Evaporation from free water surfaces and bare soil and evapotranspiration from vegetated surfaces support upward directed energy and mass fluxes that complement downward directed precipitation in climate of the second kind and the terrestrial branch of the hydrologic cycle. Furthermore, evaporation and evapotranspiration have an important role in determining surface temperatures, surface pressure, rainfall, and atmospheric motion. The upward directed energy and water vapor fluxes from the Earth's surface involve the passage of water from the liquid to the gaseous state. It may be thought of as the mass flux that is opposite of precipitation but because it is water vapor it is not visible in the same way as precipitation. The water vapor flux occurs as evaporation from free water surfaces (i.e. lakes, rivers, and the oceans) and moist soil surfaces and as transpiration from living plants. Evaporation from free water surfaces and moist soil surfaces occurs when the ambient air vapor pressure gradient is less than the vapor pressure at the evaporating surface and an external source of energy is present.
Transpiration is a more complex process and varies considerably from one plant species to another largely in response to the plant rooting depth and the vegetative area. Water is transported by the plant vascular system from the roots to the stomata on the underside of the leaves where it is extruded. Water exiting the stomata is evaporated by available energy, and this loss of water is plant transpiration. The combined evaporation from the soil, plant, and other surfaces and the transpiration from plants covering the ground constitute evapotranspiration. When the ground is well covered with plants, transpiration is the dominant moisture exchange process and evaporation is a small fraction of the total moisture flux (Szilagyi and Parlange, 1999). The physical process is the same in either case, and it is common to use either evaporation or evapotranspiration to embrace both processes. Evaporation is favored in Europe and evaporation and evapotranspiration are both widely used in the United States (Ward and Robinson, 2000). In the discussion that follows, evaporation and evapotranspiration are treated separately in an effort to maximize clarity.
The evaporation process can be described by a relatively simple generic equation analogous to Ohm's characterization of electric current expressed in terms of electric potential and resistance. The potential for evaporation is directly proportional to the concentration of water vapor at the surface and in the air above the surface or the vapor pressure gradient. Resistance to the vapor transfer occurs in the form of the relative difficulty the surface and the atmosphere present to the net movement of water vapor away from the surface. Within this framework, evaporation (E) from a surface into the atmosphere is expressed as
where pa is air density, e* is the ratio of the molecular weights of water vapor and air, P is atmospheric pressure, e*s is the saturation vapor pressure of the surface, ea is the vapor pressure of air, and rs and ra are the resistance to evaporation by the surface and the air, respectively. This expression clearly illustrates that the highest potential evaporation rate for any given atmospheric state will occur when the surface is completely wet, and the constraint on achieving that potential rate is due to the resistance to water vapor transfer presented by the environment (Willmott, 1996).
Free water surfaces present the least resistance to water molecule exchange with the air since the water-surface vapor pressure is a maximum for any given temperature. Snow and ice surfaces present greater resistance relative to a free water surface because water molecules in snow and ice are bound in a more rigid molecular structure. Land surface resistance to evaporation varies with the surface roughness and the structure of the plant canopy related to the nature of the vegetation, with the soil type and texture, and with the degree to which the vegetation and soil are wet. Wind is the primary atmospheric resistance factor, but surface geometry and atmospheric stability also contribute. In essence, wind promotes efficient transport of water molecules away from the surface and maintains a vapor pressure gradient that supports the maximum evaporation determined by available energy.
The fundamental role evapotranspiration plays in the hydrologic cycle is evident in that about two-thirds of the land surface precipitation is allocated to evapotranspiration (Szilagyiand Parlange, 1999). However, the importance of the energy flux that accompanies evapotranspiration must be acknowledged. Since this vapor flux involves a phase change of water, evapotranspiration accounts for a significant transfer of energy from the Earth's surface to the atmosphere. Both the energy and vapor transfers influence atmospheric behavior and Earth's climate.
Although the entire troposphere is influenced by solar radiation absorbed at the Earth's surface, atmospheric responses to energy and mass fluxes at the Earth's surface are particularly evident in the atmospheric boundary layer. The atmospheric boundary layer is the lowest 1 km of the atmosphere above the Earth's surface (Andrews, 2000). Atmospheric motion in this region is directly influenced by frictional effects related to the nature of the underlying Earth's surface. Equally important is the boundary layer's role in providing an environment that encourages or inhibits energy and mass fluxes at the surface. Interactions between the Earth's surface and the boundary layer provide the
atmosphere with water, provide the major cause of diurnal temperature change, and contribute to atmospheric mixing and turbulence.
Evaporation is measured using evaporation pans or tanks of various sizes, atmometers, and inflow and outflow measurements of lakes. These techniques are constrained by a number of physical factors that influence evaporation and make extrapolation of data problematic. Only selected instruments are presented here to illustrate common characteristics.
The U.S. National Weather Service Class A pan (Fig. 4.12) is 120.7cm in diameter, 25.4 cm deep, is supported 4 cm above the ground surface, and is initially filled with water up to 5 cm of the rim. The unpainted, galvanized steel pan is set on a wooden platform to allow free air circulation under the pan. Water is added to the pan each day until the surface is level with the spike tip in the stilling cylinder. Evaporation is the daily difference between observed water levels corrected for any precipitation measured by a nearby rain gauge. The evaporation data in Figure 4.13 show variations in amounts related to daily changes in available energy and to a generally decreasing energy availability over the course of the month.
Turbulence created by the pan, heat transfer through the sides of the container and small heat storage in the limited water volume all tend to cause the water loss from the pan to be different from that over an open water surface. Use of evaporation pan data to estimate lake evaporation or evaporation from a land surface requires application of an empirical pan coefficient to reduce values to realistically represent lake or vegetation evaporation (Ward and Robinson, 2000). Nevertheless, evaporation pans are the most commonly used device for measuring evaporation.
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The Russian 20 m2 evaporation tank is recommended by the World Meteorological Organization as the international standard reference evapori-meter. This flat-bottomed cylinder has a diameter of 5 m, a surface area of 20 m2, and is 2 m deep. It is buried in the soil with its rim 7.5 cm above the ground. The tank has a replenishing vessel and a stilling well with an index pipe on which a volumetric burette is placed to measure the water level in the tank. A needle point inside the stilling well indicates the height to which the water level is to be adjusted to determine the moisture loss (WMO, 1996).
Atmometers measure water loss from a standard moistened surface (Guyot, 1998). These devices use a small water-filled porous porcelain bulb or wetted pieces of paper to serve as the evaporating surface. Either a tube filled with water or an attached container of water maintains the wetness of the evaporating surface mounted on top of the cylindrical water reservoir. Utilization of atm-ometer data is constrained in that data are not comparable unless they come from identical instruments exposed in similar conditions (Guyot, 1998). In addition, atmometers indicate the drying power of the air, but the water loss cannot be converted to a depth of water loss over the ground (Ward and Robinson, 2000).
The determination of evaporation using lake or reservoir levels and inflow and outflow data is theoretically possible, but in these cases evaporation is not actually measured. Evaporation from water bodies is a residual in a mass balance equation and is subject to considerable uncertainty and error if the evaporation quantity is small compared to the other variables. Seepage is an especially troublesome variable that introduces errors in mass balance equations for lakes and reservoirs. Under the best circumstances, the mass balance computation contains the net sum of all measurement errors as well as evaporation.
4.8.2 Estimating evaporation
The physics of the evaporation process relate to the climatic forcing that supplies the energy for the latent heat of vaporization and to diffusion of water vapor between the Earth's surface and the atmosphere as illustrated in Equation 4.11. The thermodynamic perspective of evaporation addresses the energy balance characteristics of the evaporating surface and the allocation of energy to latent heat. The mass transport and aerodynamic approaches emphasize the vapor flux from the evaporating surface.
Dalton is credited with introducing in 1802 a general formula now known as the mass transport method that predicts evaporation as a function of vapor pressure. Dalton recognized that the rate at which water molecules leave a water surface is dependent on the temperature of the water surface and the atmospheric partial pressure due to water vapor. For the evaporation process to continue efficiently, atmospheric motion or wind is needed to carry away the water molecules from the evaporating surface. Evaporation from open water (Eo) is expressed as
where u is an empirically determined constant involving some function of windiness, eo is the vapor pressure at the surface and ea is the actual vapor pressure in the air at some point above the surface. This method offers the advantage of simplicity in calculation once the empirical constants are developed. Numerous applications have shown that the mass transport method works well when u is locally determined in advective and non-advective cases.
The evaporation of water from a given surface is greatest in warm, dry conditions because the air is warm, the saturation vapor pressure of water is high, and the actual vapor pressure of the air is low. Aerodynamic or profile techniques for estimating evaporation are based on the physical processes governing the turbulent diffusion of momentum, sensible heat, and water vapor in the atmosphere. Each of these fluxes is estimated by analogous equations using turbulent exchange coefficients assumed to be identical. The water vapor flux (E) is estimated by
where Mw and Ma are the mole weights of water vapor and air, respectively, P is atmospheric pressure, pa is air density, Kw is the turbulent exchange coefficient for water vapor, and dejdz is the vertical gradient of water vapor (Rosenberg et al., 1983). However, research has shown that the assumption of identity for the exchange coefficients is only valid under neutral atmospheric stability, and the effects of non-neutral conditions must be determined experimentally. The likelihood of large errors occurring in determining each of the fluxes limits the use of this technique (Guyot, 1998).
Penman (1948) introduced a method for estimating evaporation from open water surfaces based on both energy budget and aerodynamic approaches and eliminating terms not commonly measured. In essence, this formulation is a weighted sum of an evaporation rate due to net radiation as defined in Equation 2.11 and an evaporation rate due to turbulent transfer. The formulation assumes no advected energy and no heat storage effects. Only meteorological measurements made at one level above the surface are required, and Eo is expressed as
where D is the slope of the saturation vapor pressure curve at the mean wet bulb temperature of the air, Rno is the net radiation over open water, 7 is the psychrometric constant expressed as 7 - PCpILe, where P is the atmospheric pressure, Cp is the specific heat of air at constant pressure, and e* - Mw |Ma where Mw and Ma are defined above. In this form, evaporation due to the energy balance is represented by Rn and evaporation due to the aerodynamic component is represented by Ea - f (U)(ea - ea) in whichf(U) - 0.27(1 - U|100), U is the wind run in km per day at 2 m, and ea and e*a are the vapor pressure and saturation vapor pressure of the air in hPa at some height above the surface, respectively. The required weather variables are measured routinely at most weather stations except Rn and it can be estimated. The D and 7 terms are weighting factors to determine the relative importance of the energy balance and aerodynamic terms in accounting for total evaporation.
Measuring evapotranspiration is difficult because of its upward directed orientation and the influence of various surface materials on the nature of the process. It is measured in equivalent depth of water returned to the atmosphere over a specified period to make it comparable with precipitation. Although commercial gauges with a surface that simulates a well-watered leaf are available for estimating local evapotranspiration, the most accurate evapotranspiration measurement is achieved using lysimeters or soil-filled tanks covered with vegetation. In general, lysimeters are categorized as weighing or non-weighing types. There is no universal international standard lysimeter for measuring evapotranspiration (WMO, 1996).
A lysimeter is an instrument that integrates the influences of temperature, wind speed, solar radiation, and available moisture on the evapotranspiration
process. Weighing lysimeters consist of a soil-filled container several meters in diameter and 1 or 2 m deep. The container is buried at ground level and the surface is planted with the same vegetation as the surrounding area (Fig. 4.14). The vegetation can include orchard and vine crops as reported by Johnson et al. (2005). The bottom of the container is positioned on highly sensitive hydraulic weighing systems or on load cells with strain gauges of variable electrical resistance (WMO, 1996; Barani and Khanjani, 2002). The container is constantly weighed and weight changes are equated to the change in moisture content of the soil-filled tank. An alternative design is to float the lysimeter tank in water and use the change in liquid displacement as a measure of the weight gain or loss from the lysimeter tank related to changes in soil water. Any precipitation or irrigation on the lysimeter is measured at ground level and any percolation from the soil in the lysimeter is recorded. By this method, evapotranspiration equals precipitation plus irrigation minus percolation minus change in soil storage. A weighing lysimeter can determine evapotranspiration accurately for periods as short as one hour using mechanical scales or for periods of 24 hours using hydraulic weighing systems (Barani and Khanjani, 2002). Units are expressed in mm of water for the appropriate time interval to correspond with measures of precipitation and irrigation. Unfortunately, the expense of installing and operating lysimeters limits their use to research centers.
Evapotranspiration is controlled by the energy demand for moisture, water availability, and the extent of plant cover and its growth stage. Operated under natural conditions allowing moisture to be replenished by precipitation only, the weighing lysimeter provides a measure of the physical water loss from the surface called actual evapotranspiration (ETa). Natural moisture loss depends on climatic factors related to net radiation, wind velocity, and humidity and to other physical influences like soil type, soil moisture content, vegetation rooting depth, and land management practices. Application of a constant water supply to the lysimeter by surface or subsurface irrigation so that the water loss is never restricted by a lack of available water permits the lysimeter to measure the moisture loss limited only by available energy. Under these conditions, the lysimeter provides a measure of the maximum evapotranspiration flux or potential evapotranspiration (ETp). This is the moisture flux occurring from an extended surface of short green vegetation that fully shades the ground, exerts little or negligible resistance to the flow of water, and is always well supplied with water (Rosenberg et al., 1983). The possibility that evapotranspiration may not be satisfied by the available moisture supply creates the need for the two designations for evapotranspiration. ETp is a climatically defined quantity independent of surface characteristics. ETa is the moisture flux occurring from a vegetated surface to the atmosphere in response to the coincidence of energy and moisture. Due to the defining role moisture plays in these two expressions, ETa can be equal to or less than ETp but it can never exceed ETp.
Reference evapotranspiration (ETo) is a term used to relate the evapotranspiration concept to crop water requirements. ETo is essentially equivalent to ETp with the exception that the leaf surfaces are typically not wet and a reference crop of short grass or alfalfa is specified (Jensen et al., 1990). Even though ETp and ETo have technical distinctions, McKenney and Rosenberg (1993) assert they are basically similar conceptually. ETp is emphasized in the following discussions because natural landscapes are the dominant focus of hydroclimatological studies. ETo is used in those instances where agricultural applications are the major focus.
Non-weighing or percolation-type lysimeters measure ETa by indicating volumetric change in the container water balance. A simple design is a petroleum barrel filled with soil and placed in a hole so that its top is level with the surrounding surface. Excess water draining to a pebble layer at the bottom of the barrel is removed through a small tube either by a gravity drain or by a suction hand pump (WMO 1996). A percolation lysimeter uses direct sampling of soil moisture changes or indirect sampling with a device such as a neutron probe along with water drainage out of the bottom of the root zone to determine ETa. In locations with a high water table, the water table in the lysimeter is maintained at a constant level and the water added to maintain the water level is a measure of ETa (Nokes, 1995). Non-weighing lysimeters can be used only for long-term measurements unless the soil moisture content is measured by some independent technique (WMO, 1996).
The difficulty in measuring evapotranspiration has promoted the use of various approaches for estimating evapotranspiration. The specific application of evapotranspiration information is an important determinant in choosing an estimating technique because not all techniques perform equally well in all settings. The space and time purposes of the evapotranspiration data are important in defining the nature of the required meteorological data and the likelihood of it being available. Estimating techniques that provide excellent results for 30-minute time steps are not readily extrapolated for decadal time-series studies. Techniques providing excellent evapotranspiration assessments for irrigated agriculture may not perform well for heterogeneous natural vegetation experiencing soil drying. Because application characteristics vary, estimating techniques favored by agriculture, climatology, engineering, forestry, hydrology, and meteorology differ. However, the physical basis for estimating the evapotranspiration process is the same.
Evapotranspiration is estimated with considerable accuracy using energy balance concepts, highly sensitive and efficient instrument arrays, and a variety of indirect techniques for computing evapotranspiration based on the physics of the phase change process. These techniques are described in detail in the micrometeorological and hydrological literature (e.g. Rosenberg et al., 1983; Shuttleworth, 1993; Guyot, 1998), and selected examples are discussed here to illustrate the nature of these techniques.
There are a number of equations in common use for estimating evapotranspiration that share a focus on the energy balance at the Earth's surface. All of these approaches have some basis in theory with one or more experimentally determined or estimated variables. The form of the equation is dictated by its application to a type of land surface, climatic setting, or vegetation cover. The common element linking these equations is their focus on the energy balance at the Earth's surface as shown in Equation 2.12, which expresses the energy balance as the algebraic sum of the energy fluxes. The energy balance approach is commonly used for daily estimates of evapotranspiration, and it enjoys a considerable degree ofsuccess when applied locally. However, detailed meteorological measurements are needed for these estimates, and the effect of atmospheric stability is important and must be included in the computation for short-term estimates.
The energy balance approach to estimating evapotranspiration is concerned with estimating the portion of net radiation available for conversion into latent heat. A simple expression of this condition is the ratio of the sensible heat flux (H) to the latent heat flux (LE). This relationship is commonly termed the Bowen ratio (/3) and is expressed as
where 7 is the psychrometric constant which varies weakly with temperature, Ts is the mean surface temperature, Ta is mean air temperature at a given height, es is the saturation vapor pressure of the evaporating surface at temperature Ts, and ea is the actual vapor pressure of the air at the height where Ta is measured. Accurate measures of net radiation, soil heat flux, and vertical profiles of temperature and humidity are needed for this approach. These measurements are relatively simple and rapid response instruments are not needed for most research purposes, but routine field measurements for these evapotranspiration calculations may be difficult to acquire (Ward and Robinson, 2000). The sign of H often changes in the evening and morning so that Equation 4.15 is not defined at these times. The Bowen ratio estimates ETp when the surface is well watered and LE is limited only by Rn. When moisture is a limiting factor for energy partitioning at the surface, then the Bowen ratio estimates ETa.
The energy balance can be coupled with empirical relationships depicting various surface conditions to estimate evapotranspiration. Priestly and Taylor (1972) proposed a method using an empirically derived constant as an advective term so that evapotranspiration from a moist surface (ETp) depends only on measured temperature and available energy. The equation takes the general form of
where c is an empirically derived constant, A is the slope of the saturation vapor pressure curve at the mean wet-bulb temperature of the air, 7 is the psychro-metric constant, Rn is net radiation, and G is the soil heat flux. The Priestly-Taylor method is most reliable in humid areas using a constant value of 1.26. In arid climates, a constant of 1.74 is recommended (Shuttleworth, 1993). Other empirical radiation-based equations have been proposed for use in either humid climates (Turc, 1961) or arid climates (Doorenbos and Pruitt, 1977).
Parlange et al. (1995) conclude that the fundamental difference among energy balance equations for estimating ETa is in their bases for partitioning available energy to determine evaporation as a residual of the measured terms. They propose a general form of the various equations is
where LE is the latent heat flux in Wm 2; L is the latent heat of vaporization with a value of2.45 x 106Jkg-1 at typical temperatures; E is the evaporation rate in kgm-2 s-1; A is the slope of the saturation vapor pressure curve taken at the temperature of interest; Rn is net all-wave radiation incident on the surface; G is the soil heat flux into the ground; ea and e*a are the vapor pressure and saturation vapor pressure of the air at some height above the surface, respectively; g is the ratio of the specific heat of air at constant pressure to the latent heat of vaporization generally taken to be a constant of 0.67 hPaK-1 at standard temperature and pressure; f(u) is some function of the wind velocity historically taken to be of the linear form f(u) = a + bu with a and b being constants; A, B, and J are parameters that take on various values depending on the particular formulation; B' is the Budyko-Thornthwaite-Mather parameter, which is a function of the availability of surface water and is generally taken to be 1.0 until some measure of field capacity is reached and then allowed to decrease to zero with limited water availability (Parlange et al., 1995). Since ET is linked to the energy balance through LE, ETa is derived from Equation 4.17 by
where all of the variables are defined above.
Penman's Eo is converted into ETp for a vegetated land surface by employing empirically derived coefficients for a particular site and time of the year using a modified form of Equation 4.13. A widely used formulation by Monteith (1965) incorporates vegetation-canopy conductance, and it characterizes the vegetation surface as one big leaf. ETp from land surfaces by the Penman-Monteith method is estimated by
where A is the slope ofthe saturation vapor pressure curve at the mean wet-bulb temperature of the air; Rn is net radiation incident on the surface; G is the soil heat flux into the ground; pa is air density (kg m-3); cp is specific heat at constant pressure (Jkg-1K-1); ea and e*a are the vapor pressure and saturation vapor pressure of the air at some height above the surface, respectively (hPa); ra is the aerodynamic resistance to vapor transfer (sm-1); g is the psychrometric constant or the ratio of the specific heat of air at constant pressure to the latent heat of vaporization, generally taken to be a constant of 0.67 at standard temperature and pressure (hPaK-1); and rs is minimum canopy resistance (s 1). This equation is remarkably successful in estimating ETp in many environments and for periods as short as 20 minutes. However, the surface resistance must be determined by botanical methods that are difficult to extrapolate to other areas or types of vegetation, and the surface resistance can vary dramatically over a short period in response to environmental variables. Nevertheless,
Fig. 4.15. Daily reference evapotranspiration (ETo) for August 2006 at Indio, California (34° N). (Data courtesy of the California Department of Water Resources from their website at http://wwwcimis.water.ca.gov/.)
Fig. 4.15. Daily reference evapotranspiration (ETo) for August 2006 at Indio, California (34° N). (Data courtesy of the California Department of Water Resources from their website at http://wwwcimis.water.ca.gov/.)
this approach produced the best results in an extensive comparison by Jensen et al. (1990) of 19 methods for estimating potential evapotranspiration compared to lysimeter and well-watered alfalfa data.
The Food and Agriculture Organization of the United Nations (FAO) recommends a modified form of the Penman-Monteith equation for ETo whose foundation is based on water needs associated with well-managed irrigated agriculture. The reference surface is defined as a hypothetical grass reference crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70sm~\ and an albedo of 0.23. This reference surface closely resembles an extensive green, well-watered grass of uniform height, actively growing, and completely shading the ground. The fixed surface resistance of 70 s m_1 implies a moderately dry soil resulting from a weekly irrigation frequency (Allen et al., 1998). The FAO Penman-Monteith equation applied on a daily basis and resulting in mmd-1 has the form
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