Mesh type runoff model by
GIS Ryuzo Yokoyama, Luo Xiao Bo
Department of Computer Science I wate University Morioka, I wate , Japan 020 Abstract A mesh type run-off model (MR model) is proposed. A basin is divided into square meshes with an uniform size. The runoff characteristics of each mesh are described as tank models. Each mesh is related to its adjacent meshes under the flow-down connection and the total meshes form a tree graph under the connection, of which root is the mesh at dam site of the run-off volume. The MR model can directly describe the spatial and temporal variations of precipitation and runoff parameters, which observed /estimated by remotely sensed data and derived from a GIS of the basin .The model is applied to Yuta dam basin located in northern Japan and demonstrated promising results. Introduction A mathematical model to describe the relationship between a precipitation and a runoff volume in a basin, a runoff model, is one of the most important topics in the hydrology. Various types of runoff models, e.g. tank model, kinematic wave method, unit diagram method, etc, have been popularly used. The run-off is a complicated process depending upon spatial and temporal factors of precipitation and run-off conditions. The mathematical models of those, those, however, have been described by a lumped parameters systems with limited number of state described by a lumped parameters systems with limited number of state variable due to the restricted observation techniques. In recent years, however, we have gotten new technologies to describe a run-off model more precisely as follows.
Structure of MR model The conditions related to the run-off dynamics of a basin such as topography, land cover/use, distribution of rain, etc, are not homogeneous but vary spatially and temporarily. MR model is directed to describe those in homogeneities of run-off characteristics. A basin is divided into square meshes with a suitable size. A run-off dynamics of each mesh is to be described by the tank models with one hole or two holes. Each mesh is related to its adjacent mesh existing at the flow direction of the run-off water . Depending upon the topographical condition of meshes, two kinds of tank models are assumed as follows
Yuta dam, which is one of the flood control dams in the Kitakami river network in northern Honshu, Japan as shown in Figure 4. It has the area of 583Km2, and its maximum and minimum elevations are 1500m and 250m, respectively. In the basin, a rain telemetering system with seven ground stations is installed. The run-off volume has been measured at the dam site. The basin was divided into 1 km square meshes. Figure 5 shows the tree graph of the meshes. The geographic information's for the meshes are organized into a file with a two-dimensional multi-layer structure and used as the fundamental data of the MR model as shown in Figure 6. Simulation of the MR model Four cases of flood in the past observation data, which were all precipitations in summer as in Table 1, were considered as the examples of the model simulation. The rain rate for each mesh was assumed to the observed rain rate at its nearest ground station. For each run-off observation data, the optimal parameters of ;, B and h under the performance index of eq.(3) were calculated by the iteration method. Figure 7 shows the results of the simulation of the four cases. In each case, the run-off from the MR model efficiently follows to the observed one. This means that the MR model might be excellent when appropriate parameters were applied. The ptimal parameters, however , vary for each rain . In practical applications of the model, unified values of optimal parameters are necessary. In this paper, the MR model could only consider the spatial characteristics of the precipitation, but it could not consider those of the run-off characteristics since the unified values of parameters were specified to all slope meshes . In the next step, the algorithms to determine optimal run-off parameters depending upon the run-off conditions are necessary to be developed. Conclusions The MR model can directly describes the spatial and temporal variation of runoff in a basin well. By applying the model to Yuta dam basin, the results of the simulation of the past rains relevantly realized the observed run-offs and the model could fundamentally demonstrate promising results. The optimal parameters for thefor case studies were unified but changed in a rather wide ranges. In this sense, further investigations are expected to improve the model to have unified parameters for rains. Table 1: Optimal parameters for the slope meshes of Yuta Dam MR mode 1.
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