Spatial downscaling of radar-derived rainfall field by two-dimensional wavelet transform

Downscaling of rainfall fields, either as images or products of global circulation models, have been the motive of many hydrologists and hydro-meteorologists. The main concern in downscaling is to transform high-resolution properties of the rainfall field to lower resolution without introducing erroneous information. In this paper, rainfall fields obtained from Next Generation Weather Surveillance Radar (NEXRAD) Level III were examined in the wavelet domain which revealed sparsity for wavelet coefficients. The proposed methodology in this work employs a concept named Standardized Rainfall Fluctuation (SRF) to overcome the sparsity of rainfall fields in wavelet domain which also exhibited scaling behaviors in a range of scales. SRFs utilizes such scaling behaviors where upscaled versions of the rainfall fields are downscaled to their actual size, using a two-dimensional discrete wavelet transform, to examine the reproduction of the rainfall fields. Furthermore, model modifications were employed to enhance the accuracy. These modifications include removing the negative values while conserving the mean and applying a non-overlapping kernel to restore high-gradient clusters of rainfall fields. The calculated correlation coefficient, statistical moments, determination coefficient and spatial pattern display a good agreement between the outputs of the downscaling method and the observed rainfall fields.