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United States Department of Agriculture

Agricultural Research Service


Location: Wind Erosion and Water Conservation Research

Title: A field test of recursive calculation of crop evapotranspiration)

item Lascano, Robert
item Van bavel, Cornelius
item Evett, Steven - Steve

Submitted to: Transactions of the ASABE
Publication Type: Peer reviewed journal
Publication Acceptance Date: 7/1/2010
Publication Date: 7/15/2010
Citation: Lascano, R.J., Van Bavel, C., Evett, S.R. 2010. A field test of recursive calculation of crop evapotranspiration. Transactions of the ASABE. 53(4):1117-1126.

Interpretive Summary: In irrigated agriculture the amount of water that a crop uses on a daily basis must be known to schedule irrigation events. Currently, the most popular method that is worldwide used is based on a concept that was introduced in 1948 by a well-known scientist, Howard Penman, and named his concept a combination method to calculate crop evapotranspiration (ET). The ET represents the amount of water that is lost by evaporation from the soil surface and from the crop. It is called combination because it combines the energy balance, inputs and outputs, of the crop surface with another equation that calculates ET above the crop. By doing so, Penman was able to eliminate the surface temperature of the evaporating crop, a difficult value to measure, from all of the calculations. The problem is that the error that is introduced by this simplification increases as the air temperature increases and the air humidity decreases, which corresponds to semi-arid and arid climates, where irrigation is normally practiced. In our previous work we showed that this error can be substantial resulting in a 25% under-calculation of crop ET and that a simpler calculation method, without the assumptions introduced by Penman, can give accurate values of crop ET. In this paper, we experimentally show that the iterative method we introduced to calculate crop ET is accurate. We tested our method with alfalfa in Bushland TX and Tempe AZ. Our results show that for a well-watered crop the iterative method we proposed to calculate crop ET is accurate. Our method is simple to implement and requires no more computing power than a spreadsheet such as Microsoft' Excel. This is a preferred method to calculate crop ET and requires as input values that are routinely measured in weather stations that are part of regional ET networks.

Technical Abstract: Numerous methods to calculate the evapotranspiration (ET) rate from field crops have been proposed, but few have convincingly demonstrated to be usefully accurate. The direct measurement of ET requires weighable lysimeters. However, the use of a surface energy balance to calculate ET requires a correct value for the crop surface temperature. An alternative for the latter is to solve the energy balance equation by iteration, as we proposed in 2007 (Lascano and Van Bavel, Agron. J. 99, 585–590). The validity of such a recursive method was examined in a three-month experiment in 1999 on an hourly, daily and monthly basis in Bushland TX on a well-watered alfalfa field, exposed to a hot and dry summer climate. The ET was measured half-hourly with lysimeters, accurate to 0.05 mm. Daily amounts of ET were found to be correctly calculated from the weather data using the recursive method to within 0.8 mm as indicated by the root mean squared difference (RMSD) between calculated and measured values of ET. The sum of the 26 daily-calculated values of ET was found to be within 7 mm of the measured amount. We also applied the recursive method to data collected in a similar experiment with alfalfa conducted in July 1964, in Tempe AZ. Daily ET was measured with lysimeters and calculated with the same recursive formula from the hourly weather data over a period of 20 days after a flood irrigation that kept the crop in a well-watered condition. The RMSD was 0.6 mm and the calculated total amount of ET was within 2 mm of the measured value. We conclude that an iterative formulation can give very good accuracy to the measurement of ET of a well-watered crop and that similar studies with other irrigated crops grown in hot and dry climates should be made.

Last Modified: 8/24/2016
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