CHAPTER 1

THE HYDROLOGICAL CYCLE

1.1 Definition of Hydrology

Water is vital for all living organisms on Earth. For centuries, people have been investigating where
water comes from and where it goes, why some of it is salty and some is fresh, why sometimes there
is not enough and sometimes too much. All questions and answers related to water have been
grouped together into a discipline. The name of the discipline is hydrology and is formed by two Greek
words: "hydro" and "logos" meaning "water" and "science". Hydrology is the science concerned with
the occurrence, distribution, movement and properties of all the waters of the Earth.

A good understanding of the hydrologic processes is important for the assessment of the water
resources, their management and conservation on global and regional scales.

1.2 Water Distribution on Earth

The "Blue Planet", as the Earth is called, is easily identified in the solar system due to its distinctive
element: water.

Oceans and seas cover 71% of the planet's surface. The remaining 29% are land, but water can be
found here as well in lakes and rivers, in the soil cover, underground and bound up in the composition
of minerals of the Earth's crust and core. The biosphere contains water and cannot exist without it.
Water is held in the atmosphere together with other gases.

Water exists in three states: liquid, solid (ice and snow) and gas (water vapour). Due to the energy
supplied by the sun it is in permanent transformation from one state to another, and in constant motion
between oceans, land, atmosphere and biosphere.

A reliable assessment of the water storage on Earth considers the amount of water as an average
over a long period of time, contained in the hydrosphere. Current estimations weigh up to 1386 million
cubic kilometres of water that are divided as shown in Figure 1.1 and Table 1.1.
 Figure 1.1. Distribution of water on Earth

Table 1.1. Distribution of freshwater on Earth

Component of % of the hydrosphere

freshwater content
Glaciers and Permanent
1.74 %
Snow Cover
Groundwater 0.75 %
Freshwater Lakes 0.0066 %
Rivers 0.0002 %
Atmosphere 0.0009 %
Biosphere 0.0001 %

Freshwater is only 2.5% from the total, yet most of it is out of human reach. Freshwater usable by
humans represents 0.3% of all water on Earth and is drawn from underground, lakes and rivers (Figure
1.2).

Figure 1.2. Freshwater available for human use (0.3 % of Earth's water)

Groundwater is the second largest storage of freshwater and the most used by humans. People in the
arid and semi-arid regions, use groundwater exclusively for all their needs. Still, groundwater is not
always within easy reach. The withdrawal of groundwater becomes difficult and expensive when it is
confined over 800m depth.

The surface water bodies, as lakes and rivers, hold a very small amount of freshwater. Unlike
groundwater it is easily accessible, but liable to pollution. At the same time, it is unevenly distributed
with regard to continent surfaces and population. For example, 30 % of the world freshwater storage
and 6 % of runoff are located in Canada alone.

1.3 The Hydrologic Cycle

The total amount of water on Earth is invariable. At the same time water is continuously renewed while
circulating between oceans, land and atmosphere. All processes like evaporation, condensation,
precipitation, interception, transpiration, infiltration, storage, runoff, groundwater flow, which keep
water in motion constitute the hydrologic cycle. Those processes are stimulated by solar energy. They
take place simultaneously and, except for precipitation, continuously. Consider Figure 1.3.

Figure 1.3. The hydrologic cycle (Musy, 2001)

Water from rivers is replenished every year. Simultaneously the quality of water is restored. The
assessment of water resources availability or deficiency for a specific region is based on the volume
of runoff in that region. The water volume of each water body in the hydrosphere is fully replenished
during the hydrologic cycle, but the time period required varies as is shown in Table 1.2.

Table 1.2. Period of renewal of water in the hydrosphere (UNESCO, 2004)

Water body Period of renewal

Polar ice 9700 years

Oceans 2500 years

Mountain glaciers 1600 years

Groundwater 1400 years

Lakes 17 years

Rivers 16 days

Atmospheric moisture 8 days

Water in the biosphere Several hours

Water from rivers is completely renewed every year. Simultaneously its quality is restored.

1.4 The Water Budget

The water budget represents the inventory of water for a specific water body (or hydrologic region)
during a certain time interval.

It can be estimated using the continuity equation, which expresses the balance between the inflows,
outflows and change of storage in any water body / hydrologic region over a period of time:

P - R - G - E - T = ΔS (1.1)

where:

P precipitation, [unit of height] or [unit of volume / unit of time]

 R runoff, [unit of height] or [unit of volume / unit of time]

R = Rout - Rin

Rout = runoff as outflow from the water body / hydrologic region

Rin = runoff as influx into the water body / hydrologic region

G groundwater flow, [unit of height] or [unit of volume / unit of time]

G = Gout - Gin

Gout = groundwater as outflow from the water body / hydrologic region

Gin = groundwater as influx into the water body / hydrologic region

E evaporation, [unit of height] or [unit of volume / unit of time]

T transpiration, [unit of height] or [unit of volume / unit of time]

ΔS change in storage, [unit of height] or [unit of volume / unit of time]

Equation 1.1 is the basic equation of hydrology. In practice it is successfully applied for local studies
when the various hydrologic terms can be properly measured or estimated. Nevertheless estimation
is usually rough on a global scale.

1.4.1 Annual water budget of the Earth

Every year approximately 577'000 km3 are transported through the hydrosphere. The annual water
budget is displayed on Figure 1.4.

Figure 1.4. Annual water budget of the Earth

1.4.2 Annual budget of some hydrologic regions
Table 1.3. Annual water budget of Switzerland (Musy, 2001)

Precipitation 1546 mm / year

Total runoff Runoff 978 mm / year 1296 mm / year

Influx into Switzerland 318 mm / year

evaporation 484 mm / year

Table 1.4. Annual water budget of Romania (National Institute

of Meteorology and Hydrology, Regional Office, Timisoara)

Precipitation 850 mm / year

Runoff 300 mm / year

evaporation 550 mm / year

Table 1.5. Annual water budget of Bulgaria (Geography of

Bulgaria, monograph, Bulgarian Academy of Sciences , 1989)

Precipitation 690 mm / year

Runoff 176 mm / year

evaporation 514 mm / year

Table 1.6. Annual water budget of Ukraine

Precipitation 625 mm / year

Runoff 86.8 mm / year

evaporation 538 mm / year

1.5 A Brief History of Hydrology

In ancient times various hydrologic principles were successfully applied in practice. Early Chinese
irrigation and flood control works and Greek and Roman aqueducts are worth mentioning. On the other
hand ancient science was based only on logic and intuition, without measurements and observations,
and the theories were faulty most of the time.

Homer (8th century B.C.) believed in the existence of large subterranean reservoirs that supplied rivers,
seas, springs and wells. The Roman engineer Marcus Vitruvius (1st century B.C.) developed an early
theory of the hydrologic cycle in his treatise 'On Architecture'. According to his theory the rain and
snow falling in mountains infiltrated into the ground and later appeared in the lowland as streams and
springs. During the Middle Ages, Vitruvius's work was the standard reference book on Hydrology.

In the late 15th century Leonardo da Vinci and Bernard Palissy gave, independently of each other, an
accurate explanation of the hydrologic cycle. The theories were based on observations of hydrologic
phenomena. In the 17th century the modern science of hydrology was established by Perrault, Mariotte
and Halley. Perrault measured the rainfall and runoff in the Seine River and proved that rainfall
contributes significantly to river flow. He also measured evaporation and capillarity. Mariotte recorded
the velocity of flow in the Seine River and made measurements of the cross section, estimating the
discharge. Halley measured evaporation of the Mediterranean Sea.

The Bernoulli piezometer and theorem, the Pitot tube and Chezy's formula are representative
achievements of the 18th century. During 19th century experimental hydrology made considerable
progress: Darcy's law of flow in porous media and Dupuit-Thiem's well formula were elaborated.

Early 20th-century governmental agencies developed their own programs of hydrologic research.
Sherman's unit hydrograph, Horton's infiltration theory and Theis's non-equilibrium approach to well
hydraulics were based on their analyses and were the results of research programs. After 1950 the
progress in sciences and the high-speed digital computers opened new perspectives in hydrology.

CHAPTER 2

WATERSHED CHARACTERISTICS
2.1. Watershed defined

2.1.1. Definition

A watershed is a geographical unit in which the hydrological cycle and its components can be
analysed. The equation is applied in the form of water-balance equation to a geographical region, in
order to establish the basic hydrologic characteristics of the region. Usually a watershed is defined as
the area that appears, on the basis of topography, to contribute all the water that passes through a
given cross section of a stream.

The surface trace of the boundary that delimits a watershed is called a divide. The horizontal projection
of the area of a watershed is called the drainage area of a stream at that cross section. The location
of the stream cross section that defines the watershed is determined by the analysis.

2.1.2. Delineation

If a permeable soil covers an impermeable substrate, the topographical division of watershed will not
always correspond to the line that is effectively delimiting the groundwater.

Figure 2.1. The difference between the real watershed and the topographical one [Musy,
2001]
Thus the watershed is different from the topographically delimited watershed. In this case it is called
a real watershed. This difference between the two kinds of watershed is of particular importance in the
karst areas.

In the delineation of a watershed artificial barriers (e.g. roads, railways) must also be taken into
consideration. The hydrological process takes place especially on the surface, and it can be modified
by artificial inflow (e.g. artificial derivation, drinking and wastewater networks, roads, pumps,
reservoirs).

Figure 2.2. Artificial changes that occur in a watershed [Musy, 2001]

The conventional method of watershed delineation requires a topographic map. To start the divide we
should start from the location of the chosen stream cross section, then we draw a line away from the
left bank or the right bank always maintaining an angle of 90° to the contour lines. We continue the
line until it is generally above the headwaters of the stream network. Finally we return to the starting
point and we trace the divide from the other bank, eventually connecting it with the first line.
 Figure 2.3. Watershed delimitation method - detail

2.2. Watershed characteristics

2.2.1. Physical characteristics

The physiographical characteristics of a watershed influence to a large degree its hydrological

responses and especially the flow regime during floods and periods of drought.

The concentration time, which characterizes the speed and intensity of the watershed's reaction to
stress (rainfall), is influenced by the different morphological characteristics.

2.2.1.1. Geomorphology

Watershed Surface

A watershed is the area of reception of the rainfalls and of supplying the watercourse; the outlet flows
depending thus on its surface. The surface of a watershed can be measured using a variety of
methods: superposing a grid over the watershed map, using a planimeter or digitalizing methods.

Watershed Shape

The shape of a watershed influences the shape of its characteristic hydrograph. For example, a long
shape watershed generates, for the same rainfall, a lower outlet flow, as the concentration time is
higher. A watershed having a fan-shape presents a lower concentration time, and it generates higher
flow.
 Figure 2.4. The influence of watershed shape on the hydrograph [Musy, 2001]

Different geomorphologic indices can be used for the analysis of a watershed if its shape is taken into
consideration. The most frequently used index is the Gravelius's index KG, which is defined as the
relation between the perimeter of the watershed and that of a circle having a surface equal to that of
a watershed.

(2.1)

where:

KG Gravelius's shape index

A watershed area [km2]

P watershed perimeter [km]

Several values of the Gravelius's index for various shapes of watershed can be found in Figure 2.5.
 Figure 2.5. Some KG values for different watershed shapes [Musy, 2001]

Watershed orientation

The orientation of a watershed influences the melting speed of snow. Watersheds developed
especially in North-South direction have an alternative exposure to sunrays; the melting speed of snow
thus being smaller than in cases of watersheds developed towards East-West.

For a precise determination of the influence of watershed orientation, it is necessary to know the
direction and frequency of the dominant wind.

2.2.1.2. Topography

The relief influences the reaction of the watershed through the following characteristics:

Watershed hypsographical curve

Watershed hypsographical curve gives a general synthetic view of the watershed relief. This curve
represents the repartition of the watershed, taking its altitude into consideration.
 Figure 2.6. Hypsographical curve of a watershed [Musy, 2001]

The hypsographical curve has practical utility in the comparison of watersheds or of different sections
of a watershed. The hypsographical curve also helps to establish the average amount of precipitation
over the watershed, and can give information about the hydrologic and hydraulic behaviour of the
watershed, and about its hydrographic network.

Characteristic altitudes for watershed

a) The extreme altitudes of the watershed, such as minimum and maximum, are obtained as a starting
step for topographic maps. The maximum altitude is the elevation of the highest point of the watershed,
while the minimum altitude is the elevation of the lowest point, this being generally the outlet section
of the watershed. These values determine the altimetry amplitude of a watershed and help to calculate
the slope.

b) The average altitude of a watershed - can be deduced directly from the hypsographical curve or
from reading the topographical map. The average altitude of a watershed is often used in the
evaluation of certain hydro-meteorological parameters and can be calculated with relation 2.2.

(2.2)

where:

Ha average altitude of the watershed [m]

Ai;i+1 area between two consecutive contour lines [km2]

hi ; hi+1 altitudes of the contour line [m]

 A watershed area [km2]

c) The medium altitude of a watershed, represents the arithmetic mean of the values of maximum and
minimum altitudes of a watershed, and is expressed by the following relation:

(2.3)

where:

Hm medium altitude of the watershed [m]

Hmax maximum altitude of the watershed [m]

Hmin minimum altitude of the watershed [m]

Watershed average slope

Watershed average slope offers information about the watershed topography. It is considered an
independent variable. The average slope of a watershed influences radically the value of the time of
concentration and, directly, the runoff generated by a rainfall.

Series of methods have been developed to estimate the average slope of the watershed. The method
proposed by Carlier and Leclerc (1964) consists of calculating the weighted mean of all the elementary
surfaces that exist between two contour lines. [Musy, 2001]

(2.4)

where:

ia average slope of the watershed [m/km] or [‰]

D the equidistance between two consecutive contour lines [m]

L total length of the contour lines [km]

A surface of the watershed [km2]

2.2.1.3. Hydrography

The hydrographic network is defined as the sum of all the watercourses, natural or artificial, permanent
or temporary, which contribute to the runoff. The characteristics of a hydrographic network of a
watershed are influenced by four main factors: geology, climate, relief and environment. The
hydrographic network is one of the most important characteristics of a watershed.
Hydrographic network topology

The classification of the watercourses was introduced by Strahler (1957). The order of the
watercourses reflects the degree of ramification of the hydrographic network from upstream to
downstream and it is based on the following principles: [Musy, 2001]

 all watercourses without tributaries are of 1st order;

 the watercourse formed by the confluence of two watercourses of different order is going to
keep the highest order of the two;

 the watercourse formed by the confluence of two watercourses of same order is going to have
an order higher with one than the other two.

Figure 2.7. Strahler's system of hydrographic network classification [Musy, 2001]

Characteristic slopes and length for hydrographic network

The steep slope of a watercourse favours and accelerates the runoff, while a small slope gives the
water the necessary time to infiltrate totally or partially into the soil. The calculation of the average
slope is obtained from the longitudinal profile of the main stream and its tributaries.
 Figure 2.8. Longitudinal profile of a hydrographic network [Musy, 2001]

The most frequent method used to calculate the longitudinal slope of a watercourse consists of
correlating the difference of altitude of the extreme points of the stream with its length.

(2.5)

where:

s1 longitudinal slope of stream [m/km] or [‰]

ΔH difference of altitude of the extreme points of the stream [m]

L total length of the stream between its extreme points [km]

The degree of development of the hydrographic network

The degree of development of the hydrographic network, introduced by Horton, is given by the rapport
between the total length of the hydrographic network and the watershed surface.

(2.6)

where:

Dd degree of development of the hydrographic network [km/km2]

Li length of the stream [m]

A watershed surface [km]

The stability constant of a stream, introduced by Schumm, represents the opposite of the development
degree of the hydrographical network.

2.2.1.4. Agro-pedo-geological factors

Soil types and vegetal covering

The type of soil influences the infiltration rate, the retention capacity and the runoff coefficient. The
humidity degree of the soil is one of the main factors that determine the concentration time. It is very
difficult to measure this parameter because it has great variations in time and space. Most often other
parameters are used. They reflect the soil moisture and can be obtained more easily. One of these is
the antecedent precipitation index (API), expressed by the relation:

(2.7)

where:

API0 the API initial values [mm]

APIt API values after t days [mm]

t time [days]

K regression factor (K<1), characteristic for each watershed and varies from one season
to another [km]

The type and density of vegetal covering directly determines the quantity of water intercepted and
retained by the soil. For example, the forest retains a certain part of the precipitation by the tree
canopy. Vegetation regularizes the runoff in conditions that are meteorologically normal. Its action in
extreme conditions (floods and droughts) is relatively reduced. In cases of soils without vegetation the
capacity of water retention is reduced, which leads to torrential runoff and to apparition of riverbed
erosion phenomena.

For estimating the influence of vegetal covering, a coefficient for various cultures must be calculated:

(2.8)

Watershed geology

The geology of the watershed must be known in order to estimate the watershed hydrological reaction.
The geology of the watershed substrate influences both the runoff and the groundwater flow. For the
runoff the main geologic characteristic is the permeability of the soil substrate. In case of rainfall a
watershed that has an impermeable substrate presents a faster and more violent increase of the runoff
in comparison to a watershed with a permeable substrate. A watershed with a permeable substrate
will provide a base runoff during dry periods that will last longer. Watershed geology is essential for
groundwater flow, through the identification of the karst areas. These karst areas may modify even the
real watershed delimitation.

2.2.2. Hydrological characteristics

The analysis of the hydrologic behaviour of a watershed is done in order to study the hydrologic
reaction of the watershed in relation to rainfall. This reaction is measured by observing the quantity of
water that is drained from the system. The graphical representation of the evolution of the discharge
Q versus time is called a hydrograph. The hydrologic reaction of a watershed to a particular rainfall is
characterized by its speed and its intensity. Figure 2.10 gives an example of a hydrograph resulting
from a given rainfall.

Figure 2.9. The hydrograph resulted from a rainfall [Musy, 2001]

2.2.2.1. Concentration time

The concentration time tc, of the water in a watershed is defined as being the maximum of duration
necessary for a water drop falling on the watershed surface to reach the outlet section of the
watershed. The concentration time is made up of three different terms:

 th - humidification time - the time necessary for the soil to absorb the water;

 tr - runoff time - the time that corresponds to the water flow from the surface or from the first
soil horizon to a hydrographical network;
  ta - moving time - the time necessary for the water drop to move through the hydrographical
network to the outlet section of the watershed.

Concentration time is thus equal to the maximum sum of the three elements:

(2.9)

The concentration time may be deduced through field measurements or may be estimated with
empirical formulas. [Musy, 2001]

2.2.2.2. Isochrones

The isochrone is a contour joining points of equal concentration time of the water in a watershed. The
farthest isochrones from the outlet section represent the time passed for which the whole watershed
surface contributes to the flow towards the outlet section after a uniform rainfall.

Thus, the tracing of the isochrones network allows partial the comprehension of the hydrologic
behaviour of a watershed and the relative importance of each of its sub watersheds. [Musy, 2001]

Figure 2.10. Representation of isochrones from a watershed [Musy, 2001]

These curves allow, for different hypotheses, the determination of the hydrograph resulting from
rainfall over the watershed.
 CHAPTER 3
RAINFALL

3.1. Generalities

Water is the most widespread and mobile elements and has a very important role in all the physical,
chemical and biological processes. It serves as a vital substance for human existence and also for the
economical and social development of the community. In nature water is present in three aggregation
states:

 solid: snow and ice;

 liquid: pure water and solutions;

 gaseous: vapours under different grades of pressure and saturation

The change of phase depends essentially on temperature and pressure, and also on the degree of
pollution in the atmosphere. The water exists in the atmosphere in these three aggregation states.

3.2. Mechanism of formation and development of rainfall

3.2.1. The condensation process

The water is present in nature in three aggregation states: solid, liquid and gaseous. The equilibrium
states and the phase transformation of the water depend on the following parameters:

 temperature of the water and the air;

 vapour pressure e measured above the water or above the ice (dew point)

 maximum vapour pressure E given by: E= 1/2

where: e and e0 represent the partial tensions of the corresponding pressures P0 and P.
Because the maximum vapour pressure corresponds to the equilibrium state between vapours and
the evaporative surface of the water or the ice, it is called "the saturation pressure", in the first case
Ea and in the second case E0. The saturation tension increases with the temperature and at the same
temperature, it is smaller above ice than above a plane water surface. The dependence of the water
phases on the temperature and the vapour pressure is depicted in Figure 3.1.

Figure 3.1 - The transformation phases of the water

One can notice that the three phases of water are in equilibrium (at the point called triple point) only
for a certain temperature (T = 76.10-4 °C) and a certain vapour tension (e = 6,1 mb = 4,58 mmHg). In
nature the reverse process of evaporation is the transformation of water vapours into liquid state, and
is called "condensation". The transformation of vapours directly into the solid state is called
"sublimation".

The condensation of water vapours from the atmosphere depends on many factors. These factors
ensure the proper physical and thermodynamical conditions for the transformation of water's phases,
and they are:

 the cooling of the air up to the condensation temperature;

 the guarantee of the saturation state with water vapours of atmospheric air;

 the ascendant movements of warm air (convection phenomenon);

 the existence of ice crystals;

  the existence of condensation nuclei.

3.2.2. The aerosol particles spectrum size

The nuclei of condensation are minuscule particles of hygroscopic substances, which can be fine
crystals of sea salt, powders of mineral, industrial, or volcanic origin, acidic droplets. The clouds are
colloidal systems formed from very fine particles (1 - 20 μm) which are maintained in suspension due
to atmospheric turbulence.

3.2.3. The Bergeron process

According to the Bergeron theory, in order for water vapour condensation and the formation of the
droplets of atmospheric precipitations to take place, it is necessary to have in the cloud mass
supercooled particles and ice crystals around which minuscule particles agglomerate. These
agglomerations move randomly within clouds and they increase their volume (the weight) continuously
by attracting new particles. When they reach weights that surmount the sustaining forces in the cloud
mass, they fall under the action of the gravitational force with a speed between 0.3 - 8 m/s.

When clouds are present, if the air temperature is positive we get rain, and if it is negative we get
snowflakes. The size of the precipitation droplets (200 - 5000 μm) depends on the length of their path
through the clouds and on atmospheric turbulence.

3.2.4. Condensation physics and types of rainfall

If a cloud were totally exhausted, it would supply only a small quantity of the precipitation that reaches
the ground. Yet any cloud regenerates continuously during precipitation through the ascendant
currents of warm air filled with water vapour. Precipitation happens when the temperature of big
masses of air decreases below the condensation point. This cannot happen through simple cooling of
air due to the loss of heat through radiation during the night, it is necessary for a big mass of air to rise
to higher altitudes.

The air that rises from the ground surface suffers a decrease in temperature, even if it does not lose
caloric energy outwards. The decrease in temperature is due to the reduction of atmospheric pressure
at high altitudes, which allows the ascendant air to expand.

The individual molecules of gas are more diffused and do not collide so often, therefore gas has a
sensibly lower temperature. If condensation does not take place the decrease in temperature rate (dry
adiabatic lapse) is approximately 1 °C for 100 m elevation, and the dewpoint temperature decreases
with air rising, of 0,2 °C for 100 m.
If water vapours from the air condense, the adiabatic lapse is smaller (approximately 0,6 °C for 100
m) due to partial attenuation of the loss of temperature through the release of latent heat during the
condensation process. This modified gradient is called moist adiabatic lapse (of saturation).
Precipitation occurs when the air that rises cools adiabatically under the dewpoint so quickly that it
determines not only the formation of clouds but also the formation of rain, snow, and hail.

The lifting of huge masses of air to high altitudes can be convective, orographic, cyclonic or frontal.
Convective precipitation results from a simple convection cell, which is just an ascendant current of
warm air that rises to higher altitudes by being lighter than the surrounding air (figure 3.2)

Figure 3.2 - The formation of convective precipitation

A descendent colder and denser air current completes the cell. Bare grounds warm up quickly and
convey the radiant heat from the upper air. Thus the air above a warm surface becomes hotter than
the air from the surrounding area and starts to rise in a column shape, the same way as hot air and
smoke rises through a chimney. As the air rises, it becomes adiabatically cooler, so that in the end its
temperature is equal to the temperature of the surrounding air, and becomes stationary.

Before reaching this stage air can cool under the dewpoint. The condensation process then begins
immediately and the column of ascendant air becomes a cumulonimbus cloud. Its plate base indicates
the critical point at which the condensation takes place. The peak with a cauliflower shape represents
the upper part of the warm air column, which penetrates to higher layers of the atmosphere. If this
convective column continues to develop, the cloud can become a cumulonimbus mass that is a storm,
capable of producing a pouring rain.

Uneven warming of the soil is a factor that unleashes a spontaneous ascendant current, fed by latent
caloric energy released through the condensation of water vapours. For each gramme of water formed
through condensation 600 calories are released.
Unstable air, favourable to spontaneous convection that can determine precipitation as
thundershowers, can often be found in warm and humid regions, above the equatorial and tropical
oceans and above the land that surrounds them, during the whole year or during the summer for
medium altitudes.

The second mechanism that generates precipitation is the orographic type. The dominant winds and
other masses of moving air can be forced to circulate above mountain ranges. As the air rises along
the slope it cools with adiabatic speed. If the cooling is sufficient, precipitation begins. After the air
passes the mountain ridge it descends on the opposite slope. Thereafter the air is subjected to the
adiabatic heating process and, not having any humidity, source becomes very dry. These regions can
become arid, being "protected against precipitation".

Foehn-ul, the dry and warm wind from Europe, can determine the sudden evaporation of snow or the
humidity of the soil. These winds come into existence from the turbulent composition of the inferior
and superior layers of air on the leewardside of the mountain. Upper layers that had little humidity at
the beginning become drier and drier and warm up in their way to the lower layers.

The third type of precipitation is the cyclonic type. At medium and high latitudes most of the
precipitation is produced by cyclonic storms, or in low-pressure centres in an eastward motion, where
air converges and is forced to rise. Cyclonic precipitation comes into existence in the contact zone
between the warm and cold masses of air; the warm and humid air rises energetically and then cools
suddenly and therefore the water vapours condense and the resulting precipitation has a pouring
character.

3.2.5. Types of precipitation: dew, rain, ice, snow, hail, fog

Precipitation takes place when there is quick condensation inside a cloud. Rain comes from the
reunion of a big number of small droplets into big drops, too heavy to be suspended in the air. These
drops can subsequently develop, colliding with one another, reaching 7 mm in diameter. The bigger
ones are unstable and separate into smaller ones. Droplets with a diameter smaller than 0.5 mm form
drizzle.

The graupel is formed from small ice spheres resulting from the freezing of rain. Rain droplets are
formed in the warm superior layers, then fall into the cold inferior layers.

Sleet is a mixture of rain and snow.

Snow is formed from ice crystal masses, which result directly from water vapours in the atmosphere
in regions where the air temperature is below the freezing point. The ice crystals, which can be
captured on a black surface and examined under a strong magnifying glass, have a hexagonal or
prismatic shape, with an infinite range of symmetrical variations.
Hail is precipitation in the form of small balls or lumps usually consisting of concentric layers of clear
ice and compact snow. This kind of ice is usually opaque, not transparent. Hail varies from 0.5 to 5
cm in diameter and can be damaging crops and small buildings. The hail falls from cumulonimbus
clouds only, because of the strong updrafts inside the clouds. Rain droplets are raised to high altitudes
where they freeze, then form ice grains, and then fall towards the Earth, by passing through the cloud.
Suspended by strong updrafts balls of hail develop through the accumulation of new droplets of water
that freeze. Finally hail gets free from the air current and falls to the ground.

When it rains over a cold surface with temperature below freezing, water becomes a layer of thin
transparent ice. This layer of ice is called glazed frost, and the formation phenomenon is called rain
with glazed frost. This can damage trees and especially telephone and electricity poles. Roads
become dangerous and driving is very difficult.

3.3. Global distribution of rainfall

3.3.1. Influence of geographic conditions

The annual average of rainfall is recorded on maps. A line on a map or chart connecting areas of equal
rainfall is called isohyets. These maps show the distribution of rainfall on the globe.

Precipitation is very abundant (over 200 cm) in equatorial zones, where high temperatures and vast
surfaces of ocean provide large quantities of water vapours and unstable atmospheric conditions.
Almost all of precipitation is convective. If it happens close to mountainous ranges it might also be
orographic.

Precipitation is poor in subtropical zones of high pressure, due to the descendent movements of
adiabatically heated air and at the same time subjected to a strong drying process. The North African,
Arabian and Iranian deserts are in this area and so are those in Australia, South Africa and the West
Coast of South America.

Monsoon winds in Asia affect precipitation on the SE side of the continent. During the summer time
humid tropical air from the Indian Ocean comes across mountain ranges and abundant orographic
precipitation takes place. This kind of precipitation of over 200 cm is recorded in the Himalayan
Mountains, in northern India and also in the SE part of Birma and the Malacca peninsula. The
Indonesian Mountains receive orographic precipitations from both groups of monsoons: australian and
asian. At medium altitudes precipitation is affected by the dominant winds from the west. Between 35°
and 60° latitude, on the west coasts of the continents narrow strips appear with abundant
precipitations.
In arctic region, the annual average of rainfall is very low. Here the temperature is low and therefore it
doesn't contain big amounts of water vapours that can produce precipitation. At the same time low
temperatures reduce the evaporation process so that during the summer there is more soil humidity
and surface water, and during the winter, snow and ice.

3.3.2. Distribution of vegetation

The profound effect of precipitation on vegetation, drain systems, soil humidity, groundwater, and also
the quantity and seasonal distribution is important in establishing the climatic zones. The climatic map
largely coincides with a map of medium annual rainfall.

Plants react promptly to climatic changes. Every vegetal species is associated with a certain
combination of climatic elements favourable to its growth, but also with certain extremes of warmth,
cloudiness and drought beyond which the plants cannot survive. Vegetation tends to adapt to the
morphological characteristics varying with the climate, hence the large variety of vegetal species.

All land vegetation can be divided into four structural formations:

a) The forest can be defined as a vegetal formation composed of trees growing close to one another
and forming a canopy, which shades the ground. Usually there is more than one layer of vegetation in
a forest. This necessitates abundant annual precipitation, which does not need to be distributed
uniformly during the year. The necessary precipitation depends on the temperature and humidity of
the air. Forests can be found from the equatorial climate up to the subartic zones.

b) The savanna is a combination of trees and hay fields in variable proportions. The appearance of
this vegetation is similar to that of a park, with scattered bushes surrounded by grassy areas or an
area of small bushes or annual plants. The climate in these regions is characterized by low and
randomly distributed annual precipitation.

c) The meadow (hay field) consists of vegetation of higher regions, being composed partially or totally
of grasses and gramineous and subshrubs. The degree of covering varies from continuous to
discontinuous. The meadow may also have trees in humid zones of valleys and along rivers. The total
annual precipitation is low; variations from excessive heat to excessive cold can be recorded.

b) The desert is associated with a very arid climate, and consists of rare plants; there is a large barren
surface exposed to direct sunlight, to winds and running water and the frosting-defrosting effect. Here
and there one can find wooden plants. These plants are usually small and consist of grasses,
bryophyte and lichens. The vegetable habitat presents a large range due to the climate that varies
from hot tropical deserts to cold arctic deserts. In conclusion one can say that the vegetation zones
are determined by the humidity available for plants (varying from abundant-forests, to the total lack-
deserts). Temperature conditions vary greatly with the latitude and the altitude.
3.3.3. Influence of oceans on precipitation formation

Oceans cover about 7/10 of the total surface of the globe. The ocean surface has an important role in
the absorption and emission of heat. The surface of water warms up moderately and slowly, in
comparison with the surface of land, which warms up quickly and intensely. On the other hand land
cools down quickly and reaches very low temperatures compared with the surface of water when the
solar radiation ceases.

The temperature contrasts are moderate on water surfaces. Water is transparent and permits caloric
radiations to penetrate more deeply into the ocean, heat being distributed in thick layers of water.
Waters of the ocean mix continuously due to vertical movements in the surface layer, which allows the
distribution and storage of heat into a bigger mass of water.

The ocean surface allows continuous evaporation, which is accompanied by a cooling process and so
the temperature of water decreases. Moreover, water has to absorb 5 times more caloric energy than
soil and rocks in order to increase the temperature to the same level. The quantity of water vapour in
the air at a specific time varies from one place to another. In the cold and dry air of the arctic regions
it can be zero, while in the warm and humid equatorial regions it can represent 4-5 % of the volume of
the atmosphere. The oceans supply the air masses that produce precipitation through evaporation.

3.3.4. The global water cycle

Water from the oceans, from the atmosphere and from the land is subjected to a large number of
continuous transformations, also as a geographical position and as physical state.

Of the approximately 510 millions km2 of the Earth surface, land has 149 millions km2 (29.2%), and
oceans 361 millions km2 (70.8%). There is a volume of approximately 2.0 billions of water on Earth, of
which 1.369 billions km3 is the planetary ocean. The total volume of water in the land represents
751'200 km3 of which 750'000 km3 are in lake basins, and the water in riverbeds represents only 1'200
km3. The annual volume of the drainage in river waters is approximately 35'000 km3.

The circulation of water in nature is a complex process and implies other processes: evaporation,
condensation, precipitation, superficial drainage, infiltration, underground drainage, which determines
the transformation of water from one aggregation state to another. This circulation conditions the
drainage on land, contributes to the formation of underground reserves of water and at the same time
ensures the necessary water for vegetation. Without the circulation of water in nature there would be
no precipitation and life would not be possible.

Water circulation in nature is a closed continuous circuit called the global hydrologic cycle, in which
water from the atmosphere, the hydrosphere and the lithosphere participates. Huge quantities of water
evaporate from the hydrosphere (84%), the lithosphere - the humid zone (10%) and from the
lithosphere - arid zone (6%) because of solar energy. The air currents, which go from hydrosphere to
lithosphere, transport 9% of the vapours, and those that go in the reverse direction, only 2%. Therefore
there is a surplus of vapours in the lithosphere of 7%.

Under certain temperature and pressure conditions water vapours condense and fall due to gravitation,
and the precipitation is distributed as follows: 77% in the hydrosphere, 17 % in the humid lithosphere
and 6% in the arid lithosphere. In the hydrosphere precipitation (77%) is lower than evaporation (84%),
and in the lithosphere precipitation (23%) is higher than evaporation (16%).

In the lithosphere some of the fallen water comes together to form streams, brooks, creeks, rivers that
are tributary to the oceans and seas. Another part of the water infiltrates and supplies the underground
currents, coming to the surface after a while as springs. These springs also contribute to the running
water, and it finally arrives at seas and oceans after covering long distances.

3.3.5. The water budget

The water budget is the variation of water reserves ±ΔW and can be calculated as the difference
between the quantity of the incoming water I and the quantity of the emerging water E in a controlled
domain and in a determined time interval. It can be written as follows:

±ΔW=I-E (3.1)

The positive and the negative signs correspond to the increase and decrease of the water reserves
belonging to the analysed domain in the time interval. To analyse the water budget over a global year
period, the following elements are necessary:

 zm: the average annual quantity of water evaporated from the seas and oceans (the
hydrosphere space);

 zu :the average annual quantity of water evaporated from the land (the lithosphere space);

 xm: the average rainfall over the seas and oceans;

 xu: the average rainfall over the land;

 Y : the average annual quantity of water transferred by rivers into the seas and the oceans.

For every space there are the following balance relations:

 Hydrosphere zm=xm+Y

 Lithosphere zu=xu-Y
Adding up these equations we obtain:

zm + zu=xu + xm (3.2)

so that the total quantity of evaporated water equals the total quantity of fallen precipitation.

Globally, for an average year, the components of the water budget (mil. km3) are:

Table 3.1 Annual values of the components of the water budget

Oceans zm=0,425
The quantity of the evaporated water Land zu=0,078
Oceans xm=0,385
Rainfall
Land xu=0,118
The drainage from the continents Y=0,04

3.4. The measurement of rainfall

3.4.1. The measurement system of rainfall

Rainfall and other forms of precipitation are measured in terms of depth, the values being expressed
in millimetres. One millimetre of precipitation represents the quantity of water needed to cover the land
with a 1mm layer of water, taking into account that nothing is lost through drainage, evaporation or
absorption.

3.4.2. The rain gauge

The rain gauge (figure 3.3) consists of a hollow cylindrical vessel. Rain (or other form of precipitation)
falls into the vessel and its depth is measured. The evaporation process can influence the
measurements if the time interval is too long. Wetting the sides of the gauge or the measuring tube
when the quantity of the precipitation is very small may cause loss of some of the precipitation. In
order to avoid this problem the rain gauge has a funnel connected to a thinner tube. A small quantity
of precipitation can fill the scaled thinner tube, making the reading easier. The rain gauge needs
frequent emptying if it does not have an automatic device.

To know the intensity of rainfall (which is important in the maximum flow capacity calculation) the
hourly measurements are performed at specific climatologic terms for the station.
 Figure 3.3 - Precipitation gauge, showing the overflow can
1-pole; 2-collector; 3-support- galvanized metal sheet ; 4 - funnel; 5 - steel ring

3.4.3. The graphic rain gauge

Another instrument that can be used for the measurement of precipitation is the graphic rain gauge
(figure 3.4). The instrument records the graphical variation of the fallen precipitation, the total fallen
quantity in a certain time interval and the intensity of the rainfall (mm/hour). It allows continuous
measurement of the rainfall.

The general principle of the graphic rain gauge is:

 the water is collected in a funnel and is directed to a reservoir; the water level in the reservoir
(with an equivalent capacity of 10 l/mp) is controlled through a floater coupled with a recording
arm;

 the recording arm rests on a diagram, which is wrapped around a clock-driven drum, this
cylinder performs a complete rotation in 24 hours;

 when the reservoir is full the value is recorded on the diagram, the reservoir is emptied through
a siphon device and the recording arm comes to the initial position and continues to record if
rain still falls.
 Figure 3.4 - The graphic rain gauge. 1-receiver; 2-floater; 3-siphon; 4-recording needle;
5-drum with diagram; 6-clock mechanism

3.4.4. Tele-rain gauge with tilting baskets

The tele-rain gauge (figure 3.5) is used to transmit measurements of precipitation through electric or
radio signals. The sensor device consists of a system with two tilting baskets, which fill alternatively
with water from the collecting funnel, establishing the electric contact.

The number of tiltings is proportional to the quantity of precipitation hp:

hp=k n (3.3)

where:

n represents the number of tiltings (signals),

k the gauging constant of the device;

The advantage of this device is the possibility to automatically collect the data.
 Figure 3.5 - The tele-rain-gauge. 1 - collecting funnel, 2- tilting baskets;
3- electric signal; 4 -evacuation

3.4.5. Meteorological radar

Radar is an indispensable instrument for investigation and measurement in atmospheric physics. The
measurement of precipitation can be done using the theory of the electromagnetic wave propagation
of short wavelets. The ability to determine aerial distribution and cloud movements depends on the
type of radar employed. Some types of radar can estimate the intensity of precipitation, even though
there are calibration difficulties.

The advantage of radar, compared with the classical rain-gauge networks, consists of the covering
capacity from a fixed point, with information about the cloud system states for very large surfaces (over
100.000 km2). The radar range can reach 150-400 km.

Estimation of the parameters of precipitation using radar is affected by errors. One of the challenges
is the way to find the correct intensity of precipitation. In spite of all the problems, radar is still a good
way to measure the parameters of cloud systems in real time for the whole hydrographic basins and
for a range of 100 km.

3.4.6. Measurement system of snowfall

Snowfalls are measured by melting a unit-column of snow and reducing it to the water equivalent.
Thus the records for rainfall and snowfall can be compared. A 10 cm layer of snow is equivalent to a
1 cm rainfall, but the ratio varies from 30/1 for loose snow to 2/1 for old snow or melted snow.

Snow layer has a variety of densities from fresh loose snow to old moist snow. The density is measured
by weighting the snow probe, using a pentadic densimeter or through melting at room temperature.
The gravimetric densimeter consists of a cylinder similar to that of the rain gauge, which can be stuck
in the snow, the probe being measured by a scale with weight (figure 3.6).

Figure 3.6 Snow densimeter. 1- receiver cylinder with gradations; 2- gliding weight;
3- rod with gradations; 4- fastening system

To determine the density the following relation is used dz=m/v [g/cm3], dz is the weighted mass over
the volume of the probe, which can be read on the cylinder with gradations.

The area of the cylinder is 50 cm2, and measuring the depth hz we can calculate the volume V=50 hz
[cm3] and the density dz=m/50 hz [g/cm3], where m is the mass resulting through weighing. The water
equivalent in the snow, namely the reserve of the water in the snow, can be calculated using: ha=hz dz
[l/m2 or mm]. The water equivalent can also be obtained through the slow melting of the snow probe
at room temperature and weighing the water amount with the can of the rain gauge. Using this method
the density is:

dz=ha/hz (3.4)

If necessary the thickness of the ice crust can be measured.

3.5. Punctual rainfall

Rainfall fallen in a certain time interval is recorded in mm water column or litres per square meter. The
two measurement units are equivalent:

(3.5)

Rainfall at the station is recorded on rain gauges. They measure total values recorded in a time interval
or using the records on rain gauge graphs (figure 3.7):
 Figure 3.7 - Rain gauge graphs

By measuring the rainfall fallen in an equal time interval we obtain a graph called histogram. The
histogram represents the graph of rainfall intensity.

The following values represent the height of rainfall in time interval Δt; where Δt may be in minutes (1
minute, 5 minutes) or in hours (1 hour, 2 hours, 3 hours etc.):

(3.6)

Therefore, the histogram is derived from the rain gauge graph. This can be written as following (cf.
Figure 3.8):

(3.7)

The average intensity of rainfall is the ratio between the total rainfall and the duration of the rain.
According to necessities the rain intensity can be expressed in the following units: mm/minute-1; mm/k
or ls-1ha-1 or m3s-1km-2.
 Figure 3.8 - Rain gauge graph and histogram

The monthly rainfall (total rainfall for a month) or the annual rainfall (total rainfall for a year) are
calculated using the rainfall fallen in a 24 hour period. The resulting values are kept in archives as
tables.

The values hijdaily are null when there is no precipitation and above zero when there is precipitation.
One can get to monthly rainfall by adding up the values of rainfall on a column.

Daily precipitation and monthly precipitation may be processed statistically. The daily values are used
for gauging calculations regarding the hydrotechnic works or the evacuation of the meteorite water
works. The monthly values are used for the determination of irrigation water amounts and the annual
ones for the general summary of the hydrographic basin.

3.6. Rainfall recorded on hydrographic basins

The rainfall recorded on a hydrographic basin represents values obtained by taking into account the
hypotheses regarding the spatial distribution of the uneven distribution of the precipitations. The rainfall
fallen in a time unit is maximum in the centre of the rain and decreases in a non-linear manner towards
the outskirts of the area.
The following methods are used for the calculation of the average rainfall for a basin:

 arithmetic mean;

 the method of the Thiessen polygons;

 the isohyets method;

 the square grid method.

When the area is physically and climatically homogenous and the required accuracy is small, the
average rainfall for a basin can be obtained as the arithmetic mean of the hi values recorded at
stations.

(3.8)

3.6.1. The method of Thiessen polygons

The method of Thiessen polygons consists of attributing to each station an influence zone in which it
is considered that the rainfall is equivalent to that of the station. The influence zones are represented
by convex polygons. These polygons are obtained using the mediators of the segments which link
each station to the closest neighbouring stations (figure 3.9). The ratio can be written as:

Wi=Fi/F (3.9)

where:

Fi represents the area of the Thiessen included partially or wholly in the considered basin.

F is the area of the basin

The water volume attributed to each area is:

Vi=Fi hi (3.10)

where hi represents the rainfall recorded at station i.

The average value of the rainfall is the ratio between the total volume of the rainfall (as the sum of the
partial volumes) over the area of the basin:
 (3.11)

The weights Wi are directly proportional to the area of the corresponding Thiessen polygon.

Figure 3.11 - The Thiessen polygons method

If the surfaces Fi are equal and the number of the stations is n, then and the ratio Fi/F, which

represents the weight Wi, equals to 1/n. When the surfaces of the Thiessen polygons are equal, the
method consists in calculating of the arithmetic mean for the respective basin.

The Thiessen polygons method takes into account the rainfall at stations not included in the considered
basin. The relation describing the average rainfall can be written as follows:

(3.12)

where:

i refers to stations in the considered basin,

j refers to stations outside of the considered basin.

3.6.2. The isohyets method

The isohyets method involves a linear interpolation between the punctual values of rainfall recorded
at stations. The isohyets are lines of equal rainfall value. Considering that the area between the
isohyets hi and hi+1 is fi, the partial volume Vi of the rainfall over this surface is

(3.13)

The ratio between the partial volumes and the basin surface F represents the average rainfall:

(3.14)

In reality interpolations should be done in a non-linear fashion, taking into account the characteristics
of the basin, that is: the geographic position, the vegetation type, the altitude, the topography, etc. One
should have a good knowledge of the area from the climatic and physical point of view. The method
is difficult to use for short time intervals.

3.6.3. The square grid method

The square grid method is used to calculate quickly the average rainfall for hourly time intervals. The
method takes into account the nonlinearity of the rainfall distribution over the basin area. The basin is
divided in a network of square elements with a fixed step size. The rainfall is calculated in each node
using interpolation, as a function of the measured values at the adjacent stations.

Figure 3.10 - The square grid method

First we consider the closest stations of the considered node in the four quadrants (figure 3.10). There
are not two stations in the same quadrant. The amount of rainfall in the i node is:
 (3.15)

where:

hj represents the recorded rainfall in the nodes 1, 2, 3, 4

hi are computed values.

dij distance between nodes i and j (j = 1, 2, 3, 4)

The following ratio signifies a weight, representing the influence of the stations j against the stations i:

(3.16)

With this notation hi becomes:

(3.17)

The values hi are computed for every Δt time interval; the average rainfall over the basin for the current
interval is computed as the arithmetic mean of the hik values; the calculation for each node is:

(3.18)

where:

N is the number of nodes of the basin

k the index of the time step.

3.6.4. I-D-F curves

The calculation of maximum rainfall is necessary for the designing of evacuation works of rainwater in
cities, or on the premises of storm flow correction, or constructions and hydrotechnic installations. For
this purpose one can use the intensity-duration-frequency lines (figure 3.11). The intensity of
calculated rainfall is a function of the standardized frequency and the duration of the calculated rainfall.

Figure 3.11 - The intensity-duration-frequency curves (Musy, 2001)

The standardized frequency is the annual number of rains of duration t, whose intensity exceeds the
computed intensity. The computed frequency is calculated as a function of the class importance of the
analysed objective. Thus for populated centres and industrial units we have the following values of
standardized frequencies (table 3.1).

Table 3.2 Standardized frequencies

Class of the Industrial units and

importance of the production units of a Populated centres
objective different nature
I 1/5 1/2...1/1
II 1/3...1/2 1/1...2/1
III 1/2...1/1 2/1
IV 1/1...2/1 -
V 2/1

In expressing frequency the numerator represents the numbers of rains and the denominator
represents the number of years. The values in the table represent frequencies, not probabilities.

CHAPTER 4
EVAPORATION AND TRANSPIRATION
4.1. Evaporation process

4.1.1. Definition

evaporation (E), from the hydrological point of view, is the process in which water from open water
surfaces (oceans, seas, lakes and rivers), from uncovered soil and from surfaces covered by snow
and glaciers goes into the atmosphere in vapour state. [Musy, 2001]

Transpiration is the process in which a fraction from the water assimilated by vegetation is set free
into the atmosphere in vapour state.

Evapotranspiration (ET) is the sum of those two processes, evaporation and transpiration. So the
evapotranspiration is the total quantity of water, in the shape of vapour, transferred from atmosphere,
hydrosphere, biosphere, lithosphere and anthroposphere.

(4.1)

where:

ET evapotranspiration [unit of height] or [unit of volume / unit of time]

Ew evaporation from water surface [unit of height] or [unit of volume / unit of time]

Et transpiration produced by the vegetation biological process [unit of height] or [unit of

volume / unit of time]

Es evaporation from soil surface without vegetation [unit of height] or [unit of volume / unit of
time]

Ei evaporation of rainfall quantity intercepted by vegetal covering and also by constructions

[unit of height] or [unit of volume / unit of time]

Ed evaporation of rainfall quantity accumulated in ground depressions without possibilities of

infiltration [unit of height] or [unit of volume / unit of time]

Eg evaporation from snow and glacier surface [unit of height] or [unit of volume / unit of time]
 Figure 4.1 The components of evapotranspiration

The evaporation and evapotranspiration processes play a major role in the hydrological cycle and in
maintaining a climatical balance at planetary level. The evaporation and evapotranspiration role is
explained by the fact that these processes are associated with an important energetic consumption.

4.1.2. Physical process of evaporation

For evaporation to take place the presence of water inflow is assumed. Water will evaporate from free
open surfaces like land, lakes, reservoirs, open streams, but also from soils covered with vegetation,
trees, etc. Precipitation that reaches the ground surface returns to the atmosphere in vapour shape.

Natural evaporation is an energy-exchange process. Energy input is necessary for evaporation to

proceed. The quantity of energy necessary to start the transition from liquid state to vapour state is
called vapourization latent heat (Le).

(4.2)

With continuous heat flow evaporation will continue, and it will produce an accumulation of molecules
in vapour state on the air-water interface. As is known from the gas formula, at constant speed and
temperature the gas pressure will increase with the molecule number accumulated on the water
surface. This increasing of water vapours (e) will continue to the end, when the condensation
phenomenon appears. In a hypothetical situation, where the condensation rate is equal to the
vaporization rate, there will be balance, and the molecules will pierce the air layer from the water
surface in both ways, layer which has a maximum vapour pressure (es).

In reality this balance situation cannot exist, because the air volume is unlimited compared to the water
volume. For this reason the concentration of molecules from the water surface to atmosphere will be
different and circulation will take place under a certain gradient of vapour pressure (e) with respect to
the height (z) above the air liquid interface.
If we note K as the vapours transport coefficient, we can express the evaporation in this way:

(4.3)

The wind influence on evaporation is evident when the turbulent diffusion increases it causes an
increased vapour transfer coefficient K. The graphic of Figure 4.2 expresses the combined effect of
temperature, air pressure, air stability and other factors, in variation with height.

Figure 4.2. The correlation between daily evaporation, temperature

and elevation. (Serban, Stanescu, Roman, 1989)

The vapour pressure (e) at constant air pressure, with respect to the temperature is presented in
Figure 4.3.

Figure 4.3. The correlation between water vapour pressure and

temperature. (Serban, Stanescu, Roman, 1989)
Dalton (1802), after studying this phenomenon, established a law that expresses the evaporation rate
from a water surface, depending on the air saturation deficit (the water quantity es - ea which air can
store) and on the wind speed (u). This law has the following expression (Musy, 2001):

(4.4)

where:

E evaporation rate (evaporation speed) characteristically to the time T [unit of height / unit
of time]

f(u) constant of proportionality which takes into account the wind influence in the evaporation
process

es vapour pressure at the saturation state, at the temperature of evaporation surface

ea vapour pressure on the time interval T

Vapour pressure at the saturation state can be expressed by the relation:

(4.5)

Where, from P results the pressure of the water vapours in natural state and the temperature of the
evaporation surface is expressed in °C (Musy, 2001).

4.1.3. Meteorological factors

The meteorological factors that influence the evaporation process are: the available quantity of water,
solar radiation, air pressure and wind, the specific and relative air humidity and also the air and water
temperatures.

4.1.3.1. Available water quantity

Basically, for the evaporation phenomenon takes place a water supply is necessary.

4.1.3.2. Solar radiation

The quantity of water evaporated from a surface depends mainly on the heat quantity that the surface
receives from the sun. The heat quantity received by a surface alternates depending on the geographic
conditions (latitude gradient) and altitude (altitude gradient) where the surface is located (Musy, 2001).
This heat exchange between the atmosphere, the soil surface and the water surface is achieved
through heat convection and conduction. This energy exchange is compensated in all points by a
transfer into the atmosphere of evaporated water, which through condensation returns as rainfall.
These heat exchanges maintain the hydrological cycle. The solar radiation received by the soil surface
during a day with clear sky can be expressed using the relation:

(4.6)

where:

RA is the Angot value of solar radiation

n/D the day clouding rate

a,
coefficients, in Penman relation a = 0.18 and b = 0.55
b

A part of solar radiation received by the Earth (Rc) is reflected like short radiation waves, the reflection
coefficient is r = 0.06.

The net quantity of absorbed radiation, Rn results in the relation:

(4.7)

A fraction of the net quantity of absorbed radiation by Earth surface is lost during nights with a clear
sky. Empirically, the net flux in the outside (RB) can be expressed as follows:

(4.8)

where:

σ Lummer and Pringsheim constant (117.74×10-9 [g·cal/cm2·day])

Ta absolute temperature (t °C + 273 [K])

u air vapours pressure [mm Hg]

c,
d, coefficients, Beuman relation c = 0.47, d = 0.077, e = 0.20, f = 0.80
e, f

Consequently, the net quantity of energy (H) that finally stays on the water surface is given by the
relation:
 (4.9)

4.1.3.3. Atmospheric pressure and wind (air movement)

The weather pattern indicated by atmospheric pressure affects evaporation. The edge of an
anticyclone provides ideal conditions for evaporation as long as some air movement is operating in
conjunction with high air pressure. Low atmospheric pressure is usually associated with weather in
which the air is charged with water vapour and conditions are not conducive to aid evaporation.

Wind plays an important role in the evaporation process. The amount of evaporation increases as drier
air replaces humid air accumulated above the evaporating surface [Shaw, 1988].

4.1.3.4. Water & air temperature and air humidity

Temperature of both air and evaporating surface is an important factor in evaporation. The higher the
air temperature, the more water vapour it can hold, and similarly, if the temperature of evaporating
water is high, it vaporizes faster. Thus evaporation amounts are high in tropical climates and tend to
be low in Polar Regions. Similar contrasts are found between summer and winter evaporation
quantities in temperate climate.

The water vapour capacity of air is directly related to temperature. Evaporation is dependent on the
saturation deficit of the air, which is given by the difference between the saturation vapour pressure at
the surface temperature and the actual vapour pressure of the air.

(4.10)

Hence more evaporation occurs in inland areas where the air tends to be drier than in coastal regions
with damp air from the oceans [Shaw, 1988].

4.1.4. Physical factors

The physical factors that have a major interference in the evaporation process are: the depth of the
free water surface, the shape of the free water surface and the water salinity.

Depth of open water surface

This characteristic plays an important role in energy storage. The essential difference between a
shallow water surface and a deep-water surface results from the sensitivity of the shallow surface to
seasonal climatic variations. A shallow water surface will follow closely meteorological variations, and
the deep-water surface with an important temperature delay will present a different answer to climatic
exchanges [Musy, 2001].

Shape of open water surface

The nature of the evaporating surface affects evaporation by modifying the wind pattern. Over a rough,
irregular surface, friction reduces the wind speed but tends to cause turbulence so that, with an
induced vertical component of the wind, evaporation is enhanced.

Water salinity

An increase of salinity concentration by 1% reduces the evaporation by 1% by reducing water

pressure. This decreased pressure is directly proportional to the concentration of saline solution [
Musy, 2001].

4.2. Evapotranspiration process

By the definition, this process groups direct water evaporation from the soil surface and from the open
water surfaces with vegetation transpiration.

4.2.1. Transpiration process

The plants assimilate water from soil through the roots. The development of the roots system is
connected to the water quantity available in soil. The water absorption is accomplished through
osmosis. The water circulates through vegetation's vascular system to the leaves. The transpiration
process takes place at the leaf level.

Figure 4.4. The pathway of water through vegetation. [Musy, 2001]

In addition to the participation of the transpiration process in the water hydrological cycle, transpiration
has multiple functions, the most important of which is to maintain a thermal balance in the leaf. The
water quantity transpired depends on meteorological factors (the same as the physical process of
evaporation), on the soil humidity in the roots zone, on the plant's age and species, and also on leaf
growth and on the depth of the roots.

4.2.2. Evapotranspiration factors

In general, evapotranspiration is conditioned by climatic conditions, soil type and also vegetation type.
Starting from the vegetal covering degree, two kinds of evaporation flux resistance have been
observed: the aerodynamic resistance and the diffusion resistance of the evaporated surface. In
physical terms the aerodynamic resistance is the resistance from water vapours transferred from the
vegetation surface to the atmosphere. The values of aerodynamic resistance are generally between
10 and 100 [s/m]. The dynamic resistance can be expressed by the following relation:

(4.11)

where:

ra aerodynamic resistance [s/m]

κ von Karman constant

u wind speed [m/s]

z anemometer height (=h+2 or h is the vegetation height) [m]

z0 contact height [m]

d0 translation of plan origin from the logarithmically relation between the wind speed and
height [m]

The diffusion resistance from the evaporation surface rs depends on the vegetation type and on the
available humidity of the soil. After research, Jaworski proposed a relation to estimate this resistance:

(4.12)

where:

rs diffusion resistance of the evaporation surface [s/m]

 c coefficient depending on vegetation type (e.g. for the turf c = 76.5)

Zg water quantity existing in the superior layer of the aerated zone [mm]

P rainfall quantity [mm]

4.2.3. Evapotranspiration notions

The authors used three distinct notions for evapotranspiration:

Potential evapotranspiration (ET0) is defined as the total water losses through evaporation and
transpiration of a surface with grass of uniform height completely covering the ground surface, in
period of growth, and abundantly fed with water.

Maximal Evapotranspiration (ETM) of a given crop is defined using different growing studies in which
the quantity of water and the agronomic conditions are optimal.

Real Evapotranspiration (ETR) is the sum of the quantity of water evaporated from soils and the
quantity of water evaporated from vegetation, when the soil is at actual specific humidity and the
vegetation is in real physiological and sanitary growing phases. [Musy, 2001]

4.3. Estimating evaporation and evapotranspiration

For the quantitative estimation of the evaporation and evapotranspiration processes, direct and
indirect methods exist that measure the processes with adequate equipment. These evaporation and
evapotranspiration values can also be determined using empirical and semi-empirical formulas.

4.3.1. Estimating evaporation

PRIMAULT formula for open water surfaces:

(4.13)

where:

E evaporation [mm]

es vapour pressure at saturation state at the evaporation surface temperature [kPa]

ea vapour pressure during the estimation time interval [kPa]

 N effective sunstroke duration during the estimation interval [h]

nd total number of days of the estimation interval

ROHWER Formula:

(4.14)

where:

E evaporation [mm]

es vapour pressure at saturation state at the evaporation surface temperature [kPa]

ea vapour pressure during the estimation time interval [kPa]

u wind speed [m/s]

PENMAN Formula:

(4.15)

(4.16)

where:

E evaporation [mm]

γ Bowen constant [kPa/ °C]

Δ slope of the maximum curve tension of the saturated air with vapour depending on
temperature

λ vaporization constant heat at constant pressure, (= 2.45 [MJ/kg])

ε report vapour molecule weight /air sec, (= 0.622)

P atmospheric pressure [kPa]

Cp vaporization constant heat at constant pressure, Cp = 1.013×10-3 [MJ/kg/ °C]

Ea evaporation calculated by Rohwer formula [mm]

Ec evaporation measured by Colorado bank [mm]

Among these three empirical and semi-empirical formulas the Penman formula is the most rigorous if
the values for the parameters that occur in relation are correctly introduced.

4.3.2. Estimating evapotranspiration

To estimate the evapotranspiration process, empirical or semi-empirical relations can be used, and
also deterministic relations that express more exactly the physical process.

4.3.2.1. Empirical and semi-empirical formulas

The empirical and semi-empirical formulas are obtained for certain particular climatic conditions and
extrapolated in some cases for other climatic conditions, but only after a previous control and
adaptation. These formulas are easy to apply, but they can estimate only the evaporation during large
time intervals (decades, months, season). An example is developed by Turc (1961) who expresses
the evapotranspiration potential depending only on average air temperature t and global solar radiation
Rg, estimated through the sunshine duration:

- for soil with relative moisture U bigger or equal to 50%

for 10 days
(4.17)
for one month

- for soil with relative moisture U smaller than 50%

for 10 days
(4.18)
for one month

Between the illustrative empirical and semi-empirical relations, that give similar results with values
resulted by direct determination, we can evoke the formulas of Meier, Thornthwaite, Bouchet,
Papadakis.

4.3.2.2. Formulas with physical base

These theoretical formulas for evapotranspiration estimation define more exactly the physical process.
Bouchet used the energetic balance, Penman (1948) in addition has introduced the aerodynamic
influence, and Monteith (1981) has improved the Penman formula by introducing the effect of diffusion
resistance of evaporation surface: [Serban, Stanescu, Roman, 1989]

PENMAN Equation

(4.19)

PENMAN-MONTEITH Equation

(4.20)

where:

Rn net solar radiation [W/m2]

γ Bowen constant [kPa/ °C]

Δ slope of the maximum curve tension of saturated air with vapour depending on
temperature

λ vaporization constant heat at constant pressure, (= 2.45 [MJ/kg])

ρ air volume mass [kg/m3]

δe humidity deficit [kPa]

cp moist air heat capacity [MJ/kg/ °C]

ra aerodynamic resistance [s/m]

rs diffusion resistance of evaporation surface [s/ m]

CHAPTER 5
INFILTRATION
5.1 Infiltration Processes

5.1.1 Definition

Infiltration is the flow of water through the soil surface into a porous medium under gravity action and
pressure effects.

5.1.2 Infiltration characteristics

The infiltration capacity is the maximum rate at which water can be absorbed by a given soil per unit
area under given conditions.

Figure 5.1 The infiltration process depending on soil type and flow [Musy,2001]

Infiltration regime i(t) depends on the supply regime (irrigation, rain), but also on soil properties. The
cumulative infiltration I(t), is the total amount of water infiltrated during a given period.

(5.1)
where:

I(t) the cumulative infiltration during the t period (mm)

i(t) the infiltration regime during the t period (mm/h)

Hydraulic conductivity at saturation ks, is an essential parameter of infiltration. It represents the limiting
value of infiltration if the soil is saturated and homogenous. Percolation is the vertical water flow in
soils (porous unsaturated environment) on the groundwater layer under the influence of gravity. This
process follows infiltration and has a major influence on the underground layer water supply.

Net rain is the amount of rain that falls to the ground surface during a shower. The clear rain is deduced
from the total rain, diminished by the intercepted fraction of vegetation and that which is stored in
ground depressions. The difference between the infiltrated rain and the drained rain on the ground
surface is called production function.

5.1.3 Factors which influence infiltration

The main factors that influence the infiltration are:

 the soil type (texture, structure, hydrodynamic characteristics). The soil characteristics
influence capillary forces and adsorption;

 the soil coverage. Vegetation has positive influence on infiltration by increasing the time of
water penetration in soil;

 the topography and morphology of slopes;

 the flow supply (rain intensity, irrigation flow);

 the initial condition of soil humidity. Soil humidity is an important factor of infiltration regime.
The infiltration regime evolves differently in time for dry or wet soils;

 soil compaction due to rain drop impact and other effects. The use of hard agricultural
equipment can have consequences on the surface layer of soil.
 Figure 5.2 The infiltration regime depending on time for different types of soil [Musy,2001]

5.2 Models Used to Estimate Infiltration Rates

Infiltration processes can be estimated by means of different models:

 models based on empirical relations involving 2, 3 or 4 parameters;

 physically based models

5.2.1 Models based on empirical relations

Empirical relations show a decrease of infiltration depending on initial time (either exponential or
quadratic function of time), which tends to a limit value, generally ks, but near 0. An empirical relation
is the Horton formula, where the infiltration capacity can be expressed as following [Drobot, 1999]:

(5.2)
or

(5.3)

where:

i(t) infiltration capacity at time t (mm/h)

i0 initial infiltration capacity depending on soil type (mm/h)

 t time from the beginning of the shower (h)

I(t) total quantity of infiltrated water from initial time until the moment t (mm water column)

γ empirical constant depending on soil type (min-1)

This formula is not linear and it presents certain practical difficulties. Through linearization, we obtain:

(5.4)

As logarith, we get:

(5.5)

The formula of the Institute of Soil and Water Management of the EPFL is:

(5.6)

where:

i(t) infiltration capacity at time t (mm/h)

if final infiltration capacity (mm/h)

a,
correction coefficients
b

The relation is a little different from that of Horton. There are just two parameters. This relation has the
advantage of allowing the search of functional relations between the limit/final capacity of infiltration
and soil texture, and also between the parameter a and the amount of soil humidity. Other formulas
can be used to determine the infiltration regime of water from soil.

5.2.2 Physically based models

These models describe in a simplified manner the water movement in soils, especially at the humidity
front level, depending on certain physical parameters.

Table 5.1 Main functions used at infiltration [Musy,2001]

Author Function Legend

 i(t) - infiltration capacity during time [cm/s]
i0 - initial infiltration capacity [cm/s]
Horton
if - final infiltration capacity [cm/s]
γ - constant depending on the soil type

Kostiakov α - parameter depending on soil conditions

i1 - infiltration capacity at time t=1min [cm/s]

Dvorak-
Mezencev t - time [s]
b - constant

c - factor variable from 0.25 to 0.8

Holtan w - Holtan equation flow factor
n - experimental constant approximately = 1.4

s - sorptivity [cms-0.5]
Philip A - gravity component depending on hydraulic
conductivity at saturation [cm/s]

a - constant
Dooge Fmax - maximal retention capacity
Ft - water quantity retained on soil at time t

ks - hydraulic conductivity at saturation [mm/h]

h0 - surface pressure load [mm]
Green&Ampt
hf - pressure load at the humidity front [mm]
zf - humidity front depths [mm]

From the models presented in Table 5.1 the following two models have been used most often:

The Philip model

Philip proposed a method of resolving the vertical infiltration for certain initial and boundary conditions.
This model has introduced the notion of "sorption" that represents the soil capacity to absorb water
when the flow is produced only under gradient pressure [Musy, 1998]. The infiltration can be simplified
as follows:

(5.7)
where:

i(t) infiltration rate (cm s-1)

s sorption (cm s-0.5)

t time (s)

A the gravity component, depending on hydraulic conductivity on saturation (cm s-1)

For horizontal infiltration the gravity gradient is not involved. Infiltration will have the following
expression:

(5.8)

(5.9)

The Green and Ampt model

This model is based on hypotheses that involve a schematisation of infiltration processes (Figure 5.3):

Figure 5.3 Infiltration process schematisation according to Green and Ampt [Musy,2001]

The method's main hypotheses are:

 a humidity front is perfectly defined;

 a transmission zone, where in time and space water storage and hydraulic conductivity are
constant;
  the suction forces of the humidity front are constant;

Based on the Darcy law the model includes the hydrodynamic parameters of soil:

(5.10)

where:

i(t) infiltration rate (mm)

t time (h)

ks hydraulic conductivity at saturation (mm/h)

H0 hydraulic total head at surface (mm)

Hf(t) hydraulic total head at the humidity front level (mm)

zf maximum depth of the humidity front

h0 pressure head at surface (mm)

hf pressure head of the humidity front (mm)

One of Green's and Ampt's model hypotheses stipulates that water storage from the transition zone is
uniform. The cumulative infiltration I(t) results from the product of water storage and the depth of the
humidity front.

(5.11)

where:

I(t) cumulate infiltration

θ0 quantity of water imposed on the surface

θ initial quantity of water in soil

zf maximum depth of humidity front

The last two relations result in:

(5.12)
For horizontal flow infiltration has the relation:

(5.13)

For vertical flow infiltration becomes:

(5.14)

This model is satisfactory when applied to a soil with coarse texture, but it is an empirical method in
which it is necessary to determine the pressure head of humidification front.

5.2.3 Variation of infiltration rates during a rainfall

The spatial and temporal variability of water quantity existing in soil is described by infiltration curves
or hydric profile (Figure 5.4). These represent the vertical water distribution in soil at different periods
t. In a homogeneous (uniform) soil when the soil surface is flooded, the hydric profile has three zones:
a saturation zone, a transition zone and a humidity zone.

Figure 5.4 Characteristics of the hydric profile during infiltration [Musy,2001]

During a rainfall the infiltration capacity of soil decreases to a limiting value, which represents the
infiltration potential at saturation. If we compare the rain intensity and the infiltration capacity of the
soil, there are two possibilities:

 when the rain intensity is inferior to infiltration capacity, water infiltrates faster due to the supply
regime. The necessary time to equalize the infiltration capacity is variable and depends on
 existing soil humidity conditions or on the shower. The time taken is longer when the soil is
dry and the water supply regime is similar to the hydraulic conductivity at saturation ks;

 when the rain intensity is superior to the infiltration capacity of the soil the water surplus is
stocked on the surface or in ground depressions. The infiltration regime and the infiltration
capacity for net storm rain are presented in the next Figure (Figure 5.5) [Musy,2001].

Figure 5.5 Infiltration regime and net storm rain [Musy,2001]

CHAPTER 6
 RUNOFF AND SUBSURFACE FLOW

6.1 Hydrological regime

6.1.1 Definition

Stream hydrological regime is defined by means of flow variations, usually represented by the monthly
average flow graphics (calculated for a certain number of years). Monthly flow coefficient is the monthly
rapport of the inter-annual, which allows repartition representation, in percents, of the monthly flows
during the year.

The hydrological regime of a stream is defined by the flow variations usually represented by the
monthly average flow graphic (calculated for a certain number of years and called inter-annual module-
rainfall):

(6.1)

It can be defined as the annual flow coefficient:

(6.2)

The curve of monthly flow coefficients shows the systematic character of seasonal variations and
compares the streams between them.
 Figure 6.1 Examples of average flow curves [Musy, 2001]

Average annual flow can be represented by the following relation:

(6.3)

6.1.2 Classification

A simple classification of hydrological regimes has been done by Pardé (1933), who distinguished
three regime types:

 simple regime: characterized by a maximum and generally only one water supply (glacial
regime, snow regime, gauging regime)

 mixed regime: characterized by two maximums and two minimums per year, with several ways
of water supply (snow-glacial regime, snow-gauging regime)

 complex regime: many extremes and many ways of water supply

In a first step two flow types can be distinguished: "rapid" flows (surface and subsurface flow) and
"slow" flows (groundwater flow).

6.1.3 Annual flow balance

The annual flow Et represents the water quantity that flows every year through a basin. Total flow can
be expressed by means of the following relation:

(6.4)

where:

Es superficial flow

Eh hypodermic flow

Eb base flow

For important rainfall Es >> Eh. For this reason when it cannot always be distinguished quantitatively
on the field, Es and Eh, is often adopted:

(6.5)

where:

Cr surface flow coefficient

Ces superficial flow coefficient

P rainfall
 Figure 6.2 Rain heights repartition during a shower of constant intensity [Musy, 2001]

6.2 Runoff (Overland flow)

Overland flow is a phenomenon that appears when the rain intensity exceeds the soil's maximum
capacity to absorb water. This capacity decreases in time until it reaches a constant value. In
homogenous soils, with a deep underground layer, this maximum capacity is equal to the hydraulic
conductivity at saturation. Natural soils with an increased hydraulic conductivity in temperate and
humid climate have an infiltration capacity inferior to the maximum intensity of rain.

Otherwise the flow process is developed in two phases:

1. At the beginning of the shower, the infiltration capacity is generally superior to the rain intensity;
water will be completely infiltrated. Rain is retained in the soil until the soil saturation capacity
is achieved. The submersion time (ts), can be defined as the duration between the beginning
of rainfall and the instant when the soil achieves saturation capacity. The submersion time
also indicates the flow beginning. For soils the submersion time is variable and depends on
rainfall intensity and initial soil humidity.

2. The rainfall intensity exceeds the infiltration capacity. The subsurface flow is constituted by the
difference between these two terms.
 Figure 6.3 Infiltration rate and cumulate infiltration for a uniform
rain and submersion time definition [Musy, 2001]

When the runoff process exceeds the infiltration capacity water flows into another area of the
watershed with a superior infiltration capacity. Using mathematical models and site experiments, the
resultant runoff process explains the hydrological basin's answer in semi-arid climates and also in
conditions of important rainfall intensity.

The flow on saturated surfaces is produced when it exceeds the soil capacity to retain water and the
capacity to transmit laterally the water flux. Figure 6.4 shows these two situations: flow on saturated
surfaces and flows that exceed the infiltration capacity .

Figure 6.4 Flow process generated through exceeding the infiltration capacity
and through flows on saturated surfaces [Musy, 2001]

Generally the flow is indirectly estimated from the hydrographical network.

6.3 Subsurface flow

Part of the infiltrated effective rainfall circulates more or less horizontally in the superior soil layer and
appears at the surface through drain channels. This flow is called subsurface flow (in the past it was
called hypodermic flow). The presence of a relatively impermeable shallow layer favours this flow.
Subsurface flows in water bearing formations have a drainage capacity slower than superficial flows,
but faster than groundwater flows. The essential condition for the appearance of the subsurface flows
is: the hydraulic lateral conductivity of the environment has to be superior to the vertical conductivity.
The subsurface flow in unsaturated regimes can be the base flow in the area with large slopes, and it
is dominant in humid regions with vegetal covering and well-drained soils.

Figure 6.5 Different flow types [Musy, 2001]

6.3.1 Piston effect

Piston effect permits analysis of the subsurface flow. The existence was assumed of a mechanism to
transmit a quasi-instantaneous pressure wave. This mechanism, called "the piston effect" assumes
that water that falls on a slope is transmitted downstream with a pressure wave and causes a sudden
exfiltration on the watershed.

This phenomena principle can be explained by analogy with a saturated soil column to which known
quantity of water is added. Due to the gravitation effect water moves to the bottom of the column.

6.3.2 Flow through macro pores

Macro pores are pores in which the capillarity phenomena are inexistent.
The origin of macro pores

We can distinguish:

 pores formed due to soil micro fauna: with dimension of 1-50 mm. In general they are located
in the superior soil layer (0-100 cm).

 pores formed due to vegetation roots. These pores become free when the plants die. The
structure of macro pores network will depend on vegetation type and also on the growing
state.

 natural macro pores: appears when the initial hydraulic conductivity is large.

 cracks.

Subsurface flow is carried through macro pores. Which lead the water to unsaturated areas.

6.3.3 Pipe flow

Pipe flow emphasizes soil drainage and water flow. It is difficult to establish the exact difference
between pipes and macro pores. Pipes are considered to be larger than macro pores. Also pipes
present a higher connectivity degree than pores, without saying that the pipes are forming a continuous
network. Pipes lead the water to an unsaturated environment.

6.4 Groundwater flow

Since the aeration zone has enough humidity to allow deep-water infiltration a part of the rainfall
penetrates into the phreatic layer. The amount of water depends on the underground structure and
geology and also on the water volume that comes from rainfall. The water flow passes through the
aquifer with a speed of several meters per day before it returns to the stream. This flow, wich comes
from the phreatic layer, is called base flow or groundwater flow. The groundwater flows generally
maintain stream discharge in the absence of rainfall.
 Figure 6.6 Two distinct situations in which the underground layer can contribute
to stream discharge or drain the stream [Musy, 2001]

Darcy's Law and the continuity principle govern the non-steady state movement of water in the ground.
For the difference between inflow and outflow, the following equation can be written:

Inflow = Outflow +/- Variation in Storage

6.5 Flow resulting from ice and snow melting

The flow resulting from ice and snow melting dominates generally in glaciers and mountain regions,
where the climate is cold. The snow melting process reloads the water layer and also saturates the
soil. In some cases it can contribute to the surface flow. The increase in the surface flow will depend
on water equivalent to snow or ice layer, on the melting regime, and finally on the snow's
characteristics.

6.6 Sediment transport

Alluviums are particles of different shapes and dimensions transported by the stream current. They
come from the soil layers, from the slopes and also from the ground of the streambed. The alluviums
from slopes are gravel and small boulders disintegrated by the hitting of raindrops or other atmospheric
agents and they are carried to the streambed by overland flow.

The solid transport is the sediment quantity (or solid discharge) transported by the stream. This
phenomenon is regulated by two stream properties:

 its competence - it is measured using the maximum diameter of rocks that can be transported
by the stream. This characteristic depends on water speed.
 Figure 6.7. Hjulstrom diagram shows the competence
depending on water speed [Musy, 2001]

 its capacity - it represents the maximum quantity of materials that can be transported to a
given point and instant of the water stream. Capacity depends on the water speed, on the
flow and on the section characteristics (shape, roughness)

These two properties are not directly connected. The silt transport of a water stream is determined by
the particle characteristics (shape, size, concentration, the drop speed and particles density). These
allow us to determine:

 The suspended load is composed of those materials whose size and density allow them to
move without touching the stream bottom. Suspended load transport is generally made up of
silts, clays, and colloidal substances. This solid discharge can be measured and extrapolated
in certain conditions for the entire sector. In many cases the suspension load represents a
high percentage of the total transport. These particles make the water turbid. The particles
have a prismatic shape, sharp edges and the smaller ones reach several microns.
  The bed load is composed of gross matter that cannot be found in suspension because of its
weight and of the speed of flow. These particles move by rolling. They have round edges and
flattened shapes due to friction and collision of the particles.

Notions about specific transport and mechanical erosion on watershed

The notion of specific transport and mechanical erosion on watershed regroups two different
processes. These two notions show the difference between the processes of alluvium detachment and
transport, before going back into the stream, and also the transport into the stream.

The first notion concerns erosion agents, which are rain, wind, flow and also factors that condition the
quantity of dragged particles: rain characteristics, soils, vegetation, topography and human activity.
The quantity of dragged particles will be also determined by a number of factors like water speed,
streambed characteristics, aggregate grading. Bank erosion can contribute to the suspension load
measured in streams, and the presence of lakes and reservoirs leads to particle sedimentation. The
sedimentation of solid matters transported by a stream is introduced into the reservoir. And to the
downstream of dams erosion of the streambed takes place.

The following aspects emerge out from the second notion:

 the stream bed is the transit way for alluviums in their movement from upstream to downstream

 the alluvium quantity grows when the water flow is over a critical value

 the alluvium movement within the stream takes place intermittently, being influenced by the
flow.

Figure 6.8. Classification of different types of riverbed sediments [Musy, 2001]

 CHAPTER 7
SURFACE AND SUBSURFACE STORAGE

7.1 Surface Water Storage

7.1.1 Definition

Surface water storage includes water accumulated on the soil surface or underground, intercepted
water, i.e. the rainfall quantity retained by vegetal coverage, and water retained in depressions
(flooded plains, lakes, swamps, pools).

Figure 7.1. Surface storage [Musy, 2001]

On a temporal scale (hours ,season, year) and spatial scale (depression type) we can distinguish:

 Small depressions that are filled with water when rain intensity is bigger than the soil
absorption capacity. The total volume that can be retained in these depressions is called the
surface retention capacity. After a shower water stocked in depressions flows into the soil.
These depressions can have an important role in flood attenuation on a watershed.
  Lakes, pools or flooded plains are natural or artificial surface water reservoirs that can store
important amounts of water. They influence in hydrological balance through surface water -
groundwater relations, favouring evaporation processes and slowing down river flow.

7.1.2 General characteristics of lakes

Limnology is the discipline that studies hydrological and biological phenomena in lakes, together with
their environment. It also studies lakes' origins, morphology, physical and biological properties and
hydrological balance.

The main morphological elements of lakes and pools are depth, length, size and shape of water
surfaces, and also water volume. The study of the lakes' state requires the understanding of a certain
number of physical characteristics such as:

 volume;

 useful volume (volume that can be exploited during a year);

 surface;

 maximum and average depth;

 dimensions (length and width);

 altitude;

 orientation with regard to dominant winds;

Water plan level variations are an important factor. All lacustrine surfaces are submitted to level
variations, evaporation and water flow. Inflows into a lake depend on seasons.

7.2 Subsurface Water Storage

This represents the portion of water that penetrates into the soil and stagnates for a short period of
time or for many years.

7.2.1 Saturated / unsaturated zone

Saturated zone - is a system with two phases (solid and liquid) where all pores are filled with water.

Unsaturated zone - is a system with three phases (solid, liquid and gas) where only a part of the
ground is filled with water.
 Figure 7.2. Distinction between saturated and unsaturated zones [Musy, 2001]

The fundamental difference between saturated and unsaturated zones consists in different hydraulic
conductivities.

It can be distinguished:

 water from soil representing water from the unsaturated zone, and which is the transit bond
between matter and substances. These processes are part of a continuous cycle soil-plants-
atmosphere.

 subsurface water level is influenced by rain percolation regime or irrigation water that crosses
through the unsaturated zone.

7.2.1.1 Water from soil

Spatial and temporal variability of the liquid phase is emphasized by quantity and quality level. The
evolution of quantity (volume) and quality (water composition) results from a dynamic transfer coupled
with water properties and soil characteristics.

Characteristics of the soil liquid phase

The description of the liquid phase is based on the notion of soil humidity, this variation depending on
soil structure and porosity. With reference to mass or volume, soil humidity can be expressed by:
 θ Volumic humidity is the ratio between water volume present in the soil on apparent soil
volume. This varies between minimal values (residual humidity), and maximal values
(saturation humidity). This principle is equal to effective porosity (defined as the ratio
between void volume and total environment volume).
θr Residual humidity.
θs Saturation humidity.
Sw Saturation index is defined as the ratio between water volume and pore volume. The value
of this ratio expresses the pore volume filled with water, and it varies between a residual
minimum and 100%.
w Weight humidity represents the ratio between the water amount (mass) contained in a soil
sample and the mass of the dry soil particles.

Spatial and temporal variability is described by hydric profiles that represent vertical distribution of soil
humidity at given instants. The surface included between two successive hydric profiles in the interval
t1 and t2 represents the volume of water stored or lost from the considered surface.

Figure 7.3. An example of hydric profiles at

time t1 and t2 [Musy and Soutter, 1991]

Subsurface water energetic state

Water dynamics results from the action of different force fields: gravity, capillarity, and absorption. The
sum of internal, kinetic, and potential energy characterizes the energetic state of the subsurface water.
The concept of total potential of liquid phase allows quantifying the energetic state of subsurface water,
and describes the behaviour inside the system "soil - plants - atmosphere". In a general manner it can
be written as the ratio of the sum of potential energies (pressure, gravity) on weight liquid unit and it
can be expressed by the notion of hydraulic charge H.

(6.1)

where:

H hydraulic charge [m] is the pressure expressed by water equivalent height or the pressure
exerted by a water column of same height

h pressure charge [m] is the ratio between the effective pressure of subsurface water and
the air pressure

z gravity charge [m], is the water height above the reference plan

The distribution of pressure potential, gravity and total potential in soil is graphically represented by
profiles of pressure charge, gravity and total charge.

Figure 7.4. Profiles of pressure charge, gravity charge and total charge
of a system in hydrostatic equilibrium [Musy, 2001]

Dynamics behaviour: Darcy's law

Darcy's law proposes calculation of the total water outflow as a yield between the constant of
proportionality (hydraulic conductivity at saturation) and a gradient of hydraulic charge, depending on
depth. Darcy's law can be written as following:
 (6.2)

where:

q transition flux [mm/h]

H total hydraulic charge [m]

z depth below the soil surface [m]

Ks hydraulic conductivity at saturation [mm/h]

Two cases are distinguished:

 in case of an unsaturated environment, hydraulic conductivity varies with soil humidity and
water effective pressure, which is negative.

 in case of a saturated environment, effective water pressure in soil is positive and depends on
the depth of submersion below the free water surface.

Water stock estimation

The quantification of flux is achieved with hydric profiles, and is based on the continuity equation:

(6.3)

where:

Δθ humidity variation [m3/m3]= 100[%], positive or negative value

Δq transit flux variation [mm/h]

Δz depth variation [mm]

Δt time variation [h]

Two hydric profiles are taken into account, measured between t1 and t2, and between the altimetric
cote z1 and z2. This results in the following equation:

(6.4)

(6.5)
 (6.6)

where:

qz2, qz1 represent the average water flux throughout t1 and t2, and z1 and z2

Δt time interval throughout t1 and t2

(ΔS)z2-z1 surface throughout two hydric profiles and z1 and z2

ΔS stock variations between the altimetric level

Figure 7.5. Estimation of water stock in soil [Musy, 2001]

7.2.1.2 Subsurface water

An aquifer is a permeable geological pattern (soil or rock) with pores or communicating fissures large
enough to allow water to circulate under the effect of gravity (sand, gravel, gritstone). The aquifer is
therefore a groundwater reservoir.

Suspended and phreatic groundwater tables.

Suspended formations appear in aeration zones above local impermeable lentils of clay or marl; these
groundwater tables are of shallow depth with volume variations depending on the air temperature and
the rainfall atmospheric regime.

Different types of groundwater tables can be distinguished:

 a free groundwater table is that in which the superior limit is the free surface.

 a captive groundwater table (artesian) is created by rainfall infiltration into permeable rocks
and accumulation between two impermeable layers. Usually water is under pressure. For this
 reason the hydrostatic level is above the captive groundwater table or even above ground
level. Captive underground waters can be frequently found in isolated deposits. They have
physical and chemical qualities that make them valuable for urban centre water supply.

 A semi-captive groundwater table has a semi-permeable coverage.

 A karstic groundwater table is formed in a region composed of carbonated and soluble rocks
(CaCO3). Due to the solubility process, new fissures (which allow free water circulation through
watershed) and caves (where water is stored) are created.

Subsurface water main characteristics

The aquifer can be characterized by the following indexes:

 Effective porosity is the ratio between the "mobile" water volume at saturation (liberated under
gravity effect) and total volume of environment. Generally it varies between 0.1 and 30%. The
effective porosity is a parameter determined in the laboratory or on the field.

 Storage coefficient is the ratio between the free or stored water volume of an aquifer and
hydraulic charge variations. The storage coefficient is used to characterize the exploited water
volume, and to regulate the groundwater storage in reservoir voids. For captive groundwater
this coefficient is extremely low.

 Hydraulic conductivity at saturation is a coefficient of Darcy's law and characterizes the effect
of flow resistance under friction forces. It is determined in the laboratory or on the field.

 Transmissivity is the product between hydraulic conductivity at saturation and the groundwater
table's height.

 Diffusion characterizes the reaction speed of a groundwater table when disturbed (stream level
variation, aquifer level variation). It can be expressed by a ratio between transmissivity and
storage coefficient.

Real and hypothetical flow speed, subsurface water flow

Water flow speed depends on hypothetical water speed.

 Figure 7.6 Real flow and hypothetical flow (Musy, 2001)

Groundwater flow Q is the volume of water per time unit that crosses a section of the subsurface water
under the effect of a hydraulic gradient. It can be expressed by the following relation:

(6.7)

where:

Q subsurface water flow

Ks hydraulic conductivity [m3/s]

i hydraulic charge gradient [m/m]

A section of soil [m2], A = H.1m

H subsurface water width [m]

l flow section average width [m]

T transmissivity [m2/s]

Water stock estimation

The estimation of the subsurface water volume begins by a geological study of the impermeable level,
or by determination of the rock or storage coefficient, or by measuring the piezometric level.

Recession curve

Without rain, evaporation and transpiration processes progressively reduce the subsurface water
reserve of the watershed. One of the most common laws is the simple exponential law:

(6.8)
where:

Q water flow at time t [m3/s]

α drainage coefficient

Q0 initial water flow at time t0 [m3/s]

This relation can be applied to determine the useful volume of water stored at a given instant, and also
to determine the storage capacity. The available water volume at an instant t can be found with the
following equation:

(6.9)

where:

V available water volume contained in the watershed reserve

In the particular case of an exponential decreasing law and at instant t = 0, one obtains:

(6.10)

Figure 7.7. Watershed storage capacity (Musy, 2001)

7.3 Water storage in solid phase

7.3.1 Snow coverage

Snow coverage is an essential component of the storage in mountain regions. Accumulated snow on
a watershed is a potentially useful stock for a region's water supply.

Evaluation of snow storage

The snow storage can be evaluated by:

 photogrammetry, which can give information about the snow layer and its distribution in
mountain regions with poor forestation. The flow width is estimated through subtraction of the
snow surface level and soil level. It is determined in certain points marked before the first snow
falls.

 utilization of topographical copies, which allows estimation of the altitude of the snow layer
limits on mountainsides.

 utilization of photos from satellites (digital or analogical), which allows estimation of the snow
layer in mountain and plain regions.

 site measurements, which are also used to estimate the snow width variations.

Snow layer measurements on large surfaces, combined with snow density values locally estimated,
permit an evaluation of the water equivalent for an entire region; but it is also necessary to estimate
the snow melting time and the flow of this storage.

During the snow melting period snow coverage is composed of two separate parts: the upper part
which is unsaturated and can contain a certain quantity of water, and the lower part which is in contact
with the soil and is saturated with water.
 Figure 7.8. Flow process of a snow layer [Musy, 2001]

Snow melting

Snow melting is caused by heat transfer to the snow layer and depends on the following elements:

 Solar radiation

 Heat transfer (convection and conduction)

 Latent heat transfer through evaporation and condensation

Snow melting rate calculation is a difficult process that requires different simplified hypotheses. It is
assumed that the latent ice heat is 80 cal/g, that the snow is pure ice, and that the snow temperature
is 0 °C. It can be admitted that this last hypothesis is not real during winter, because snow temperature
is negative.

A simple method of calculating the snow-melting rate in the United States is the method of the
temperature index or the method of the daily degree. This method takes into consideration the air
temperature, and has the advantage of using general accessible meteorological records. Water height
resulting through snow melting can be estimated by the following relation:

(6.11)

where:

hfiday water height resulting through snow melting during the day i [cm]

k coefficient which expresses the influence of natural and climatic conditions of the basin
(excepting the temperature) above snow melting [cm/ °C]

Ti daily average air temperature, over 0 [ °C] for the day j, determined for the average
altitude of the basin

T0 reference temperature, generally admitted as equal to freezing temperature [ °C]

7.3.2 Ice coverage

Two types of ice coverage can be distinguished: permanent glaciers and ice formed on the surface of
lakes and rivers.
 CHAPTER 8
HYDROGRAPH / HYDROLOGICAL PROCESSES

8.1 Hydrological response analysis

The way a catchment reacts when it is subjected to a rainfall event is called hydrological response.

Figure 8.1 Hydrological response of a catchment [Musy, 2001]

A shower that falls on a catchment can have a powerful effect by modifying the flow regime. The
hydrological response can be:

 fast - important in case of surface flow

 delayed - important in case of subsurface flow

  total - hydrological response is composed of the surface and subsurface flow

 partial - hydrological response results from the surface flow or subsurface flow

Hydrological response on a catchment is influenced by many factors that are related to:

 climatic conditions of the environment

 rain (spatial and temporal distribution, intensity and rain duration)

 catchment morphology (shape, dimension, slopes' orientation)

 physical properties of the catchment (soil nature, vegetal coverage)

 structure of the hydrographic network (dimensions, hydraulic properties)

 previous soil humidity state.

8.1.1 Rainfall related factors

8.1.1.1 Influence of the rainfall duration

The response of a catchment depends on the rainfall volume and the intensity variations during the
rainfall. For a simple catchment, divided into four areas (A, B, C and D) of equal surface and delineated
by isochrones, a variable flow time can be allocated for each sector (1 hour for zone A and 4 hours for
zone D) (Linsley & Crowford, 1966).

Figure 8.2 Catchment representation [Musy, 2001]

A rain with a volume of 10 mm constant for every case is considered.

Figure 8.3 presents three cases:

 Uniform rainfall of 10 mm / 1 hour (i = 10 mm/h) on the catchment

 Uniform rainfall of 10 mm / 4 hours (i = 2,5 mm/h) on the catchment

  Uniform rainfall of 10 mm / 20 minutes (i = 30 mm/h) on the catchment

Figure 8.3 The rainfall influence in time, on the hydrological response of a catchment
(Réménérias, 1976). Hyetograms are represented on the left side, and hydrographs on the
right side

It can be observed that there is a rainfall critical time when the peak flow is at its maximum.

8.1.1.2 The influence of spatial distribution

The average rainfall of 10 mm / 1 hour is equally distributed over the catchment. Figure 8.4 shows the
influence of shower spatial distribution over the hydrograph form. Hyetograms are represented on the
left side, and hydrographs on the right side.
 Figure 8.4 The influence of rainfall spatial distribution on
the hydrological response of a catchment [Musy, 2001]

8.1.1.3 Influence of intensity variations

The total rainfall of 10 mm / 1 hour is uniformly distributed over the catchment, but it is not equally
distributed in time. Figure 8.5 shows the influence of intensity variations over the hydrograph form.
Hyetograms are represented on the left side and hydrographs on the right side.

Figure 8.5 The influence of rainfall intensity variations on

the hydrological response on a catchment [Musy, 2001]

8.1.2 Importance of initial humidity conditions

The hydrologic response depends also on the initial hydric state of the catchment. In relating effective
rainfall to surface runoff, the amount of effective rainfall depends on the state of the catchment before
the storm event. If the ground is saturated or the catchment is impervious, then a high proportion of
the rain becomes effective runoff. By absorbing rainfall an unsaturated ground has a certain capacity
before responding to effective rainfall that contributes to the surface runoff. Once the ground
deficiencies have been made up the rainfall becomes fully effective. In a second period of effective
rain the response of the catchment will depend on the effects of the first input. An example for these
cases is given in Figure 8.6.
 Figure 8.6 Influence of initial humidity conditions on the
hydrograph's response of a catchment. [Musy, 2001]

8.2 Relation rainfall - runoff

A rainfall defined in time and space that falls on a catchment produces a hydrograph. Figure 8.7
defines certain essential elements of the hydrograph resulting from a hyetogram.

Figure 8.7 Hyetogram and hydrograph resulting from a storm event (rain - flow) [Musy,
2001]
To describe the processes that occur when the rain is transformed into a flow hydrograph (by Horton's
postulate), we apply two functions called production function and transfer function. The production
function allows determination of the net rain hyetogram starting from the total rain. The transfer
function allows determination of the hydrograph resulting from the net rain. The net rain represents
the part of total rain that contributes to the flow process.

Figure 8.8 Transformation of total rain in hydrograph. [Musy, 2001]

The hydrograph is represented by an asymmetric curve. Peak flow is represented by the following
formula:

(8.1)

where:

C runoff coefficient (depends on the catchment characteristics)

i rainfall intensity in time tc

A area of catchment

It can be defined:
  Response time of the catchment tr - represents the time interval that separates the net rain
gravity centre from the peak flow or sometimes the gravity centre of the flow hydrograph.

 Time of concentration tc - is the time required by rain fallen on the catchment to flow from the
farthest point to the measuring point of the river. Thus, after time tc from the beginning of the
rainfall, the whole catchment is considered to contribute to the flow. The value of i, the main
intensity, assumes that the rate of rainfall is constant during tc, and that all measured rainfall
over the area contributes to the flow. The peak flow Qp occurs after the period tc.

 Rising limb tm - is the time from the beginning of the rain to the peak of the hydrograph

 Base time tb - represents the direct flow duration.

8.3 Flow hydrograph

The hydrograph describes the whole time history of changing rate of flow from a catchment due to a
rainfall event. It is essential to appreciate some of its simple components.

In Figure 8.7, rainfall intensity (i, in mm/h) is shown in discrete block intervals of time (t). The lower
continuous curve of discharge (Q in m3/s) is the hydrograph resulting from the event. The discharge
hydrograph is obtained from continuously recorded river levels and the level-discharge relationship
appropriate to a river gauging station. The discharge hydrograph has two main components: the area
under the hump, labelled surface runoff (which is produced by a volume of water derived from the
storm event), and the broad band near the time axis, representing the baseflow.

At the beginning of the rainfall the river level is low and a period of time passes before the river begins
to rise. During this period the rainfall is intercepted by vegetation or soaks into the ground, making up
soil-moisture deficits. The length of the delay before the river rises depends on the humidity of the
catchment before the storm and the intensity of the rainfall itself.

When the rainfall has made up catchment deficits and when surfaces and soil are saturated, the rain
begins to contribute to the stream flow. The portion of rainfall that finds its way to a river is known as
the effective rainfall, the rest being lost in evaporation, detention on the surface or retention in the soil.
As the storm proceeds, the proportion of effective rainfall increases and the lost rainfall decreases.

The volume of surface runoff, represented by the upper area of the hydrograph minus the baseflow,
can be considered in two main subdivisions in order to simplify the complex water movements over
the surface and in the ground. Effective rainfall makes the immediate contribution to the rising limb
unto the peak of the hydrograph and, even when rainfall ceases, it continues to contribute until the
inflection point. Beyond this point, it is generally considered that the flow comes from water temporarily
stored in the soil. This so-called interflow continues to provide the flow of the recession curve until
water from the whole effective rainfall is completely depleted.

One final term, lag time, requires explanation. There are many definitions of lag, which is a measure
of the catchment response time, but here it is considered from the gravity centre of the effective rainfall
to the gravity centre of the direct surface runoff.

The boundary between surface runoff and baseflow is difficult to define and depends on the geological
structure and composition of the catchment. During an individual rainfall event, the baseflow
component of the hydrograph continues to go down even after river levels have begun to rise. Only
when the storm rainfall has time to percolate down to the water table does the baseflow division curve
begin to rise.

Unit Hydrograph

Unit hydrograph is the hydrograph of surface runoff resulting from a rain that falls in a unit of time (1
hour or 1 day) and produced uniformly in space and time over the total catchment area (Sherman,
1942).

In practice, a t hours unit hydrograph is defined as resulting from a unit depth of effective rainfall falling
in t h over the catchment. The chosen magnitude for t depends on the size of the catchment and the
response time to major rainfall events. The standard depth of effective rainfall was chosen by Sherman
to be 1mm or 10mm.

The response hydrograph of a catchment varies according to the season: the same amount of effective
rainfall will be longer in appearing as surface runoff in the summer season when vegetation is at its
maximum development, and the hydraulic behaviour of the catchment will be "rougher". In countries
with no marked seasonal rainfall or temperature differences and constant catchment conditions
throughout the year, the unit hydrograph will be a much more consistent tool to use in deriving surface
runoff from effective rainfall. Another weakness of the unit hydrograph is the assumption that effective
rainfall is produced uniformly both in time and over the area of the catchment. Indeed, real distribution
of rainfall within a storm is very rarely uniform. For small or medium size catchments (up to 500 km2),
a significant rainfall event may extend over the whole area, and if the catchment is homogeneous in
composition, even a fairly even distribution of effective rainfall may be produced. More often, storms
that cause large river discharges vary in intensity, in space, as well as in time. The storm movement
often affects the consequent response over the catchment area. Making T smaller can reduce the
effect of variable rainfall intensities.

The unit hydrograph method has the advantage of great simplicity. Once a unit hydrograph of specified
duration T has been derived for a catchment area, then, for any sequence of effective rainfalls in
periods of T, an estimation of the surface runoff can be obtained by the simple properties outlined
above. The technique was adopted and used worldwide for many years.

Many researchers from all over the world have studied extensions of the unit hydrograph principles.
Dooge (1959) brought one of the most researched and fundamental contributions. Concentrating on
linear mechanism, he suggested that the response of the catchment could be modelled by combining
the storage effects with translation effects.

Further simplification of the Dooge approach using linear theory was also made by Diskin (1964) who
modelled the catchment response by means of two series of equal linear reservoirs in parallel. Singh
developed another linear catchment model, and showed that in practice it is possible to use simple
geometrical forms instead of the real time-area curve. Kulandaiswamy produced a non-linear
catchment response function using a non-linear storage expression and hence incorporated non-linear
relationships that have been recognized for a long time as being more realistic in the description of a
catchment's behaviour.

The unit hydrograph and its derivative models are mostly based on a single rainfall input, as usually
an effective or excess rainfall after losses is deducted. Sometimes the input value comes from
measurements of a single rain gauge or from the rainfall area over the catchment computed from
several point rainfall measurements. In both cases a single value represents the catchment rainfall,
which is called lumped input (Shaw, 1988).
 CHAPTER 9
INSTRUMENTATION AND MONITORING

9.1 Rainfall measurement

Of all the components of the hydrological cycle the elements of precipitation, particularly rain and
snow, are the most commonly measured. Precipitation is generally expressed as accumulated depths
of water caught over a horizontal surface (mm) in a time interval.

1 mm = 1 l/m2 = 10 m3/ha (9.1)

The commonest instruments used to measure rainfall are rain gauges and rainfall recorders.

9.1.1 Rain gauges

It is not physically possible to catch all rainfall or snowfall over a drainage basin; the precipitation over
the area can only be sampled by rain gauges. Rain gauges have different capacities depending on
the readings (daily or monthly). The rain gauge shows the total quantity of rainfall or snow collected
usually in a day, or in a month (if the rain gauge is placed where the access is difficult).

Its components are:

 a sampling orifice made of brass

 a slowdown funnel that forms the top part of the gauge and an inner part that are made of
copper.

 a graduated glass gives a direct reading of the depth of rain that falls on the area.

Choosing the site where the collector will be set is very important, and must be representative for the
area and characterized by the absence of obstacles in the neighbourhood. The OMM standards (1996)
stipulate that the receptive surface of a rain gauge must be horizontal and placed at 1.50m above the
soil surface.
 Figure 9.1 Hellmann's rain gauges [Musy, 2001]

9.1.2 Rainfall Recorders

The need for continuous recording of precipitation arose from the need to know, not just how much
rain has fallen, but also when it fell and over what period.

Siphon rain recorder (float recording gauges)

Rain is stored in a cylindrical collecting chamber containing a float. Movements of the float are
recorded by a pen trace on a chart. When no rain is falling the pen draws a continuous horizontal line
on the chart; during rainfall, the float rises and the pen traces slopes upwards on the chart according
to the intensity of rainfall. When the chamber is full the pen arm lifts off the top of the chart and the
rising float releases a trigger interrupting the balance of the chamber, which tips over and activates
the siphon. A counter-weight brings the empty chamber back into an upright position and the pen
returns to the bottom of the chart.

Tipping-bucket rain gauge

Rain caught in the collector flows down a funnel into a two-compartment bucket of fixed capacity.
When full the bucket tips to empty, and a twin adjoining bucket begins to fill. As the bucket is tipped,
it activates an electric circuit, and the ensuing pulse is recorded on a counter. In many stations,
particularly in remote locations, measurements are recorded on magnetic tape or solid-state event
recorders and the cassette is usually changed at monthly intervals.

Optical precipitation gauge

The optical precipitation gauge can measure rain or snow; it measures the precipitation rate in relation
to disturbance to a beam between an infrared light emitting diode and a sensor. These gauges can
record directly on a data storage device that can be accessed by computer [Dingman, 2002].

9.2 Evaporation, transpiration and evapotranspiration

measurements

9.2.1 Evaporometers

Atmometers

These instruments can give direct measurement of evaporation, are simple, inexpensive, and easy to
operate, but clean the porous surfaces from which the evaporation takes place.

Two types are described here:

The Piche evaporometer consists of a glass tube with one end closed. A circular disc of absorbent
blotting paper is held against the open end by a small circular metal disc with a spring collar. Water in
the tube hangs-up by its closed end, feeding it constantly. The tube is graduated in millimetres, and
will give a direct reading of evaporation over a chosen period of time, usually a day. The tube holds
an equivalent of 20 mm of evaporation; Water is replenished when necessary.

The Bellani atmometer consists of a graduated burette and a thin ceramic disc that provides the porous
surface. The difference in burette readings over a specified time gives the measure of evaporation.

Percolation gauges

These instruments measure evaporation and transpiration from a vegetal surface, Et, and compare
the tanks and pans used for measuring E0. There are different types of tanks and pans, having
between 1-5 m diameter and 10-70 cm depth. They can be set at the soil surface, partially into the
ground or in water. In all of these cases a distance between water and the upper part of the tank has
to be maintained. Water variations in the tank, measured at established time intervals, reflect the
evaporation. (More details can be found in Linsley, Kohler and Paulhus - "Hydrology for engineers",
1988)

There are many different designs and, in general, these are regarded as research tools. A cylindrical
or rectangular tank about 1 m deep is set into the ground and filled with a representative soil sample
supporting a vegetal surface [Shaw, 1988]. A pipe from the bottom of the tank leads surplus percolating
water to a collecting container. Evaporation plus transpiration is given by the following equation:

Et = Rainfall - Percolation (9.2)

Percolation gauges do not take into account changes in soil moisture storage. The measurements
should be taken over a time period defined by instances when the gauge is separated, so that any
difference in the soil moisture storage would be small.

Lysimetres

The lysimetre is an recipient set into the ground, open at the top, with drainpipe at the bottom and a
weighing device underneath that improves Et measurements of percolation gauges. However, it is
much more complex and more expensive to construct and maintain [Shaw, 1988].

Then:

Et = Rainfall - Percolation ± Weight change (9.3)

All units of measurements are referred to the area of the lysimeter orifice at ground level.

Figure 9.2 Lysimeter [Musy, 2001]

9.3 Infiltration measurement

9.3.1 Mûntz Infiltrometre

This method is based on the principle of constant charge. A graduated cylinder is set into the ground
and maintains a constant water level (about 30 mm). Water level variations during a time interval
determine the infiltration rate.

Figure 9.3 Mûntz's infiltrometre [Musy, 2001]

9.3.2 Infiltrometre with double cylinders

Two cylinders are set into the ground. Measurement is based on the principle of variable charge and
allows assessment of vertical water infiltration.

Figure 9.4 Infiltrometre with two cylinders [Musy, 2001]

9.3.3 Guelph Infiltrometre

This instrument is made of two concentric tubes. The inner tube allows air circulation and the outer
tube allows water supply. Water introduced with a constant charge (3-25cm) passes through a small
cylinder (~10 cm) fixed in soil. This method allows determination of hydraulic conductivity and
sorptivity.

9.3.4 Infiltrometre with aspersion.

This instrument uses the principle of rainfall simulation. Infiltration is indirectly measured through the
estimation of the groundwater table level.

9.4 Flow measurement (liquid and solid discharges)

9.4.1 Stage

The staff gauge is a base element for reading the level of a stream. A graduated staff is fixed vertically
to the riverbank or according to the angle of slope, (but values obtained in this case must be corrected
depending on the angle) at a stable point in the river, unaffected by turbulence or wave actions. The
meter graduation should extend from the datum or lowest stage to the highest stage expected. The
stage is read with an accuracy of ± 3 mm. All staffs should be made of durable material resistant to
temperature changes and they should be kept clean especially in the range of average water levels
[Shaw, 1988].

Depending on the regime of the river and on the availability of reliable observers, single readings of
the stage at fixed time can provide a useful regular record.
 Figure 9.5 Staff gauges [Musy, 2001]

Crest gauges

There are several simple devices for marking the peak flood level in places where there is no
continuous level recorder. The standard crest gauge consists of a 50 mm diameter steel tube
perforated near the bottom and closed at the top with one or two holes under a lid to allow air to
escape. Inside the tube is a removable rod that retains the highest watermark by means of a floating
granular cork supplied near the base. The crest gauge is levelled into a normal staff gauge or
benchmarked on the bank. The rod is cleaned and the crest gauge is reset after each reading. The
main disadvantage of this device is that a sequence of minor peaks over a short period might be
missed, the reading after such events giving only the highest peak level.

Autographic Recorders

The most reliable means of recording water level is the float operated chart recorder. To ensure
accurate sensing of small changes in water level the float must be installed in a stilling well to avoid
waves and turbulence from the main river flow. There are two basic mechanisms used by
manufacturers:

The moving float looped over a geared pulley with a counterweight that activates a pen marking the
level on a chart driven round on a horizontal clockwork drum.
 Figure 9.6 Scheme of a float recorder [Musy, 2001]

The level calibration of the chart should accommodate the whole range of water levels, but extreme
peaks are sometimes lost. The time scale of the chart is usually designed to last a week, but the trace
continues around the drum until the chart is changed or the clock stops.

The float with its geared pulley and counterweight turns the chart drum set horizontally, and the pen
arm is moved across the chart by clockwork. With this instrument all levels are recorded, but the time
scale is limited.

9.4.2 Discharge measurements

The most direct method to obtain a value of discharge that corresponds with a stage measurement is
the use of the velocity-area method, in which flow velocities are measured at selected verticals of
known depth across a measured section of the river.

The simplest method to determine flow velocity is timing the movement of a float over a known
distance. Surface floats comprising any available floating object are often used in rough preliminary
surveys; these measurements give only the surface velocity and a correction factor must be applied
to give the average velocity over a depth.

Current meters

Current meters are reasonably precise instrument that can give a nearly instantaneous and consistent
response to velocity changes, and the construction is simple and robust enough to withstand rough
treatment in debris-laden flood flows. The instrument needs to be calibrated to obtain the relationship
between the rate of revolutions of the cups or propeller, and the water velocity.
 Figure 9.7 Flow and field of velocities through a cross section [Musy, 2001]

Electromagnetic method

The electromagnetic flow measurement method and the following ultrasonic method, are now well
established:

The ultrasonic method uses pulses to measure the mean velocity at a prescribed depth across the
river. This is a sophisticated form of the velocity-area method; the cross-section must be surveyed and
water levels must be recorded.

The integrating-float technique developed recently [Sargent, 1981] uses the principle of moving floats
by releasing compressed-air bubbles at regular intervals from special nozzles (From a pipe laid across
the bed of the stream). Bubbles rising to the surface with a constant terminal speed Vr are displaced
downstream, at a distance L from the surface by the effects of the flow velocity.

Dilution Gauging

This method of measuring the discharge in a stream or pipe is made by adding a chemical solution or
tracer of known concentration to the flow and then measuring the dilution of this solution downstream
where the chemical solution is completely mixed with stream water.
Figure 9.8 Principle of dilution measuring [Musy, 2001]
 CHAPTER 10
HYDROLOGICAL DATA

10.1 Data organization

To understand processes that intervene in the water cycle and to study their spatial and temporal
variations, a database is essential. Field observations are very important for climatic statistics, for
planning and management of water resources.

Measurements are recorded using a wide range of methods, from the simple writing of a number by a
single observer to the invisible marking of electronic impulses on a magnetic tape. Although the most
advanced techniques are used in developed countries, many nations of the third world employ only
direct manual methods [Shaw, 1988].

Data Archives and Publication

Old meteorological measurements were tabulated on specially designed forms and are stored in boxes
occupying considerable shelf space at headquarters. These are historical data valuable for students
or hydrologists who study past extreme rainfalls. Instead of abstracting the figures manually the
potential user must be able to define precisely his requirements from a system embodied in a computer
software. Nowadays computer programs are written to abstract information.

Considerable attention is now given to the present need for data. The technique used to solve
problems in ungauged catchments, by using information from neighbouring catchments, continues to
be investigated [Shaw, 1988]. Although data publication is highly desirable, the time taken for a
yearbook to appear means that data are only of historic value, useful for assessing past conditions.
Operationally hydrometric data are disseminated to users for the customer's own analysis. The USA
has an excellent record of data publication; its series of Water Supply Papers being well known at
international levels.

The Hydrological and Geological National Service publishes the Switzerland Hydrologic yearbooks.
The Natural Environment Research Council of U.K. publishes yearbooks entitled Hydrological Data.
The yearbooks regroup the following results:

 daily rainfall depth;

  monthly rainfall depth;

 annual rainfall depth;

 annual average rainfall;

 average number of rainy days and variability of rainy days;

 ratio between the monthly considered module and the annual module

 maps of monthly and annual rainfall

Some of these values can be presented in an isohyets map.

The measurement results can be written as a random variable:

(10.1)

For a random variable the following characteristics can be calculated [Musy, 2001]:

- median value

(10.2)

- average value

(10.3)

- average deviation

(10.4)

- dispersion

(10.5)
- square average deviation

(10.6)

- impulses of superior order

(10.7)

- coefficient of variations

(10.8)

- centred impulses

(10.9)

- coefficient of asymmetry

(10.10)

10.2 Data control

10.2.1 Rainfall data quality control

The data are received in specialized offices by:

 postcards from observers (monthly)

 tapes from Water Authorities

 computer copying from other data set: climatic network returns

The value of rainfall data depends on the instrument, its installation, its site characteristics, and its
operation by an observer. Before publishing the data it is necessary to verify missing values, correct
errors, etc. This can be done starting from the original documents (filed formularies, diagrams - which
constitute archives) that are accessible only to specialized personnel.

Archives are then transformed into working files to allow data visualization and verification of the data
precision and quality tests. The files are then operational and can be published and distributed to users
[Musy, 2001]. The hydrometric data gathering agencies are national or local government authorities,
and it is their duty to publish the data and make them available to the public.

To check the daily rainfall at a station neighbouring stations data will be used through interpolation.
Suspect values are discarded and then each of the daily totals is converted to a percentage of the
relevant station's annual average rainfall and the interpolated percentage rainfall (R) for the testing
station is given by the following relation [Shaw, 1988]:

(10.11)

where:

Ri rainfall percentage of annual average at station i

Di distance between station i and control station (km)

The estimated value from the interpolated percentage will then be compared with the recorded value.
The difference (DIFF) is considered insignificant and the record acceptable if DIFF < or = 2.5 mm and
DIFF < or = 2 x error in estimation.

This checking procedure corrects automatically:

 Wrong days;

 Indicated accumulations with a simple proportioning routine to allocate the measured total
among the rain days;

 Unindicated accumulations that require a searching procedure before applying the

apportioning routine;

 Transposed values;

 Erroneous daily totals due to incorrect time of observation.

10.2.2 Quality control of river flow data

For each river flow station the expected response of the catchment to rainfall inputs depends on the
catchment's characteristics that can be assessed, and thus a limit to the difference between
consecutive stage readings can be fixed.

The daily mean discharge (m3s-1), representing the flow volumes in a day (m3) averaged over the
number of seconds, is the final product of the data processing program. They should be checked every
month. Discrepancies may be found when the following checking are made:

 Comparison of the daily mean discharge with stage hydrograph traces from an autographic
recorder chart, which can be made with a computer.

 The correct stage-discharge relationship has been used for the data. Different relationships
may be required for different periods of the year.

 The range of flows produced is within the calibration range for the gauging station.

 The discharge converted into runoff (mm) from the catchment is commensurate with the
catchment rainfall and with the runoff from neighbouring catchments.

A quality-control computer routine is designed to deal with known conditions and events. It requires
different structure depending on countries and climates.

10.3 Error research and measurement corrections

There are several types of errors that can occur; on a first inspection, some of these may be identified
and corrected at once, some are noted and marked, and others may remain undetected. They are:

1. "In situ"

 Misreading, misplaced decimal points, copying errors and arithmetic mistakes.

 Accumulated readings over several days entered as a one-day total.

 Correct readings entered on wrong days, persistently or only occasionally.

 Inadvertent omissions of observations made but not noted.

 Occasional errors due to temporary disturbance of the gauge or its exposure.

 Systematic errors caused by gradual alteration of exposure over a long period (years) or a
leaking gauge with increasing losses.

2. Statistical investigations based on specific hypotheses. Hypotheses for a statistical analysis are:
  Measurements reflect the real values - this hypothesis is not used in practice.

 Consistency of the data - there are no modifications in the internal conditions of the system
during the observation period.

 Data series is stationary - the properties of the statistic law do not change in time.

 Data are homogenous - a data series is considered homogenous when:

o it reflects two or many different events (e.g. the stream regime downstream the
confluence of two subbasins with different hydrologic behaviours)

o the event is non-stationary (e.g. climatic variations, variation of the flow regime)

 Data series is random and simple. If all observations issue from the same population and are
independent of each other, the series is random and simple.

 The series must be long enough - the length of a series influences the sample errors.

Statistical tests

The following categories are of statistical tests:

1. Tests subsequent to their mathematic properties. In most cases, these tests are based on the
normal law and assume the existence of a reference random variable X. The question is whether
results are valid if X is not normal: if results are valid, the test is "robust". This means that the test
remains almost insensitive to certain modifications of the model.

2. Tests subsequent to their object are classified in four categories:

 homogeneity tests or tests of samples comparison

If two samples are given, of n1 and n2 size, can it be admitted that these samples were part of the
same population, but independent between them ?

Mathematically, the problem can be expressed as following: it can be observed on the first sample the
realization of a random variable X1 and the repartition function F1(x), and on the second sample the
realization of a random variable X2 and the repartition function F2(x).

It can be tested:

if

if

 conformity test
The comparison of a sample characteristic values with a reference value means verifying whether the
characteristic can be admitted equally to the reference value. For example H0 : μ = μ0 where μ0 is the
reference value, and μ is the unknown value.

 adjustment test

Verifies whether a given sample is part of a certain population.

 autocorrelation test

Verifies whether a bond exists between the chronological data of an observation series. Anderson has
studied the distribution of the autocorrelation coefficient for a normal population. In this case, the
autocorrelation coefficient can be calculated for n-values pairs (x1, x2), (x2, x3), …, (xn-1, xn), and (xn,
x1). For a series n, Anderson limited the values at 75. The autocorrelation coefficient, after a normal
law will be [Musy, 2001]:

(10.12)

After Anderson, Wald and Wolhowitz developed a non-parameters test of the autocorrelation
coefficient, calculated by means of the following relation:

(10.13)

(10.14)

(10.15)

with:

(10.16)

Autocorrelation discrepancies kρk of a stationary temporal series is defined by:

 (10.17)

Autocovariance is estimated through a n observation series x1, x2, ..., xn:

(10.18)

3. Tests subsequent to the nature of information. In hydrology there are different situations depending
on particular hydrological situations. Sometimes it is necessary to control just one type of data (rainfall,
temperature, and evaporation) for local flow or regional flow, and sometimes it is necessary to control
different types of data (rainfall-discharge, temperature-wind velocity) for local and regional flow. (More
details can be found in Musy, "e-drology", 2001)