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)

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 (L_e).

(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 (e_s).

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 e_s - e_a which air can store) and on the wind speed (u). This law has the following expression (Musy, 2001):

(4.4)

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)

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

The net quantity of absorbed radiation, R_n 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 (R_B) can be expressed as follows:

(4.8)

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)

The diffusion resistance from the evaporation surface r_s 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)

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)

ROHWER Formula:

(4.14)

PENMAN Formula:

	(4.15)
	(4.16)

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 R_g, 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)

Bibliography

Musy, A. 1998. Hydrologie appliquée, Cours polycopié d'hydrologie générale, Lausanne, Suisse.

Musy, A. 2001. e-drologie. Ecole Polytechnique Fédérale, Lausanne, Suisse.

Serban, P., V. A. Stanescu, and P. Roman. 1989. Hidrologie Dinamica (Dynamic Hydrology). Editura Tehnica, Bucuresti, Romania.

Shaw, E. M. 1988. Hydrology in practice. Van Nostrand Reinhold International, London, United Kingdom.