3:30 PM - 3:45 PM
[AHW21-01] Development of a vertical quasi-two-dimensional surface-subsurface flow model and its application to basin-scale rainfall-runoff simulation
★Invited Papers
Keywords:rainfall-runoff model, quasi-2D model, Richards' equation, hydraulic gradient
In recent years, runoff prediction has become increasingly important as the increased severity and frequency of heavy rainfall disasters. However, practical rainfall-runoff models often contain assumptions or simplifications and require model parameter optimization due to declining accuracy depending on the applied catchment and flood scale. Conversely, sophisticated physical models based on Richards’ equation have the advantage that parameters can be determined directly from observable soil properties but are difficult to use for basin-scale runoff prediction due to their high computational cost.
In this study, we developed a vertical quasi-two-dimensional surface-subsurface flow model (quasi-2D model), aiming to achieve both physically-based modeling of rainfall-runoff processes and a computational cost applicable to basin-scale runoff prediction. In the quasi-2D model, grid cells are set up on the slope, as shown in Figure 1, and computations are performed one column at a time, starting from the upstream. The subsurface flow is described by the vertical two-dimensional Richards’ equation, in which the hydraulic gradient in the downward direction is approximated by the slope gradient, thus simplifying the modeling of rainfall-runoff processes. Surface flow is represented by the kinematic wave equation and is computed separately from subsurface flow. This allows the time steps to be set according to the velocity of each flow. For subsurface flow, which is slow and requires iterative computation, the amount of computation can be reduced by using a large time step.
The quasi-2D model was validated on a single slope by comparing it with a model that solves the vertical two-dimensional Richards’ equation without simplification (2D model). The quasi-2D model accurately reproduced runoff height and soil moisture profile computed by the 2D model. However, the quasi-2D model did not consider the downstream soil moisture conditions at each location on the slope, which could easily affect the accuracy, especially on a gentle slope. The computation time of the quasi-2D model was reduced to about 1/10 of that of the 2D model. These results demonstrate that the quasi-2D model can significantly reduce the computational costs while maintaining the accuracy of saturated-unsaturated flow computations.
When deploying the quasi-2D model to a river basin, we considered the stability and amount of computation. At the slope junction, the upper limit of the inflow into the soil layer is determined based on the conditions at the most upstream part of the slope. If the runoff from the upstream area exceeds this limit, the same amount of water as the excess inflow is added to the rainfall intensity to supply the entire slope. This process ensures stable computation against the rapid changes in runoff from the upstream area. The analysis of the size of the computational cells on a single slope indicated that the accuracy does not grow worse easily on steep slopes if the cell size is enlarged in the slope direction. Therefore, computational cells were increased to the maximum size that maintained accuracy based on slope gradient, thereby reducing the computational costs.
The quasi-2D model was applied to the upstream area from the confluence of the Kamo and Takano Rivers in Kyoto, Japan. The catchment area totals 138.1 km2. Model parameters were determined by actual observed soil properties, albeit in other catchments. Figure 2 compares the quasi-2D model simulation and observation for the July 2020 flood. The model was generally able to reproduce the observed hydrograph, including the time of rise and peak of the hydrograph, although it tended to overestimate peak discharge. The flood event for 11 days shown in Figure 2 was simulated in about one day. In the target basin, simulations for the Kamo and Takano rivers can be carried out in parallel, taking about 1/10 of the actual time.
In this study, we developed a vertical quasi-two-dimensional surface-subsurface flow model (quasi-2D model), aiming to achieve both physically-based modeling of rainfall-runoff processes and a computational cost applicable to basin-scale runoff prediction. In the quasi-2D model, grid cells are set up on the slope, as shown in Figure 1, and computations are performed one column at a time, starting from the upstream. The subsurface flow is described by the vertical two-dimensional Richards’ equation, in which the hydraulic gradient in the downward direction is approximated by the slope gradient, thus simplifying the modeling of rainfall-runoff processes. Surface flow is represented by the kinematic wave equation and is computed separately from subsurface flow. This allows the time steps to be set according to the velocity of each flow. For subsurface flow, which is slow and requires iterative computation, the amount of computation can be reduced by using a large time step.
The quasi-2D model was validated on a single slope by comparing it with a model that solves the vertical two-dimensional Richards’ equation without simplification (2D model). The quasi-2D model accurately reproduced runoff height and soil moisture profile computed by the 2D model. However, the quasi-2D model did not consider the downstream soil moisture conditions at each location on the slope, which could easily affect the accuracy, especially on a gentle slope. The computation time of the quasi-2D model was reduced to about 1/10 of that of the 2D model. These results demonstrate that the quasi-2D model can significantly reduce the computational costs while maintaining the accuracy of saturated-unsaturated flow computations.
When deploying the quasi-2D model to a river basin, we considered the stability and amount of computation. At the slope junction, the upper limit of the inflow into the soil layer is determined based on the conditions at the most upstream part of the slope. If the runoff from the upstream area exceeds this limit, the same amount of water as the excess inflow is added to the rainfall intensity to supply the entire slope. This process ensures stable computation against the rapid changes in runoff from the upstream area. The analysis of the size of the computational cells on a single slope indicated that the accuracy does not grow worse easily on steep slopes if the cell size is enlarged in the slope direction. Therefore, computational cells were increased to the maximum size that maintained accuracy based on slope gradient, thereby reducing the computational costs.
The quasi-2D model was applied to the upstream area from the confluence of the Kamo and Takano Rivers in Kyoto, Japan. The catchment area totals 138.1 km2. Model parameters were determined by actual observed soil properties, albeit in other catchments. Figure 2 compares the quasi-2D model simulation and observation for the July 2020 flood. The model was generally able to reproduce the observed hydrograph, including the time of rise and peak of the hydrograph, although it tended to overestimate peak discharge. The flood event for 11 days shown in Figure 2 was simulated in about one day. In the target basin, simulations for the Kamo and Takano rivers can be carried out in parallel, taking about 1/10 of the actual time.