Penman–Monteith equation
The Penman–Monteith equation approximates net evapotranspiration (ET) from meteorological data, as a replacement for direct measurement of evapotranspiration. The equation is widely used, and is the standard method for modeling evapotranspiration used by the United Nations Food and Agriculture Organization. The resulting estimate is reference evapotranspiration, ETo. Significance. Evapotranspiration contributions are very significant in a watershed's water balance, yet are often not emphasized in results because the precision of this component is often weak relative to more directly measured phenomena, e.g. rain and stream flow. In addition to weather uncertainties, the Penman–Monteith equation is  sensitive to vegetation specific parameters, e.g. stomatal resistance or conductance. Various forms of crop coefficients (K) account for differences between specific vegetation modeled and a "reference evapotranspiration" (RET or ET) standard. Stress coefficients (K) account for reductions in ET due to environmental stress (e.g. soil saturation reduces root-zone O, low soil moisture induces wilt, air pollution effects, and salinity). Models of native vegetation cannot assume crop management to avoid recurring stress. Equation. Per Monteith’s "Evaporation and Environment", the equation is: Note: Often resistances are used rather than conductivities. where r refers to the resistance to flux from  a vegetation canopy to the extent of some defined boundary layer. Also note that formula_3 varies over each day, and in response to conditions as plants adjust such traits as stoma openings. Being sensitive to this parameter value, the Penman–Monteith equation obviates the need for more rigorous treatment of formula_3 perhaps varying within each day. Penman's equation was derived to estimate daily ET from daily averages. This also explains relations used to obtain formula_5 & formula_6 in addition to assumptions key to reaching this simplified equation. Accuracy. While the Penman-Monteith method is widely considered accurate for practical purposes  and is recommended by the Food and Agriculture Organization of the United Nations, errors when compared to direct measurement or other techniques can range from -9 to 40%. Variations and alternatives. Variations. The standard methods of the American Society of Civil Engineers modify the standard Penman–Monteith equation for use with an hourly time step. The SWAT model is one of many GIS-integrated hydrologic models estimating ET using Penman–Monteith equations. Priestley–Taylor. The Priestley–Taylor equation was developed as a substitute to the Penman–Monteith equation to remove dependence on observations. For Priestley–Taylor, only radiation (irradiance) observations  are required. This is done by removing the aerodynamic terms from the Penman–Monteith equation and adding an empirically derived constant factor, formula_7. The underlying concept behind the Priestley–Taylor model is that an air mass moving above a vegetated area with abundant water would become saturated with water. In these conditions, the actual evapotranspiration would match the Penman rate of potential evapotranspiration. However, observations revealed that actual evaporation was 1.26 times greater than potential evaporation, and therefore the equation for actual evaporation was found by taking potential evapotranspiration and multiplying it by formula_7. The assumption here is for vegetation  with an abundant water supply (i.e. the plants have low moisture stress). Areas like arid regions with high moisture stress are estimated to have higher formula_7 values. The assumption that an air mass moving over a vegetated surface with abundant water saturates has been questioned later. The lowest and turbulent part of the atmosphere, the atmospheric boundary layer, is not a closed box, but constantly brings in dry air from higher up in the atmosphere towards the surface. As water evaporates more easily into a dry atmosphere, evapotranspiration is enhanced. This explains the larger than unity value of the Priestley -Taylor parameter formula_7. The proper equilibrium of the system has been derived and involves the characteristics of the interface of the atmospheric boundary layer and the overlying free atmosphere. History. The equation is named after Howard Penman and John Monteith. Penman first published his equation in 1948 and Monteith revised it in 1965.