A comparison of the discrete cosine and wavelet transforms for hydrologic model input data reduction

Abstract

The treatment of input data uncertainty in hydrologic models is of crucial importance in the analysis, diagnosis and detection of model structural errors. Data reduction techniques decrease the dimensionality of input data, thus allowing modern parameter estimation algorithms to more efficiently estimate errors associated with input uncertainty and model structure. The discrete cosine transform (DCT) and discrete wavelet transform (DWT) are used to reduce the dimensionality of observed rainfall time series for the 438 catchments in the Model Parameter Estimation Experiment (MOPEX) data set. The rainfall time signals are then reconstructed and compared to the observed hyetographs using standard simulation performance summary metrics and descriptive statistics. The results convincingly demonstrate that the DWT is superior to the DCT in preserving and characterizing the observed rainfall data records. It is recommended that the DWT be used for model input data reduction in hydrology in preference over the DCT.