Selection of predictors for statistical downscaling using wavelet techniques

Selection of predictors for statistical downscaling using wavelet techniques

Selection of predictors for statistical downscaling is crucial as the relationship between the predictors (temperature, humidity and geopotential height) and predictands (local scale meteorological variables such as rainfall) forms the basis of statistical downscaling. While selection of predictors based on correlation analysis is common for statistical downscaling, the traditional correlation analysis has limited ability for interpreting non-stationary and non-linear relationships. Wavelet coherence analysis can be used for identifying the strength of the relationship between two time series for both the time and frequency domains simultaneously. In this study a methodology has been developed to identify the potential predictors for statistical downscaling using continuous wavelet transforms (CWT) and square wavelet coherence (WTC). First CWT was used to identify the dominant periodicity in the predictand series and then the predictors were selected by examining the WTC between the predictors and predictands for that dominant periodicity. Scale average wavelet coherency (SAC) was found to be useful for selecting the predictor domain. It was also observed that CWT is useful for identifying the predictors for which the predictor-predictand relationship is nearly stationary over a long period, which is an important criteria for predictor selection. For a case study, monthly rainfall from nine rainfall stations in the Onkaparinga catchment in South Australia was considered as the predictands whereas NCEP/NCAR reanalysis variables were considered as the predictors. Overall, the methodology introduced in this study could be applied for selecting potential predictors for statistical downscaling of hydro-climatic variables.