Quoted from:L.A. Hunt, L. Kuchar, C.J. Swanton,Estimation of solar radiation for use in crop modelling,Agricultural and Forest Meteorology,Volume 91, Issues 3–4,1998,Pages 293-300,ISSN 0168-1923,

https://doi.org/10.1016/S0168-1923(98)00055-0.

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.

The fitted coeffcientsfrom each station in turn were used to estimate solar radiation values for each of the other stations for each day over the full span of data available. Correlation coeffcients (R2) between computed and real values and root mean square errors (RMSE), were then calculated using data from 12- month periods. Overall means and standard deviations were calculated using the available 12-month correlations and RMSE values. Correlations between the daily solar radiation data measured at each site and that measured at each of the other seven sites, together with RMSE values, were also computed for all 12-month periods. Averages and error terms were calculated from the 12-month period computations.

The finding that radiation data from a nearby station can be used quite widely has implications relative to the deployment of resources in agricultural, silvicultural, and ecological research. Currently, many researchers are making efforts to record radiation at experimental sites that are often not visited at frequent intervals. Because of the problem of radiation measurement, the data from such sites may be of questionable quality either because some values are in error due to instrument malfunctioning or temporary shading of the sensor, or because all values are biased due to calibration and instrument siting problems, or both. It may be preferable, therefore, for agricultural and ecological researchers to concentrate their efforts to measure daily radiation at a central site for an agroecological region, rather than to dissipate resources by trying to measure at a number of poorly maintained sites. The definition of regions within which such an approach could be adopted will depend on the error that is acceptable for particular applications, as well as the characteristics of a region. For Ontario, the presented curve relating RMSE to separation of sites could be used to establish a `critical distance within which measurements should be made for particular applications. For other regions, definition of a similar curve may require the establishment of temporary stations that could be well monitored for a period of time, the data from which could be used to define the `climatological topography' of the region (a resultant of climate, landscape, reservoirs and lakes, etc.), but that would not necessarily need to be maintained indefinitely as an adjunct to field research efforts.