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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/hess-2019-115
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2019-115
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Technical note 28 Mar 2019

Technical note | 28 Mar 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Hydrology and Earth System Sciences (HESS).

Technical note: Comparison between two generalized Nash models with a non-zero initial condition

Baowei Yan, Aoyu Yuan, Zhengkun Li, and Chen Cao Baowei Yan et al.
  • School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan, China

Abstract. 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), 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 case of n = 1, it was shown theoretically that the difference between the two models is whether the current outflow is estimated (DLCM) or observed (GNM). The GNM is the unique solution of the Nash cascade model with a non-zero initial condition, 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. At last, 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 depending on the estimate accuracy of the current state.

Baowei Yan et al.
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Short summary
This paper attempts to find the relationship and further discusses the difference between two type generalized Nash models – the DLCM and the GNM. It is found that the main difference lies in the way to estimate the initial storage state. The GNM is the unique analytical solution of the Nash cascade model with a non-zero initial condition, and the DLCM is an approximate solution.
This paper attempts to find the relationship and further discusses the difference between two...
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