Testing the spatial applicability of the Johnson–Woodward method for estimating solar radiation from sunshine duration data

Solar radiation is a driving variable for a wide range of processes in both natural and human systems. On-site measurement of solar radiation is much rarer than for other meteorological variables (approximately 40 sites of more than 2000 in the current UK network, with many of these only having records in the last 10 years). Hence a number of models have been developed to estimate solar radiation values based on more frequently observed variables such as temperature and sunshine hours. One of the principal limitations of these methods is that they require calibration using on-site measured solar radiation data and it is therefore open to question how transferable these calibration values are to other locations. This paper follows on from previous research that compared the performance of three models to estimate solar radiation (Campbell–Donatelli, Donatelli–Bellocchi and Johnson–Woodward), and that concluded the Johnson–Woodward (JW) model, estimating solar radiation values from sunshine hours duration, had an overall superior performance for UK sites. The JW model has a single empirical parameter (F) that indicates the intensity of diffuse solar radiation from cloudy skies. We investigate the use of spatial interpolation methods to provide estimates of F at locations without solar radiation measurements. Six simple spatial interpolation methods were tested with the best found to be ordinary kriging with first order polynomial trend removal. The performance of the interpolations was assessed using cross-validation. The magnitudes of the errors from cross-validation were compared with the year-to-year variability of the F parameter and found to be acceptable for the intended application. The analysis indicated the importance of stations near the geographic and altitudinal boundaries of the region, with significant errors associated for sites that have greater cloud cover than would be expected from other sites in their immediate vicinity. This suggested that other local factors may need to be included within the spatial interpolation. The paper concludes by suggesting possible improvements to the spatial interpolation methodology.