Statistical downscaling of rainfall: a non-stationary and multi-resolution approach

A novel downscaling technique is proposed in this study whereby the original rainfall and reanalysis variables are first decomposed by wavelet transforms and rainfall is modelled using the semi-parametric additive model formulation of Generalized Additive Model in Location, Scale and Shape (GAMLSS). The flexibility of the GAMLSS model makes it feasible as a framework for non-stationary modelling. Decomposition of a rainfall series into different components is useful to separate the scale-dependent properties of the rainfall as this varies both temporally and spatially. The study was conducted at the Onkaparinga river catchment in South Australia. The model was calibrated over the period 1960 to 1990 and validated over the period 1991 to 2010. The model reproduced the monthly variability and statistics of the observed rainfall well with Nash-Sutcliffe efficiency (NSE) values of 0.66 and 0.65 for the calibration and validation periods, respectively. It also reproduced well the seasonal rainfall over the calibration (NSE = 0.37) and validation (NSE = 0.69) periods for all seasons. The proposed model was better than the tradition modelling approach (application of GAMLSS to the original rainfall series without decomposition) at reproducing the time-frequency properties of the observed rainfall, and yet it still preserved the statistics produced by the traditional modelling approach. When downscaling models were developed with general circulation model (GCM) historical output datasets, the proposed wavelet-based downscaling model outperformed the traditional downscaling model in terms of reproducing monthly rainfall for both the calibration and validation periods.