Impact of different regression frameworks on the estimation of the scaling properties of radar rainfall

Rainfall is characterized by high variability both in space and time. Despite continuous technological progress, the available instruments that are used to measure rainfall across several spatio-temporal scales remain inaccurate. To remedy this situation, scaling relationships of spatial rainfall offer the potential to link the observed or predicted precipitation quantities at one scale to those of interest at other scales. This paper focuses on the estimation of the spatial rainfall scaling functions. Standard scaling analysis constructed by means of the ordinary least squares method often violates such basic assumptions implicit in its use and interpretation as homoschedasticity, independence, and normality of the errors. Consequently, the authors consider alternative regression frameworks i.e. bootstrapping regression, semi parametric linear model, and multilevel normal linear model to show how these different approaches exert a significant impact on the multifractal analysis of radar rainfall. In addition, the uncertainties associated with the construction of the scaling function due solely to the regression procedure are quantified. The radar data come from the polarimetric C-band weather radar located in Rome, Italy, and the scaling properties are computed for a square domain centred on the radar site with a side length of 128 km and a finest resolution of 1 km².