Explicit and Recursive Calculation of Potential and Actual Evapotranspiration

The explicit combination method (ECM; Penman, 1948) to calculate potential evapotranspiration (ETp) is a physically based model using standard climatological data. It is based on an assumption regarding the temperature and humidity at the evaporating surface that is not made in a recursive combination method (RCM; Budyko, 1958). Our objective was to compare the two methods by calculating values of ETp and of actual evapotranspiration (ETa) using hourly weather data collected on 45 d during the warm season in Lubbock, TX. Results show that on hot summer days ECM underestimated the daily value of ETp and of ETa by as much as 25% compared with RCM. The proposed RCM procedure is based on the same physical principles as ECM, but uses iteration to find an accurate answer. It can easily be used with commercially available mathematical software that has proven to be stable. The RCM needs experimental verification before implementation for crop irrigation. T HE TERM POTENTIAL EVAPOTRANSPIRATION, due to Thornthwaite (1948), stands for the maximum rate of water loss by evaporation from the land surface under given atmospheric conditions. The ETa represents values of evapotranspiration (ET) that, applied to well-watered agricultural crops, facilitate the planning and efficient use of water in crop production. It takes account of the role of leaf stomata in causing ETa to be less than ETp. Historically, the methods of relating ETp to weather parameters were empirical and lacked general validity. However, Penman (1948) and Budyko (1958) independently proposed methods to calculate ETp based on known physical principles and standard climatological data, commonly referred to as the combination method. The solution was obtained by combining the equations for the transport of water vapor and sensible heat from or to the land surface with an expression for the radiative energy balance of that surface. For reviews of methods to calculate ETp, see Sellers (1965) and Brutsaert (1982). Penman (1948) derived an explicit equation for ETp by making the assumption that the ratio between the temperature gradient between the surface and the air above and the corresponding humidity gradient, given saturation at the surface, would equal the value of the Clausius-Clapeyron equation at the ambient air temperature. The object of this assumption was the elimination of the surface temperature from the set of equations used in the calculation of ETp (Milly, 1991). However,

[1]  I. A. Walter,et al.  The ASCE standardized reference evapotranspiration equation , 2005 .

[2]  S. B. Idso,et al.  A model of thermal radiation from partly cloudy and overcast skies , 1982 .

[3]  Dan R. Upchurch,et al.  Energy and water balance of a sparse crop: simulated and measured soil and crop evaporation , 1987 .

[4]  Steven R. Evett,et al.  ASIMPLIFIED WEIGHING LYSIMETER FOR MONOLITHIC OR RECONSTRUCTED SOILS , 1998 .

[5]  A. G. Azpeitia,et al.  Introduction to Numerical Analysis. , 1968 .

[6]  C. H. M. van Bavel,et al.  Water Loss from a Sorghum Field and Stomatal Control1 , 1968 .

[7]  U. KyawThaPaw,et al.  Applications of solutions to non-linear energy budget equations , 1988 .

[8]  C. H. M. van Bavel,et al.  Potential evaporation: The combination concept and its experimental verification , 1966 .

[9]  C. H. M. van Bavel,et al.  Experimental Verification of a Model to Predict Soil Moisture and Temperature Profiles 1 , 1983 .

[10]  M. Budyko.  The heat balance of the earth's surface , 1958 .

[11]  H. L. Penman.  The physical bases of irrigation control , 1952 .

[12]  R. Lascano.  A General System to Measure and Calculate Daily Crop Water Use , 2000 .

[13]  P. Milly.  A refinement of the combination equations for evaporation , 1991 .

[14]  Terry A. Howell,et al.  An Evapotranspiration Research Facility Using Monolithic Lysimeters from Three Soils , 1993 .

[15]  L. S. Pereira,et al.  Crop evapotranspiration : guidelines for computing crop water requirements , 1998 .

[16]  Paul R. Lowe,et al.  The Computation of Saturation Vapor Pressure , 1974 .

[17]  C. W. Thornthwaite.  An approach toward a rational classification of climate. , 1948 .

[18]  F. S. Nakayama,et al.  Measuring Transpiration Resistance of Leaves. , 1965, Plant physiology.

[19]  K. Bristow.  On solving the surface energy balance equation for surface temperature , 1987 .

[20]  A. J. Mcarthur.  The Penman form equations and the value of Delta : a small difference of opinion or a matter of fact? , 1992 .

[21]  H. L. Penman.  Natural evaporation from open water, bare soil and grass , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[22]  C. H. M. van Bavel,et al.  Simulation and measurement of evaporation from a bare soil , 1986 .

[23]  R. Huey,et al.  Errors resulting from linear approximations in energy balance equations , 1984 .

[24]  A. J. Mcarthur.  An accurate solution to the Penman equation , 1990 .

[25]  U Paw,et al.  A discussion of the Penman form equations and comparisons of some equations to estimate latent energy flux density , 1992 .

[26]  W. Ehrler,et al.  Sorghum Foliar Responses to Changes in Soil Water Content 1 , 1967 .