Evaluating the Performance of Hydrological Models via Cross-Spectral Analysis: Case Study of the Thames Basin, United Kingdom

Abstract

Nine distributed hydrological models, forced with common meteorological inputs, simulated naturalized daily discharge from the Thames basin for . While model-dependent evaporative losses are critical for modeling mean discharge, multiple physical processes at many time scales influence the variability and timing of discharge. Here the use of cross-spectral analysis is advocated to measure how the average amplitude-and independently, the average phase-of modeled 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 modeled transformation involves runoff generation and routing that amplify the annual cycle, while subsurface storage and routing of runoff between grid boxes introduces most of the autocorrelation and delays. Too much or too little modeled evaporation affects discharge variability, as do the capacity and time constants of modeled stores. Additionally, the performance of specific models would improve if four issues were tackled: 1) nonsinusoidal annual variations in model discharge (prolonged low base flow and shortened high base flow; three models), 2) excessive attenuation of highfrequency variability (three models), 3) excessive short-term variability in winter half years but too little variability in summer half years (two models), and 4) introduction of phase delays at the annual scale only during runoff generation (three models) or only during routing (one model). Cross-spectral analysis reveals how reruns 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.

Towards the representation of groundwater in the Joint UK Land Environment Simulator

“…The model performance was poor and only for one catchment the Nash Sutcliffe efficiency for the optimized simulations was higher than 0.5. Weedon et al (2015) applied nine distributed hydrological models, including JULES, to simulate the daily runoff at the Thames catchment. The evaluation was based on the cross‐spectral analysis and they found that JULES’ performance depended on the configuration that was used (i.e., JULES‐TOPMODEL, JULES‐PDM, JULES) with JULES‐TOPMODEL producing a slightly better performance.…”

Improving river flow generation over Great Britain in a land surface model required for coupled land-atmosphere interactions

“…10. If a time series is 15 compared to itself, but offset by a few time steps, there is a resulting trend in the high frequency part of the phase difference spectrum (equation A10 in Weedon et al, 2015). The theoretical phase difference trends that approximate the results are shown using black dashed lines in Fig.…”

“…In order to further assess the model performance at time scales longer than daily and relevant for the studied catchments, and reinforce findings using NS at the daily time scale and mean bias, we use a cross-spectral analysis (Weedon et al, 2015) that provides measures on how the average amplitude and phase of modelled river flow differ from observed river flow at those time scales.…”

“…In particular, this allows assessment of the average amplitude of discharge at different time scales and separately the average phase difference (lead or lag) of the modelled compared to the observed discharge (Weedon et al, 2015). The time scales investigated range from 2 days to the length of the time series or 10 years.…”

“…10. Note that phase differences distinguishable from zero degrees can result from both simple offsets in the timing of model output compared to observations (causing phase difference trends) and from incorrect modelling of the response times of hydrological stores (Weedon et al, 2015). 20…”