Evaluation of a radiation-based empirical model for estimating hourly reference evapotranspiration for high-altitude climatic conditions: A case study for the state of California

Abstract

High-altitude (>800 m) climatic conditions for the four stations in arid, semiarid and subhumid climatic zones were examined to evaluate their influence on radiation-based empirical estimations of reference evapotranspiration ( $${ET}_{\mathrm{o}}$$ ) on an hourly time step. The empirical method utilises the incoming solar radiation and the relationship between a function of relative humidity and vapour pressure deficit. The empirical method overestimated $${ET}_{\mathrm{o}}$$ by 21.4%, on a yearly basis, 27.0% for the winter period and 16.3% for the summer period, compared with the estimations of the American Society of Civil Engineers Penman Monteith (ASCE PM) (2005) method. Various meteorological variables included in the energy and the aerodynamic term of the ASCE PM (2005) method were investigated with respect to altitude. The increasing trend of incoming solar radiation combined with the decreasing trend of relative humidity, both with respect to altitude were the main causes for the underestimation of the empirical radiation method. The empirical method was adjusted for high-altitude climatic conditions by multiplying the values by the ratio of the atmospheric pressure corresponding to the altitude of the station to the atmospheric pressure at sea level. The adjusted values were overestimated by 3.4% compared to the estimations of the ASCE PM (2005) method (higher overestimation: 9.1% and lower overestimation: 0.8%). The value of $$0.073\hbox { mm h}^{-1}$$ was considered as the upper limit for the satisfactory performance of the empirical method. The root mean square error (RMSE) values ranged from 0.038 to $$0.054\hbox { mm h}^{-1}$$ and the $$R^{2}$$ values ranged from 0.95 to 0.97. The values of the wind speed and vapour pressure deficit (not included in the empirical method) were divided into intervals and the RMSE values between the values of the estimations of the empirical method and the values of the estimations of the ASCE PM (2005) were calculated for each interval. The RMSE values calculated for the intervals of the values of the wind speed ranged from 0.036 to $$0.065\hbox { mm h}^{-1}$$ and were satisfactory. The vapour pressure deficit values <2.5 kPa also yielded satisfactory RMSE values and accounted for 96.1% of the data.