Predicting Daily Net Radiation Using Minimum Climatological Data

Net radiation $\left(R_n\right)$ is a key variable for computing reference evapotranspiration and is a driving force in many other physical and biological processes. The procedures outlined in the Food and Agriculture Organization Irrigation and Drainage Paper No. 56 [FAO56 (reported by Allen et al. in 1998)] for predicting daily $R_n$ have been widely used. However, when the paucity of detailed climatological data in the United States and around the world is considered, it appears that there is a need for methods that can predict daily $R_n$ with fewer input and computation. The objective of this study was to develop two alternative equations to reduce the input and computation intensity of the $\mathrm{FAO}56-R_n$ procedures to predict daily $R_n$ and evaluate the performance of these equations in the humid regions of the southeast and two arid regions in the United States. Two equations were developed. The first equation [measured-$R_s$-based $\left(R_{s-M}\right)]$ requires measured maximum and minimum air temperatures $(T_{\max }$ and $T_{\min })\text{,}$ measured solar radiation $\left(R_s\right)\text{,}$ and inverse relative distance from Earth to sun $\left(d_r\right)\text{.}$ The second equation [predicted-$R_s$-based $\left(R_{s-P}\right)]$ requires $T_{\max }\text{,}$ $T_{\min }\text{,}$ mean relative humidity $\left({\mathrm{RH}}_{\mathrm{mean}}\right)\text{,}$ and predicted $R_s\text{.}$ The performance of both equations was evaluated in different locations including humid and arid, and coastal and inland regions (Gainesville, Fla.; Miami, Fla.; Tampa, Fla.; Tifton, Ga.; Watkinsville, Ga.; Mobile, Ala.; Logan, Utah; and Bushland, Tex.) in the United States. The daily $R_n$ values predicted by the $R_{s-M}$ equation were in close agreement with those obtained from the FAO56-$R_n$ in all locations and for all years evaluated. In general, the standard error of daily $R_n$ predictions (SEP) were relatively small, ranging from 0.35 to 0.73 MJ m⁻² d⁻¹ with coastal regions having lower SEP values. The coefficients of determination were high, ranging from 0.96 for Gainesville to 0.99 for Miami and Tampa. Similar results, with approximately 30% lower SEP values, were obtained when daily predictions were averaged over a three-day period. Comparisons of $R_{s-M}$ equation and $\mathrm{FAO}56-R_n$ predictions with the measured $R_n$ values showed that the $R_{s-M}$ equations’ predictions were as good or better than the $\mathrm{FAO}56-R_n$ in most cases. The performance of the $R_{s-P}$ equation was quite good when compared with the measured $R_n$ in Gainesville, Watkinsville, Logan, and Bushland locations and provided similar or better daily $R_n$ predictions than the $\mathrm{FAO}56-R_n$ procedures. The $R_{s-P}$ equation was able to explain at least 79% of the variability in $R_n$ predictions using only $T_{\max }\text{,}$ $T_{\min }\text{,}$ and RH data for all locations. It was concluded that both proposed equations are simple, reliable, and practical to predict daily $R_n\text{.}$ The significant advantage of the $R_{s-P}$ equation is that it can be used to predict daily $R_n$ with a reasonable precision when measured $R_s$ is not available. This is a significant improvement and contribution for engineers, agronomists, climatologists, and others when working with National Weather Service climatological datasets that only record $T_{\max }$ and $T_{\min }$ on a regular basis.