# Bathymetric Survey for Enhancing the Volumetric Capacity of Tagwai Dam in Nigeria via Leapfrogging Approach

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Material and Method

#### 2.1. Study Area

#### 2.2. Source of Data

^{2}(302.035 hectares) with a perimeter of 8728.358 m. The maximum depth observed was 20.800 m. The reduced water level at the moment of sounding was 250.170 m, as referenced to a sounding datum established around the corridor of the reservoir. The maximum and minimum elevation was 250.260 m and 229.460 m, respectively. The datum used was the Minna-UTM zone 32 projection system. The Minna datum was established based on Clark 1880 ellipsoidal parameters.

#### 2.3. Setting Criteria and Scenario via Leapfrogging

#### 2.4. Interpolation and Kriging

#### 2.5. Ordinary Kriging Interpolation Experiment

#### 2.6. Evaluation of Interpolation Surface

#### 2.7. Volume Computation via Simpson 3/8 Integration Techniques

## 3. Results and Analysis

^{2}or coefficient of determination, but partial agreement in the coefficient of variance in all cases. The cross-validation result indicates a spatial trend of homogeneity in the estimation model in all classes. Furthermore, Table 3 shows the interactive cross-validation experiment in each case, five points were omitted from the original data and after interpolation, the points were tracked and their difference computed.

^{3}, which is 23.79% of the total volume, as shown in Table 2. Subsequently, in Table 2 are the enhanced volume of other stages. Scenarios B and C account for 1.16% and 1.25% increases in volume above the present stage (A). Either B or C can be achieved by dredging or erecting an embankment around the dam of 2 m at any instant. Similarly, D is the combination of Scenario B and C, while A remains constant. Stage D has the edge over B and C of 2.43%, which is a 9,502,144 m

^{3}increment above the present stage when implemented.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Describing leapfrogging criteria (Source: Research lab). A: Stage A was taken to be the present state of the dam (leapfrog at rest) with space covered. Knowing the spatial information (X, Y, and depth) of all the leapfrogs, the volume occupied was computed. B: At Stage B, it was assumed that the leapfrogs dug downward 2 m from their existing water-based level (dam bed). Thus, the depths were increased downward independently by 2 m and the capacity determined. C: Additionally, at Stage C, it was assumed that the leapfrogs leapt upward above the present water level by 2 m. Hence, the depth was increased above the current level by 2 m. The embankment, as shown in this figure, is a presentation of the increase. Consequently, the volume was calculated. D: Furthermore, at Stage D, the whole scenario (A, B, and C) was considered and the cumulative volume was computed.

**Figure 7.**Randomly selected points for cross-validation for the four scenarios considered. In each of the Scenerio A, B, C, and D 400 points were randomly selected for cross-validation. The points in red show the value; the gray line indicates the reference line; while the blue line represents the best fit line. The upper and lower diagonal represents the measured and estimated value respectively.

**Figure 9.**Digital Elevation Model of Scenarios (

**A**–

**D**) (Source: Research lab, generated from the interpolated data with a pixel size of 10 m by 10 m using Surfer 2021 software).

Model | Nugget | Sill | Range | R-Squared | RMSE | |
---|---|---|---|---|---|---|

Figure 5a | Exponential | 0.075 | 0.421 | 1702.12 | 91.01% | 0.165 |

Figure 5b | - | 0.062 | 0.253 | 1425.20 | 92.63% | 0.065 |

Figure 6 | - | 0.0451 | 0.157 | 775.21 | 99.58% | 0.006 |

Scenario | ME | MSE | RMSE | R^{2} | Coef. of Va. | Volume (m^{3}) | % Volume |
---|---|---|---|---|---|---|---|

A | 0.008 | 0.138 | 0.371 | 0.965 | 0.015 | 93,129,808 | 23.79 |

B | 0.008 | 0.148 | 0.385 | 0.962 | 0.017 | 97,668,974 | 24.95 |

C | 0.008 | 0.148 | 0.385 | 0.951 | 0.014 | 98,030,602 | 25.04 |

D | 0.008 | 0.168 | 0.410 | 0.959 | 0.018 | 102,631,952 | 26.22 |

Easting (m) | Northing (m) | Reduced Depth (m) | Residuals (m) |
---|---|---|---|

242,502.387 | 1,058,741.722 | 242.414 | 0.006 |

243,107.042 | 1,058,271.965 | 244.086 | −0.130 |

244,246.156 | 1,059,864.163 | 244.877 | −0.004 |

242,885.429 | 1,059,116.951 | 236.219 | 0.207 |

243,209.73 | 1,059,435.427 | 242.708 | −0.012 |

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**MDPI and ACS Style**

Ibrahim, P.O.; Sternberg, H. Bathymetric Survey for Enhancing the Volumetric Capacity of Tagwai Dam in Nigeria via Leapfrogging Approach. *Geomatics* **2021**, *1*, 246-257.
https://doi.org/10.3390/geomatics1020014

**AMA Style**

Ibrahim PO, Sternberg H. Bathymetric Survey for Enhancing the Volumetric Capacity of Tagwai Dam in Nigeria via Leapfrogging Approach. *Geomatics*. 2021; 1(2):246-257.
https://doi.org/10.3390/geomatics1020014

**Chicago/Turabian Style**

Ibrahim, Pius Onoja, and Harald Sternberg. 2021. "Bathymetric Survey for Enhancing the Volumetric Capacity of Tagwai Dam in Nigeria via Leapfrogging Approach" *Geomatics* 1, no. 2: 246-257.
https://doi.org/10.3390/geomatics1020014