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Submitted to: Biological Systems Simulation Group Proceedings
Publication Type: Abstract Only
Publication Acceptance Date: 4/18/2011
Publication Date: 4/21/2011
Citation: Lascano, R.J. 2011. Recursive Calculation of Crop Evaptranspiration[abstract]. Biological Systems Simulation Group. April 18-21, 2011, Austin, Texas. p. 22-24.

Interpretive Summary:

Technical Abstract: In 1948 three papers were published that introduced methods to calculate evaporation of water from land and water surfaces. The first paper was by Charles Thornthwaite (geographer and climatologist) that devised a climate classification system and introduced the concept of potential evapotranspiration (ETp). He defined ETp as the maximum rate of water loss by evaporation from the land surface under given atmospheric conditions. The second paper was by Howard Penman (physicist and mathematician) that wrote the landmark paper where the combination method was introduced to calculate water evaporation from different surfaces. The third and final paper was by Mikhail Budyko (physical climatologist) where he pioneered studies on global climate and calculated the temperature of the earth using a simple energy balance model. In addition, Budyko (1956) published a paper where he described evaporation of water using what he called the complex method. Interestingly, the complex and combination methods are similar, except that the complex method uses an iterative solution to find the surface temperature (Ts) that satisfies the energy balance.
The genius of Penman (1948) was that he derived an explicit equation to calculate ETp by eliminating the Ts from the pertinent equations and by using measurements of air temperature and humidity, wind-speed, and incoming short-wave irradiance. The elimination of Ts was possible by assuming a linear relation between vapor pressure and temperature of water, within the ranges of air/water temperature normally found in field situations. This error increases as air temperature increases and dewpoint temperature decreases, i.e., arid conditions, where irrigation of crops is normally practiced. Many, have questioned the linearity assumption e.g., Budyko (1951); Ferguson (1952); Sellers (1964); Tracy et al. (1984); Paw U and Gao (1988); Milly (1991) and alternative solutions to calculate ET have been proposed. For example, Paw U and Gao (1988) gave quadratic and quartic equations that relate vapor pressure and air temperature relations. Milly (1991) derived a higher-order Taylor series term relating vapor pressure and air temperature. Using these terms to calculate ET are an improvement over the linear assumption, but the solutions are complex and convergence is not always assured. All these methods are classified as “first-order combination equations” and hereafter are referred to as Explicit Combination Methods (ECM).
The two most common ECM to calculate crop ET have been developed by agricultural engineers and are: 1) FAO–56 (Allen et al., 1998), and 2) the American Society of Civil Engineers (2005). These two methods use the well-known Penman-Monteith equation (Monteith, 1965). The values of crop ET obtained from these methods are “standardized” and refer to a short reference crop (grass) or to a tall reference crop (alfalfa), which are defined by parameters (crop and zero plane displacement heights) that characterize the aerodynamic properties and by surface resistance values for day and for nighttime conditions. Furthermore, values of reference grass and/or alfalfa ET are then empirically related to different crops by crop-specific coefficients.
As first proposed by Budyko (1948, 1956) crop ET can be calculated by iteration. This calculation makes no assumption of the linear relation between vapor pressure and temperature and instead recursively finds a value of Ts that satisfies the energy balance. Hereafter we refer to this method as the Recursive Combination Method (RCM). The contribution of Budyko to calculate crop ET cannot be underestimated and the statement of Sellers (1964) summarizes my thoughts as well:
“The treatment will be a slight modification of that presented by Budyko (1956), who, in the author’s mind, has come closer to giving a complete physical picture of potential evapotranspiration