Estimation of solar radiation for use in crop modelling

Abstract

The aim of this study was to determine the accuracy and applicability of a number of existing and newly developed formulae for calculating solar radiation from other weather variables. Data were taken from eight sites in Ontario, Canada, that had long-term daily weather data sets which included solar radiation. Daily recorded values of minimum and maximum air temperature and precipitation, together with calculated values for clear sky radiation, were used in the formulae. Clear sky radiation was calculated as a function of latitude, day of year, solar angle, and solar constant. Coefficients for five formulae were fitted using data from Elora, Canada. Correlation coefficients between values calculated for individual days and measured data, and errors, were then computed. A newly developed formula that included the maximum temperature, the difference between maximum and minimum temperature, precipitation, and precipitation squared, provided estimates with less error than other formulae. Coefficients for this model and for one other formula were then fitted to data from seven sites. The root mean square error (RMSE) between values calculated for individual days with the newly developed model and measured data for Ontario (Elora) was 4.1 MJ m −2 day −1 with a standard deviation of 0.29 MJ m −2 day −1. When coefficients from one site were used for other sites, the RMSE increased as a linear function of distance between sites; in contrast, when measurements from one site were used for other sites, the RMSE increased curvilinearly with distance. Comparison of errors involved when using coefficients from one site as contrasted to using measured solar radiation indicated that it would be preferable to use measured radiation values if the distance between sites was less than 390 km. Because the RMSE at this separation may not be acceptable for some applications, it was suggested that the curve relating RMSE to separation of sites could be used to establish a `critical' distance within which measurements should be made.