# Improving the Accuracy of Hydrodynamic Simulations in Data Scarce Environments Using Bayesian Model Averaging: A Case Study of the Inner Niger Delta, Mali, West Africa

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## Abstract

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## 1. Introduction

^{2}during wet years [1]. Its main water sources are the Niger and Bani Rivers, which enter the study area at Ké-Macina and Sofara, respectively, flowing through the Delta over several hundred kilometers, before both exit at Diré (Figure 1). The maximum inundation area shrinks to around 10,000 km

^{2}in dry years [2] under the combined impacts of climate variability, irrigation withdrawals, and dam operation. The IND faces many environmental challenges due to upstream water interventions on the river system, as well as high precipitation variability.

## 2. Materials and Methods

#### 2.1. Available Data

#### 2.1.1. Discharge and Water Level

#### 2.1.2. Topographic Data Sources

#### 2.1.3. DEM Derivation Using the Waterline Method

- Seven inundation extent polygons derived from Landsat satellite images by Zwarts et al. [2] for dates 5 July 1985, 10 June 2001, 8 August 1984, 28 July 2001, 25 October 1984, 16 October 2001, and 28 November 1999 were selected to represent the range of possible water elevations in the Inner Delta.
- For each of the seven flood inundation maps, water levels at Ké-Macina, Mopti, Akka, and Diré were used to calculate the slope of the water surface along principal flow paths between Ké-Macina and Akka, between Mopti and Akka, and between Akka and Diré. In the absence of additional information, it was further assumed that the water level variation between any two stations is linear.
- A series of orthogonal lines were drawn at 30 m intervals along principal flow paths.
- It was assumed that water levels along these lines are constant. Therefore, an elevation value could be set at the intersection points between water extent polygon and the orthogonal lines.
- At the end of the process, an altitude was estimated for each point within the flood extent polygons.
- Areas outside the larger polygon were populated using SRTM elevation data.
- GIS was used to interpolate the elevation data inside the study area.

#### 2.1.4. Satellite Imagery

#### 2.2. River Network

#### 2.3. Channel Geometry

#### 2.4. Estimation of Inflow at Ungauged Inlets

#### 2.5. Floodplain Friction

#### 2.6. Hydrodynamic Model Setup

#### 2.6.1. Mesh Generation

#### 2.6.2. Model Boundary Conditions

#### 2.6.3. Initial Conditions

#### 2.6.4. Model Configurations

#### 2.7. Calibration

#### 2.8. Bayesian Model Averaging

## 3. Results and Discussion

#### 3.1. Calibration Results

#### 3.1.1. BMA Weights

#### 3.1.2. BMA Estimates of Water Levels and Discharge in the Calibration Period

#### 3.2. Hydrodynamic Models Validation

#### 3.3. BMA Validation

#### 3.4. Simulated Inundation Extent from Best Individual Models

#### 3.5. Potential Usages of the Developed Model

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Digital elevation model derived from the waterline method (

**left**), Shuttle Radar Topography Mission (SRTM) (

**middle**), and Multi-Error-Removed Improved-Terrain (MERIT DEM) (

**right**).

**Figure 4.**Satellite Images of inundation extents of the Delta on 28 July 2001 (

**left**) and 16 October 2001 (

**right**) (Source: Zwarts, et al., 2005).

**Figure 6.**(

**a**) Extent of the SWAT model with calibration stations (Source: Seidou, 2019) and (

**b**) locations of the liquid boundaries in the hydrodynamic model.

**Figure 9.**Comparison of the Nash-Sutcliffe (NS) coefficient of BMA and the three best individual models.

**Figure 11.**Comparison of discharge (

**top**) and water level (

**bottom**) from the best individual models and BMA prediction at the validation.

**Figure 12.**Inundation extent on 28 August 2008 (

**left**panel), 7 October 2008 (

**middle**), and 17 January 2009 (

**right**panel).

Image Source/Name | Satellite | Path/Row | Purpose | Date Captured | Resolution |
---|---|---|---|---|---|

Several images from Zwart et al. [2] | Landsat 5 TM | 197/49 and 197/50 | Model setup, Calibration | 1984 to 2001 | 30 m |

MOD09A1.A2008241 MOD09A1.A2008281 MOD09A1.A2009017 | MODIS | - | Model validation | 28 August 2008 7 October 2008 17 January 2009 | 500 m |

Monitoring Stations | Bankfull Discharge (m^{3}/s) | Bankfull Stage (mIGN) | Bankfull Depth (m) | Bed Elevation (mIGN) |
---|---|---|---|---|

KeMacina | 3518.00 | 274.31 | 5.81 | 268.50 |

Mopti | 2340.00 | 266.42 | 5.04 | 261.38 |

Akka | 1816.00 | 262.81 | 4.61 | 258.20 |

Dire | 1760.00 | 261.45 | 4.56 | 256.89 |

Monitoring Station | Latitude | Longitude | NS at Calibration | NS at Validation |
---|---|---|---|---|

Kankan | 10.38 | −9.31 | 0.65 | 0.8 |

Baro | 10.51 | −9.72 | 0.68 | 0.73 |

Kouroussa | 10.64 | −9.88 | 0.68 | 0.78 |

Banankoro | 11.68 | −8.67 | 0.86 | 0.9 |

Sélingué | 11.64 | −8.24 | 0.45 | 0.64 |

Koulikoro | 12.85 | −7.56 | 0.87 | 0.93 |

Kirango | 13.69 | −6.08 | 0.86 | 0.82 |

Ké-Macina | 13.95 | −5.36 | 0.9 | 0.91 |

Bougouni | 11.39 | −7.45 | 0.77 | 0.78 |

Pankourou | 11.44 | −6.58 | 0.74 | 0.6 |

Douna | 13.21 | −5.9 | 0.79 | 0.9 |

Mopti | 14.49 | −4.21 | 0.8 | 0.78 |

Akka | 15.4 | −4.24 | 0.87 | 0.84 |

Diré | 16.27 | −3.39 | 0.9 | 0.75 |

Inlet Point Location | SWAT Model Subbasin(s) | Remarks |
---|---|---|

Inlet boundary 1 (Inlet B. 1) | Watershed 9 | 60% of the outflow of watershed 9 |

Inlet boundary 2 (Inlet B. 2) | Watershed 9 | 40% of the outflow of watershed 9 |

Inlet boundary 4 (Inlet B. 4) | Watershed 1 | 0.2126 * (Inflow of watershed 1-Outflow of watershed 1) |

Inlet boundary 5 (Inlet B. 5) | Watershed 2 | Outflow of watershed 2 |

Inlet boundary 6 (Inlet B. 6) | Watershed 1 | 0.125 * (Inflow of watershed 1-Outflow of watershed 1) |

Inlet boundary 7 (Inlet B. 7) | Watershed 3 | Outflow of watershed 3 |

Inlet boundary 8 (Inlet B. 8) | Watershed 6 and watershed 7 | Outflow of watershed 6 + Outflow of watershed 7 |

Model Number | Elevation Data | Downstream Boundary Condition |
---|---|---|

Model 1 | Merit DEM | Rating curve in the form of water level as a function of discharge, R = 0.02 |

Model 2 | Merit DEM | Rating curve in the form of discharge as a function of water level |

Model 3 | SRTM DEM | Rating curve in the form of water level as a function of discharge, R = 0.02 |

Model 4 | SRTM DEM | Rating curve in the form of discharge as a function of water level |

Model 5 | Waterline DEM | Rating curve in the form of water level as a function of discharge, R = 0.02 |

Model 6 | Waterline DEM | Rating curve in the form of discharge as a function of water level |

**Table 6.**Correlation (r) and Nash-Sutcliffe (NS) coefficients for simulated discharge and water level at the calibration.

Models | Discharge | Water Level | ||||||
---|---|---|---|---|---|---|---|---|

Mopti | Akka | Mopti | Akka | |||||

NS | r | NS | R | NS | r | NS | r | |

Model 1 | 0.975 | 0.996 | 0.879 | 0.944 | 0.984 | 0.992 | 0.946 | 0.988 |

Model 2 | 0.975 | 0.995 | 0.863 | 0.983 | 0.984 | 0.999 | 0.941 | 0.992 |

Model 3 | 0.954 | 0.995 | 0.908 | 0.983 | 0.951 | 0.999 | 0.907 | 0.992 |

Model 4 | 0.954 | 0.995 | 0.871 | 0.974 | 0.954 | 0.999 | 0.915 | 0.986 |

Model 5 | 0.956 | 0.994 | 0.958 | 0.986 | 0.981 | 0.997 | 0.871 | 0.998 |

Model 6 | 0.956 | 0.994 | 0.945 | 0.983 | 0.981 | 0.997 | 0.838 | 0.994 |

Hydrometric Station | MOPTI | AKKA | ||||||
---|---|---|---|---|---|---|---|---|

Variable | Discharge | Discharge | ||||||

d/s Boundary Condition | Type 1 ^{a} | Type 1 | Type 2 ^{b} | Type 2 | Type 1 | Type 1 | Type 2 | Type 2 |

Performance Criteria | NS | r | NS | r | NS | r | NS | r |

Best models/associated DEM | MERIT ^{d} (M1 ^{c}) | MERIT (M1) | MERIT (M2) | MERIT (M2) and SRTM(M4) | Waterline (M5) | Waterline (M5) | Waterline (M6) | Waterline (M6) and MERIT(M2) |

Second model/corresponding DEM | Waterline (M5) | SRTM (M3) | Waterline (M6) | - | SRTM (M5) | SRTM (M3) | SRTM (M4) | - |

Third model/Corresponding DEM | SRTM (M3) | Waterline (M5) | SRTM (4) | Waterline (M6) | MERIT (M1) | MERIT (M1) | MERIT (M2) | SRTM (M4) |

^{a}Type 1: d/s Boundary condition—water level as a function of discharge;

^{b}Type 2: d/s Boundary condition—discharge as a function of water level;

^{c}M1, M2…: Model 1 and Model 2 and so on;

^{d}MERIT DEM.

Hydrometric Station | MOPTI | AKKA | ||||||
---|---|---|---|---|---|---|---|---|

Variable | Water Level | Water Level | ||||||

Boundary Condition | Type 1 ^{a} | Type 1 | Type 2 ^{b} | Type 2 | Type 1 | Type 1 | Type 2 | Type 2 |

Performance Criteria | NS | r | NS | r | NS | r | NS | r |

Best model/associated DEM | MERIT ^{d} (M1 ^{c}) | SRTM (M3) | MERIT (M2) | MERIT (M2) and SRTM (M4) | MERIT (M1) | Waterline (M5) | MERIT (M2) | Waterline (M6) |

Second model/corresponding DEM | Waterline (M5) | Waterline (M5) | Waterline (M6) | Waterline (M6) | SRTM (M3) | SRTM (M3) | SRTM (M4) | MERIT (M2) |

Third model/Corresponding DEM | SRTM (M3) | MERIT (M1) | SRTM (M4) | Waterline (M5) | MERIT (M1) | Waterline (M6) | SRTM (M4) |

^{a}Type 1: d/s Boundary condition—water level as a function of discharge;

^{b}Type 2: d/s Boundary condition—discharge as a function of water level;

^{c}M1, M2...: Model 1 and Model 2 and so on,

^{d}MERIT DEM.

Model | BMA Weight to Obtain Discharge | BMA Weight to Obtain Water Level | ||
---|---|---|---|---|

Mopti | Akka | Mopti | Akka | |

Model 1 | 0.0002 | 0.1177 | 0.3650 | 0.9602 |

Model 2 | 0.7931 | 0.0000 | 0.1820 | 0.0000 |

Model 3 | 0.1417 | 0.0000 | 0.0001 | 0.0000 |

Model 4 | 0.0000 | 0.0000 | 0.0000 | 0.0398 |

Model 5 | 0.0614 | 0.8823 | 0.3320 | 0.0000 |

Model 6 | 0.0017 | 0.0000 | 0.1200 | 0.0000 |

**Table 10.**Correlation (r) and NS coefficients for simulated discharge and water level in the validation period.

Models | Discharge | Water Level | ||||||
---|---|---|---|---|---|---|---|---|

Mopti | Akka | Mopti | Akka | |||||

NS | r | NS | R | NS | r | NS | r | |

Model 1 | 0.982 | 0.995 | 0.836 | 0.918 | 0.962 | 0.984 | 0.940 | 0.992 |

Model 2 | 0.982 | 0.995 | 0.803 | 0.979 | 0.964 | 0.997 | 0.975 | 0.994 |

Model 3 | 0.939 | 0.995 | 0.830 | 0.979 | 0.933 | 0.997 | 0.917 | 0.994 |

Model 4 | 0.939 | 0.995 | 0.800 | 0.975 | 0.939 | 0.997 | 0.953 | 0.996 |

Model 5 | 0.935 | 0.990 | 0.882 | 0.976 | 0.973 | 0.993 | 0.876 | 0.988 |

Model 6 | 0.935 | 0.990 | 0.857 | 0.975 | 0.974 | 0.993 | 0.881 | 0.995 |

BMA | 0.972 | 0.995 | 0.887 | 0.972 | 0.978 | 0.990 | 0.940 | 0.983 |

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**MDPI and ACS Style**

Haque, M.M.; Seidou, O.; Mohammadian, A.; Djibo, A.G.; Liersch, S.; Fournet, S.; Karam, S.; Perera, E.D.P.; Kleynhans, M.
Improving the Accuracy of Hydrodynamic Simulations in Data Scarce Environments Using Bayesian Model Averaging: A Case Study of the Inner Niger Delta, Mali, West Africa. *Water* **2019**, *11*, 1766.
https://doi.org/10.3390/w11091766

**AMA Style**

Haque MM, Seidou O, Mohammadian A, Djibo AG, Liersch S, Fournet S, Karam S, Perera EDP, Kleynhans M.
Improving the Accuracy of Hydrodynamic Simulations in Data Scarce Environments Using Bayesian Model Averaging: A Case Study of the Inner Niger Delta, Mali, West Africa. *Water*. 2019; 11(9):1766.
https://doi.org/10.3390/w11091766

**Chicago/Turabian Style**

Haque, Md Mominul, Ousmane Seidou, Abdolmajid Mohammadian, Abdouramane Gado Djibo, Stefan Liersch, Samuel Fournet, Sara Karam, Edangodage Duminda Pradeep Perera, and Martin Kleynhans.
2019. "Improving the Accuracy of Hydrodynamic Simulations in Data Scarce Environments Using Bayesian Model Averaging: A Case Study of the Inner Niger Delta, Mali, West Africa" *Water* 11, no. 9: 1766.
https://doi.org/10.3390/w11091766