A Time-Based Framework for Evaluating Hydrologic Routing Methodologies Using Wavelet Transform

Abstract

In this study we explore a method which provides an insight into the effectiveness of various hydrologic models’ routing components based on their ability to accurately represent flood peak times and shapes. The method is based on using Cross-Wavelet Transforms to estimate the phase (time) difference between the time series of the observed and the simulated discharges. In this article we evaluate two routing components, the Routing Application for Parallel Computation of Discharge (RAPID), which is based on the simplified Muskingum routing method, and the routing component of the non-linear Hillslope-Link hydrologic Model (HLM) produced in the Iowa Flood Center (IFC). Both routing components are driven by the same source of runoff and used the same channel network to ensure that the discrepancies between the simulated stream discharges are due to channel routing alone. We also explore the suitability of different wavelet shapes for our application, and how the difference in wavelet shape can affect our evaluation results. Unlike the conventional statistical skill scores used to evaluate model performance (e.g. Root Mean Squared Error, correlation coefficient, and Nash Sutcliff efficiency index), which give an estimate of the overall hydrograph performance, our method conveniently provides time-localized information with higher resolution at peak location. We perform our evaluation at multiple stream gauge locations, covering a wide range of scales (700 to 16,862 km2), located in the eastern part of the state of Iowa. Our results show that the proposed wavelet method is effective in evaluating the performance of the routing components in simulating peak times across spatial scales. Generally, the non-linear routing method employed in the HLM outperformed the Muskingum based method employed in RAPID. In addition, our results suggest that the Paul wavelet is more effective in detecting and separating individual peaks than the Morlet wavelet, which in turn leads to a more accurate evaluation of the routing components.