Comparison between two generalized Nash models with a same non-zero initial condition
Initial condition can impact the forecast precision especially in a real-time forecasting stage. The discrete linear cascade model (DLCM) and the generalized Nash model (GNM), though expressed in different ways, are both the generalization of the Nash cascade model considering the initial condition....
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IWA Publishing
2021-12-01
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| Series: | Hydrology Research |
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| Online Access: | http://hr.iwaponline.com/content/52/6/1216 |
| _version_ | 1818971038282678272 |
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| author | Baowei Yan Yu Liu Zhengkun Li Huining Jiang |
| author_facet | Baowei Yan Yu Liu Zhengkun Li Huining Jiang |
| author_sort | Baowei Yan |
| collection | DOAJ |
| description | Initial condition can impact the forecast precision especially in a real-time forecasting stage. The discrete linear cascade model (DLCM) and the generalized Nash model (GNM), though expressed in different ways, are both the generalization of the Nash cascade model considering the initial condition. This paper investigates the relationship and difference between DLCM and GNM both mathematically and experimentally. Mathematically, the main difference lies in the way to estimate the initial storage state. In the DLCM, the initial state is estimated and not unique, while that in the GNM is observed and unique. Hence, the GNM is the exact solution of the Nash cascade model, while the DLCM is an approximate solution and it can be transformed to the GNM when the initial storage state is calculated by the approach suggested in the GNM. As a discrete solution, the DLCM can be directly applied to the practical discrete streamflow data system. However, the numerical calculation approach such as the finite difference method is often used to make the GNM practically applicable. Finally, a test example obtained by the solution of the Saint-Venant equations is used to illustrate this difference. The results show that the GNM provides a unique solution while the DLCM has multiple solutions, whose forecast precision depends upon the estimate accuracy of the current state. HIGHLIGHTS
The main difference lies in the way to estimate the initial storage state.;
The GNM is the unique solution of the Nash cascade model.;
The DLCM is an approximate solution of the Nash cascade model.;
The DLCM can be transformed to the GNM.; |
| first_indexed | 2024-12-20T14:46:01Z |
| format | Article |
| id | doaj.art-b6fa630ceb804ab5a5a20217d69f4a69 |
| institution | Directory Open Access Journal |
| issn | 1998-9563 2224-7955 |
| language | English |
| last_indexed | 2024-12-20T14:46:01Z |
| publishDate | 2021-12-01 |
| publisher | IWA Publishing |
| record_format | Article |
| series | Hydrology Research |
| spelling | doaj.art-b6fa630ceb804ab5a5a20217d69f4a692022-12-21T19:37:07ZengIWA PublishingHydrology Research1998-95632224-79552021-12-015261216122210.2166/nh.2021.172172Comparison between two generalized Nash models with a same non-zero initial conditionBaowei Yan0Yu Liu1Zhengkun Li2Huining Jiang3 School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China Initial condition can impact the forecast precision especially in a real-time forecasting stage. The discrete linear cascade model (DLCM) and the generalized Nash model (GNM), though expressed in different ways, are both the generalization of the Nash cascade model considering the initial condition. This paper investigates the relationship and difference between DLCM and GNM both mathematically and experimentally. Mathematically, the main difference lies in the way to estimate the initial storage state. In the DLCM, the initial state is estimated and not unique, while that in the GNM is observed and unique. Hence, the GNM is the exact solution of the Nash cascade model, while the DLCM is an approximate solution and it can be transformed to the GNM when the initial storage state is calculated by the approach suggested in the GNM. As a discrete solution, the DLCM can be directly applied to the practical discrete streamflow data system. However, the numerical calculation approach such as the finite difference method is often used to make the GNM practically applicable. Finally, a test example obtained by the solution of the Saint-Venant equations is used to illustrate this difference. The results show that the GNM provides a unique solution while the DLCM has multiple solutions, whose forecast precision depends upon the estimate accuracy of the current state. HIGHLIGHTS The main difference lies in the way to estimate the initial storage state.; The GNM is the unique solution of the Nash cascade model.; The DLCM is an approximate solution of the Nash cascade model.; The DLCM can be transformed to the GNM.;http://hr.iwaponline.com/content/52/6/1216discrete linear cascade modelgeneralized nash modelinitial storage stateunique solution |
| spellingShingle | Baowei Yan Yu Liu Zhengkun Li Huining Jiang Comparison between two generalized Nash models with a same non-zero initial condition Hydrology Research discrete linear cascade model generalized nash model initial storage state unique solution |
| title | Comparison between two generalized Nash models with a same non-zero initial condition |
| title_full | Comparison between two generalized Nash models with a same non-zero initial condition |
| title_fullStr | Comparison between two generalized Nash models with a same non-zero initial condition |
| title_full_unstemmed | Comparison between two generalized Nash models with a same non-zero initial condition |
| title_short | Comparison between two generalized Nash models with a same non-zero initial condition |
| title_sort | comparison between two generalized nash models with a same non zero initial condition |
| topic | discrete linear cascade model generalized nash model initial storage state unique solution |
| url | http://hr.iwaponline.com/content/52/6/1216 |
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