A cross-spectral approach to assessing the performance of hydrological models: observed v modelled daily discharge of the River Thames, UK

Nine distributed hydrological models, forced with common meteorological inputs, simulated observed daily discharge from the Thames Basin, S.E. England for 1963-2001. Standard metrics are of limited use for diagnosing model deficiencies because of the wide range of time scales having large variations in discharge. We used a cross-spectral approach to analyse model performance in terms of reproducing average amplitude and phase of discharge variations at the different time scales. The different time scales are characteristic of different physical processes.

Overall evaporative losses are critical for successfully modelling mean discharge, but sub-annual processes, represented differently in different models, also partly dictate the amplitude of the annual cycle of discharge. One model was re-run with alternative methods of runoff generation - designed to improve model performance over time scales of days to weeks. Despite improvements compared to observations on short time scales in the two subsequent runs, the cross-spectral analysis clarifies the degradation of model performance over longer time scales including the annual cycle.

Spectrally the transformation of precipitation variability into discharge variability within the real basin - and as modelled - involves both amplification of an annual cycle, predominantly due to the seasonal cycle in evapotranspiration and introduction of substantial serial correlation. In the land surface models and global hydrological models analysed, this transformation occurs by: a) runoff generation creating the annual cycle and b) routing of runoff between model grid boxes introducing most of the serial correlation. Three of the models also introduce excessive suppression of high-frequency discharge variability; indicative of a unwanted moving average property added during the modelling of routing. Quantitative assessment of modelled amplitude and phase at distinct time scales via the cross-spectral approach facilitates hydrological model diagnoses and development.