Global solar radiation in Central European lowlands estimated by various empirical formulae

Abstract

Seven methods for estimating daily global radiation, R G, were tested in the Central Europe case study area (lowlands of Austria and the Czech Republic) assuming that no measured global radiation data for parameterisation are available, i.e. with all empirical coefficients required by the selected methods being obtained from previously published studies. The variability explained ( R 2), the root mean square error (RMSE) and mean bias error (MBE) indicated that the highest precision could be expected when sunshine duration was used as predictor. The method generally known as the Ångström–Prescott method explained 96% of the R G variability with the RMSE value (annual mean) equalling 1.6 MJ m −2 day −1 and MBE being 0.1 MJ m −2 day −1. It was found to be ultimately the best of all tested methods. Where there were no reliable estimates of the empirical coefficients necessary for this equation, the multiple regression method between measured sunshine duration and R G, was found to perform satisfactory from April to August. Where there were no sunshine duration data, the formula including cloud term and daily temperature range, yielded a sufficiently precise estimates ( R 2 = 0.91; RMSE = 2.3 MJ m −2 day −1; MBE = 0.2 MJ m −2 day −1). Where the cloud cover records were not available, the one of the methods employing the total daily precipitation might be used ( R 2 = 0.86; RMSE = 3.1 MJ m −2 day −1; MBE = 0.2 MJ m −2 day −1). Where the precipitation data are not available, the temperature-based method despite the relatively large deviations ( R 2 = 0.82; RMSE = 3.5 MJ m −2 day −1; MBE = 0.3 MJ m −2 day −1) might be considered as an alternative. The missing R G data could also be substituted by the values measured in a nearby station. The precision of the radiation estimated in this way decreased with increasing distance between the two stations: R 2 decreased from 0.95 to 0.60 as the distance increased from 17 to 369 km. When the annual mean RMSE was studied it was found that it increased by approximately 0.15 MJ m −2 day −1 per 10 km in the study region and variability explained decreased by approximately 1% for the same distance. The R G estimates based on temperature or combination of temperature and precipitation were biased by about 10% during several months. The value of RMSE of these methods reached up to 30%, and even the best estimates based on sunshine duration hours were loaded by RMSE to the extent of 10–20% during the growing season. Therefore, any further application relying on these estimates, especially if they are based on literature derived coefficients, might be significantly distorted and error propagation analysis is strongly recommended to any user of estimated R G data.