Climate and Groundwater Depth Relationships in Selected Breede Gouritz Water Management Area Subregions Between 2009 and 2020

Abstract

Groundwater resources are changing under the current climate change trajectory. Mitigation and adaptation measures include understanding the inter-working relationships among all climate variables and water resources, specifically groundwater, since it has less direct impacts than surface waters due to its nature. The Breede Gouritz Water Management Area provides an interesting platform to assess these interdependencies, since they have not been assessed before. To assess any underlying dependencies, a multivariate analysis of independent variables including monthly average temperature, summative precipitation, and average evapotranspiration, and a dependent monthly variable, i.e., average groundwater depth, from 14 boreholes was conducted. Moreover, a groundwater depth near-future prediction for each relevant borehole was made. The Multiple Linear Regression model was chosen as the appropriate one since it is cost- and time-effective, entry-level, easy to interpret, and provides a simple and basic understanding of the relationship dependencies. The Kruskal-Wallis test was also performed to elaborate on findings from the Multiple Linear Regression models. Simple linear models incorporating independent and dependent variables can only account for up to 41.7% of the variation in groundwater depth. Groundwater depth is mainly influenced by temperature and evapotranspiration and is expected to be lower for ten dependent variables. The more arid regions in the study area can expect groundwater depth to lower soon and need to use alternative water resources. The temperate west of the study area could expect more favorable outcomes regarding groundwater depth in the near future. Incorporating more variables and using a multi-modal approach to combat non-linear relationships is recommended in future.

1. Introduction

The impact of the changing climate on the hydrologic system is far-reaching (depending on the location), but it will intensify; hot places will get hotter, cold places colder, wet places wetter, stormy places stormier and so forth [1,2,3,4,5,6]. The global average temperature is also increasing in some places more rapidly than others [1,7,8,9]. Surface waters are generally declining; based on satellite imagery, it has been estimated that large water bodies and lakes globally reduced in volume by 53% between 1992 and 2020 [10]. Groundwater depth is expected to generally decrease [11,12,13,14,15], but the rate and extent of decline needs to be assessed locally.

The groundwater system is not isolated; it forms part of the more extensive hydrologic system and is highly dependent on precipitation; without rain, aquifers cannot recharge [16,17,18,19]. However, evapotranspiration has also been linked to increasing or decreasing groundwater depth, determined by the location [20,21,22]. Temperature indirectly plays a role due to its strong correlation with evapotranspiration [1,7,23]. It is essential to define and quantify these inter-relationships to steward groundwater resources adequately.

Several authors have considered statistical methods to determine groundwater depth variance and predict groundwater depth for the near future [24,25,26]. Ardana et al. [24] determined whether multiple linear regression (MLR) or artificial neural networks (ANN) performed better for two monitoring wells in Denpasar, Bali, Indonesia. Hodgson [26] simulated groundwater depth responses using the MLR and validated the response to the Vryburg aquifer. He could simulate groundwater depth responses six years ahead using precipitation and discharge. Bloomfield et al. [25] developed an MLR model to determine groundwater depth response to different climate change (CC) scenarios using only precipitation and groundwater depth. Haaf et al. [27] correlated the physiographic properties of groundwater with climatic variables via simple empirical models despite a large and heterogeneous study area. They found that effective predictive models can be developed via statistical means at regional scales.

It has become increasingly common to use empirical statistical models like regression and ANN over process-based models due to the need for dynamic predictive models that are less data- and time-intensive and that are essentially cheaper [28,29]. These dynamic predictive models can handle trends that are time-dependent and variable patterns with less input data. The MLR is generally used but cannot always handle non-linear behavior between model inputs and outputs [30,31]. Nonetheless, using models such as the MLR and ANN is simple and profitable [32]. The MLR illustrates the cause-and-effect relationship between the observation and response variables through a linear equation that fits best through the data [33]. Moreover, the MLR is easy to use and simple to interpret [30].

The Breede Gouritz Water Management Area (BGWMA) is a vast catchment with different climates, populations, land uses, and economies. The catchment plays a critical economic role in South Africa, notably in Cape Town. Even though the western border is adjacent to the Cape Metropolitan area, the BGWMA supplies water to Cape Town and needs substantial water to feed its agricultural sector [34]. It is essential to know which climate variables could influence future groundwater depth due to the existing correlations.

This study aimed to define and quantify the relationships between temperature, precipitation, evapotranspiration, and groundwater depth (from different boreholes) in selected subregions in the BGWMA. The main objective was to perform a multivariate analysis of temperature, precipitation, evapotranspiration, and groundwater depth in order to delve deeper into underlying dependencies. A near future groundwater depth prediction for each relevant borehole analyzed was also made.

2. Study Area

The selected study area was the BGWMA, governed by the Breede-Gouritz Catchment Management Agency (BGCMA). The boundaries are the Indian Ocean to the south, the Berg-Olifants Water Management Area (WMA) to the west, the Orange WMA to the north and the Mzimvubu-Tsitsikama WMA to the east (Figure 1a). This WMA is mainly in the Western Cape, with overlaps in the Eastern and Northern Cape. It covers an area of about 72,000 km² [34]. The protection, conservation, management, and control of water resources in the catchment are mandated by the BGCMA.

The BGWMA provides an exciting platform to assess CC impacts on groundwater due to the complexity of the catchment, representing different climatic, geologic, hydrologic, and geohydrologic regimes. It is also a strategically important WMA in South Africa due to the extent of agricultural activity and the tourism industry in the region. Moreover, the BGWMA is essential to water resources in the City of Cape Town [34]. The BGWMA is susceptible to occasional drought; therefore, water management and planning, including for groundwater, are essential.

The study area was subdivided into smaller subregions based on the Köppen-Geiger climate classification system [36], since the study area is large. Four subregions (Figure 1b), i.e., BWh, BWk, Csa and Cfb, for which overarching temperature, precipitation, evapotranspiration, and groundwater depth data were available were selected for further analysis. These subregions include the BWh and BWk in the north-east of the study area in the semi-arid to arid Karoo, the Cfb temperate subregion toward the south coast, and lastly, the Csa subregion in the temperate west of the study area.

The BWh subregion is characterized by an arid, desert environment and hot conditions (Figure 1). The mean annual temperature (MAT) is 18.6 °C and the mean annual precipitation (MAP) is less than 256 mm a year [36]. The average annual precipitation between 2014 and 2020 was 121 mm (Prince Albert) (en.climate-data.org). The BWk subregion (Figure 1) has cold, arid, desert-like conditions. The MAT is lower than 18 °C and the MAP is a function of the MAT depending on the precipitation season. In this summer precipitation area, the MAP is less than ten times the MAT plus 28 [36]. The MAP for Beaufort West between 1994 and 2020 was 258.6 mm (en.climate-data.org).

The Cfb subregion is characterized by a temperate climate, with a warm summer and without a dry season (Figure 1). The air T of the warmest month is above 10 °C, whereas the air T of the coldest month is between 0 and 18 °C. Furthermore, the number of months where the air T is more than 10 °C is four or more [36]. The MAP for George between 2013 and 2019 was 670 mm (en.climate-data.org). The Csa subregion is a temperate area with dry and hot summers (Figure 1). The MAT is 18.7 °C and the precipitation in the wettest month (June) is more than three times that of the precipitation in the driest month [36]. This winter precipitation area receives a MAP of 272.31 mm (between 1999 and 2020) (en.climate-data.org, accessed 1 September 2021).

3. Material and Methods

3.1. Materials

3.1.1. Climate Data

Climate data were obtained from the South African Weather Service (SAWS) and the Agricultural Research Council (ARC) in Pretoria, South Africa. The average daily temperature (T) was used (in °C) but averaged monthly. If there was missing information, linear interpolation or a neighboring station’s value were used to account for it. The monthly summative precipitation (in mm) was used. If there were missing gaps in the precipitation (P) data, a neighboring station with a good correlation was used by applying the regression equation. Please refer to Figure 1b to view the stations selected for this study.

Monthly evapotranspiration (ET) was extracted from the WaPOR site (https://data.apps.fao.org/wapor/?lang=en (accessed on 1 September 2022) as GeoTIFF maps (Rome, Italy). The maps were in raster format (measured in mm) and dated from January 2009. The maps had a resolution of 250 m. Monthly totals were obtained by estimating ET in mm/day, multiplying it by the number of days in a ten-day period, and then using each month’s average. Relevant data were extracted for the Köppen-Geiger climate subregion. Moreover, individual shapefiles were created for the four selected subregions, from which average monthly spatial ET could be calculated.

3.1.2. Groundwater Data

Groundwater depth (GWD) data from the Breede and Gouritz Catchments were obtained from the Hydstra database from the Department of Water and Sanitation (DWS) in Cape Town, South Africa. For most boreholes, monthly observations were recorded. After filtering the Hydstra dataset, only 14 borehole locations across four subregions (

Table 1. The chosen boreholes, their respective subregions, the period for which data were available, their location relative to the subregions chosen weather station, and the elevation and status of the borehole.

Station	Borehole ID	Subregion According to Köppen-Geiger Classification	Period Analyzed	Distance and Direction from the Station	Elevation (m)	Usage Status
Beaufort West	J2N0001	BWk	1963–2021	10.1 km N	944	Local municipal use
	J2N0019		1974–2019	1.5 km E	852
	J2N0041		1974–2021	4.7 km SW	860
	J2N0043		2007–2021	9.1 km NNW	1074
	J2N0550		1975–present	22.6 km NE	979	In use: Unknown consumer
	J2N0618		2004–present	1 km WNW	869
George	K3N0001	Cfb	2014–2022	9.8 km NE	334	In use: Unknown consumer
Prins Albert	J2N0580	BWh	2005–2022	13.1 km S	705	In use: Unknown consumer
	J2N0582		2005–2022	15.5 km S	762
	J2N0620		2006–2022	15.6 km S	742
	J2N0621		2007–2022	11.3 km S	674
Worcester	H1N0018	Csa	1981–2022	3.8 km SW	205	In use: Unknown consumer
	H1N0055		1978–2022	1 km SE	209
	H2N0521		2004–2022	5.2 km NE	247

) were selected for further analysis (Figure 1b). The selected boreholes were chosen based on specific criteria, which included proximity to a chosen weather station, preferably in the same quaternary catchment and on the same side of a watershed (at least the latter if the former was not possible), and the number of consistent data points available (over at least ten years). Monthly averages were used for GWD. Where there was missing information, linear interpolation was used to fill in the gaps, assuming no significant change occurred between the previous and the subsequent measurement. Every effort was made to choose appropriate boreholes with significant data and minimal missing values. However, only a few were deemed appropriate, since their periods had to overlap with the other variables’ periods for our multivariate analysis.

A few assumptions about the observed GWD (in meters) were made during the analysis phase of this study: GWD’s seasonal patterns indicated recharge patterns and were closely compared to P in each subregion; The observed GWD was due to CC, mainly P (since no abstraction data were available) and based on the supposition that GWD had increased, in other words, the point at which water was first encountered was closer to the surface than expected. In the latter case, it was assumed that the respective aquifer had experienced recharge and a resultant increase in storage.

In the BWh subregion, the aquifers are fractured with a minimal yield [35]. The BWk subregion also has fractured aquifers, albeit with differing yields [35]. The single borehole in the Cfb subregion is from an intergranular aquifer. In the Csa subregion, all aquifers in question are fractured aquifers [35]. In this area, fractured aquifers are secondary aquifers primarily associated with the Table Mountain Group (TMG). Their borehole yields are between 0.1 and 2.0 L/s [37]. Intergranular aquifers are the primary aquifers in the area and are porous, sandy aquifers that can hold substantial amounts of groundwater [37].

3.2. Methods

3.2.1. Multiple Linear Regression (MLR)

A multivariate analysis determined which independent variables (T, P, or ET) affected the dependent variables (each respective borehole) and to what extent. The raw data were tested for consistency according to domain knowledge. Outliers were removed using a z-score of 3, meaning values outside of 3 standard deviations of the mean. A total of 14 records across all subregions were removed.

MLR was chosen as the appropriate statistical test since it can incorporate multiple variables and assess underlying linear relationships, if any [38]. Also, it is simple to use and easy to interpret, making it suitable for use in an area where knowledge was being built systematically to assess and quantify the relationships among the variables. MLR helps to elucidate each independent variable’s contribution to the total variance [39]. The test incorporates the strength and the significance of the model (R², adjusted R², F-statistic, probability F statistic), the complexity of the model (Akaike Information Criterion (AIC) and Bayesian Information Criteria (BIC)), the GWD constant when all the other variables are zero, the coefficients which measure the unit change in GWD for each of the other variable changes, the significance of the contribution of each variable on GWD fluctuations (p-value), and a few other tests to determine the distribution of the data (Omnibus and its probability, skewness, Jacque Bera and its probability, and kurtosis) and the collinearity of the data (conditioning number). The classical assumptions are that the data are normally distributed, there are no correlations between variables, there are no multicollinear variables, and that there is no heteroscedasticity [24].

According to findings from a previous paper [40], some independent variables are strongly correlated. Due to this, the results of MLR could be influenced. Therefore, a best-subset analysis was run for each dependent variable to determine which variables, or combination of variables, were determining. This subset analysis was done automatically (and manually for validation) to confirm the results by looping through all possibilities among the independent variables and choosing the best one based on the model’s results. Usually, including at least two variables, i.e., T and ET, determines the best possible variation for the dependent variable. Multicollinearity between certain variables is anticipated in this case. The outcomes of the models will be discussed for each subregion.

The test was run for each borehole (dependent variable) from each subregion. The formula was as follows [38]:

$$y={\beta }_0+{\beta }_1{X}_1+{\beta }_{2 }{X}_2+\dots +{\beta }_n{X}_n+ϵ$$

(1)

where:

y = dependent/predicted variable

β₀ = y-intercept (value when all other parameters are zero)

β₁ and β₂ = regression coefficients that represent the change in y relative to one-unit change in Xi and Xi, respectively

β_nXn = regression coefficient for the last independant variable

ϵ = random error of the model

3.2.2. Kruskal-Wallis Test

The Kruskal-Wallis (KW) test, a non-parametric and rank test used to compare two or more independent groups for a distinct variable, was also performed [41]. The null hypothesis (H₀) assumed that the category medians were equal. In contrast, the alternative hypothesis (H₁) was that the medians were unequal or that the medians from the groups differed [41]. The data were assumed to have a non-normal distribution, and the dependent variable had two or more independent variables [41]. The KW test was performed to test the validity of the MLR results, since the data residuals might not have met all the classical assumptions.

The KW test is the non-parametric version of the one-way ANOVA that determines stochastic dominance in a group [42]. The test can handle a random or stochastic distribution and is usually combined with a multiple pairwise comparison test such as Dunn’s. Dunn’s test uses the rank sums from the KW test to determine a z-test statistic to the precise rank-sum statistic [43] by making multiple pairwise comparisons [42].

The independent variables were categorized into low, medium, and high (

Table 2. Categories that were used to separate temperature (T), precipitation (P), and evapotranspiration (ET) into low, medium, and high categories, with the additional category of ‘abnormal’ for extreme P for each of the respective subregions, i.e., BWh, BWk, Csa, and Cfb (N/A = Not applicable).

Category	T (°C)	P (mm)	ET (mm)
BWh
Low (also minimum)	9.7	0	19.9
Medium	13.2	1.6	25.8
High	24	5.2	45.1
Abnormal	N/A	13.6	N/A
Maximum	27.1	43.8	63.8
BWk
Low (also minimum)	9.2	0	24.2
Medium	13.8	5.5	33.7
High	23.01	13	56.9
Abnormal	N/A	25.7	N/A
Maximum	25.9	72.2	71
Csa
Low (also minimum)	10.3	0	28.2
Medium	14	1.2	43.6
High	23.4	9.4	88.3
Abnormal	N/A	30.8	N/A
Maximum	27	99.2	107.1
Cfb
Low (also minimum)	11.55	0	32.33
Medium	14.07	26.41	53.21
High	19.33	39.75	88.53
Abnormal	N/A	74.93	N/A
Maximum	21.31	185.41	104.91

). Depending on the area, p had an additional category, i.e., ‘abnormal,’ for abnormally high P. The T and ET categories were chosen based on the dataset’s minimum, maximum, mean, and standard deviation. P was subdivided according to the dataset’s minimum, maximum, and 25%, 50%, and 75% percentiles. For each category, the regional climate was considered. Please refer to Table 2 for a summary of the different categories for each variable in each subregion.

The KW test was run for all categories from each borehole from each subregion. The formula was as follows [41]:

$$H=\left[{\displaystyle \frac{12}{n(n+1)}} {\sum }_{j=1}^c{\displaystyle \frac{T_j^2}{n_j}}\right]-3(n+1)$$

(2)

where:

n = total number of samples/observations

T_j = rank total for each group

n_j = number of observations in each group

4. Results

The descriptive statistics in

Table 3. Basic descriptive statistics, including the count, mean, standard deviation (std), minimum (min), 25% percentile, 50% percentile, 75% percentile, and maximum (max) of all variables from all four subregions. Climate variables included temperature (T), precipitation (P), and evapotranspiration (ET). Boreholes from each subregion included J2N0580, J2N0582, J2N0620, and J2N0621 in the BWh subregion, J2N0001, J2N0019, J2N0041, J2N0043, J2N0550, and J2N0618 in the BWk subregion, H1N0018, H1N0055, and H2N0521 in the Csa subregion, and lastly, K3N0001 in the Cfb subregion.

	BWh							BWk									Csa						Cfb
	T	P	ET	J2N0580	J2N0582	J2N0620	J2N0621	T	P	ET	J2N0001	J2N0019	J2N0041	J2N0043	J2N0550	J2N0618	T	P	ET	H1N0018	H1N0055	H2N0521	T	P	ET	K3N0001
Units	°C	mm	mm	m	m	m	m	°C	mm	Mm	m	m	m	m	m	m	°C	mm	mm	m	m	m	°C	mm	mm	m
count	89							127									141						96
mean	18.6	9.0	35.4	−13	−11.4	−10.2	−8.9	18.4	17.8	45.30	−18.1	−18.2	−26.2	−23.4	−15.9	−28.8	18.7	20.0	65.9	−2.5	−2.3	−13.4	16.7	54.2	70.9	−23.5
std	5.4	10.3	9.6	6.9	6.8	1.4	3.7	4.6	16.4	11.6	19.3	10.7	12.2	12.8	3.2	7.8	4.7	24.4	22.4	0.6	0.3	1.4	2.6	41.4	17.7	6.3
min	9.7	0.0	19.6	−34.3	−28.2	−15.8	−14.3	9.2	0.0	24.2	−55.7	−42.0	−49.1	−57.4	−19.5	−39.2	10.3	0.0	28.2	−3.4	−2.9	−15.9	11.6	0.0	32.3	−27.7
25%	13.8	1.6	28.9	−11.1	−17.2	−11.1	−11.9	14.6	5.5	36.4	−29.8	−26.2	−35.1	−30.6	−18.6	−35.4	14.4	1.2	44.9	−2.9	−2.5	−14.9	14.5	26.4	57.1	−26.6
50%	18.8	5.2	34.6	−10.5	−9.5	−10.3	−9.3	18.3	13.0	46.8	−8.1	−16.1	−27.8	−26.5	−16.9	−31.5	18.9	9.4	65.6	−2.6	−2.3	−12.8	16.5	39.8	72.8	−262
75%	23.8	13.6	39.6	−9.8	−5.8	−9.2	−5.1	22.5	25.7	52.7	−1.6	−8.5	−13.4	−12.6	−13.3	−20.1	23.1	30.8	84.6	−2.1	−2.0	−12.3	19.2	78.9	84.2	−25.9
max	27.1	43.8	63.8	−6.4	0.0	−7.7	−3.0	25.9	72.2	71.0	−0.1	−0.3	−6.3	−4.6	−9.8	−15.8	26.9	99.2	107.1	−0.7	−1.5	−11.7	21.3	185.4	104.9	−6.8

confirm the general climate of the area. The T moderation effect of the coast was seen in the average Ts observed in the Cfb subregion compared to the hotter and drier regions of BWh and BWk. T was most likely to deviate from the mean in the BWh subregion first, which is the hottest and driest of all, followed by Csa, BWk, and Cfb. The latter results were also seen in the average T ranges, which are typically more extensive for the hotter and drier climates. The BWk subregion had the lowest recorded average T, followed by BWh, Csa, and Cfb, which makes sense given the climatic regions and differences between maximum and minimum Ts. The highest Ts recorded was in the BWh subregion, followed by Csa, BWh, and Cfb. Despite the more temperate climate of the Csa subregion, it still had a relatively large average T range of 16.7 °C.

P was by far the most abundant in the Cfb subregion, followed by Csa, BWk, and then BWh, which once again confirmed the general climate of these subregions. The maximum recorded P in Cfb and Csa were 3 and 1.5 times higher than those in BWh. The highest variation in P was observed in the Cfb subregion, followed by the Csa, BWk, and then BWh subregions; 75% of the P in the BWh, BWk, Csa, and Cfb subregions were equal to or below 13.6 mm, 25.7 mm, 30.8 mm, and 78.9 mm, respectively.

ET was highest in the Cfb subregion, followed by Csa, BWk, and BWh, since there is more moisture to evaporate in the more temperate areas. ET showed the highest tendency to deviate from the mean in the Csa subregion, followed by the Cfb subregion, indicating more sporadic P patterns than in the Cfb subregion. Csa and Cfb indicated a far more significant standard deviation in ET than BWk and BWh (in that order); 75% of the monthly ET in the BWh, BWk, Csa, and Cfb subregions were equal to or below 39.6 mm, 52.7 mm, 84.6 mm, and 84.2 mm, respectively. Csa, followed by Cfb, hadmuch larger maximum ET levels than BWk, followed by BWh, due to more abundant general P.

The highest average GWD deviation was observed in BWk, followed by Cfb, BWh, and Csa. BWk showed the lowest recorded GWD at −55.7 m. The lowest recorded GWD for BWh was −34.3 m. The single borehole analyzed in the Cfb subregion showed the lowest recording of −26.7 m, and the lowest recording in the Csa subregion was −16 m. Boreholes that were closer in proximity tendes to share similar statistical properties.

The statistical results are shown in Table 3,

Table 4. Multiple Linear Regression (MLR) test results for each borehole from each subregion with outliers removed. The R² value indicated the extent to which the model can explain the variance in the dependent variable. The F-statistic and corresponding p-value indicated that all models were statistically significant, except for H2N0521 in the Csa subregion. The least complex models were the lowest relative Akaike Information Criterion (AIC) and Bayesian Information Criteria (BIC) values. The constant indicated the value of the respective dependent variables when all other variables were zero. The statistically significant coefficients (according to their p-values) are highlighted in green. Lastly, the resulting regression equation and the confidence intervals indicate the error range in the final result (N/A = Not applicable).

								Coefficients			p-Values
Subregion	Borehole	R2	F-Statistic	F Stat p-Value	AIC	BIC	Constant	T	P	ET	T	P	ET	Formula	Confidence Intervals
BWh	J2N0580	9.6%	4.5	0.01	593.1	600.6	−14.4	−0.4	N/A	0.2	0.02	N/A	0.0	$J2N0580=-14.4-0.4\mathrm{T}+0.2\mathrm{E}\mathrm{T}$+ ε	[−9.7; −21.7]
	J2N0582	23.8%	8.9	3.6 × 10−5	577.3	587.3	−17.6	−0.3	0.2	0.3	0.02	0.02	0.0	$J2N0582=-17.6-0.3\mathrm{T}+0.2\mathrm{P}+0.3\mathrm{E}\mathrm{T}+\mathrm{\epsilon }$	[−14.6; −25.6]
	J2N0620	17.2%	8.9	0.0003	304.6	312.1	−10.5	−0.1	N/A	0.1	0.0	N/A	0.0	$J2N0620=-10.5-0.1\mathrm{T}+0.1\mathrm{E}\mathrm{T}$+ ε	[−9.7; −12.1]
	J2N0621	29.2%	17.8	3.4 × 10−7	459.0	466.4	−14.0	−0.2	N/A	0.2	0.01	N/A	0.0	$J2N0621=-14-0.2\mathrm{T}+0.2\mathrm{E}\mathrm{T}$+ ε	[−12.3; −17.9]
BWk	J2N0001	18.9%	14.5	2.2 × 10−6	1090.0	1098.0	−15.1	−2.6	N/A	1.0	0.0	N/A	0.0	$J2N0001=-15.1-2.6\mathrm{T}+1.0\mathrm{E}\mathrm{T}+\mathrm{\epsilon }$	[−15; −41.8]
	J2N0019	29.9%	26.5	2.7 × 10−10	921.2	929.7	−5.5	−1.9	N/A	0.5	0.0	N/A	0.0	$J2N0019=-5.5-1.9\mathrm{T}+0.5\mathrm{E}\mathrm{T}+\mathrm{\epsilon }$	[−5.4; −19.2]
	J2N0041	26.2%	14.6	3.5 × 10−8	963.5	974.9	−21.9	−2.0	0.1	0.7	0.0	0.03	0.0	$J2N0041=-21.9-2\mathrm{T}+0.1\mathrm{P}+0.7\mathrm{E}\mathrm{T}$+ ε	[−30.5; −32.3]
	J2N0043	12.5%	8.9	0.0003	995.9	1004.0	−13.0	−1.5	N/A	0.4	0.0	N/A	0.01	$J2N0043=-13-1.5\mathrm{T}+0.4\mathrm{E}\mathrm{T}+\mathrm{\epsilon }$	[−8.8; −27.3]
	J2N0550	19.3%	14.8	1.7 × 10−6	632.7	641.2	−16.3	−0.4	N/A	0.2	0.0	N/A	0.0	$J2N0550=-16.3-0.4\mathrm{T}+0.2\mathrm{E}\mathrm{T}+\mathrm{\epsilon }$	[−16.4; −20.8]
	J2N0618	23.1%	12.3	4.3 × 10−7	856.9	868.2	−26.8	−1.2	0.1	0.4	0.0	0.01	0.0	$J2N0621=-26.8-1.2\mathrm{T}+0.1\mathrm{P}+0.4\mathrm{E}\mathrm{T}$+ ε	[−27; −37.7]
Csa	H1N0018	20.6%	17.9	1.3 × 10−7	213.5	222.3	−1.5	−0.2	N/A	0.03	0.0	N/A	0.0	$H1N0018=-1.5-0.2\mathrm{T}+0.03\mathrm{E}\mathrm{T}+\mathrm{\epsilon }$	[1.7; −4.2]
	H1N0055	41.7%	49.3	6.8 × 10−17	28.3	37.2	−1.3	−0.1	N/A	0.02	0.0	N/A	0.0	$H1N0055=-1.3-0.1\mathrm{T}+0.02\mathrm{E}\mathrm{T}+\mathrm{\epsilon }$	[−0.9; −1.3]
	H2N0521	0.7%	1.0	0.3	497.2	503.1	−12.9	−0.03	N/A	N/A	0.3	N/A	N/A	N/A	N/A
Cfb	K3N0001	9.8%	5.0	0.009	620.9	628.6	−21.6	−0.9	N/A	0.2	0.03	N/A	0.0	$K3N0001=-21.6-0.9\mathrm{T}+0.2\mathrm{E}\mathrm{T}$+ ε	[−21.1; −23.6]

,

Table 5. Additional information about each borehole’s Multiple Linear Regression (MLR) models. The omnibus and Jarque-Bera values (with their p-values) indicate the distribution of the residuals. The Durbin-Watson indicates autocorrelation. Skew and kurtosis provide insight into the distribution’s tails and the multicollinearity conditioning number. The standard errors and critical t-value (the critical t-value was derived from a standard t-table using the number of records for each borehole as the degrees of freedom and a 95% confidence interval) were used to calculate the confidence intervals in Table 4 (N/A = Not applicable).

								Standard Errors
Subregion	Borehole	Omnibus (p-Value)	Jarque-Bera (JB) (p-Value)	Durbin-Watson	Skewness	Kurtosis	Conditioning Number	Constant	T	P	ET	Critical t Value
BWh	J2N0580	37.7 (0.0)	64.4 (1.02 × 10−14)	0.1	−1.8	4.9	177	3.01	0.2	N/A	0.09	1.99
	J2N0582	4.8 (0.1)	6.5 (0.2)	0.5	−0.3	2.3	177	2.8	0.1	0.07	0.08	1.99
	J2N0620	66.2 (0.0)	339.5 (1.92 × 10−74)	0.6	−2.3	11.1	177	0.6	0.03	N/A	0.02	1.99
	J2N0621	1.4 (0.5)	1.3 (0.5)	0.5	0.1	2.5	177	1.4	0.07	N/A	0.04	1.99
BWk	J2N0001	16.3 (0.0)	16.8 (0.0002)	0.2	−0.8	2.4	223	6.7	0.5	N/A	0.2	1.984
	J2N0019	6.8 (0.01)	6.7 (0.04)	0.6	−0.6	3.1	220	3.5	0.3	N/A	0.1	1.984
	J2N0041	9.95 (0.01)	3.9 (0.1)	0.5	0.1	2.2	240	0.3	0.3	0.06	0.1	1.984
	J2N0043	4.8 (0.09)	4.6 (0.1)	0.5	−0.5	3.1	220	4.7	0.4	N/A	0.1	1.984
	J2N0550	19.1 (0.0)	9.2 (0.01)	0.4	0.5	2.1	220	1.1	0.1	N/A	0.03	1.984
	J2N0618	36.2 (0.0)	8.3 (0.02)	0.4	0.3	1.9	240	2.7	0.2	0.04	0.08	1.984
Csa	H1N0018	15.9 (0.0)	29.5 (3.87 × 10−7)	0.7	−0.5	4.9	327	0.2	0.03	N/A	0.01	1.984
	H1N0055	100.6 (0.0)	1167.6 (2.85 × 10−254)	1.1	−2.2	16.1	432	0.1	0.01	N/A	0.003	1.984
	H2N0521	42.3 (0.0)	18.3 (0.0001)	0.01	−0.7	1.9	76.9	0.5	0.03	N/A	N/A	N/A
Cfb	K3N0001	34.9 (0.0)	55.9 (7.3 × 10−13)	0.1	1.7	4.5	115	4.2	0.4	N/A	0.06	1.99

,

Table 6. The Kruskal-Wallis (KW) test results for variable temperature (T), precipitation (P), and evapotranspiration (ET) from each borehole. Larger H statistic values (with p-values < 0.05) render the alternative hypothesis valid, indicating that the medians across the categories differed significantly; the higher the H statistic, the more significant the difference. The highlighted cells indicate statistical significance, according to the p-value.

		T		P		ET
		H Statistic	p-Value	H Statistic	p-Value	H Statistic	p-Value
BWh	J2N0580	0.2	0.0	3.6	0.3	20.3	3.89 × 10−5
	J2N0582	1.9	0.4	2.9	0.2	6.5	0.04
	J2N0620	2.3	0.3	7.9	0.02	6.2	0.05
	J2N0621	0.6	0.8	0.9	0.6	19.7	5.26 × 10−5
BWk	J2N0001	2.01	0.4	1.7	0.6	1.6	0.5
	J2N0019	15.1	0.0005	1.8	0.6	1.9	0.4
	J2N0041	4.7	0.1	0.9	0.8	1.4	0.5
	J2N0043	7.9	0.02	1.4	0.7	0.9	0.6
	J2N0550	1.3	0.5	1.6	0.7	4.9	0.09
	J2N0618	2.4	0.3	3.7	0.3	2.4	0.3
Csa	H1N0018	4.9	0.1	10.5	0.02	2.09	0.4
	H1N0055	18.3	0.0001	13.7	0.003	6.8	0.03
	H2N0521	0.2	0.9	0.6	0.9	1.6	0.5
Cfb	K3N0001	2.4	0.3	0.1	1.0	10.6	0.01

and

Table 7. Dunn’s test results for statistically relevant variables from each subregion: temperature (T), precipitation (P), and evapotranspiration (ET). Categories 1, 2, 3, and 4 indicate low, medium, high, and abnormal respectively. Highlighted cells indicate statistically significant categories (N/A = Not applicable).

		Borehole	Categories	1	2	3	4
BWh	ET	J2N0580	1	1.0	0.8	0.006	N/A
			2	0.8	1.0	0.0009	N/A
			3	0.006	0.0009	1.0	N/A
	P	J2N0582	1	1.0	0.45	0.02	0.0007
			2	0.5	1.0	0.09	0.004
			3	0.021	0.09	1.0	0.2
			4	0.0007	0.004	0.2	1.0
	ET	J2N0582	1	1.0	0.8	0.007	N/A
			2	0.8	1.0	0.004	N/A
			3	0.007	0.004	1.0	N/A
	P	J2N0620	1	1.0	0.4	0.01	0.09
			2	0.4	1.0	0.03	0.3
			3	0.01	0.03	1.0	0.3
			4	0.09	0.3	0.3	1.0
	ET	J2N0620	1	1.0	0.9	0.007	N/A
			2	0.9	1.0	0.003	N/A
			3	0.007	0.003	1.0	N/A
	ET	J2N0621	1	1.0	0.43	0.002	N/A
			2	0.4	1.0	0.004	N/A
			3	0.002	0.004	1.0	N/A
BWk	T	J2N0019	1	1.0	0.07	0.0001	N/A
			2	0.07	1.0	0.01	N/A
			3	0.0001	0.01	1.0	N/A
	T	J2N0043	1	1.0	0.2	0.01	N/A
			2	0.2	1.0	0.05	N/A
			3	0.01	0.05	1.0	N/A
Csa	P	H1N0018	1	1.0	0.4	0.004	0.08
			2	0.4	1.0	0.01	0.2
			3	0.004	0.01	1.0	0.2
			4	0.08	0.2	0.2	1.0
	T	H1N0055	1	1.0	0.0004	0.00006	N/A
			2	0.0004	1.0	0.2	N/A
			3	0.00006	0.2	1.0	N/A
	P	H1N0055	1	1.0	0.7	0.01	0.008
			2	0.7	1.0	0.01	0.006
			3	0.01	0.01	1.0	0.8
			4	0.008	0.006	0.8	1.0
	ET	H1N0055	1	1.0	0.01	0.09	N/A
			2	0.01	1.0	0.6	N/A
			3	0.09	0.6	1.0	N/A
Cfb	ET	K3N0001	1	1.0	0.05	0.5	N/A
			2	0.05	1.0	0.004	N/A
			3	0.5	0.004	1.0	N/A

and will be discussed by climate region in Section 4.1, Section 4.2, Section 4.3 and Section 4.4.

4.1. Subregion BWh

This subregion is an already arid area with minimal amounts of P. When P does occur, it is either sporadic or very late summer rains in March. According to the MLR results in Table 4, P did not impact GWD since it did not add any value to the overall model, except for J2N0582. T might have correlated with GWD, but this was probably due to its strong correlation with ET. An increase in ET was associated with a rise in GWD, possibly indicating that vegetation indirectly impacted the GWD. Overall, the models only accounted for 9.6% and 29.2% of the variation of each borehole analyzed, with only J2N0620 having a small confidence interval.

The KW test confirmed the influence of ET on all boreholes and P on borehole J2N0620 (Table 6). According to Dunn’s test results in Table 7, ET across all categories for all four boreholes was statistically significant, meaning any variation in ET between low, medium, and high likely impacted GWD. P played a role in the vicinity of borehole J2N0582 if meagre amounts of P or high/abnormal amounts of P occurred, either positively or negatively. This effect is evident in Figure 2; initially, P seemed to induce a rise in GWD, but over 18 mm, the effect of higher P tapered off. By 30 mm of P and over, high amounts of P seemed to have a negative effect on GWD. P also played a role in the vicinity of J2N0620 between Categories 1, 2 and 3, which meant that a medium or high amount of P was probably conducive to a rise in GWD. From Figure 2, higher ET figures correlate with a rise in GWD, confirming the MLR results. For the J2N0582 and J2N0621 boreholes, ET was the variable with the single most influence on GWD (13% and 24%, respectively), according to the individual R² values.

The best model, which accounted for 29.2% of the variation in GWD, was borehole J2N0621, even though the boreholes were all close in terms of geographic location. With an expected average monthly T increase of 1 °C in the near future, an expected decrease in ET of 4 mm monthly ET, and expected decrease in P by 6 mm by 2028 [40], GWD is expected to drop to −15.7 m (−13 m average), −20.1 m (−11.4 m average), −10.9 m (−10.2 m average), and −15.1 (−8.9 m average) for boreholes J2N0580, J2N0582, J2N0620, and J2N0621, respectively. These predicted values are below the current average, with J2N0582 and J2N0621 showing the most significant decreases.

4.2. Subregion BWk

The BWk subregion is in the arid/semi-arid part of South Africa, also called the Karoo. The MLR results confirmed that T and ET affected GWD. P played a role at boreholes J2N0041 and J2N0618 as well. The KW test only confirmed J2N0019 in the case of T and J2N0043 in the case of ET (Table 6). According to Dunn’s test, any change in T could influence GWD, and high Ts could influence GWD near borehole J2N0043. Figure 3 confirms that higher T in J2N0043 could lead to cases of lower GWD. This influence was also confirmed by the individual R² values of T for both J2N0019 and J2N0043, especially for J2N0019. J2N0041 and J2N0550 had relatively small confidence intervals.

Between 12.5% and 29.9% of the variation in GWD could be accounted for by the independent variables, mainly T and ET. The best model was for borehole J2N0019, which could account for 29.9% of the variation in GWD. With an expected increase in monthly average T of 0.5 °C, a decrease in monthly ET by 12 mm, and a decrease in monthly summative P by 4 mm (by 2036) [40], average monthly GWD is expected to drop below the current average between 2.7 and 10.28 m, except for borehole J2N0019 (new average −12.3 m, old average −18.2 m) and J2N0043 (new average −18.1 m, old average −23.4 m). The sporadic locations and elevations of the boreholes may explain the variation and complexity of the models in this area. For example, J2N0043 is on a butte slope, and J2N0550 is on a riverbed.

4.3. Subregion Csa

The Csa subregion has a more temperate climate, but summers are also relatively hot and winters relatively cold. The MLR test confirmed that T and ET impacted GWD for boreholes H1N0018 and H1N0055, probably because of T’s close association with ET. The variation in GWD between 20.6% (H1N0018) and 41.7% (H1N0055) could be explained by T and ET. The model for H2N0521 was not statistically significant.

The KW test indicated that P played a significant role at H1N0018, and all three independent variables influenced H1N0055. According to Dunn’s test, for H1N0018, the low, medium, and high categories for P could statistically influence GWD. Figure 4 also illustrates this, i.e., there was a rise in GWD until high P, after which the effect tapered off in the abnormal category. For H1N0055, there were statistically significant differences amongst all categories of T, which is seen in Figure 4; the higher the T, the lower the GWD. T accounted for 20% of the variation in GWD in borehole H1N0055, according to the individual R² value. For P, the statistical significance lay between Categories 1 and 2 and Categories 3 and 4, respectively, which is also evident from Figure 4. GWD started rising from the high category (Category 3) and above. From low to medium ET, there seemed to be a lowering in GWD but a rise in Category 3 (high) ET again, which is evident in Figure 4.

The most robust model in this subregion was borehole H1N0055, which is in a commercial field area next to Worcester. This model also had the best confidence interval. H1N0018 is between the Breede River and the Brandvlei dam. The overall error metrics for the H1N0018 model were also good. With an expected decrease in T in the near future of 0.75 °C and an increase in ET by 4.2 mm by 2036 (and constant P), GWD could rise. The new monthly average for H1N0018 is −1.2 m (old average −2.5 m), and for H1N0055, it is −1.1 (old average −2.3 m). Both the new averages are expected to be higher than the norm at this point.

4.4. Subregion Cfb

The Cfb subregion is part of a more temperate and moderate climate, with large parts of the subregion bordering the ocean. Usually, this subregion does not have a dry season. T and ET are significant independent variables contributing to GWD variation at K3N0001. The KW and Dunn’s tests picked up the effect of ET. A statistically significant change occurred at medium and high ETs. GWD is expected to rise slightly to −22.3 m (average −23.5 m), which is inconsistent with the overall trend observed for this borehole.

Figure 5 indicates that between approximately −25 and −15 m, an increase in T and ET will cause a rise in GWD. Between −15 m and −10 m, GWD lowers with increasing T and ET. Above −10 m, the opposite is seen again; with increasing T and ET, GWD rises. Below −25 m, no significant effect exists from any of the variables. The individual R² indicates that ET determines 5% of the variation in GWD.

Low P was associated with lower GWD, although this same zig-zag pattern was observed. However, between −25 and −18 m, P and GWD rose, dropped between −18 m and −10 m, then rose again between −10 and 0 m. It was not clear what the patterns were in this subregion.

5. Discussion

The results of this study highlight the complexity of the groundwater system within the bigger context of a hydrologic system. Simple linear models can only account for up to 41.7% of the variation in GWD when considering T, P, and ET. Moreover, a multivariate analysis indicated that T and ET mainly affect GWD, depending on the subregion. T and ET were associated with GWD due to their close correlation. P only affected one borehole in the BWh subregion and two in the BWk subregion. Some of the multivariate models were stronger than others; however, all the boreholes displayed statistical models that were significant enough, according to the f-statistic and corresponding p-value (Table 4). The most significant model was H1N0055 in the Csa subregion; the variance in T and ET could explain 41.7% of the variance in borehole H1N0055.

Across the board, a positive correlation was observed between GWD and ET. In some cases, GWD is expected to rise; the most significant anticipated increase can be seen in the BWk subregion. In theory [23], elevated ET should cause a lowering in GWD; therefore, this correlation only makes sense if ET is indirectly correlated to the abundance of specific vegetation. According to the MLR equations, GWD is expected to be lower except for J2N0019 and J2N0043 from the BWK subregion and H1N0018 and H1N0055 from the Csa subregion. A decrease in ET is expected in the BWh, BWk, and Cfb subregions [40] in the near future. In contrast, an increase is expected in the Csa subregion.

Reduced grasslands and increased shrublands [40] also indicate that the vegetation of these drier, more arid areas (BWh and BWk) is changing, which could lead to an over-reliance on groundwater and a corresponding groundwater decline. This change in vegetation from grass to shrubs is a sign of desertification [44,45]. Shrubs have deeper roots than grasslands and can reach underground water stores to sustain themselves—possibly another reason for the decline expected in GWD. Moreover, it was found that T plays a critical role in GWD in hotter climate scenarios where aquifers are exposed to surface evaporation [23]. The near future scenarios for these areas and less P are not conducive to groundwater recharge. Less groundwater will be available for human consumption.

The BWk subregion is more complex and, for most boreholes, could not be adequately explained by the MLR. The MLR test indicated that T and ET impacted the GWD of all boreholes, and P for only two. However, the KW test only confirmed T for J2N0019 and ET for J2N0043. Since 1990, forests have substantially decreased in scope, as have wetlands and dryland agriculture [40]. Grasslands decreased in size starting in 1990 but have increased since 2013/14. Increases in shrubland, plantations, and irrigated agriculture are all signs of desertification [44,45], since there is an increasing reliance on irrigation. Although there have been more abundant water resources since 1990, available surface water resources have decreased since 2013/14, which is not a positive sign. The relationship between T, P, ET, and GWD seems more complex to explain via simple linear models; it could be due to the location and elevation of the boreholes. Topography also plays a role in GWD; it was found that the mean of the regional slope correlated positively with GWD [27]. Therefore, a more in-depth physical or statistical model that handles non-linearity better may be able to explain the variation in GWD in this area.

The statistical tests of the Csa subregion confirmed the robust control that T, and subsequently ET, has on weather-related processes. Despite the more temperate setting, this subregion still experiences hot summers and icy winters, with mainly winter P. T is expected to decrease in this area in the near future and ET to increase. In contrast, no trend is expected for P [40]. The combination of the latter results should statistically see a rise in GWD in the area. In certain areas, development is taking place in the form of urbanization, increasing surface water through the building of dams, dryland, and irrigated agriculture. In other areas, the increase of bare lands and losses in forests and grasslands indicate a drying climate. However, this could just be due to development. Plantations and shrublands have decreased since 1990 but increased since 2013/14, which could indicate desertification or just, once again, development taking place. However, the future of groundwater in this subregion looks optimistic.

For the Cfb subregion, the KW and Dunn’s test determined ET to be a significant variable. Relationships among variables are very complex, and some specific sets of optimal conditions between T, P, and ET are conducive to groundwater recharge. T and ET are expected to increase and decrease, albeit to a minimal amount. No change in P is expected. However, according to previous results [40], GWD is expected to lower but based on the MLR, it is expected to rise. Only one borehole was measured for this area, making it difficult to draw significant conclusions, and the results were inconsistent with the overall trend.

Another study found similar results; the MLR of the Ngurah Rai monitoring well in Bali, Indonesia could explain 25.7% of the variation in the GWD due to barometric pressure, evaporation, T, and P [24]. The rest of the variation was probably due to the activities of the community, especially concerning the shallow aquifers. It is evident that for some climates (in this case, subregions), it is simpler to explain variations in GWD (for example, Csa) than others (for example, Cfb), since relationships among climate and climate-related variables are generally not linear. An intricate interplay exists between T, P, and ET for optimal groundwater recharge. These interworking relationships differ from location to location. Despite the use of several significant models that can quantify near-future GWD predictions under the influence of mainly T and ET, only a certain amount of variance was accounted for, which indicates the importance of incorporating the total environment when analyzing groundwater systems. It wasfound that groundwater is affected by barometric pressure, evaporation, T, wind, bright sunshine, and P, as well as urbanization, seismicity, tidal influence, and external stress [46]. Groundwater abstractions likely also play a significant role in the observed GWD.

The models themselves were insufficient to explain the total variance of GWD. Nonetheless, they provided valuable insights into the underlying variables that control groundwater processes, at least in the present study. The difficulty in modelling climate and climate-related processes is due to the fact that relationships among variables are usually non-linear and multicollinear (mainly T and ET) (Table 5), which can negatively affect the final model. However, in this study, looking at the variables independently did not significantly improve the final results.

The omnibus value (Table 5) tests the distribution of the residuals. For most of the boreholes (p-value < 0.05), with three exceptions in the BWh and BWk subregions, the data were not normally distributed, which is one of the assumptions of the MLR test. All models were positively autocorrelated (Durbin-Watson values between 0 and 2), which was expected. The skewness measures the asymmetry of the residuals’ distribution, with a positive number indicating a longer right tail and a negative number indicating a longer left tail. All of the models had some measure of skewness. Similarly, kurtosis measures how heavy the tails are in the distribution of the residuals; the higher the kurtosis, the heavier the tails. Most of the boreholes displayed heavier tails, especially J2N0620 and H1N0055.

The conditioning number is a measure of multicollinearity among the independent variables; the higher the value, the stronger the multicollinearity and the more difficult it is to interpret the regression coefficients. All models displayed multicollinearity, which was also an expected outcome. Therefore, the p-values of each independent coefficient from each independent variable were considered in the final regression equation in Table 4. Some metrics were more favorable to the model than others. However, in general, the models were statistically significant and served as a stepping stone in evaluating the overall variance of GWD.

6. Conclusions

This study highlighted the firm control that temperature and evapotranspiration have on groundwater-related processes. With limited variable datasets and over a short period, a simple linear model could explain up to 41.7% of the variation in groundwater depth due to the effects of T and ET. It is also evident that these inter-relationships are, in most cases, not linear and would need to be further analyzed via statistical methods that can account for non-linear behavior and randomly distributed datasets. The MLR gave an adequate general estimation of what can be expected in the near future. However, site-specific and more local estimations need to be made.

In the more arid subregions to the north of the study area, where an increase in temperature and decrease in evapotranspiration are expected in the near future, lower groundwater depth can also be expected in most cases. Government bodies need to explore alternative water resources. The more temperate areas to the west of the study area can expect more favorable outcomes for groundwater depth in the near future. With an anticipated decrease in temperature and an increase in evapotranspiration, groundwater depth is expected to rise under constant precipitation. Temperature and evapotranspiration are the most significant independent variables that influence groundwater depth, and any change in these variables should influence groundwater depth either positively or negatively, depending on the variable and the area.