Parameter optimization of physically based distributed hydrological model

Abstract:

1 Introduction

The catchment structure is complex, so the hydrological process on it is complex also. In the past decades the lumped conceptual model is the dominating models in modeling catchment hydrological processes that can not consider the catchment structures explicitly. Physically based distributed hydrological models(PBDHMs) simulate the catchment hydrological process based on the catchment structure using physical equations, has the promising to better represent the hydrological processes. A few models have been proposed such as the SHE model, VIC model and others.

PBDHMs discretize the catchment terrain into a number of squared cells, and assign different model parameters to different cells, so the model parameters to be determined will be huge even to a small or medium-sized catchment. Principally the values of the model parameters should be derived from the catchment structures such as the topography, soil types and vegetations, but practically are difficult due to the current limitation to the understanding of the impacts of the catchment structures to the hydrological processes. For this reason, parameter optimization is still needed. As the parameters of the PBDHMs are huge, it is impossible to calibrate the model parameters like the lumped model, a method to optimize the model parameters considering the physical meaning in the PBDHMs is needed. This paper, based on the physical meanings, proposed a method for model parameter optimization for PBDHMs, and has been tested in several catchments ranging from 100km² to 1000km²in southern China.

2 Proposed Methodologies

2.1 Basic assumptions

The methodologies proposed in this paper are based on the following assumptions.

1) The model parameters of PBDHMs have physical meanings

The parameters in the PBDHMs are regarded as to have physical meanings, and the values of the model parameters are related to one or more catchment characteristics, including the topography, soil type and vegetation.

2) The uncertainty of model parameters of PBDHMs

The values of the model parameters of PBDHMs could be derived directly from the catchment characteristics, and there is a real value for all model parameters. But in practice, due to the current limitation to the understanding of the impacts of the catchment characteristics to the hydrological processes and the parameters deriving methods, bias between the derived value and real value of the model parameters exists, that means there is uncertainty in deriving model parameters of PBDHMs.

3) Parameter sensitivities

In PBDHMs, the impact of the model parameter bias to the model simulation result are different, for the parameters, a small bias will result in great changes of the model simulation results, these parameters are called sensitive parameters; while for some other parameters, even a reasonable big bias will not result in corresponding or obvious changes of the model simulation results, these parameters are called insensitivity parameters.

4) Parameter values are determinable

It is difficult to determine the real values of the model parameters of the PBDHMs, but a value approximating the real value at an unlimited extent could be determined, these parameters should enable the model to have reasonable performances for engineering application, such as for the flood forecasting, water cycle, etc. This value could be regarded as the real value of the model parameters, and could be determined by optimization method.

2.2 Parameter generalization

In PBDHMs, there are different parameter in different cells, so even for a small sized catchment, the total parameter numbers could be over millions, it is impossible to calibrate all the parameters as doing in lumped models, and to generalize and propose the independent and sensitive parameters for optimization based on the above assumptions is key for the parameter optimization.

In this study, the parameters of the PBDHMs are classified into 4 types, including climate related parameters, topography related parameters, soil related parameters and vegetation related parameters, every type parameters are only related to the catchment characteristics belong to it. For example, for the soil related parameters, the values of the parameters are only related to the soil type of the cell. With this treatment, for all the parameters with the same soil type will have the same parameter values even they are belong to different cells, and the parameters need to be optimized will be largely reduced, and the automated parameter optimization will be feasible from the point of practice.

2.3 Parameter optimization

Currently there is no parameter optimization method for PBDHMs, but several method have been used successfully in lumped model parameter calibration, such as Generic Algorithm, Adaptive Random Search, Simulated Annealing, Particle Swarm Optimization, Ant Colony System, Shuffle Complex Evolution Algorithm. The method proposed in this paper do not require any specific method, different model may employ different method. In this study, the Particle Swarm Optimization algorithm is tested for Liuxihe Model.

3 Liuxihe Model and parameters optimization method

3.1 Liuxihen Model

Liuxihe Model is a physically-based distributed hydrological model proposed mianly for catchment flood forecasting, which has several sub-models, including Basin Digitization Model (BDM), Data Preparation Model(DPM), Evaportranspiration Model (EM), Runoff Production Model (RPM), Runoff Routing Model (RRM) and Parameter Deriving Model(PDM). The BDM divides the studied basin into a number of cells horizontally, which are further divided into 3 layers vertically. All cells are classified as hillslope cells, river cells and reservoir cells according to their flow accumulation while having its own properties and model parameters. The DPM prepares data for every cell including DEM, soil type, land cover type, channel cross-section size, which is used to derive model parameters, and rainfall, which is either estimated from weather radar or interpolated from rain gauge measurements. EM calculates the evaportranspiration occurring in the cells, and RPM determines the runoff produced in every cell. The runoff modeled includes surface runoff, interflow and underground flow. The saturation excess mechanism is employed to determine the surface runoff while the interflow is calculated using Campbell equation. Cell by cell RRM routes the runoff produced to the basin outlet. The runoff routing is divided into hillslope routing and river routing. For the hillslope routing, the kinematics wave approximation algorithm is employed, while river routing adopts the diffusive wave approximation assuming the river shape is trapezoid.

3.2 Parameter classification

The parameters of Liuxihe Model are classified into 4 types, including climate related parameters, topography related parameters, soil related parameters and vegetation related parameters. Climate related parameters are Potential Evaportranspiration, topography related parameters are Flow direction and Hill Slope, soil related parameters are Water content at saturation, Water content at field condition, Water content at wilting condition, Soil thickness, Saturated conductivity and Soil porosity characteristics, the vegetation related parameters are Manning coefficient and Evaportranspiration coefficient.

4 Case Study

4.1 Study case and introduction and Liuxihe Model set up

The studied catchment is the first order branch of North River, the Lechangxia Catchment in Southern China with a drainage area of 3622km², as shown in Figure 2. There are 17 rain gauges installed and data of 14 flood events including the discharge in the catchment outlet and precipitation at 17 rain gauges have been collected for this study. The terrain data including the DEM, soil type and vegetation type also have been collected first, and the Liuxihe Model is then set up and the initial model parameters are derived based on the above terrain data.

4.2 Parameter Optimization

From the above collected 14 flood event data, one is selected for parameter optimization, and five different optimization objectives are tested. Figure 1 and Figure 2 show the evolution processes of the objective functions and parameters respectively, while Figure 3 shows the simulated results of two observed flood events. The results show that the model has a very reasonable simulation results. Also the simulated results are compared with that simulated with no parameter optimization, and the model performance has been improved much with the parameter optimization.

5 Conclusions

From this study, the following conclusions could be proposed.

1) For the physically based distributed hydrological models, the parameter optimization is necessary and feasible, the model performance could be improved largely by parameter optimization

2) The method proposed in this study for distributed hydrological models parameter optimization is successful, and could be used also for other distributed hydrological models

3) The parameters of physically based distributed hydrological models are physically based, that is theoretic basis for the parameter optimization of physically based distributed hydrological models.