Probability Weighted Moments–Based Parameter Estimation for Kinematic Diffusion and Muskingum-Based Distributions
Publication: Journal of Hydrologic Engineering
Volume 24, Issue 12
Abstract
Hydrologic series in arid and semiarid areas often contain zero values. For such data, the unit impulse response function (irf) of a kinematic diffusion model and a Muskingum flood routing model have been employed as probability distribution functions for frequency analysis. However, the probability weighted moments (PWMs) of these distributions have not been derived for parameter estimation. In this study, the parameter estimation formulas of a two-parameter kinematic diffusion distribution (KD2), a two-parameter Muskingum-based distribution (M-like), and three Muskingum-based three-parameter distributions based on PWMs are derived using mathematical transformation and numerical calculation principles. The fitting effects of PWMs of these distributions are evaluated and compared with the method of moments (MOM) and maximum likelihood method (MLM) using ordinary least square (OLS) criterion, residual square sum criterion (RSS), and Akaike information criterion (AIC). Precipitation data collected from six gauging stations were used as a case study. Results show that for each distribution, PWM yields the smallest OLS, RSS, and AIC values among the three methods and improves the accuracy of estimation.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
The present study is financially supported by the National Natural Science Foundation of China (Grant Nos. 51479171, 41501022, and 51409222). The authors appreciate the editor and anonymous reviewers for their constructive comments, which greatly improved the quality of this manuscript.
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Published In
Journal of Hydrologic Engineering
Volume 24 • Issue 12 • December 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Mar 23, 2019
Accepted: Aug 5, 2019
Published online: Sep 28, 2019
Published in print: Dec 1, 2019
Discussion open until: Feb 28, 2020
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