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Flood simulation of a region in southern Thailand during January 2017 is presented in this work. The study area covers the Tapi river, the longest river in southern Thailand. The simulation is performed by applying the two-dimensional shallow water model in the presence of strong source terms to the local bottom topography. The model is solved numerically by our finite volume method with well-balanced property and linear reconstruction technique. This technique is accurate and efficient at solving for complex flows in the wet/dry interface problem. Measurements of flows are collected from two gauging stations in the area. The initial conditions are prepared to match the simulated flow to the measurements recorded at the gauging stations. The accuracy of the numerical simulations is demonstrated by comparing the simulated flood area to satellite images from the same period. The results are in good agreement, indicating the suitability of the shallow water model and the presented numerical method for simulating floodplain inundation.

To simulate flooding over an affected area of terrain, the two-dimensional shallow water model is one of the most efficient models. Since the nonlinear shallow water model is complicated, an efficient and accurate numerical method is required to find approximate solutions in terms of water depth and velocity. The finite volume method is an accurate numerical method that can be developed to solve the problem (for more details and reviews, see [

In this work, we will apply the finite volume method with the WAF approximation for simulating a flood. The accuracy of numerical scheme depends on the method for approximating the bottom slope as discussed in [

The paper is organized as follows. We describe the finite volume method with the weighted average flux and linear reconstruction for two-dimensional shallow water equations in Sections

Flood over a large area can be simulated by considering the two-dimensional shallow water equations. The governing equations are given by

The conservative form of equations (

Next, we will apply our developed scheme to numerically approximate the water level and velocity at each location and time of our studied area.

A discretized form of (

The discretization in time is performed by the second-order Runge-Kutta (RK2) method to ensure the second-order accuracy in time of our method.

We first consider the approximation of numerical flux in the

The weighted average flux in two dimensions is proposed by [

To avoid unexpected oscillations near a discontinuous water level profile, the WAF can be applied while enforcing the total variation diminishing (TVD); more details can be found in [

Second-order accuracy in space from constant data can be obtained by applying linear reconstruction [

By the same concept, the linear reconstruction in the

A well-balanced concept is included in our developing scheme for preserving the stationary solution at the steady state. The concept is obtained from considering just the one-dimensional flow at the steady state where the stationary solution must satisfy the following conditions:

Following Bermudez and Vazquez [

Similarly, for the two-dimensional flow problem, the conditions are

To obtain the well-balanced scheme, we follow the reconstruction approach proposed by Audusse et al. [

The advantage of these reconstructions is that it can preserve the non-negativity of the water depth [

In this work, we propose a technique to modify the conservative variables to be

The finite volume scheme is then expressed by

Similarly, the numerical flux in the

Moreover, to overcome the difficulties in calculating the source term for wet/dry problem, the friction term is approximated by the splitting implicit technique (see more details in [

In this work, the scheme without linear reconstruction is referred to as scheme I, and the scheme with linear reconstruction is referred to as scheme II. Scheme II is second-order accurate in space for a smooth flow over a smooth bottom (see numerical experiment in [

This experiment is performed to check the well-balanced property of the present scheme. The scheme is a well-balanced scheme if it satisfies the exact C-property; that is, the numerical solution should preserve the still water stationary solution at steady state. In this experiment, we consider a rectangular domain of 1500 m long with the discontinuous bottom defined by

The initial water depth is

Water depth (a) and velocity (b) of still water stationary state at final time 100 s.

To test the ability of the scheme to handle wet/dry still water stationary state, an additional experiment is performed on the same domain with initial conditions

Water depth (a) and velocity (b) of wet/dry still water stationary state at final time 100 s.

The numerical results from this experiment show that the present scheme satisfies the exact C-property for both wet and wet/dry problems over a discontinuous bottom; hence, the present scheme is a well-balanced scheme.

To test the convergence of flow whether it reaches the still water stationary state, we perform a numerical experiment by considering a rectangular domain of 1500 m long with the discontinuous bottom defined in (

Initial velocity is zero in the entire domain. Simulation is run on 1000 cells. The numerical results obtained by scheme II at time 0 s, 150 s, 400 s, and 1000 s are shown in Figure

Numerical results at time 0 s (a), 150 s (b), 400 s (c), and 1000 s (d).

Water depth (a) and velocity (b) at final time 4000 s.

This problem is considered on a 200 m × 200 m rectangular domain as shown in Figure

Top view of partial dam-break domain.

The simulation is performed using scheme II on

Water level (a) and its contour plot of

Water level (a) and its contour plot of

Velocity vector field of the partial dam-break problem at 7.2 s.

Velocity vector field of the partial dam-break problem at 10 s.

For the simulation of dry bed case, the initial water level is set to be 10 m on the upstream side and zero on the downstream side. The water level and its contour plot at the final time 7.2 s is shown in Figure

Water level (a) and its contour plot of

Velocity field of partial dam-break problem at 7.2 s, wet/dry case.

This numerical experiment is considered to show the applicability of the present scheme for solving strong interaction between high-gradient water depth and friction bottoms in wet and dry case. The problem is dam-break flow over three humps defined by

The computational domain is rectangular with 75 m × 30 m. The dam is located at 16 m from the upstream boundary with initial water depth

The water depth profile, the contour plot, and the velocity fields at

Water surface profile using

Contour plots of

Velocity field using

The comparison between scheme I and scheme II in terms of accuracy is shown in Figure

Contour plots of

Generally, the numerical schemes without conservative property may suffer from mass-lost problem during wet/dry simulations. Thus, we have checked this issue by performing the next simulation using

The water surface profile (a) and its contour plot (b) of a dam-break flow over three humps at

It should be noted that the rectangular grid cells are used in this simulation and the water depth profile is relatively fitted to the circular dry bottom domain at steady state. More accurate solution can be obtained by applying more mesh refinements at the discretization step.

In this section, we will apply the developed scheme to simulate the flooding in the Tapi basin (Figure ^{2} with 8 tributaries. Most of the area is high and used for agriculture, especially fruit trees and rubber plantations. Since the bottom topography is not smooth, the numerical results obtained from schemes I and II are slightly different as discussed in Section

Tapi basin in the south of Thailand [

In our simulation, we consider the smaller area shown in Figure ^{2}. This area includes a 96 km stretch of the Tapi river. There are two gauging stations, X37A in Phrasaeng district and X217 in Khian Sa district, separated by about 96 kilometers. The input topography obtained from the NASA Shuttle Radar Topographic Mission (SRTM) is in the digital elevation model (DEM) format (Figure

Data elevation model (DEM) for Tapi basin in the south of Thailand.

The cause of flood event is prolonged due to heavy rainfall within the basin. The amount of water entering the basin can be assessed from the measured discharge.

The observed discharge rates at both gauging stations on January 9–13, 2017, are shown in Table

Real discharge data on January 9–13, 2017.

Gauging station | Discharge (m^{3}/s) |
Average | ||||
---|---|---|---|---|---|---|

9 (Monday) | 10 (Tuesday) | 11 (Wednesday) | 12 (Thursday) | 13 (Friday) | ||

X37A | 570.2 | 655.6 | 673.8 | 636 | 582.8 | 575.8 |

X217 | 523.2 | 675.2 | 788.8 | 860.8 | 876.8 | 655.89 |

Contour plot of simulated water depth on January 8, 2017, used for the initial condition.

From the initial conditions established for January 8, we run the first simulation to predict the flooded area on January 11. The discharge observed at station X37A is set as an input or upstream condition throughout the simulation. We assume a constant discharge value throughout each day and update the value daily for each of the 3 days simulated. The result is displayed on the Google Earth along the Tapi river. The satellite image of the area on the same day can be obtained from [

The simulation and real data of flooded area images on January 11, 2017. (a) The real data from satellite image on January 11, 2017. (b) The difference between the real data and the simulation result.

Next, we continue the simulation to predict the flooded area on January 13. Heavy rainfall over the Tapi river basin continued during this period. This can be observed from the discharge value which reaches the maximum value 876.8 at station X217 on January 13. Severity of flooding is expected to increase as a direct result. The real satellite image data and the difference between simulation and real data are shown in Figures

The result on January 13, 2017, for the case simulation for 5 consecutive days. (a) The real data from satellite image on January 13, 2017. (b) The difference between real data and the simulation result.

Flood simulation during January 2017 in Thailand is presented in this work. The study area is the Tapi river basin which covers many provinces in southern Thailand. We apply the well-balanced finite volume method to solve the two-dimensional shallow water model with strong source term from an irregular bottom profile in DEM format. The simulated period is from January 9 to 13. Discharge data are collected from two gauging stations. The initial conditions are difficult to obtain, and here, we use the data from January 8 and then run numerical simulations until the numerical results are close to the observed data. The simulation results show flooded area on January 11 and 13 that agree well with the satellite images displayed by the Google Earth program. The range of predicted water depth at some locations is in the same range as that indicated by news photos. All of these simulation results show the capability and the performance of our numerical scheme to solve complex shallow water flows in real situations that can be applied to study other areas further.

The image and time series data supporting this manuscript are from previously reported studies and datasets, which have been cited by references [

The authors declare that they have no conflicts of interest.

The authors would like to thank the Hydro and Agro Informatics Institute (HAII) for supporting data. They would also like to thank Mr. Brian Kubera at the Faculty of Science, Kasetsart University, for proof reading throughout the paper.