Evaluating the performance of hydrological models via cross-spectral analysis: case study of the Thames Basin, United Kingdom

Nine distributed hydrological models, forced with common meteorological inputs, simulated naturalised daily discharge from the Thames Basin for 1963-2001. While model-dependent evaporative losses are critical for modelling mean discharge, multiple physical processes at many time scales influence the variability and timing of discharge. Here we advocate the use of cross-spectral analysis to measure how the average amplitude, and independently the average phase, of modelled discharge differ from observed discharge at daily to decadal time scales. Simulation of the spectral properties of the model discharge via numerical manipulation of precipitation confirms that modelled transformation involves runoff generation and routing that amplify the annual cycle, while subsurface storage and routing of runoff between grid boxes introduces most autocorrelation and delays. Too much or too little modelled evaporation affects discharge variability as do the capacity and time constants of modelled stores. Additionally the performance of specific models would improve if four issues were tackled: a) non-sinusoidal annual variations in model discharge (prolonged low baseflow and shortened high baseflow, 3 models), b) excessive attenuation of high frequency variability (3 models), c) excessive short-term variability in winter half years but too little variability in summer half years (2 models) and d) introduction of phase delays at the annual scale only during runoff generation (3 models) or only during routing (1 model). Cross-spectral analysis reveals how re-runs of one model using alternative methods of runoff generation - designed to improve performance at the weekly to monthly time scales - degraded performance at the annual scale. The cross-spectral approach facilitates hydrological model diagnoses and development.