SPATIAL STRUCTURE OF SOLAR-RADIATION IN WISCONSIN

Insolation at the earth's surface varies in time and space. Applications that require daily insolation values at specific locations, e.g. irrigation scheduling on coarse textured soils, require pyranometer networks denser than those typically deployed to date. We used satellite derived measurements of daily insolation to investigate effects of network density on errors of prediction when only sparse data are available. The satellite data provided spatial resolution much higher than that obtained with typical pyranometer networks. Insolation was estimated from the satellite imagery on a grid of 567 locations, separated by about 20 km; 44 days during the growing season were studied. Subsets of the complete daily datasets were extracted to serve as hypothetical sparse pyranometer networks and used as input for kriging. One simulated network had about 270 km of separation between measurements and the other about 100 km. On individual days, all locations in the complete dataset were estimated by kriging, using the variogram from that day, and variograms from other days that represented the range of spatial structures observed. Variograms of insolation on individual days during the growing season were essentially linear, but differed 350-fold in their values at one-half maximum data point spatial separation. Using the variogram from the day with the greatest variation, errors less than 4.6 MJ m-2 day-1 can be expected for 80% of the area within the measurement grid on 90% of the days, given a 270 km spacing between pyranometers. Absolute errors of estimation were typically halved by increasing network density four-fold.