Modification of the Hargreaves–Samani Model for Estimating Solar Radiation from Temperature and Humidity Data

A new formula is introduced to estimate solar radiation, $R_S$ ($\mathrm{MJ}/{\mathrm{m}}^2/\mathrm{d}$), using maximum and minimum air temperature, $T_{\max }$ (°C) and $T_{\min }$ (°C), respectively, as well as relative humidity, $RH$ (%). This technical note describes a modification to the original equation of the Hargreaves–Samani model. The new formula is obtained by calibration using data obtained from a global database. The new version of the formula is: $R_S\approx 0.338\times R_A\times {(T_{\max }-T_{\min })}^{0.3}\times {(1.001-RH/100)}^{0.2}$ where $R_A$ is the extraterrestrial radiation ($\mathrm{MJ}/{\mathrm{m}}^2/\mathrm{d}$). The proposed modification was tested under various climatic conditions using high-quality daily weather data from 32 stations across California, Florida, Arizona, and Greece, showing improvement of the accuracy of estimates of solar radiation. The proposed modification is not as generalized as the original Hargreaves–Samani equation that allows estimation of $Rs$ using widely available $T_{\max }$ and $T_{\min }$ data because it is restricted to locations where good quality $RH$ data is measured.