# 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

- David, D.; Hart, N.; Leroy, P. A Special Section on Dam Removal and River Restoration. BioScience
**2002**, 52, 653–655. [Google Scholar] [CrossRef] - Ajith, A.V. Bathymetric Survey to Study the Sediment Deposit in Reservoir of Peechi Dam. IOSR J. Mech. Civ. Eng.
**2016**, 12, 34–38. [Google Scholar] [CrossRef] - Amano, K. Water Quality Enhancement Techniques in Dam Reservoirs. J. Soc. Mech. Eng.
**2003**, 106, 454–455. [Google Scholar] [CrossRef] - Girish, G.; Ashitha, M.K.; Jayakumar, K.V. Sedimentation assessment in a multipurpose reservoir in Central Kerala, India. Environ. Earth Sci.
**2014**, 72, 4441–4449. [Google Scholar] [CrossRef] - Estigoni, M.; Matos, A.; Mauad, F. Assessment of the accuracy of different standard methods for determining reservoir capacity and sedimentation. J. Soils Sediments
**2014**, 14, 1224–1234. [Google Scholar] [CrossRef] - Hart, D.D.; Johnson, T.E.; Bushaw-Newton, K.L.; Horwitz, R.J.; Bednarek, A.T.; Charles, D.F.; Kreeger, D.A.; Velinsky, D.J. Dam Removal: Challenges and Opportunities for Ecological Research and River Restoration. BioScience
**2002**, 52, 669–682. [Google Scholar] [CrossRef] - Badejo, O.T.; Adewuyi, K.G. Bathymetric Survey and Topography Changes Investigation of Part of Badagry Creek and Yewa River, Lagos State, Southwest Nigeria. J. Geogr. Environ. Earth Sci. Int.
**2019**, 22, 1–16. [Google Scholar] [CrossRef] [Green Version] - Khattab, M.F.; Abo, R.K.; Al-Muqdadi, S.W.; Merkel, B.J. Generate Reservoir Depths Mapping by Using Digital Elevation Model: A Case Study of Mosul Dam Lake, Northern Iraq. Adv. Remote Sens.
**2017**, 6, 161–174. [Google Scholar] [CrossRef] [Green Version] - Morris, L.M.; Fan, J. Reservoir Sedimentation Handbook: Design and Management of Dams, Reservoirs, and Watersheds for Sustainable Use; McGraw-Hill: New York, NY, USA, 1998; p. 4.17. [Google Scholar]
- Lampe, D.C.; Morlock, S.E. Collection of bathymetric data along two reaches of the Lost River within Bluespring Cavern near Bedford, Lawrence County, Indiana. Sci. Investig. Rep.
**2007**, 142, 2008–5023. Available online: http://pubs.water.usgs.gov/sir (accessed on 15 August 2020). - Silveira, D.T.; Portugal, J.L.; de Oliveira Vital, S.R. Análise estatística espacial aplicada a construção de superfícies batimétricas. Geociências
**2014**, 33, 596–615. [Google Scholar] - Farrira, I.O.; Dalto, D.R.; Gérson, R.S.; Lidiane, M.F. In Bathymetric Surfaces: IDW Or Kriging. Bol. Ciênc. Geod.
**2017**, 23, 493–508. [Google Scholar] [CrossRef] [Green Version] - McIntire, J.P.; Webber, F.C.; Nguyen, D.K.; Li, Y.; Foong, S.H.; Schafer, K.; Chue, W.Y.; Ang, K.; Vinande, E.T. LeapFrogging: A technique for accurate long-distance ground navigation and positioning without GPS. J. Inst. Navig.
**2018**, 65, 35–47. [Google Scholar] [CrossRef] - Fudenberg, D.; Gilbert, R.; Stiglitz, J.; Tirole, J. Preemption, Leapfrogging, and Competition in Patent Races. Eur. Econ. Rev.
**1983**, 22, 3–31. [Google Scholar] [CrossRef] [Green Version] - Brezis, E.; Krugman, P.; Tsiddon, D. Leapfrogging: A Theory of Cycles in National Technological Leadership. Am. Econ. Rev.
**1993**, 1211–1219. [Google Scholar] [CrossRef] - Brezis, E.S.; Krugman, P. Technology and Life Cycle of Cities. J. Econ. Growth
**1997**, 2, 369–383. [Google Scholar] [CrossRef] - Munasinghe, M. Is environmental degradation an inevitable consequence of economic growth: Tunneling through the environmental Kuznets curve. Ecol. Econ.
**1999**, 29, 89–109. [Google Scholar] [CrossRef] - Barro, R.; Sala-i-Martin, X. Economic Growth; MIT Press: Cambridge, MA, USA, 2003; p. 375. ISBN 9780262025539. [Google Scholar]
- Arseni, M.; Voiculescu, M.; Georgescu, L.P.; Iticescu, C.; Rosu, A. Testing Different Interpolation Methods Based on Single Beam Echosounder River Surveying. Case Study: Siret River. Int. J. Geo-Inf.
**2019**, 8, 507. [Google Scholar] [CrossRef] [Green Version] - Parente, C.; Vallario, A. Interpolation of Single Beam Echo Sounder Data for 3D Bathymetric Model. Int. J. Adv. Comput. Sci. Appl.
**2019**, 10, 6–13. [Google Scholar] [CrossRef] - IHO Manual on Hydrography. International Hydrographic Organization Publication C-13; International Hydrographic Bureal: Monaco City, Monaco, 2011. [Google Scholar]
- Hare, R.; Eakins, B.; Amante, C. Modelling Bathymetric Uncertainty. Int. Hydrogr. Rev.
**2011**, 6, 31–42. Available online: https://coast.noaa.gov/data/digitalcoast/pdf/topo-bathy-data-considerations.pdf (accessed on 15 August 2020). - Williams, C.K.I. Prediction with Gaussian Processes: From Linear Regression to Linear Prediction and Beyond. Learn. Graph. Models
**1998**, 599–621. [Google Scholar] [CrossRef] - Marcelo, C.; Joaquim, L.; Igor, O.; Joao, L.; Jose, S. Assessment of Spatial Interpolation Methods to Map Bathymetry of an Amazonian Hydroelectric reservoir to Aid in decision marking for water Management. ISPRS Int. J. Geo-Inform.
**2015**, 4, 220–235. [Google Scholar] [CrossRef] - Ferreira, I.O.; Domingos, R.D.; Santos, G.R. Coleta, Processamento e Análise de Dados Batimétricos; Novas Edições Acadêmicas: do Paraná, Brazil, 2015. [Google Scholar]
- Li, J.; Heap, A.D. Spatial interpolation methods applied in the environmental sciences: A review. Environ. Model Softw.
**2014**, 53, 173–189. [Google Scholar] [CrossRef] - Wu, C.; Joann, M.; Liang, M.; Mohammad, A. Comparison of different spatial interpolation methods for historical hydrographic data of the lowermost Mississippi River. Ann. GIS
**2019**, 25, 133–151. [Google Scholar] [CrossRef] - Santos, G.R.; Oliveira, M.S.; Louzada, J.M.; Santos, A.M.R.T. Krigagem simples versus krigagem universal: Qual o preditor mais precison. Energy Agric.
**2011**, 26, 49–55. [Google Scholar] [CrossRef] [Green Version] - Webster, R.; Oliver, M. Geostatistics for Environmental Scientists; John Wiley & Sons, Ltd.: Chichester, UK, 2001; p. 271. [Google Scholar]
- Eriksson, M.; Siska, P.P. Understanding Anisotropy Computations. Math. Geol.
**2000**, 32, 683–700. [Google Scholar] [CrossRef] - Merwade, V.M.; Maidment, D.R.; Goff, J.A. Anisotropic considerations while interpolating river channel bathymetry. J. Hydrol.
**2006**, 331, 731–741. [Google Scholar] [CrossRef] - Canadian Hydrographic Service (CHS). CHS Standards for Hydrographic Surveys, 1st ed.; Fisheries and Oceans: Ottawa, ON, Canada, 2005. [Google Scholar]
- Hernandez-Stefanoni, J.L.; Ponce-Hernandez, R. Mapping the spatial variability of plant diversity in a tropical forest: Comparison of spatial interpolation methods. Environ. Monit. Assess.
**2006**, 117, 307–334. [Google Scholar] [CrossRef] - Isaaks, E.H.; Srivastava, R.M. Applied Geostatistics; Oxford University Press: New York, NY, USA, 1989; p. 561. [Google Scholar]
- Nalder, I.A.; Wein, R.W. Spatial interpolation of climatic Normals: Test of a new method in the Canadian boreal forest. Agric. For. Meteorol.
**1998**, 92, 211–225. [Google Scholar] [CrossRef] - Ahmed, S.; De Marsily, G. Comparison of geostatistical methods for estimating transmissivity using data on transmissivity and specific capacity. Water Resour. Res.
**1987**, 23, 1717–1737. [Google Scholar] [CrossRef] - Burrough, P.A.; McDonnell, R.A. Principles of Geographical Information Systems; Oxford University Press: Oxford, UK, 1998; p. 333. [Google Scholar]
- Hu, K.; Li, B.; Lu, Y.; Zhang, F. Comparison of various spatial interpolation methods for non-stationary regional soil mercury content. Environ. Sci.
**2004**, 25, 132–137. [Google Scholar] - Vicente-Serrano, S.M.; Saz-Sánchez, M.A.; Cuadrat, J.M. Comparative analysis of interpolation methods in the middle Ebro Valley (Spain): Application to annual precipitation and temperature. Clim. Res.
**2003**, 24, 161–180. [Google Scholar] [CrossRef] [Green Version]

**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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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