Geog 595 Ecological ModelingSpring 2010Lecture NotesEvapotranspiration1. Moisture Measurement in the AtmosphereWater vapor is a variable component in atmosphere. It varies from almost nothing to nearly 20 g of water per kg of dry air. There are several ways measuring the moisture content of the atmosphere. (1) Vapor Pressure (Pa)The pressure in the atmosphere that is created by water vapor is called the vapor pressure. The standard air pressure at sea level is 101325 Pascal, which is created by all gases in the air (primarily N2, O2, Ar, and H2O). There are many other trace gases in the atmosphere, such as CO2, CH4, NO2, etc. Though their presence may have significant environmental effects, such as the greenhouse effects, but their pressure is negligible. In the figure above, if one add some pure water into a container with dry air only. Some of the water molecules will overcome the pull by other water molecules and enter into thedry air. This will lead to the increase in the gas pressure. As the water vapor molecules increase in the air, some of the water molecules will be pulled back into the water. But there are more molecules leaving the water surface than returning in the beginning. Givenenough time, the number of water molecules leaves the water surface entering the air, andthat returns to the water will be balanced. The vapor pressure at this time is called the saturated vapor pressure. Due to the fact that the number of water molecules leaving the water surface is determined by the kinetic energy of the molecules, i.e. its temperature, we call the saturated air pressure at temperature T, es or es(T). The relationship of air temperature and es(T) can be modeled asPure waterDry air (Pair)Pure waterWet air (Pair+PH2O)cTbTexpa(T)esWhere a=610.7 Pa, b=17.502, c=240.97oC, and T is air temperature in degrees Celsius. (2) Relative Humidity and Vapor Pressure DeficitIn the natural open air, the air is almost always not saturated with water vapor, i.e. the actual water vapor pressure (e) is less than the saturated vapor pressure (es). The relative humidity is therefore defined as%100eehsThus, we have relative humidity as 50%, 60%, etc. Vapor pressure deficit (D) is the deficit in pressure needed to make the air reach saturation.)h1(eeeDss(3) Specific Humidity (gH2O/kg moist air)vvCC378.01622.0qWhere Cv=e/Pair, , where e is in Pa and Pair is in kPa, i.e. the mole ratio of water vapor to total atmosphere in mmol/mol.2. EvapotranspirationEvapotranpiration (ET) refers to the total amount of water vapor enter into the atmosphere through either the evaporation of water from open water and soil surface or transpiration of water from vegetation leaves. It is either measured in mm water from the surface into the atmosphere as in water balance equation or as the amount of heat used in transferring the same amount of liquid water into water vapor per unit area (w/m2) as used in the energy balance equation. Estimating ET has been a major scientific challenge for many years until Penman (1948) came up with the combination approach which solved the problem for open water or wet soil surface, and Penman (1953) further improved the model for unsaturated surface of single leaf by introducing resistance. Monteith (1965) applied the Penman Equation for the canopy. The Penman equation since become the famous Penman-Monteith equation. The amount of ET is almost equally expressed in two units: the amount of water left the surface in ET (mm) or the amount of energy used in ET (W/m2). 1. The Penman Equation.Two conditions are need to continued evaporation to occur: (1) availability of energy for latent heat of vaporization and (2) the mechanism for removing the vapor, i.e. a sink for water vapor. One has to start with one of the two in address the problem.(1) The Sink Strength ApproachThe best known sink strength approach is the Dalton equation, which shows the rate of evaporation is a function vapor pressured deficit and wind speed as)f(u)e(eEdsWhere es is the saturated vapor pressure at the surface temperature, and ed is the vapor pressure of the air above the surface. The wind speed is u, and f(u) is a function of wind speed. One such empirical function is)0.17u)(1e(e4.0E2dsmm/day,Where es and ed are measured in mm mercury and u2 is the wind speed at 2 meter height in miles per hour. Similar empirical functions can be derived based on aerodynamic equations.(2) Energy Balance ApproachThe total amount of energy available for all biophysical processes is the net radiation (Rn), which can be estimates assurfaceairLLQ  )1(Rn This equation takes different forms for vegetation canopy and the ground underneath the canopy. The amount of energy (Rn) can be used for ET (E), sensible heat (H), heating the ground (G) and fixed in photosynthesis (A), AGHERnA is often a small fraction of Rn, thus can be ignored in the energy balance equation. G usually does not change very much within a whole day (it gains heat to warm up during daytime, and loses heat to cool down during nighttime. The net change is small.). The energy balance equation can then be simplified asHERnBowen (1926) defined a ratio, later called Bowen ratio, β=H/EdsaseeTTγEHβThus the energy balance equation can be written as Rn=E+βE=E(1+β), therefore,β1REn(3) The Combination ApproachAccording to Dalton equation, )f(u)e(eEdsIf we replace es with ea, i.e. the saturated vapor pressure at air temperature instead of surface temperature, we have)f(u)e(eEdaaThen we can get a ratio asdsasdsasdssdaaeeee1eeeeeeeeeEEdeRecall Energy balance Equation:)e)/(eTγ(T1Rβ1REdsasnnLet aaTessTe, then (Ts-Ta)=(es-ea)/Δ, then we haveEEREEReeeeReeTTRanandsasnasasn111)()(1)()(1ESolving the above equation for EnaREEE  1naREEE ThusanEREThis is the famous Penman equation, which works for open water or well wet surface, i.e.evaporation that is not limited by supply of water. ET is determined by two factors, the available energy, Rn, and the drying power of the air, Ea.2. “Penman-Monteith” Equation (Penman Equation)The 1948 Penman equation is valid only for open water surface or