Scale dependence of radar-rainfall rates - An assessment based on raindrop spectra

Scale differences may introduce a bias when comparing, merging, or assimilating rainfall measurements because the dynamic range of values representing the underlying physical process strongly depends on the resolution of the data. The present study addresses this issue from the perspective of how well coarser-resolution radar-rainfall observations may be used for evaluation of hydrologic point processes occurring at the land surface, such as rainfall erosion, infiltration, ponding, and runoff. Conceptual and quantitative analyses reveal that scale differences may yield substantial biases. Even for perfect measurements, the overall bias is composed of two contributing factors: one related to a reduction of dynamic range of rain rates and the other related to a dependence of the relationship between observed radar reflectivity factor and retrieved rainfall rate on the scale of observation. The effects of scale differences are evaluated empirically from a perspective of averaging in time based on raindrop spectra observations. Averaging drop spectra over 5 min, on average over a large dataset, resulted in an underestimation of median and maximum rainfall rates of approximately 50% compared to the corresponding 1-min values. Overall, standard deviations of rain rates retrieved from 5-min-averaged radar reflectivity factors may easily be off a corresponding high-resolution ( 1 min) rainfall rate by a factor 2 or more. This magnitude is larger than the uncertainty resulting from limitations of the radar measurement precision. Scale-difference effects are thus important and should be considered when comparing, merging, or assimilating data from very different spatial and temporal scales. A similar challenge arises for downscaling schemes attempting to recover subgrid-scale features from coarse-resolution information.