Calibration of the Angström-Prescott solar radiation model for accurate estimation of reference evapotranspiration in the absence of observed solar radiation

Abstract

The Angström-Prescott (AP) model is widely suggested for estimating global solar radiation (R _s), especially for reference crop evapotranspiration (ET₀) calculations. Many previous studies indicated that the coefficients of the AP model depend on the climatic and geographical characteristics of study sites. In the present work, calibrated AP models were developed in some climates in Iran. Different radiation scenarios from estimated and measured R _s were applied to calibrate the AP coefficients. Radiation scenarios included measured R _s (M) and estimated R _s from the models of Daneshyar (D) and Hargreaves (H). Daily reference evapotranspiration was calculated using the coefficients obtained from different R _s scenarios. The estimated daily ET₀ values were compared with field lysimeter data for validation. Results showed that scenarios D and H present the minimum ET₀ deviation from lysimeter data. Findings suggested that at the majority of the study sites, calibration of the AP model improved the accuracy of estimated ET₀. Results also indicated the applicability of reliable R _s estimation methods to calibrate the AP model. Apart from applied R _s scenarios, the daily ET₀ is underestimated by the FAO56 Penman-Monteith model.

Appendix

The statistical methods used were as follows:

$$ \mathrm{RMSE}=\sqrt{\frac{{\displaystyle \sum_{i=1}^n{\left({P}_i-{O}_i\right)}^2}}{n}} $$

(10)

$$ \mathrm{MBE}=1/n\times {\displaystyle \sum_{i=1}^n\left({P}_i-{O}_i\right)} $$

(11)

$$ \mathrm{MPE}=1/n\times \frac{{\displaystyle \sum_{i=1}^n\left({P}_i-{O}_i\right)}}{\overline{O}}\times 100\kern0.5em \% $$

(12)

$$ \mathrm{MAE}=1/n\times {\displaystyle \sum_{i=1}^n\left|{P}_i-{O}_i\right|} $$

(13)

where P _i and O _i are the ith predicted and observed values, respectively; $\overline{O}$ is the observed daily averaged value; and n is the total number of observations.