CART Regression Models for Predicting UV Radiation at the Ground in the Presence of Cloud and Other Environmental Factors

Abstract

The goal was to build models for predicting ground-level biologically weighted ultraviolet radiation (UV index, shortened to UV here) that would not require substantial execution time in weather and climate models and yet be reasonably accurate. Recent advances in modeling data make this goal possible. UV data computed from Brewer spectrophotometer measurements at Toronto were matched with observed meteorological predictors for 1989?93. Data were stratified into three sets by solar zenith angle 70° and time between 1000 and 1400 LST. Stepwise linear regression (SLR) and CART (nonlinear) tree-based regression models were built for UV and N(UV) (ratio: observed UV to clear-sky UV). CART models required fewer predictors to achieve minimum error, and that minimum was lower than SLR. For zenith angle less than 70° CART regression models were superior to SLR by 5%?10% error after regression. The CART model had 31% relative error (ratio: estimated mean-squared error after regression to sample variance) and three predictors: total opacity, liquid precipitation, and snow cover. Including five next predictors decreased error only another 1%. For zenith angle 70° or greater, SLR could not produce a useful model, whereas CART gave a model with 15% relative error using three predictors. Total opacity is by far the most important predictor throughout. Snow cover enhances UV at the ground by 11%?13% even in cloudy conditions, but its relative influence decreases with zenith angle. For general use at other locations models with as few predictors as possible are desirable. CART models with 34%?35% relative error were built with three predictors: total opacity, zenith angle, and clear-sky UV. Tests were done at 11 stations for several months in 1995. Averaged root-mean-squared discrepancy between predicted and observed UV is reduced about 40% when observed opacity is used for the CART prediction compared to using clear-sky UV. When an 18-h forecast opacity is used the reduction is about 25%. Improvement over clear-sky UV is substantially greater than this on cloudy days. Thus, CART three-predictor models for N(UV) can be used poleward of Toronto in a variety of cloud conditions in analysis or forecast modes. A predictor representing smoke from forest fires was not included. Several cases during the test period showed clear-sky UV was reduced by smoke 30%?50% near to the fires and 20%?30% far downwind.