speeds as high as 75 m s- 1 at the 10m level have been recorded
• wind speeds on surfaces and structures increases roughly in proportion to the kinetic
energy of the flow

2.24.6 LOW-LATITUDE CLIMATES

• This covers the largely barotropic region across which the sun is within about 10° of
the zenith at least once per year
• when sharpened by sea breezes or monsoon flows on the equatorial sides of the
subtropical anticyclones
• There are very large meridional gradients of water content, cloud and precipitation
between the arid subtropics
• the wet equatorial zone, and comparable zonal gradients reflecting distributions of
land and sea hot land deserts of the Earth

111
El Nino-Southern Oscillation (ENSO)
• Southern Oscillation because they influence weather over a large part of the south
central Pacific
• Walker circulation, uplift and rainfall are encouraged over Indonesia
• Subsidence along the Equator can split the local ITCZ by a cloud-free lane centred
along the Equator, which is clearly visible in satellite pictures

112
 UNIT III GLOBAL CLIMATE
Components and phenomena in the climate system: Time and space scales – interaction and
parameterization problem. Gradients of Radiative forcing and energy transports by
atmosphere and ocean – atmospheric circulation – latitude structure of the circulation -
latitude – longitude dependence of climate features. Ocean circulation: latitude – longitude
dependence of climate features – ocean vertical structure – ocean thermohaline circulation –
land surface processes – carbon cycle

COMPONENTS AND PHENOMENA IN THE CLIMATE SYSTEM

• One of the fundamental difficulties faced by climate models is that a huge range of
scales
• The main features (components) of the climate system is:
• the atmosphere
• the ocean
• land surfaces
• The cryosphere
• the biosphere
• the lithosphere
• The cryosphere consists of land ice snow and sea ice
• The biosphere, the sum total of all living things on the planet spread throughout the
oceans and land surfaces
• The lithosphere - the “solid” Earth, creates the distribution of ocean basins, mountain
ranges etc., not to mention the occasional volcanic eruption
• One could view the chemical composition to be an additional set of variables
associated with each of the other climate system components
• chemical interactions relevant for climate often involve interactions across these
traditional boundaries
• biogeochemistry is used for the complex interactions of biology with the chemistry of
the climate system
• carbon dioxide and other carbon compounds are exchanged at the ocean and land
surface
• there are a great number of climate processes
• The solar heating acts to create a warm surface layer
• regions is less dense than the colder deep waters below, and thus tends to remain near
the surface
• This mixing carries surface warming down as far as the thermocline, the layer of rapid
transition of temperature to the colder abyssal waters below.

113
 • the absorption of solar heating at the surface results in the atmosphere being heated
from below by heat fluxes from the surface
• moist convection dominates vertical transfer of heat in large parts of the atmosphere
• Contrast between warmer and colder latitudes creates thermally driven circulations at
larger scales. Infrared radiation, also known as longwave radiation
• upward infrared radiation at the top of the atmosphere is termed outgoing longwave
radiation (OLR)
• Exchanges between the atmosphere and the upper ocean include exchanges of several
forms of heat energy,
TIME AND SPACE SCALES
• Period: For phenomena that oscillate in a periodic manner
• Externally e.g. the seasonal cycle (period one year, highly periodic).
• this period is internally determined, e.g. El Niño
• Response time: When the sun comes out, land surfaces heat up in hours, but the ocean
surface has a much longer response time
• the ocean surface layer warms up to the new equilibrium temperature on a time scale
of months
• Lifetime: For phenomena that have an identifiable beginning and end
• The lifetime of a convective cloud is on the order of hours
• the response time of the upper ocean to heating depends on a
• number of factors that influence heat exchange, on the depth of the layer through
which the heating is mixed
• weather system may have a lifetime of days, but a random sequence of weather
events can still affect climate at longer time scales
• scale separation where the slower component can be treated as constant
• land surface vegetation type can be taken as fixed, or changes of vegetation can be
prescribed

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INTERACTION AND PARAMETERIZATION PROBLEM

• Separation of time and space scales does not always guarantee

• for weather systems and convective clouds interacting with the larger scales of the
global circulation
• The image is for visible light that is reflected from clouds and surfaces on the Earth
and detected at the satellite
• The regions of large climatological convection in the tropics can actually be seen on
the particular day
• At mid latitudes, the main regions of climatological precipitation are known as storm
tracks, occurring about 30–50 ◦ N in both Pacific and Atlantic oceans

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• individual storms, and only by averaging over many of these does the shape of the
storm tracks emerge
• climate models represent the atmosphere, dividing up the continuous atmosphere
into a series of discrete boxes
• Rates of change of the average values of temperature, moisture, wind, etc. within
each grid box are computed
• A new value of each variable is computed a short time later, and the operation is
repeated until a simulated year, decade or century has been reached

• the computer representation, only an average across the grid box is included
• These include phenomena such as squall lines, mesoscale convective complexes,
tower-anvil cumulonimbus clouds, etc
• averages must change with the parameters of large-scale fields that affect the
clouds, such as moisture and temperature

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 • The method of representing average effects of clouds over a grid box interactively
with the other variables is an example of what is known as parameterization.
• The horizontal scale of the system would be on the order of 10 km
• the area covered would fit on the order of 100 times into the area of a single GCM
grid box of, say 100 km×100 km

GRADIENTS OF RADIATIVE FORCING AND ENERGY TRANSPORTS

Basics of radiative forcing:
• The essence of radiation in the Earth’s atmosphere is simple: solar radiation comes in
reaching the surface
• Infrared radiation (IR) is the only way this heat input can be balanced by heat loss to
space
• IR emissions depend on the Earth’s temperature; the planet tends to adjust until it
reaches a temperature where this balance is achieved
• This occurs when the upward flux of long wavelength infrared radiation, integrated
over the Earth, balances the flux of incoming short wavelength solar radiation
• when the upward flux of long wavelength infrared radiation, integrated over
• the Earth, balances the flux of incoming short wavelength solar radiation
• the intensity of the radiation (light) as a flux in units of watts per square meter
(Wm−2)
• The electromagnetic spectrum includes, in order of decreasing
• wavelength: radio waves, microwaves, IR, visible light, ultraviolet, X-rays, and
gamma Rays
• radiation depends on temperature in an approximation that does not depend on the
particular substance doing the emitting. This is known as blackbody radiation.
• The differences in input of solar energy between different latitudes tend to create
temperature gradients
• the surface temperatures that would occur at the North Pole in winter time if there
were no atmosphere or ocean.
• There is no incoming sunlight, so there is no direct solar radiative heating
• no ocean, there would be little heat storage since land surfaces have small heat
capacity
• If there were no atmospheric or oceanic motions transporting heat, the infrared
radiation required to balance

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 • longwave radiation varies much less as a function of latitude
(i) the atmospheric and oceanic transports are very effective at reducing
temperature gradients
(ii) the ocean stores some heat from the previous summer and returns it to the Arctic
atmosphere in winter as temperatures start to cool
(iii)Both effects act to reduce extremes
• In the annual average climatology, the rate of heat storage by the ocean is small

ATMOSPHERIC CIRCULATION

• Vertical structure
• Latitude structure of the circulation
• Latitude–longitude dependence of atmospheric climate features
VERTICAL STRUCTURE
• Pressure can be used as a vertical coordinate
• Pressure is proportional to the mass (per unit area) above each level
• In terms of mass, the upper layers of the atmosphere are small
• the stratosphere counts somewhat because of ultraviolet radiation absorption by ozone
• The thermosphere and mesosphere have very little mass.
• Interaction with charged particles from the Sun and the Aurora Borealis occurs at
these levels
• Heating by absorption of ultraviolet radiation by stratospheric ozone is the reason for
the temperature increase with height in the stratosphere

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LATITUDE STRUCTURE OF THE CIRCULATION
• latitudinal gradients in solar energy input are a dominant driver of atmospheric
circulation
• both in a latitude–height plane and in the horizontal, longitudinal variations due to
continents, oceans etc
• This represents the circulation in an average over all longitudes, known as a zonal
average
Main features
• The Hadley cell is a thermally driven, overturning circulation that tends to rise in the
tropics and sink at slightly higher latitudes.
• Warming from the surface near the equator is transferred upward through a deep layer
by convection

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• The descending motion occurs over a broader region than the ascending motion
• descending regions have little rainfall; roughly speaking, they are
• on the losing end of a competition with the deep convective regions that involves
moisture and heat transport feedbacks
• Poleward of the Hadley cell there is a weak zonal average overturning circulation that
appears to run backwards from the point of view of heat transfer
• the Hadley circulation transports heat to about 30 degrees latitude
• The trade winds in the tropics blow westward as they converge slowly toward the
equator

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LATITUDE–LONGITUDE DEPENDENCE OF ATMOSPHERIC CLIMATE
FEATURES
• El Niño depends on east–west contrasts in the Pacific
• A view of the latitude–longitude dependence of the precipitation climatology for
January and July, corresponding to southern and northern summer
Features :
• The intertropical convergence zones (ITCZs)
• The term convergence refers to the low-level winds that converge into these regions is
tropical convection zones
• The tropical convection zones move northward in northern summer, and southward in
southern summer

• These are the monsoon circulations

• From the global scale view, there is the Asian-Austral monsoon, the Pan-American
monsoon and the African monsoon
• The climate is not perfectly symmetric about the equator
• There are substantial variations in longitude the eastern Pacific has little rain the
western Pacific has intense rainfall in all seasons
• In overturning circulations along the equatorial band known as the Walker circulation
• Around 30 ◦–40 ◦ N, mid latitude rainfall is organized in storm tracks over the oceans

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OCEAN CIRCULATION
• Latitude–longitude dependence of oceanic climate features
• The ocean vertical structure
• The ocean thermohaline circulation
LATITUDE–LONGITUDE DEPENDENCE OF OCEANIC CLIMATE FEATURES
• Interaction with the atmosphere is the sea surface temperature (SST)
• SST is warmest in tropics, as expected since the solar input is highest
• SST is not perfectly symmetric about the equator
• There are substantial variations in longitude. For instance, the eastern Pacific is
relatively cold, whereas the western Pacific is warm in all seasons
• rainfall over oceans has a close
• there is an Atlantic convergence zone, even though the SST there is cooler than the
western Pacific

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 • cold waters extend along the equator in the Pacific, in what is known as the
equatorial cold tongue
• the equator, the currents are in the direction of the wind-easterly winds drive
westward currents
• the equatorial counter currents which go eastward in the opposite direction of the
easterly winds
• In the interior of the ocean, currents are strongly influenced by the rate of change of
the zonal

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 • the component of the current that moves poleward is relatively small compared
with the westward component
• The wind is accelerating the water westward, but the water is also influenced by
the Coriolis force,
• which turns water to the right of its motion north of the equator, and to the left
south of the equator

THE OCEAN VERTICAL STRUCTURE

• one cannot understand the vertical structure of the ocean without understanding
• The three-dimensional circulation, including the source of deep waters
• the ocean surface is warmed from above, this tends to produce lighter water over
denser water
• This is referred to as stable stratification, where stratification is the rate of change of
density in the vertical
• this transition defines the thermocline.
• Deep ocean temperatures are as low as a few degrees Celsius

THE OCEAN THERMOHALINE CIRCULATION

• Salinity affects the ocean density
• the deep overturning circulation is termed the thermohaline circulation
• Strong evaporation occurs as it passes through the dry windy subtropics, and it cools
as it moves poleward
• It sinks and flows slowly around through the entire deep ocean
• deep water formation also occurs in the Labrador Sea and some regions around
Antarctica
• the principle remains that a few very small regions control the temperature of the deep
ocean

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LAND SURFACE PROCESSES
• the land surface covers only 30% of the Earth’s surface
The main effects
• Land does not transport or store a significant amount of heat
• The lack of heat storage produces contrast during the seasonal cycle
• Albedo - The high albedo of certain land regions can affect regional circulation and
reduces the average energy input into the climate system
• Evapotranspiration and surface hydrology. The land surface stores moisture as soil
moisture in subsurface layers of soil

• The polar regions stand out with high albedo, especially where ice caps are found
• The annual average albedo is also high in high northern latitude land surfaces
owing to winter snow cover
• regions the albedo changes greatly with season, since during the summer the
vegetated land surfaces are much less reflective
• The Sahara Desert also has high albedo
• Both the albedo and evapotranspiration depend on vegetation
• Thus, models of terrestrial ecosystems now consider carbon storage

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THE CARBON CYCLE
• It involves not only transport and storage in the physical components of the climate
system but interactions with the chemistry and biology of the Earth system
• The cycle involves transfers among reservoirs in the atmosphere, in the ocean and in
land biomass
• The size of each reservoir is given in petagrams of carbon
• One petagram is equal to 1 trillion kilograms
• The fluxes are given in petagrams of carbon per year
• These budgets keep track of the mass of carbon

• The ocean contains large amounts of carbon in various forms: dissolved inorganic
carbon dissolved compounds containing organic carbon
• he total oceanic reservoir of 38,000 PgC, 900 PgC is held in the upper ocean
• The land biomass reservoir, including vegetation, soils and vegetation detritus such as
leaf litter on the forest floor
• the ocean total, at 2300 PgC
• The atmospheric preindustrial content weighs in at only 597 PgC
• Strong exchanges of carbon occur between the atmospheric reservoir and the land and
ocean reservoirs

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 UNIT IV CLIMATE SYSTEM PROCESSES

Conservation of motion: Force – coriolis - pressure gradient- velocity equations –

Application – geotropic wind – pressure co-ordinates. Equation of State – atmosphere –
ocean. Application: thermal circulation – sea level rise. Temperature equation: Ocean – air –
Application – decay of sea surface temperature. Continuity equation: ocean – atmosphere.
Application: coastal upwelling – equatorial upwelling – conservation of warm water mass.
Moisture and salinity equation: conservation of mass – moisture. Source & sinks – latent
heat. Moist processes – saturation – convection – Wave processes in atmosphere and ocean

CONSERVATION OF MOTION
• The winds and currents by Newton’s law
ma = F
• where a is acceleration and F is the total force acting on a body of mass m
• It is convenient to deal with density rather than the mass of these arbitrary parcels
• The acceleration is the rate of change of velocity of the parcel with time

• where PGF is the pressure gradient force and Fdrag denotes friction-like forces due to
turbulent drag

• The Coriolis force is due to the rotation of the Earth and appears as a force
• choose our frame of reference to be fixed to the (rotating) surface of the Earth
• Velocity is a three-dimensional vector
• to three equations for the components of velocity in each direction: eastward,
northward and upward
• The coordinate system is chosen with atmospheric and oceanic applications

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 • in mind, so it rotates with the Earth, and the vertical direction (z) is defined as
upward,
• opposite the local direction of gravity on a surface at mean sea level

CORIOLIS FORCE
• The Coriolis force is an apparent force that acts on moving masses in a rotating
reference frame
• the Earth rotates once per day, the Coriolis force is negligible for motions
• in which other forces, such as frictional effects, operate on much shorter time scales
• Frictional forces are much smaller, and the Coriolis force becomes a leading effect
• a body moves in a straight line viewed in the nonrotating frame, points on the surface
rotate during the time of its motion
• If the motion is at the equator, the apparent force will be upward and will not affect
the horizontal motion

PROPERTIES OF THE CORIOLIS FORCE :

• It turns a body or air/water parcel to the right in the northern hemisphere; to the left in
the southern hemisphere
• Exactly on the equator, the horizontal component of the Coriolis force is zero
• It acts only for bodies moving relative to the surface of the Earth and is proportional
to velocity
• The constant of proportionality is f = (4π/1 day)sin known as the Coriolis parameter
• The northward force is −f u
• The eastward force is f v
• The Coriolis force is atmospheric and oceanic motions that even the rate of change of
the Coriolis parameter with latitude has a symbol

• The effect of this on motions is called the “beta effect”

• Since β is proportional to cos(latitude), it is always positive and maximum at the
equator
• Coriolis force is zero exactly at the equator
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PRESSURE GRADIENT FORCE
• The pressure gradient force tends to accelerate air from higher toward lower pressures
• Pressure is force per unit area
• Consider two regions a small distance δx apart
• If the pressure on both is the same, the pressure force will be in balance between the
two regions and no net force will result
• there is a pressure difference δp in the x direction
• the pressure gradient δp/δx gives the force per volume in that direction
• the pressure gradient force per mass in the x direction
• Taking the limit of small δx gives derivatives
• a rate of change in x only is simply a partial derivative in x, ∂p/∂x
• For a given pressure map, moving a unit increment in the x direction or in the y
• Direction will each be associated with a different pressure change, so ∂p/∂x and ∂p/∂y
provide two independent components of the pressure gradient

VELOCITY EQUATIONS
• the horizontal velocity equations are

• Newton’s law expresses conservation of momentum, these are also called the
horizontal momentum equations
• The time derivatives give the acceleration for a parcel of air
• denote turbulent drag on the flow due to mixing of momentum by small-scale motions
• they depend on the gradients of the wind, on its velocity and on atmospheric
stratification

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APPLICATION: GEOSTROPHIC WIND
• At large scales at mid latitudes - the Coriolis force and the pressure gradient force
are the dominant forces
• neglecting the beta effect, friction, and acceleration, gives a steady balance where
the flow goes around lows just fast enough to balance the PGF
• weather maps wind blows counter clockwise around low pressure
regions in the northern hemisphere
• If the air is initially at rest , the PGF will accelerate it toward the low

• the trade winds occur between the subtropical region

• of high surface pressure and the lower pressure near the equator. If the geostrophic
balance held perfectly and pressure changed only with latitude
• the Coriolis force does not perfectly balance the PGF

APPLICATION: PRESSURE COORDINATES

• one-to-one relation, pressure can be used as a vertical coordinate instead of height in
the atmosphere
• The pressure gradient along surfaces of constant height is obviously related to the
gradient of height along surfaces of constant pressure
• the pressure gradient force term ρ−1(∂p/∂x) in the velocity equations is just
replaced by g(∂z/∂x)
• the geopotential
Φ = gz
• to measure winds along pressure surfaces

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EQUATION OF STATE
• The atmospheric equation of state is used frequently in atmospheric applications
because the density changes with pressure are large
Equation of state for the atmosphere: ideal gas law
Equation of state for the ocean

EQUATION OF STATE FOR THE ATMOSPHERE: IDEAL GAS LAW

• For the atmosphere, the ideal gas law is used in the form

• where R = 287 J kg⁻¹ K⁻¹ is the ideal gas constant for air, and the temperature T is in
kelvin⁴
EQUATION OF STATE FOR THE OCEAN
• For the ocean, the density depends on temperature density decreases with
temperature, and more so for warmer water
• Near the freezing point, water actually gets slightly less dense as it gets colder
• Density increases with salinity
• For the sake of keeping track of the equations required in a climate model, call this
function ℘ (T , S, P) where S is salinity

• A coefficient of thermal expansion ɛT for sea water

• the upper ocean is ɛT =2.7×10−4°C⁻¹
• 1°C temperature increase water becomes 0.027% less dense
• the deep ocean a typical value is ɛT = 1.5×10⁻⁴°C⁻¹
• For small changes in temperature and density relative to reference values T0 and ρ0

APPLICATION: THERMAL CIRCULATIONS

• to small-scale circulations in the atmospheric boundary layer, such as the sea breeze
• the major circulations in the tropics of Earth’s climate
• Heating at the Earth’s surface is transferred upward through about 1 km by thermals
• Two pressure surfaces will have a greater separation in height if the layer of air
between them is warm
• region where the air column is cooler, since it is being warmed less strongly from
below
• In a sea breeze circulation, the air over the land warms during the day, resulting in

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 • relatively lower pressure over land near the surface than over the neighbouring ocean
• The surface wind blows toward the low pressure, rises and returns at the top of the
boundary layer

• A large component that runs perpendicular to the temperature gradient

• winds at the surface blow from the subtropical high pressure regions to the warmer
• hence lower pressure, tropical convergence zones, turned westward by the Coriolis
force
• The solar heating of the land surface moves with season, the atmospheric column is
warmed, and the pressure distribution
• A surface low and an upper-level high will tend to occur over
• A region where the atmospheric column is being warmed

APPLICATION: SEA LEVEL RISE

• Consider a column of water of depth h
• The mass of water in this column is approximately ρh × area , where ρ is the density
• If the mass and area of the ocean column remain constant, then ρh=constant
• Density decreases due to warming must be balanced by increases in h
• For small changes δρ and δh

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TEMPERATURE EQUATION
• the time rate of change of temperature, is a form of the first law of thermodynamics
• It expresses the conservation of thermodynamic energy as it is converted between
internal energy of the gas, work of expansion and input of heat into an air
Ocean temperature equation
Temperature equation for air

OCEAN TEMPERATURE EQUATION

• In the ocean, the temperature equation simply balances the heat capacity times the rate
of change of temperature of a water parcel

• where cw is the heat capacity of water cw =4200 J kg⁻¹ K ⁻¹, and Q is heating in J kg
⁻¹s ⁻¹
• The heating is due to heat fluxes at the surface and mixing of the heat down into the
ocean

TEMPERATURE EQUATION FOR AIR

• the compressibility of air depends on rate of change of pressure with time
• the work done in expanding or compressing the air parcel when changing the pressure
• The equation is

• where cp is the heat capacity of air at constant pressure and Q is heating

• Pressure is decreasing with height, according to hydrostatic balance
• The heating term in the global energy budget

.
• The heating is related to the fluxes by vertical integrals in pressure,
since dp/g = (increment of mass per area) in the vertical
• as multiplying by density in the ocean and integrating in z
• In the atmosphere

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APPLICATION: DECAY OF A SEA SURFACE TEMPERATURE
• there are negligible anomalous fluxes through the bottom of the surface layer
• Subtracting the climatology of SST and fluxes
• the equation for the SST anomaly is

• When SST is warmer, evaporation, infrared and sensible heat fluxes

• there is a negative heat flux anomaly Fnet sfc into the ocean
• the warmer the SST

• the magnitude of the cooling by the heat fluxes depends on the warmth of the SST
• in a way that reduces SST anomalies
• Example - negative feedback
• The coefficient γ gives the strength of the negative feedback
• the solution for SST is

• For surface layer depths on the order of 50–100m the time scale is on the order of
months
• For a deeper layer, or weaker negative feedback, the time scale could be larger

CONTINUITY EQUATION
Conservation of mass
• The rate of change of volume is given by the divergence, D3D
• horizontal divergence or convergence to horizontal motions, so the subscript 3D is to
recall that this includes the effects of vertical motions
• mass = (density × volume) is conserved
• Divergence reduces density according to

OCEANIC CONTINUITY EQUATION

• In the ocean the changes of density are small enough to neglect D3D = 0
• D be the horizontal divergence - the tendency of a parcel to expand in the two
horizontal directions, gives an oceanic continuity equation

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 • If density remains constant then conservation of mass implies that the horizontal
• divergence must be balanced by suitable changes in vertical motions

ATMOSPHERIC CONTINUITY EQUATION

• An equation of equal simplicity applies in the atmosphere if use pressure coordinates
• Let ω be the vertical velocity in pressure coordinates and let D be horizontal
divergence defined along pressure surfaces
Then the atmospheric continuity equation

• by horizontal convergence must be balanced by suitable changes in the upward

motion
• low-level convergence in tropical convection zones is balanced by rising motion
• the atmospheric continuity equation is the surface pressure equation which is
obtained
• The rate of change of surface pressure is then given by vertically integrated
divergence

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APPLICATION: COASTAL UPWELLING
• The trade winds have a component that blows parallel to the coast of Peru
• a north–south coast with a wind blowing northward
• Neglecting the d/dt term in the v equation, and assuming nothing changes very
quickly in the north–south direction

• contains the northward drag of the wind stress which tends to accelerate the ocean
currents

APPLICATION: EQUATORIAL UPWELLING

• the average conditions about which ENSO evolves
• The westward wind stress exerted on the near-surface layer of the ocean results in
westward acceleration of the currents
• north of the equator, the currents will also move westward, but the Coriolis force
• a small northward component of the flow
• Just south of the equator a similar effect will occur, except that the Coriolis force
turns the current to the left of its motion
• create a divergence in the surface layer
• Maximum upwelling occurs at the bottom of this diverging layer

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APPLICATION: CONSERVATION OF WARM WATER MASS
• The thermocline is idealized as a sudden jump in temperature at a depth −h
• The movement of the thermocline will be governed by divergence or convergence
averaged over the entire layer
• the oceanic continuity equation the whole layer and let ˆD be the vertical average
divergence

• The local partial derivative in time

• Divergence occurs where the zonal current increases to the east, convergence where it
decreases eastward
• Downward motion at the depth of the thermocline occurs where the vertical average
current is converging
• Since h measures thermocline depth ∂h/∂t is positive where the current converges

Moisture equation for the atmosphere and surface

• In the atmosphere, the budget for water vapour is usually referred
• The quantity of water vapour in the air is conveniently measured by the specific
humidity
q = (mass of water vapor)/(total mass of air parcel)
• Using P to refer to the source/sink of moisture due to these parameterized processes,
the moisture equation becomes

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 • Pconvection includes the loss of moisture by condensation and precipitation
• Pmixing includes mixing not associated with moist convection, including boundary
layer turbulence
• the lowest level of the atmosphere, Pmixing includes surface evaporation that
provides the source of moisture to the atmosphere
• Pconvection represents conversion from water vapor to cloud condensate
• In land surface or snow/ice models, the equation for water substance is usually written
for the mass of water per unit area within a given layer of soil, snow or ice
Sources and sinks of moisture, and latent heat :
• Phase changes of moisture, such as condensation or freezing, are associated with
latent heat release
• It also connects the source and sink terms for each phase to the energy budget
• water vapour condenses into water droplets in clouds, the latent heat release per unit
mass of water condensed is given by L=2.5×106 J kg−1
• the specific humidity is mass of water vapour per mass of air, when humidity is
reduced by an amount δq the latent heat per mass of air is given by Lδq

SALINITY EQUATION FOR THE OCEAN

• Salt affects ocean density, so ocean models must keep track of salinity
• the salt remains in the ocean
• The quantity of salt in the water is measured by the salinity
s = (mass of salt)/(total mass of water parcel)
• Source/sink terms for salinity occur in the interior of the ocean
• At the surface of the ocean, evaporation removes water and thus increases salinity,
• Precipitation adds fresh water to the ocean surface thus reducing salinity
• River inflow and sea ice freezing or melting create additional source or sink terms at
the surface in some locations
• the salinity equation is

• If no mixing is occurring, then water and salt will both be conserved, so ds/dt = 0.
• At the surface of the ocean, Ps mixing depends on evaporation and precipitation

MOIST PROCESSES
• the moisture equation - a number of physical processes must be taken into account
in order to calculate the sources and sinks of moisture
• the growth of ice crystals in clouds, the fall rate of raindrops, the tendency of
raindrops to aggregate when falling, and their re-evaporation
• Saturation
• Moist convection

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SATURATION
• If water vapour is continually added to air, for instance by evaporation, at a certain
point the air becomes saturated
• the equilibrium of saturated water vapour over liquid water for various temperatures.
At warmer temperatures, the molecules in the liquid water have more kinetic energy
• Relative humidity is given by the actual vapour pressure of an air parcel divided by
the saturation value at that temperature
• moisture sources and sinks and heating and cooling, an air parcel can have values of
water vapour content and temperature anywhere below the saturation line
• if temperature decreases it will eventually saturate and condensation will begin to
occur
• condensation occurs for a large air mass, it is simple to represent in a climate model
since the saturation vapor pressure is easy to calculate

MOIST CONVECTION
• A cloud parcel rising according to the moist adiabat has a temperature given by the
temperature and moisture of the boundary layer
• small-scale convective motions with rising warm air parcels to warm the troposphere
through a deep layer
• the Hadley and Walker circulations

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WAVE PROCESSES IN THE ATMOSPHERE AND OCEAN
Types of wave motions
• Gravity waves
• Kelvin waves
• Rossby waves
GRAVITY WAVES
• Gravity waves are due to the effects of gravity acting on perturbations to a density
gradient in the vertical
• Example the surface gravity waves on the surface of the ocean
• If a region of the dense fluid (water) is raised, it has negative buoyancy relative to the
surrounding fluid (air)
• vertical structures and their speed increases for waves that have larger depth scale
• If a process such as heating on a small scale by a convective cloud tends to produce
horizontal density and pressure gradients, gravity waves will act to reduce these
gradients
KELVIN WAVES
• In the north–south direction, however, it obeys geostrophic balance. This is known as
the Kelvin wave
• It has the property of traveling at a gravity wave speed, eastward along the equator
• When it encounters a coast, it can travel up the coast with the along-coast balances
• a gravity wave while being in geostrophic balance in the direction perpendicular to
the coast
• About 20 degrees of latitude in that atmosphere and 3 degrees of latitude in the ocean
ROSSBY WAVES
• climate processes such as teleconnections, communicating
• Rossby waves depend upon the variation of the Coriolis parameter with latitude,
known as the beta effect
• The pressure gradient is in balance with the Coriolis force at both the northern and
southern sides of the low
• Because f increases with latitude, it is larger on the northern side

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• the same Coriolis force balancing the pressure gradient
• the zonal wind u must be smaller on the north side than the south side
• the pressure will tend to increase on the eastern side of the low and decrease on the
western side
• The speed of propagation of the highs and lows for a sinusoidal wave is known as the
phase speed
• Rossby waves at mid latitudes are strongly affected by westerly climatological winds

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 UNIT V CLIMATE CHANGE MODELS
Constructing a climate model – climate system modeling – climate simulation and drift –
Evaluation of climate model simulation – regional (RCM) – global (GCM) – Global average
response to warming – climate change observed to date
CONSTRUCTING A CLIMATE MODEL
• Discretization is to divide the fluid up into a number of grid cells
• the continuous field by the average value across the grid cell or the value at the center
of the grid cell
• There are a number of different techniques of discretizing the equations of motion of a
continuous fluid
• An atmospheric model
• Treatment of sub-grid-scale processes
• Resolution and computational cost
• An ocean model and ocean–atmosphere coupling
AN ATMOSPHERIC MODEL

• focusing on a particular region out of a global grid

• a three-dimensional
FEATURES:
• For each of the discrete grid cells - a single value of each variable (e.g: temperature)
• The vertical coordinate is essentially a pressure coordinate, but modified so it follows
• the large-scale topography
• Grid spacing is not constant in the vertical
• The horizontal grid is in latitude and longitude

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 • The partial differential equations of motion for atmosphere and ocean are replaced by
a finite number of difference equations involving differences between values in
neighboring grid cells
• Each grid cell communicates with its neighbors
• The arrows indicate transports (or fluxes) of mass, energy, and moisture into a
particular grid cell
• The time integration proceeds one time step at a time until the desired length of
simulation (e.g. 100 years) is reached

TREATMENT OF SUB-GRID-SCALE PROCESSES

• These processes are not local in the vertical
• grid cells are affected not only by the nearest neighbors but by grid cells anywhere in
the column
• the convective and radiative processes depend only on the column, not on horizontally
adjacent columns
• the ratio of the vertical dimension to horizontal grid size: the entire troposphere is
only about 10 km deep
• the horizontal grid size is 200 km

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 • Small-scale convective motions within the grid box have updrafts in the deep
convective clouds
• convective heating is to calculate the net cumulus mass flux that would occur as an
average over the grid box for given temperature and moisture profiles over the
column
• Infrared radiation is emitted both downward and upward from every layer according
to the temperature of that layer
• The intensity of each flux depends on the temperature of the layer doing the emitting

RESOLUTION AND COMPUTATIONAL COST

• Resolution is used to describe the degree of refinement of a climate model grid
• A model with a small grid size is termed fine resolution or high resolution, while one
with a large grid size is coarse resolution
• For microscopes or photography where high resolution images can distinguish
smaller-scale
• the topographic height for the North American region
• The topography is contrasted for a larger grid size (lower resolution)
• A climate model and a smaller grid size (higher resolution)

• The grid size of 2 degrees in latitude and longitude used

• the highest resolution models had grids between 1 and 1.5 degrees in each direction.
• Two degrees of latitude corresponds to slightly over 200 km
• the high resolution case at 0.2 degrees corresponds to slightly over 20 km in
latitudinal grid size

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AN OCEAN MODEL AND OCEAN–ATMOSPHERE COUPLING
• The levels are more closely spaced (10m thick) near the surface to resolve surface
current effects
• They remain quite closely spaced through the upper ocean to resolve the thermocline
• Sloping grid cells are used in some models but the approximation shown should be
viewed in perspective
• Example the domain only about one-twentieth of the width
• The lower levels of an atmospheric model for an atmospheric model grid size of 2
degrees of longitude

• a single atmospheric column, one grid cell wide in the horizontal, and the ocean grid
cells below it
• The amount of solar radiation reaching the ocean surface depends on atmospheric
variables such as clouds
• The solar radiation penetrates into the upper few ocean levels
• Exchange of sensible heat and latent heat (evaporation) occur between the uppermost
ocean level and lowest atmospheric level
• Near-surface heating is carried down by mixing in the ocean

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LAND SURFACE, SNOW, ICE AND VEGETATION
• The variables typically include: land surface temperature; soil moisture, which
depends on precipitation and evapotranspiration; and snow cover
• biophysical land surface models
• Example the Biosphere–Atmosphere Transfer Scheme (BATS)
• Snow coverage and depth depends on atmospheric inputs such as snowfall,
temperature, surface radiation and low-level atmospheric temperature and moisture
• Sea ice models are run in close connection with the ocean model
• The melting and freezing of sea ice produces or removes fresh water

CLIMATE SYSTEM MODELING

•there is not full agreement on the terminology: Earth system modeling is an alternate
term with essentially identical usage
• Representation of the carbon cycle is typically not a single model unit but rather
implies a coordinated
• set of changes in the atmospheric model, the land surface model and the ocean model
• a set of equations for dissolved carbon compounds, both organic and inorganic, and
the biological and geochemical sources, sinks and exchanges
• The ocean biogeochemistry model may include several groupings of organisms,
concentrations of key nutrients, and the exchanges
CLIMATE SIMULATIONS AND CLIMATE DRIFT
• Each run can proceed from any reasonable set of initial conditions and a set of initial
values of all the main variables
• when the model is first run, it takes a considerable period of model simulated time
before it arrives at a state similar to the long-term mean
• This is referred to as the model spin up

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 • When a model is first run, the atmosphere might be started from constant temperature
and no wind
• the ocean is started from a simple vertical profile that has no spatial variations and no
currents
• The model then responds to the solar forcing, warming at the equator, cooling at the
poles and spinning up winds and currents
• it reaches a simulated climate that resembles the observed
• systematic model error - climate drift, because when started from observations, the
model “drifts” slowly toward its equilibrium state
• The term climate drift also refers to the steady state result of this adjustment

EVALUATION OF CLIMATE MODEL SIMULATIONS

• Atmospheric model climatology from specified SST
• Climate model simulation of climatology
• Simulation of ENSO response
Atmospheric model climatology from specified SST
• Distribution of precipitation, winds, energy fluxes at the surface and top of the
atmosphere
• the atmospheric model response to observed ENSO SST anomalies can be evaluated
• Atmospheric Model Inter comparison Project (AMIP), such runs are sometimes
referred to as “AMIP runs”
• the CPC Merged Analysis of Precipitation (CMAP) standard product is used
• The climatology starts in 1979 because satellite data are not
• available in earlier periods and station gauge data have much more limited coverage

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CLIMATE MODEL SIMULATION OF CLIMATOLOGY
• an error in the parameterized cloud cover might allow tens of Wm−2 too much solar
radiation to reach the surface in a certain region
• the coupled system, the ocean will warm, in turn affecting the cloudiness, winds, etc
• Examples NCAR CCSM3
• a comparison between precipitation from the atmospheric component of CCSM3
• The 4mm per day−1 contours are repeated for the AMIP run and the observations
• the 4mm per day−1 contour from the coupled CCSM3 simulation is added

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 • A number of regional errors are exacerbated in the coupled system. For instance, the
SPCZ in December–February,
• which extended slightly too far into the south eastern Pacific in the atmospheric
component
• It extends even further east across the basin in the coupled simulation
• the Hadley Centre model has one of the best coupled model simulations of tropical
precipitation
• In winter, Italy is as rainy as the north of France – again, a slight extension of a real
climate feature creates errors at the regional scale

SIMULATION OF ENSO RESPONSE

• El Niño/Southern Oscillation is a large climate signal
• the atmospheric response in experiments where observed SST is specified as a
function of time
• by two climate models of anomalies associated with ENSO for precipitation and for
the height of the 200 mb pressure surface in the upper troposphere
• the average over multiple events tends to reduce anomalies associated with random
weather variations
• “observations” shown here are estimates of the observed state
• Satellite systems based on microwave or radar retrieval systems provide more
accurate estimates

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• Observations based on rain gauges are available at particular locations, mostly over
land, and thus have large gaps in spatial coverage
• The 200 mb geopotential is known as a reanalysis product
• The model produces a full set of atmospheric variables with full spatial coverage
• with precipitation increases in the central to eastern equatorial Pacific and decreases
in the western Pacific
• The teleconnection to reduced equatorial precipitation in eastern South America and
the Atlantic is also clear
• as one focuses on specific regions, such as the island of New Guinea and neighboring
ocean areas near the equator just north of Australia

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GLOBAL-AVERAGE RESPONSE TO GREENHOUSE WARMING SCENARIOS
• the time dependence of radiative forcing by GHG, sulfate aerosols and both
combined, estimated
• from 1860 to present and projected into the future with a 1% per year CO2 increase
scenario
• The climate model is a coupled ocean–atmosphere model from the Hadley Centre
• The temperature change is given relative to a 130-year model control run in which
forcing was held constant at the value in 1860
• GHG effect produces an increasing warming with time in response to the ongoing
GHG increase

• the global-average surface temperature increase in 2050 due to GHG alone reaches
about 2.6 ◦C
• This is reduced to about 1.8 ◦C by sulfate aerosols when both effects are included
• GHG forcing alone produces a warming slightly less than 1 ◦C. Aerosols oppose this
and reduce it to about 0.7 ◦C
• the best estimate of the sulfate aerosol radiative forcing has been revised
• On long time scales, this natural variability is unpredictable and is not expected to
have the same time sequence for different models

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CLIMATE CHANGE OBSERVED TO DATE
Temperature trends & natural variability: scale dependence
• to natural variations depends strongly on the spatial and time averages
• annual averages and decadal averages at the hemispheric scale, at a scale of 40 or 50
thousand km2 and at the scale of a 5×5 degree latitude–longitude box
• This holds for both the year-to-year variability and decade-to-decade variability
• a slight increase in cold air transports from the north can easily have a large impact in
a particular region
• The energy transports through the edges of the larger averaging region
• At the local scale the greenhouse effect is still operating, but in a particular year, or
even a particular decade

Is the observed trend consistent with natural variability or anthropogenic forcing?

• To compare the range of variability range from an ensemble of model runs with
natural forcing only to an ensemble of runs that also have the observed twentieth-
century anthropogenic forcing
• The range in the natural forcing runs comes both from specified forcings (volcanoes,
changes in solar input, etc.)
• climate variability (like El Niño or variations in the thermohaline circulation) that
occurs
• the observed curve emerges from the range of variability in the simulations with
natural forcings only

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Sea ice, land ice, ocean heat storage and sea level rise
• The time series of observations with high spatial coverage tends to be shorter for these
quantities than for surface temperature
• Satellite observations of sea ice extent are available
• the annual average area covered by sea ice in the northern hemisphere over that time
period
• The decreasing trend amounts to about 3% of the total area per decade.
• Summer sea ice extent in the northern hemisphere has been decreasing by about 7%
of the total area per decade
• A glacier has retreated, exact mass balances for glaciers are difficult to establish
• The substantial uncertainties are due to difficulties in measuring thickness
• an indicator of warming, land ice has contributed to observed sea level rise.
• Glaciers are estimated to have contributed about 3 to 7mm per decade, and the
Greenland
• Antarctic ice sheets about 4 to 7mm per decade during 1961 to 2003
• The heat content change occurs in response to accumulated imbalance in surface heat
flux or changes in the transport to and from the deep ocean
• the observing system for subsurface temperature has imperfect coverage

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