JWARP  Vol.9 No.7 , June 2017
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.
Cite this paper: ElSaadani, M. and Krajewski, W. (2017) A Time-Based Framework for Evaluating Hydrologic Routing Methodologies Using Wavelet Transform. Journal of Water Resource and Protection, 9, 723-744. doi: 10.4236/jwarp.2017.97048.

[1]   David, C.H., Maidment, D.R., Niu, G.-Y., Yang, Z.-L., Habets, F. and Eijkhout, V. (2011) River Network Routing on the NHDPlus Dataset. Journal of Hydrometeorology, 12, 913-934.

[2]   Niu, G.-Y., et al. (2011) The Community Noah Land Surface Model with Multiparameterization Options (Noah-MP): 1. Model Description and Evaluation with Local-Scale Measurements. Journal of Geophysical Research, 116, D12109.

[3]   David, C.H., Yang, Z.L. and Famiglietti, J.S. (2013) Quantification of the Upstream-to-Downstream Influence in the Muskingum Method and Implications for Speedup in Parallel Computations of River Flow. Water Resources Research, 49, 2783-2800.

[4]   Snow, A.D. (2015) A New Global Forecasting Model to Produce High-Resolution Stream Forecasts. Master’s Thesis, BYU.

[5]   Tavakoly, A.A., Snow, A.D., David, C.H., Follum, M.L., Maidment, D.R. and Yang, Z.-L. (2016) Continental-Scale River Flow Modeling of the Mississippi River Basin Using High-Resolution NHDPlus Dataset. Journal of the American Water Resources Association (JAWRA), 53, 258-279.

[6]   Ayalew, T.B., Krajewski, W.F., Mantilla, R. and Small, S.J. (2014) Exploring the Effects of Hillslope-Channel Link Dynamics and Excess Rainfall Properties on the Scaling Structure of Peak-Discharge. Advances in Water Resources, 64, 9-20.

[7]   Cunha, L.K., Mandapaka, P.V., Krajewski, W.F., Mantilla, R. and Bradley, A.A. (2012) Impact of Radar-Rainfall Error Structure on Estimated Flood Magnitude across Scales: An Investigation Based on a Parsimonious Distributed Hydrological Model. Water Resources Research, 48, W10515.

[8]   Mantilla, R. (2007) Physical Basis of Statistical Scaling in Peak Flows and Stream Flow Hydrographs for Topologic and Spatially Embedded Random Self-Similar Channel Networks. PhD Thesis, University of Colorado, Boulder, USA.

[9]   Paik, K. and Kumar, P. (2004) Hydraulic Geometry and the Nonlinearity of the Network Instantaneous Response. Water Resources Research, 40, W03602.

[10]   Ghimire, G.R., Krajewski, W.F. and Mantilla, R. (unpublished) A Power Law Model for River Water Velocity in U.S. Upper Midwestern Basins.

[11]   Snow, A.D., Scott D.C., Swain N.R., Nelson J., Ames D.P., Jones N.L., Ding D., Noman N., David C.H., Pappenberger F. (2016) A Cloud-Based High-Resolution National Hydrologic Forecast System Downscaled from a Global Ensemble Land Surface Model. Journal of the American Water Resources Association (JAWRA), 52, 950-964.

[12]   Torrence, C. and Compo, G.P. (1998) A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society, 79, 61-78.

[13]   Labat, D. (2005) Recent Advances in Wavelet Analyses: Part 1. A Review of Concepts. Journal of Hydrology, 314, 275-288.

[14]   Foufoula-Georgiou, E. and Kumar, P., Eds. (1995) Wavelets in Geophysics. Academic Press, New York, 337.

[15]   Gochis, D.J., Yu, W. and Yates, D.N. (2015) The WRF-Hydro Model Technical Description and User’s Guide, Version 3.0. NCAR Technical Document.

[16]   Lin, Y. and Mitchell, K.E. (2005) The NCEP Stage II/IV Hourly Precipitation Analyses: Development and Applications. Preprints, 19th Conference on Hydrology, San Diego, CA, American Meteorological Society, 1.2.

[17]   Reed, S.M. and Maidment, D.R. (1999) Coordinate Transformations for Using NEXRAD Data in GIS-Based Hydrologic Modeling. Journal of Hydrologic Engineering, 4, 174-182.

[18]   Xia, Y., et al. (2012) Continental-Scale Water and Energy Flux Analysis and Validation for the North American Land Data Assimilation System Project Phase 2 (NLDAS-2): 1. Intercomparison and Application of Model Products. Journal of Geophysical Research, 117, D03109.

[19]   Xia, Y., et al. (2012) Continental-Scale Water and Energy Flux Analysis and Validation for the North American Land Data Assimilation System Project Phase 2 (NLDAS-2): 2. Validation of Model-Simulated Streamflow. Journal of Geophysical Research, 117, D03110.

[20]   Liu, Y., Brown, J.D., Demargne, J. and Seo, D.-J. (2011) A Wavelet-Based Approach to Assessing Timing Errors in Hydrologic Predictions. Journal of Hydrology, 397, 210-224.