Journal cover Journal topic
Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
https://doi.org/10.5194/gmd-2017-264
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
Development and technical paper
05 Dec 2017
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Geoscientific Model Development (GMD).
State-space representation of a bucket-type rainfall-runoff model: a case study with State-Space GR4 (version 1.0)
Léonard Santos, Guillaume Thirel, and Charles Perrin Irstea, UR HBAN, 1 rue Pierre-Gilles de Gennes, 92160 Antony, France
Abstract. In many conceptual rainfall-runoff models, the water balance differential equations are not explicitly formulated. These differential equations are solved sequentially by splitting the equations into terms that can be solved analytically with a technique called "operator splitting". As a result, only the resolutions of the split equations are used to present the different models. This article provides a methodology to make the governing water balance equations of a bucket-type rainfall-runoff model explicit. This is done by setting up a comprehensive state-space representation of the model. By representing it in this way, the operator splitting, which complexifies the structural analysis of the model, is removed. In this state-space representation, the lag functions (unit hydrographs), which are frequent in this type of model and make the resolution of the representation difficult, are replaced by a so-called "Nash cascade". This substitution also improves the lag parameter consistency across time steps. To illustrate this methodology, the GR4J model is taken as an example. The flow time series simulated by the new representation of the model are very similar to those simulated by the classic model. The state-space representation provides a more time-consistent model with time-independent parameters.

Citation: Santos, L., Thirel, G., and Perrin, C.: State-space representation of a bucket-type rainfall-runoff model: a case study with State-Space GR4 (version 1.0), Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2017-264, in review, 2017.
Léonard Santos et al.
Léonard Santos et al.
Léonard Santos et al.

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Short summary
Many rainfall-runoff models are based on stores. However, the differential equations that describe the stores evolution are rarely presented in literature. This represents an issue when the temporal resolution changes. In this work, we propose and evaluate a state-space version of a simple rainfall-runoff model within a robust resolution scheme. The results show that the proposed model performs equally well or slightly better than the original one and is independent of the temporal resolution.
Many rainfall-runoff models are based on stores. However, the differential equations that...
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