Hydrology

Hydrology means the science of water. It is the science that deals with the occurrence,
circulation and distribution of water of the earth and earth’s atmosphere. As a branch of earth
science, it is concerned with the water in streams and lakes, rainfall and snowfall, snow and ice on
the land and water occurring below the earth’s surface in the pores of the soil and rocks.

Branches:
1. Hydrometeorology – study of water in the atmosphere
2. Hydrography – study of water on the earth’s surface
a. Limnology – the scientific study of lakes including their physical and biological
features.
b. Oceanography – the scientific study of oceans including their chemistry, biology and
geology.
c. Rheology – study of running waters
3. Hydrogeology (geohydrology) – study of the movement of subsurface water through rock,
either as underground streams or percolating through porous rocks.

Hydrologic Cycle
The hydrologic cycle is a simplified accounting of the complex interactions of
meteorological, biological, chemical, and geological phenomena. It is the movement of water from
surface water, groundwater, and vegetation to the atmosphere and back to the earth in the form of
precipitation.

Solar Energy
Cumulonimbus Moving air masses
clouds
Condensation
Evaporation while falling Atmospheric
Vapor
Precipitation Evaporation from runoff
Runoff

Infiltration Transpiration
Evaporation
Ground water table Vegetation
River

ws
Percolation
Ocean/sea

The actual volume of water in air is small, ranging generally from about 0.02% in the desert
regions to about 4% in humid areas. Of the total atmospheric pressure of 14.7 psi (1013 millibars,
mb) at sea level, water vapor contributes about 0.15 psi (10 mb), whereas nitrogen contribute
about 11.03 psi (760 mb) and oxygen about 3.48 psi (240 mb). Although the moisture content of air
is seemingly insignificant, it is vital in influencing atmospheric conditions. Water vapor affects
weather and climate in three ways;
a. It is the source of all condensing water (rain, snow, hail, and frost). Water vapor is the only
gas in the atmosphere that condenses under normal atmospheric temperatures.
b. It is the most important gas in the atmosphere for absorbing both shortwave solar radiation
and long-wave terrestrial radiation (radiation by earth). Thus water vapor is critical in
regulating air temperatures near the earth’s surface.
c. It is a source of latent or stored energy. This is the energy that drives the movement of air
masses over the earth. Latent heat is the heat energy gained and stored by water
molecules as they change state (ice to water, water to vapor). Tremendous amounts of heat

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 must be supplied to water molecules to induce them to change state. Example, in changing
from ice to water to vapor, a gram of water requires about 720 calories (3010 joules). From
one gram of ice to water (80 calories), from water to near its boiling point (100 calories),
and to actually vaporize the water (540 calories).

There are several concentric atmospheric layers surrounding the earth (Troposphere,
Stratosphere, Mesosphere, and Thermosphere). The lowest layer, called the troposphere,
influences man’s activities because all weather phenomena affecting the earth’s surface occur in
this layer. The troposphere varies in thickness from about 6.4 km near the poles to about 19.3 km
near the equator. Air cools with increasing height throughout the troposphere. The rate at which it
cools is called the lapse rate and equals about 6.5oC per km. There are two adiabatic cooling rates;
dry adiabatic lapse rate (when no condensation occurs) is 9.8oC per km and the wet adiabatic rate
(when condensation occurs) averages 6oC per km.

Precipitation – all forms of water that reaches the earth surface from the atmosphere.
Moisture is always present in the atmosphere, even on cloudless days. For precipitation to
occur, some mechanism is required to cool the air sufficiently to bring it to near saturation. The
large-scale cooling needed for significant amounts of precipitation is achieved by lifting the air. This
is accomplished by convective systems resulting from unequal radiative heating or cooling of the
earth’s surface and atmosphere or by convergence caused by orographic barriers.
For precipitation to form; the atmosphere must have moisture, there must be sufficient
nuclei to aid condensation, weather conditions must be good for condensation of water vapor to
take place, and the products of condensation must reach the earth.

Forms of Precipitation
The following are the common precipitations which are referred to as falling moistures.

1. Rain – consists of liquid water drops mostly larger than 0.50 mm in diameter. The maximum
size of a raindrop is about 6 mm.
a. Light rain – for rates of fall up to 2.5 mm/hr inclusive
b. Moderate rain – from 2.5 mm/hr to 7.5 mm/hr
c. Heavy rain – greater than 7.5 mm/hr
2. Drizzle – sometimes called mist, consists of tiny liquid water droplets, usually with
diameters between 0.1 and 0.5 mm, with such slow settling rates that they occasionally
appear to float. Their intensity is less than 1 mm/hr.
3. Glaze – is the ice coating, generally clear and smooth, formed on exposed surfaces by the
freezing of supercooled water deposited by rain and drizzle. Its specific gravity may be as
high as 0.8 to 0.9.
4. Sleet – consists of transparent, globular, solid grains of ice formed by the freezing of
raindrops or refreezing of largely melted ice crystals falling through a layer of subfreezing
air near the earth’s surface.
5. Hail – it is showery precipitation in the form of irregular, spheroidal, conical pellets or lumps
of ice of size ranging from 5 to 125 mm in diameter. Hails occur in violent thunderstorms
produced in convective clouds, mostly cumulonimbus and their specific gravity is about 0.8.
6. Snow – consists of ice crystals which usually combine to form snowflakes. When new,
snow has an initial density varying from 0.06 to 0.15 g/cm3 and it is usual to assume an
average density of 0.1 g/cm3. a 125 to 500 mm of snow is generally required to equal 25
mm of liquid water.

Type of Precipitation
Convective Precipitation – in meteorology, convection refers primarily to atmospheric
motions in the vertical direction. In the atmosphere, convection enables winds to be
maintained by an upward and downward transfer of air masses of different temperatures.
Convective storms result as warm, humid air rises into cooler overlying air. A common form
of convective precipitation is the summer thunderstorm. The earth’s surface is warmed by
mid to late afternoon on a hot summer day. The surface imparts heat to the air mass
directly above. The warmed air rises through the overlying air, and if the air mass has a
moisture content equal to the condensation level, moisture will be condensed from the
rising, rapidly cooling air. This may often result in a large volume of rain from a single
thunderstorm.

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 Rain Clouds
Rain Clouds

Condensation and subsequent

thunderstorm formation
Convective
Precipitation

Air is heated and

rises

Orographic Precipitation – Orography is the study of elevation relief between highlands

(mountains) to other land and water features. Orographic precipitation results as warmer air
rises over high geographic feature such as a range of mountains and meets cooler air.
Precipitation results if the rising air mass has a condensation level of moisture.
Consequently, mountain slopes facing prevailing winds get more precipitation than the back
or leeward slopes.

Condensation
Leeward Side
Condensation Level
Orographic
Mountain Precipitation

Windward Side

Cyclonic Precipitation – Cyclonic precipitations are caused by the rising or lifting of air as it
converges on an area of low pressure. The movement of air is from high to low pressure
areas and the boundary between air masses of different pressure is called a front. Frontal
precipitation is formed from the lifting of warm air over cold air. Cold fronts are formed by
cold air advancing under warmer air; a warm front is formed by warm air advancing over
colder air. The intensity of precipitation associated with a cold front is usually heavy and
covers a relatively small area, whereas less intense precipitation is associated with a warm
front, but it covers a much larger area. Tornadoes and other violent weather phenomena
are associated with cold fronts.

Large regions in the atmosphere that have higher pressure than the surroundings
are called high-pressure areas. Regions with lower pressure than the surroundings
are called low-pressure areas. Most storms occur in low-pressure areas. Rapidly
falling pressure usually means a storm is approaching, whereas rapidly rising
pressure usually indicates that skies will clear.

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 Cold Front Warm Front

Thunderstorm is
Day-Long Drizzle
common
is common

Air forced to rise

abruptly
Cold Air
Cold Air Warm Air Warm Air

Heavy-short-duration Light-Long duration

Precipitation Precipitation
Clouds
Clouds are classified into a system that uses Latin words to describe the appearance of
clouds as seen by an observer on the ground.
a. Cumulus (heap) – ex. Fair weather cumulus
b. Stratus (layer) – ex. Altostratus
c. Cirrus (curl of hair) – ex. Cirrus
d. Nimbus (rain) – ex. Cumulonimbus
Further classification identifies clouds by height of cloud base. For example, cloud names
containing the prefix “cirr-”, as in cirrus clouds, are located at high levels while cloud names with
the prefix “alto-”, as in altostratus, are found at middle levels.
a. High-Level Clouds – form above 6 km and since the temperatures are so cold at such
high elevations, these clouds are primarily composed of ice crystals. High-level clouds
are typically thin and white in appearance, but can appear in a magnificent array of
colors when the sun is low on the horizon.
b. Mid-Level Clouds – The bases of mid-level clouds typically appear between 2 to 6 km.
Because of their lower altitudes, they are composed primarily of water droplets,
however, they can also be composed of ice crystals when temperatures are cold
enough.
c. Low-Level Clouds – are mostly composed of water droplets since their bases generally
lie below 2 km. However, when temperatures are cold enough, these clouds may also
contain ice particles and snow.
d. Vertically Developed Clouds – probably the most familiar of the classified clouds is the
cumulus cloud. Generated most commonly through either thermal convection or frontal
lifting, these clouds can grow to heights in excess of 12 km, releasing incredible
amounts of energy through the condensation of water vapor within the cloud itself.

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1. Cirrus Clouds
Cirrus clouds , sometimes called mares’ tails, are high clouds located high in the
atmosphere at about 8 km (5 mi) and have a wispy, delicate, feathery appearance
(the word cirrus means “curl” in Latin).
These feathers or curls are falling ice crystals being whipped away by winds.
Cirrus clouds reveal the presence of moisture at great heights and may indicate an
approaching storm or warm front.

2. Altocumulus Clouds
Altocumulus clouds are middle-level rows of large cumulus clouds that have darker
undersides.
Although not necessarily a warning of approaching precipitation, these clouds show
evidence of unstable air and the possibility of light snow or drizzle.
Altocumulus clouds are found at altitudes of 3-6 km (2-4 mi).

3. Stratocumulus Clouds
Stratocumulus clouds form when low-level, layered stratus clouds break up into
lumpy gray and white masses, or wavy formation, or when cumulus clouds join to
form a broken layer.
These clouds may indicate approaching precipitation, which can range from a light
sprinkle to heavy rain or snow.

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 4. Cumulonimbus Clouds
Cumulonimbus clouds are dark, towering piles of cumulus clouds, also known as
thunderclouds or thunderheads.
They bring heavy rain, hail, or snow, along with thunder and lightning and possibly
tornadoes.
They can extend the full height of the troposphere—that part of the atmosphere in
which weather occurs.

5. Cirrostratus
Cirrostratus clouds are high-level sheets of transparent clouds.
Their ice crystals scatter light and create a halo or thin veil around the Sun or Moon.
These clouds usually indicate an approaching storm or warm front.

6. Cirrocumulus
Cirrocumulus clouds are high-level clouds that appear as rows of tiny cumulus
clouds with a dappled texture.
These clouds indicate unstable air and may warn of an approaching storm.

7. Altostratus
Altostratus clouds are middle-level, thick gray clouds that cover the sky.
Because they slightly obscure the Sun or the Moon, the clouds can appear as bright
spots, but unlike cirrostratus clouds, they do not produce a halo.
These clouds occasionally produce light snow or drizzle, but they are usually so
high that their precipitation evaporates before it reaches the ground.

8. Cumulus
Cumulus clouds are fluffy white clouds with rounded tops and flattened bases.
These clouds form at low levels on warm sunny days and usually signal the
continuation of fair weather.
They can develop into cumulonimbus clouds, or thunderheads.

9. Nimbostratus
Nimbostratus clouds are ground-hugging, low-level, layered clouds bearing rain or
snow.
They derive their name from the Latin words nimbus (“rainy cloud”) and stratus
(“covered with a layer,” or “spread out”).
Nimbostratus clouds usually produce rain or snow for a long period of time.

10. Stratus
Stratus clouds are thick, gray, low-level clouds that hover at altitudes as low as 610
m (2,000 ft).
They may produce light rain or snow that can last for several days.

Measurement of Precipitation
Precipitation is expressed in terms of the depth to which rainfall water would stand on an
area if all the rain were collected on it.

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Rain Gages – used to measure rain that falls in a certain place during a specific period of time.
Rain gage is shaped like a cylinder and has a removable cover.

Site for a rain gage

a. The ground must be level and in the open and the instrument must present a
horizontal catch surface.
b. The rain gage must be set as near the ground as possible to reduce wind effects
but it must be sufficiently high to prevent splashing and flooding.
c. The instrument must be surrounded by an open fenced area of at least 5.5 m by
5.5 m. No object should be nearer to the instrument than 30 m or twice the
height of the obstruction.
Minimum densities of precipitation networks for general hydrometeorological purposes
a. For flat regions of temperate, mediterranean, and tropical zones – 600 to 900
km2 per station (ideal); 900 to 3000 km2 per station (acceptable)
b. For mountainous regions of temperate, mediterranean, and tropical zones – 100
to 250 km2 per station (ideal); 250 to 1000 km2 per station (acceptable)
c. For small mountainous islands with irregular precipitation – 25 km2 per station
d. For arid region and polar zones – 1,500 to 10,000 km2 per station

Rain Gages type:

1. Non-recording gages

a. Standard gage – the parts includes the support, overflow can, measuring tube, and
the collector or receiver. Inside the cylinder is a long narrow tube, where the rain is
measured. The top of the tube is connected with a funnel. The rain falls into the
funnel and flows into the tube. The collector or receiver has a diameter of 8 inches
(203 mm). the mouth of the funnel has an area 10 times that of the tube. The rain in
the tube is measured by a “ruler”. With this ruler, a depth of 10 inches (25 cm) gives
a reading of 1 inch (25 mm) of rainfall.

b. Symon’s gage – consists of a circular collecting area of 12.7 cm (5 inches) diameter

connected to a funnel. The rim of the collector is set in a horizontal plane at a height
of 30.5 cm above the ground level.

2. Recording rain Gages

a. Tipping bucket type – this is a 30.5 cm size rain gage. The catch from the funnel
falls onto one pair of small buckets. The buckets are so balanced that when 0.25
mm, 0.1 mm of rainfall collects in one bucket, it tips and brings the other one in
position. The water from the tipped bucket is collected in a storage can. The tipping
actuates an electrically driven pen to trace a record on clock-work-driven chart.

b. Weighing bucket type – the rain gage catch from the funnel empties into a bucket
mounted on a weighing scale. The weight of the bucket and its contents are
recorded on a clock-work –driven chart. The clock work mechanism has the
capacity to run for as long as one week. This instrument gives a plot of the
accumulated rainfall against the elapsed time.

c. Natural-Siphon type (Float type gage) – the rainfall collected by a funnel-shaped

collector is led into a float chamber (special reservoir of mercury or oil) causing a
float to rise. As the float rises, a pen attached to the float through a lever system
records the elevation of the float on a rotating drum driven by a clock-work
mechanism. A siphon arrangement empties the float chamber when the float has
reached a pre-set maximum level.

3. Radar for measuring precipitation – radar is an electronic instrument that sends out radio
waves that are reflected by raindrops. The reflected waves, called “echoes”, appear on a
screen as spots of light. The brightness of the echoes depends chiefly on the sized and
number of raindrops. The echoes indicate the amount and intensity of rainfall. Radar
measures scattered showers missed by rain gages, which are too far apart to measure
precipitation in all places.

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 4. Satellite remote sensing – satellite observations can provide information on the aerial
distribution of precipitation working on the principle that the atmosphere selectively transmit
radiation at various wavelengths, more particularly in the visible and thermal infra-red
wavelengths. The visible wavelengths are the order of 0.77 to 0.91 μm and give information
on the distribution of clouds, and therefore possible aerial location of rainfall. The infra-red
wavelengths, 8 to 9.2 μm and 17 to 22 μm, can be used to locate high clouds and their
associate convective precipitation cells. Satellite is commonly used in areas of low
inhabitation, where rain gages or radar are not available, and particularly remote island
locations.

Estimation of Missing Data

1. If the normal annual precipitation at various stations are within about 10% of the normal
annual precipitation at station X; Arithmetic mean method
1
Px  P1  P2  ...  PM 
M

2. If the normal annual precipitations vary considerably, used the normal ratio method
Nx  P1 P P 
Px    2  .....  M 
M  N1 N 2 NM 

Where:
Px = estimated precipitation volume at the missing data station X, depth
P1, P2, PM = estimated precipitation volume of the stations 1, 2, and M, depth
Nx = average annual precipitation at the missing data station X, depth
N1, N2, NM = average annual precipitation at the adjacent stations, depth

Adequacy of Rain Gage Stations

If there are already some rain gage stations in a catchments, the optimal number of stations
that should exist to have an assigned percentage of error in the estimation of the mean rainfall is
obtained by the statistical analysis as;
1/ 2
M 2 

C 
2
100 S   Pi  P  
N  v  ; Cv  ; S   i 1 
 e  P  M 1 
 
Where:
N = optimal number of stations
e = allowable degree of error in percent
Cv = Coefficient of variation in percent
S = Standard deviation
M

P i
P i 1
= mean precipitation
M

Mean Precipitation over an Area

1. Arithmetic Mean Method

M

P i
P i 1

M
Where:
P = average precipitation within the catchment area, depth
Pi = precipitation at station i within the catchment area, depth
M = total number of rain gage stations within the catchment area

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 2. Theissen’s Method

a P i i
P i 1
M

a
i 1
i

Where:
ai = estimated area coverage of rain gage station i
3. Isohyetal Method
M

a P i i
P i 1
M

a
i 1
i

Where;
ai = estimated area between two isohyets within the catchment area
Pi = average precipitation of the two isohyets bounding ai , depth

Problems:

1. The normal annual rainfall at stations A, B, C, and D in a basin are 81, 68, 76, and 92 cm
respectively. In the year 1980, the station D was inoperative and stations A, B, C recorded
annual precipitations of 91, 72, and 80 cm respectively. Estimate the rainfall at station D in
that year.

2. Part of a rain gage collector is covered during a storm event by debris. The debris reflected
rain from the collector. Upon examination of the collector, it was found that 30 % of the
collector area was covered during rainfall. If the total amount of rain recorded was 15 mm,
what would be an estimate of the actual amount assuming a standard 203 mm diameter
collector?

3. A catchment has six rain gage stations. In a month, the monthly rainfalls recorded by the
gages are as follows (given table below). For a 10% error in the estimation of the mean
rainfall, calculate the optimum number of stations in the catchment.

Station A B C D E F
Rainfall (mm) 82.6 102.9 180.3 110.3 98.8 136.7