Assessing Rainfall-Runoff Records for Time Invariance using Transfer Function Models with Time-varying Parameters

Most catchment-scale rainfall-runoff models represent as time -invariant such features of the hydrograph as lag to peak, volumetric throughput and recession time constant. While this assumption has been shown to suit many catchment-modelling purposes, it obscures any variation in response characteristics over the range of conditions in which the model is calibrated. The assumption of time invariance is tested by use of linear, transfer-function models with time-varying parameters. The approach is illustrated on seven years’ daily rainfall and streamflow records from a 10.5 km forested catchment in Virginia. Models are fitted by recursive minimum-covariance estimation with optimal smoothing, treating various subsets of the model parameters as time-varying, modelled as random walks. The extent of time variation is specified by variances for the parameter increments. These are chosen by reference to the root-mean-squared value of the residuals, the ratio of mean-square values of the one-step-prediction errors and residuals, and the credibility of the parameter variations. Care is found to be necessary because variations in gain and dominant time constant interact through the transfer-function denominator coefficients. The role of a time-varying outputoffset term in the model is examined. Significant time variation is found in volumetric throughput and recession time constant, as a consequence of non-linearity and unmodelled or incompletely modelled phenomena such as evapotranspiration, varying soil moisture and snowmelt. The broad conclusion is that a substantial reduction in residuals and improvement in short-term prediction performance is obtainable by representing the catchment behaviour as linear but time-varying. The results indicate the extent of variation of linear-model and hydrological parameters.