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Open AccessArticle

Non-Stationary Flood Frequency Analysis Using Cubic B-Spline-Based GAMLSS Model

1
College of Water Conservancy and Hydropower, Hebei University of Engineering, Handan 056021, China
2
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
3
School of Physics and Electronic Engineering, Xingtai University, Xingtai 054001, China
*
Author to whom correspondence should be addressed.
Water 2020, 12(7), 1867; https://doi.org/10.3390/w12071867 (registering DOI)
Received: 12 May 2020 / Revised: 14 June 2020 / Accepted: 22 June 2020 / Published: 29 June 2020
(This article belongs to the Section Hydrology and Hydrogeology)
Under changing environments, the most widely used non-stationary flood frequency analysis (NFFA) method is the generalized additive models for location, scale and shape (GAMLSS) model. However, the model structure of the GAMLSS model is relatively complex due to the large number of statistical parameters, and the relationship between statistical parameters and covariates is assumed to be unchanged in future, which may be unreasonable. In recent years, nonparametric methods have received increasing attention in the field of NFFA. Among them, the linear quantile regression (QR-L) model and the non-linear quantile regression model of cubic B-spline (QR-CB) have been introduced into NFFA studies because they do not need to determine statistical parameters and consider the relationship between statistical parameters and covariates. However, these two quantile regression models have difficulties in estimating non-stationary design flood, since the trend of the established model must be extrapolated infinitely to estimate design flood. Besides, the number of available observations becomes scarcer when estimating design values corresponding to higher return periods, leading to unreasonable and inaccurate design values. In this study, we attempt to propose a cubic B-spline-based GAMLSS model (GAMLSS-CB) for NFFA. In the GAMLSS-CB model, the relationship between statistical parameters and covariates is fitted by the cubic B-spline under the GAMLSS model framework. We also compare the performance of different non-stationary models, namely the QR-L, QR-CB, and GAMLSS-CB models. Finally, based on the optimal non-stationary model, the non-stationary design flood values are estimated using the average design life level method (ADLL). The annual maximum flood series of four stations in the Weihe River basin and the Pearl River basin are taken as examples. The results show that the GAMLSS-CB model displays the best model performance compared with the QR-L and QR-CB models. Moreover, it is feasible to estimate design flood values based on the GAMLSS-CB model using the ADLL method, while the estimation of design flood based on the quantile regression model requires further studies. View Full-Text
Keywords: non-stationarity; B-spline; GAMLSS-CB; quantile regression; flood frequency analysis; design flood non-stationarity; B-spline; GAMLSS-CB; quantile regression; flood frequency analysis; design flood
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MDPI and ACS Style

Qu, C.; Li, J.; Yan, L.; Yan, P.; Cheng, F.; Lu, D. Non-Stationary Flood Frequency Analysis Using Cubic B-Spline-Based GAMLSS Model. Water 2020, 12, 1867.

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