# An Integrated Hydrological-Hydraulic Model for Simulating Surface Water Flows of a Shallow Lake Surrounded by Large Floodplains

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## Abstract

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## 1. Introduction

## 2. Hydrological-Hydraulic Integrated Model

#### 2.1. Model Structure

#### 2.2. GBHM

#### 2.3. MIKE11

#### 2.4. Local Inertial Model

## 3. Numerical Scheme for the 2-D LIE

#### 3.1. Discretization

#### 3.2. Stability Analysis Results

^{1/3}, which are realistic values encountered in applications. For different values of $\Delta x$ and $\Delta t$, we compare the theoretical stability analysis results obtained through the procedure presented in Appendix A and the numerical computation results with the uniform flow perturbed with 0.01 % water depth fluctuations. In the numerical computation, the scheme is judged to be unstable if the computed water flow diverges or oscillates permanently since the true solutions are monotone and non-oscillatory. The representative results were summarized in Table 1, where the results for the explicit counterpart in which the friction slope terms are discretized in a fully-explicit manner are included in the table as well to highlight the wider stability region of the semi-implicit scheme. The results presented in the table indicate that the semi-implicit treatment clearly shows higher numerical stability than the explicit one and more importantly, lower stability than the CFL condition. Although it is empirically found that the CFL condition is insufficient to guarantee numerical stability of simulation, the above analysis clarified its mathematical evidence. According to this finding, we set a safety factor to regulate the time increment to be smaller than one determined by the CFL condition. Tanaka and Yoshioka [58] addressed theoretical stability analysis of the discretized 1-D LIEs with explicit, semi-implicit and implicit treatments for the friction term. Their results support that the CFL condition gives an optimistic stability conditions for flows with friction.

## 4. Application

#### 4.1. Study Site

#### 4.2. Remote Sensing

#### 4.3. Model Setup in the Tonle Sap Lake

#### 4.3.1. Hydrological Model GBHM

#### 4.3.2. 1-D River and Lake Routing Model MIK11

#### 4.3.3. 2-D Local Inertial Equation

#### 4.4. Results and Discussion

#### 4.5. Sensitivity Analysis

^{−1/3}s, 0.06 m

^{−1/3}s, or 0.10 m

^{−1/3}s. Although it should be dependent on land use, this analysis here sets spatially uniform value to see the magnitude of the impact over the whole TSL simulation. The bias of the water stage at the Prek Kdam station was introduced by modulating the water stage by 5%, 10%, 20%, 30% and 40%.

^{−1/3}s or 0.1 m

^{−1/3}s, the water stage at the Kampong Luong station was 1.69 times and 2.57 times larger and the flood area was 1.35 and 1.77 larger in maximum than those in the reference simulation, respectively. On the other hand, Figure 13 indicates that the bias of the water stage at the Prek Kdam station has the direct impacts on both water stage and flood area of TSL. The water stage at the Kampong Luong station and the flood area were 1.47 times and 1.37 times larger than those in the reference simulation, respectively.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

^{−10/3}in the friction slope term.

## Appendix B

#### Appendix B.1. Hillslope Module

#### Appendix B.2. River Routing Module

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**Figure 1.**A conceptual image on the model integration among GBHM, MIKE11 and 2-D LIE. The green and red areas are the simulation domains of GBHM and 2D-LIE, respectively; the blue lines are MIKE11 river network. Boundary river discharge and water stage are given by GBHM and MIKE11 as the light-green and yellow boxes, respectively.

**Figure 2.**Simulation domain and cascade system among GBHM, MIKE 11 and 2D-LIE. Brown area: simulation domain for the GBHM, blue lines: 1-D flow network for MIKE11 and brown line: boundary of simulation domain for the 2-D LIE. Rainfall and temperature are observed at blue and green circles, respectively, which are given to the GBHM and 2-D LIE. MIKE11 receives upstream tributary discharge from GBHM and observed upstream/downstream boundary water stage at light-blue and black rectangular points, respectively. Observed water stages at red points are used for the validation of the 2-D LIE.

**Figure 3.**Observed (black-dot) and simulated (light blue-line) discharges at the gauging sites. (

**a**) Chinit River, (

**b**) Sen River.

**Figure 7.**Observed (red) and simulated (blue) water level at (

**a**) the Kampong Chhnang and (

**b**) Kampong Luong stations.

**Figure 8.**Ratio of the number of flooded cells in both the simulation and satellite image and ones in satellite image.

**Figure 9.**Ratio of the number of flooded cells in only the simulation and ones in both the simulation and satellite image.

**Figure 10.**Spatial distribution of the degree of agreement on 20 August 2000. The yellow cells show the flood area in both the satellite image and simulation; the green cells show one only in the simulation; and the blue cells show one only in the satellite image.

**Figure 11.**(

**a**) The Google image of TSL and its floodplain area, (

**b**) simulated water depth overlaid with the flooded area from the Landsat image on 16 August 2000 (same period as Figure 9). The yellow and orange pixels were judged as “mixture” and “flood” (see definition in Section 4.2) in the Landsat image.

**Figure 12.**Simulated (

**a**) water stage at the Kampong Luong station and (

**b**) flood area for Manning’s roughness coefficient of 0.03 (red), 0.06 (blue), 0.10 (green). Black dots in (

**a**) shows the observed water stage.

**Figure 13.**(

**a**) water stage at the Kampong Luong station and (

**b**) flood area simulated with downstream boundary water stage at the Prek Kdam station increased (solid line) and decreased (dashed line) by 5% (red), 10% (blue), 20% (green), 30% (yellow) and 40% (purple). Black lines show simulated results with original tributary discharges.

**Table 1.**Comparison of maximum allowable time step at 500 m resolution on a slope with gradient 0.001, 0.005 and 0.01 and water depth of 0.1 m, 1.0 m and 2.0 m by the CFL conditions, one simulated using the explicit and semi-implicit treatment based on von Neumann stability analysis (see Appendix A).

Simulation Condition | |||

Gradient [-] | 0.001 | 0.005 | 0.01 |

Water depth [m] | 0.1 | 1.0 | 2.0 |

Maximum Allowable Time Step [s] | |||

CFL condition | 505 | 150 | 113 |

Explicit treatment | 23.1 | 38.8 | 23.9 |

Semi-implicit treatment | 152 | 63.9 | 45.2 |

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## Share and Cite

**MDPI and ACS Style**

Tanaka, T.; Yoshioka, H.; Siev, S.; Fujii, H.; Fujihara, Y.; Hoshikawa, K.; Ly, S.; Yoshimura, C.
An Integrated Hydrological-Hydraulic Model for Simulating Surface Water Flows of a Shallow Lake Surrounded by Large Floodplains. *Water* **2018**, *10*, 1213.
https://doi.org/10.3390/w10091213

**AMA Style**

Tanaka T, Yoshioka H, Siev S, Fujii H, Fujihara Y, Hoshikawa K, Ly S, Yoshimura C.
An Integrated Hydrological-Hydraulic Model for Simulating Surface Water Flows of a Shallow Lake Surrounded by Large Floodplains. *Water*. 2018; 10(9):1213.
https://doi.org/10.3390/w10091213

**Chicago/Turabian Style**

Tanaka, Tomohiro, Hidekazu Yoshioka, Sokly Siev, Hideto Fujii, Yoichi Fujihara, Keisuke Hoshikawa, Sarann Ly, and Chihiro Yoshimura.
2018. "An Integrated Hydrological-Hydraulic Model for Simulating Surface Water Flows of a Shallow Lake Surrounded by Large Floodplains" *Water* 10, no. 9: 1213.
https://doi.org/10.3390/w10091213