Solar radiation and relative humidity based, empirical method, to estimate hourly reference evapotranspiration

• Current methods require at least three meteorological variables to estimate ETo.
• Relation between VPD and 1/ln(RH) was investigated.
• The above was combined into a single term with an exponential function of Rs.
• The performance of the formula is similar during yearly and summer periods.
• RMSE is acceptable for almost all the observed VPD and wind speed values.

A new empirical method which estimates hourly reference evapotranspiration is proposed, that utilizes two meteorological variables, namely incoming solar radiation and relative humidity. It also utilizes a term that combines both variables. The inverse of the natural logarithm of relative humidity and the vapor pressure deficit of the atmosphere were investigated and were found to correlate quite well. The equation was calibrated in a semi arid environment, using data from Davis station (year 2000), of the CIMIS network. The estimations of both, the empirical method and the ASCE PM method, were compared. Validation of the method was performed with hourly data from the same station for 8 years, using various statistical indices. The hourly empirical equation was investigated for the whole period, for each year separately and for the summer period. It was found that it performed satisfactorily in all cases. Yearly RMSE ranged from 0.036 to 0.045 mm/h with an average for the whole period 0.042 mm/h. For the summer period RMSE ranged from 0.040 mm/h to 0.055 mm/h with an average for all the values of the summer period 0.047 mm/h. It was also validated with data from the grass reference meteorological station in the experimental field of the Agricultural University of Athens in Copais, Greece and was found to perform satisfactorily with RMSE equal to 0.043 mm/h. The deviations of the new empirical method from the ASCE PM method were investigated for various ranges of wind speed and vapor pressure deficit data values. It was found that the empirical method estimates were acceptable for practically all cases when 0.073 mm/h was considered as the threshold RMSE value. The proposed hourly empirical equation is recommended for use in semi arid climates.