# Groundwater Level Trend Analysis and Prediction in the Upper Crocodile Sub-Basin, South Africa

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}ranged from 0.795 to 0.902 for the overall period. Therefore, based on projected rainfall and antecedent groundwater levels, future GWLs can be predicted using the GB model derived in this study.

## 1. Introduction

^{3}per annum of groundwater storage was available for use by small towns, mines, villages and individuals. Moreover, this groundwater potential could be increased by recharging aquifers during wet periods and preserving groundwater supplies for use during dry/drought periods [18]. Pietersen et al. [18] further showed that over 80% of rural communities in the North West and the Kwa-Zulu Natal provinces of South Africa receive their water from groundwater sources, and the same applies to over 50% of communities in the Eastern Cape Province. In terms of urban areas, the City of Tshwane combines water from boreholes with surface water in its bulk distribution system. Some towns such as De Aar rely solely on groundwater sources for their water supply.

## 2. Materials and Methods

#### 2.1. Study Area Description

^{2}(quaternary drainage A21A to A21H). The main rivers in the Upper Crocodile are the Crocodile, Magalies, Jukskei and Hennops. The main dams are the Hartbeespoort dam in quaternary A21H and the Rietvleidam in A21A. Figure 1 below displays the study area.

^{2}.

#### 2.2. Data Sources and Acquisition

#### 2.3. Methods

#### 2.3.1. Correlation Analysis

- (a)
- Cross correlation analysis

- (b)
- Autocorrelation Analysis

- (c)
- Multiple correlation analysis

#### 2.3.2. Trend Analysis

_{i}and x

_{j}in the equations represent the values of a sequence where j is greater than i and n represents the length of the time series. The Mann–Kendall statistic (S) is given as [65]:

_{MK}measures the significance of the test. In this study, the null hypothesis (H

_{0}) assumed that there is no trend, while the alternative hypothesis (H

_{1}) assumed that there is a trend. The null H

_{0}was rejected if $\left|{Z}_{MK}\right|>{Z}_{1-\alpha}$ at a significance interval of α = 0.05. The Mann–Kendall analysis was conducted using Python.

#### 2.3.3. Gradient Boosting Regression

#### 2.3.4. Support Vector Regression

#### 2.3.5. Performance Evaluation of Predictive Models

^{2}), the Mean Squared Error (MSE) and the Mean Absolute Error (MAE). The expressions for R

^{2}and MSE are given in (9) to (11), respectively.

_{i}= observed data, S

_{i}= predicted data, $\overline{O}$ = mean of observed data, $\overline{S}$ = mean of predicted data and n = number of observations.

^{2}describes the proportion of the variance in observed data explained by the model; its values range between 0 and 1, with values close to 1 indicating a variance with less error and values close to 0 indicating a high error variance. MSE measures the average of the squares of the errors. The MSE is always positive, and it is 0 for predictions that are completely accurate. It captures the bias (i.e., the difference of estimated values from the actual values) and variance (i.e., how far are the estimates spread out). An MAE value of 0 represents a completely accurate prediction model. Figure 3 depicts the workflow of arriving at the predictive model.

## 3. Results and Discussions

#### 3.1. Correlation Analysis

_{max}), which represent the correlation between rainfall (R) and groundwater levels (GWL), were the lowest at a range of 0.145 to 0.288. The low CC

_{max}can be associated with the underlying hydrogeological parameters, as rainfall is not the only variable that affects groundwater table fluctuations, although it is the main source of recharge. Also, the weak CC

_{max}can be attributed to the spatial-temporal resolution at which the GWLs are measured, which is at a monthly time step in most of the stations. The autocorrelation coefficients (ACF) representing the response of predicted GWL to antecedent GWL were reasonably high, ranging between 0.851 and 0.940.

#### 3.2. Trend Analysis

#### 3.3. Performance Evaluation of the Predictive Model

#### 3.3.1. MSE and MAE

#### 3.3.2. Scatterplot Analysis

^{2}values, which are between 0.7 and 1, reveal a good correlation between the predicted and observed GWL. R

^{2}values for the GB model show a good performance of the model, ranging from 0.795 to 0.9, while the SVR model shows very poor R

^{2}values at a range of 0.0018 to 0.1253. Again, findings obtained from the MAE and the MSE are supported by the scatterplots and the related R

^{2}values. Again, the results agree with similar studies. For instance, Kanyama et al. [42] compared SVR, GB, ANN, Random Forest (RF) and Decision Trees (DT) in predicting GWLs. GB was the best model among the models, with R

^{2}values above 0.7 in all the stations that were studied.

## 4. Conclusions and Recommendations

_{max}were the lowest among the correlation coefficients. The low CC

_{max}were attributed to the lack of GWL measurements at a finer temporal resolution. The stations that were studied were generally shallow and thus shorter response times to rainfall were expected from these boreholes, but such data are not available. The multiple correlation coefficients showed that there is a relationship between the variables that were studied and informed the choice of the antecedent GWL and rainfall as input variables into the predictive model. The antecedent GWLs represented the hydrogeological aspect, while rainfall represented a climatic aspect. The correlation results also provided grounds to justify the GWL trends obtained using rainfall. Through trend analysis, it was deduced that 50% of the stations that were studied are undergoing a negative trend, 25% a positive trend and 25% of the stations do not indicate a trend. Thus, the negative trend was mainly attributed to low rainfall between 2012 and 2015, and the high surface-water–groundwater exchange that occurs in the stations that lie along the rivers, particularly when rainfall amounts are low. The positive trends were associated with higher rainfalls that took place around 2017. The 25% of no trend may be attributed to the heterogeneity that exists in the hydrogeological context.

^{2}when compared to the SVR model. Therefore, based on projected rainfall and existing groundwater levels, future GWLs can be predicted using the GB model derived in this study area. What is unique about this study is that data-driven approaches were employed to depict the historical trends and in predictive modelling, while most of the studies in this study area focused on the physically based models. Furthermore, the processes of input variable selection through correlation analysis and GB were not computationally intensive.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Support vector regression [30].

Station Number | Latitude | Longitude | Start Date | Quaternary |
---|---|---|---|---|

A2N0794 | −26.048 | 27.709 | 1 September 2008 | A21D |

A2N0795 | −26.047 | 27.702 | 1 September 2008 | A21D |

A2N0799 | −26.093 | 27.719 | 1 September 2008 | A21D |

A2N0800 | −26.092 | 27.712 | 1 September 2008 | A21D |

A2N0801 | −26.081 | 27.705 | 1 September 2008 | A21D |

A2N0802 | −26.073 | 27.699 | 1 September 2008 | A21D |

A2N0805 | −26.045 | 27.715 | 1 September 2008 | A21D |

A2N0806 | −26.012 | 27.727 | 1 September 2008 | A21D |

Input Variable | R | GWL | R/GWL | ||
---|---|---|---|---|---|

Station | Lag (Month) | CC_{max} | Lag (Month) | ACF | Multiple Correlation Coefficient |

A2N0794 | 3 | 0.145 | 1 | 0.94 | 0.955 |

A2N0799 | 2 | 0.288 | 1 | 0.892 | 0.91 |

A2N0800 | 2 | 0.2 | 1 | 0.865 | 0.875 |

A2N0801 | 1 | 0.239 | 1 | 0.851 | 0.858 |

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**MDPI and ACS Style**

Tladi, T.M.; Ndambuki, J.M.; Olwal, T.O.; Rwanga, S.S.
Groundwater Level Trend Analysis and Prediction in the Upper Crocodile Sub-Basin, South Africa. *Water* **2023**, *15*, 3025.
https://doi.org/10.3390/w15173025

**AMA Style**

Tladi TM, Ndambuki JM, Olwal TO, Rwanga SS.
Groundwater Level Trend Analysis and Prediction in the Upper Crocodile Sub-Basin, South Africa. *Water*. 2023; 15(17):3025.
https://doi.org/10.3390/w15173025

**Chicago/Turabian Style**

Tladi, Tsholofelo Mmankwane, Julius Musyoka Ndambuki, Thomas Otieno Olwal, and Sophia Sudi Rwanga.
2023. "Groundwater Level Trend Analysis and Prediction in the Upper Crocodile Sub-Basin, South Africa" *Water* 15, no. 17: 3025.
https://doi.org/10.3390/w15173025