An Improved Estimation of the Angstrom–Prescott Radiation Coefficients for the FAO56 Penman–Monteith Evapotranspiration Method

Abstract

The FAO56 Penman–Monteith (FAO56-PM) method is known as the standard method for estimating reference evapotranspiration (ET₀) in a variety of climate types. Global solar radiation (R_s) is one of the essential inputs of this model, which is usually estimated from the Angstrom–Prescott (AP) method. The major drawback of the FAO56 pre-defined AP coefficients application is that the AP coefficients might need local calibration, to estimate ET₀ accurately. The aim of this study is to compare the effect of the FAO56 pre-defined AP coefficients (i.e. a and b) and the locally calibrated ones, on estimating daily ET₀ in 15 sites over Iran. Using long-term (1980–2007) experimental global solar radiation data (R_s), new locally calibrated (a) and (b) coefficients are suggested and new ET₀ values are determined accordingly. It was found that the range of the calibrated AP coefficients (a, b) are climate dependent and locally different from those of recommended by the FAO56-PM method. Estimated ET₀ at daily scale, improved up to 72.7 % when the calibrated AP coefficients were applied instead of FAO56 pre-defined AP coefficients. Based on the results, applying the FAO56 pre-defined AP coefficients (i.e. a = 0.25 and b = 0.50) in northern subtropical-humid and southern hot climates caused larger ET₀ errors. By contrast, the least ET₀ errors were found in cool arid and cool semi-arid inland climates, locating about 1,330 above sea level. The correlations between the calibrated AP coefficients and geographical factors are also discussed in this research.

Appendix A (Statistics)

$$ RMSE=\sqrt{{\frac{{\sum\limits_{i=1}^n {{{{\left( {{P_i}-{O_i}} \right)}}^2}} }}{n}}} $$

(7)

$$ MBE=\frac{1}{n}\times \sum\limits_{i=1}^n {\left( {{P_i}-{O_i}} \right)} $$

(8)

$$ MPE=\frac{1}{n}\times \frac{{\sum\limits_{i=1}^n {\left( {{P_i}-{O_i}} \right)} }}{\overline{O}}\times 100\% $$

(9)

$$ t=\sqrt{{\frac{{\left( {n-1} \right){{{\left( {MBE} \right)}}^2}}}{{{{{\left( {RMSE} \right)}}^2}-{{{\left( {MBE} \right)}}^2}}}}} $$

(10)

P_i and O_i are the i^th predicted and observed values, respectively; $\overline{O}$ is the observed daily averaged value; and n is the total number of observations.