An auto-calibration procedure for empirical solar radiation models

Solar radiation data are an important input for estimating evapotranspiration and modelling crop growth. Direct measurement of solar radiation is now carried out in most European countries, but the network of measuring stations is too sparse for reliable interpolation of measured values. Instead of direct measurements, solar radiation may be estimated from empirical solar radiation models that employ more commonly measured variables or direct outputs of general and regional circulation models (such as air temperature). Coefficients for these models are site-dependent. This usually implies that they are estimated for stations with direct radiation measurements, but need to be interpolated for other locations. In this paper, we introduce a procedure to auto-calibrate empirical solar radiation models that are based on daily air temperature range, i.e. Bristow and Campbell (1984), and Hargreaves et al. (1985). Meteosat Second Generation data were used to create two static look-up tables of mean cloud cover and clear-sky transmissivity as input for the auto-calibration procedure. We demonstrate that daily solar radiation can be accurately estimated from daily air temperature range measurements without site-specific empirical coefficients that require stations that measure solar radiation. The average relative root mean square error for our auto-calibrated models was comparable to ground-measurement-based calibration; only 1% higher for the Bristow and Campbell model (p < 0.05, n = 126), and 2% higher for the Hargreaves model (p < 0.05, n = 126). The mean bias error, relative mean bias error and the slope of linear regression were not statistically different in comparison to ground-measurement-based calibration for the Bristow and Campbell model. When our new solar radiation retrieval algorithm is used to estimate evapotranspiration, we found similar accuracies when using solar radiation input from ground- and auto-calibration. We conclude that our auto-calibration procedure results in accurate solar radiation retrievals, and requires only daily air temperature time series as input. The same procedure could easily be applied to other empirical solar radiation models.