Trend analysis of selected hydro-meteorological variables for the Rietspruit sub-basin, South Africa

Identifying hydro-meteorological trends is critical for assessing climate change and variability both at a basin and regional level. This study examined the long- and short-term trends from stream discharge, temperature, and rainfall data around the Rietspruit sub-basin in South Africa. The data were subjected to homogeneity testing before performing the trend tests. Inhomogeneity was widely detected in discharge data, hence no further analyses were performed on such data. Temperature and rainfall trends and their magnitudes at yearly, seasonal, and monthly time steps were identi ﬁ ed after applying the non-para-metric Mann-Kendall and Sen ’ s slope estimator. The possible starting point of a trend was determined by performing the sequential Mann-Kendall test. This study revealed a combination of upward and downward trends in both temperature and rainfall data for the time steps under observation. For rainfall on an annual basis, there were no statistically signi ﬁ cant monotonic trends detected, although non-signi ﬁ cant downward trends were dominant. However, signi ﬁ cant decreasing rainfall trends were observed in dry and low rainfall months, which were April, August, September, and November. In contrast, signi ﬁ cant upward temperature trends were detected at the Vereeniging climate station at an annual scale and in October, November, spring, and winter. The ﬁ ndings are critical for climate risk management and reduction decisions for both near and long-term timescales. Mann-Kendall study direct in Long-term data show no signi ﬁ cant changes in rainfall while temperature is rising. Findings will improve the understanding of hydro-meteorological trends speci ﬁ c to the Rietspruit sub-basin mainly due to temperature spatial variability.


INTRODUCTION
The climate of the Earth is certainly warming and there is a rising consensus that climate change impacts will affect water availability, food security, and ecosystem services (Sintayehu 2018;Stuch et al. 2020). Climate change has a significant impact on society primarily through water-related effects, for instance, by affecting sectors such as energy, agriculture, infrastructure, and transport (IPCC 2014a). Hence, besides being an important environmental concern climate change is equally a development limitation particularly in underdeveloped nations (Banze et al. 2018;MacAlister & Subramanyam 2018). Meanwhile, the key determinants of current and future climate change impacts on freshwater supplies are rising temperatures, local rainfall variability, and shifts in the magnitude of these variables (IPCC 2014a).
In a large part of Africa, temperatures close to the earth's surface have increased by at least 0.5°C in the past 50-100 years (IPCC 2014b). Niang et al. (2014) reported that a large part of the southern African region witnessed increasing trends in minimum, maximum, and average yearly temperatures during the final half of the 20th century, whereby minimum temperatures increased faster compared with maximum temperatures. They furthermore stated that Zimbabwe, Botswana, and western South Africa experienced a slight decrease in rainfall in that period.
For society to better adapt to the different impacts associated with climatic variability and change, high-quality temporal and spatial data are needed to provide for a deeper scientific analysis and application. Identifying trends in hydrological and climatic data is critical for climate change and variability impact assessments and for understanding changes in the hydrological regimes at both regional and catchment scales (Meresa et al. 2017). Therefore, in light of basin-level water resource management, analysis of changes in the discharge, temperature, and rainfall is a necessity as these influence the available water and its quality for various and in many cases, competing uses.
The analysis of rainfall and temperature trends has continued to receive attention from researchers as a way to predict their occurrence and for water resources management for various uses (Ahmad et al. 2015;Meshram et al. 2017;Hu et al. 2019), particularly in arid and semi-arid regions which usually have higher evaporation and minimal precipitation (Forootan 2019). This is mostly the case because evaporation and rainfall are the key climate-related elements influencing freshwater resources (IPCC 2014a). In essence, reliable climate data are essential for hydrological modelling, climate forecasting, and the management of water resources (Firat et al. 2012). Hence, it is a standard requirement to use reliable data in the analysis of hydro-meteorological trends.
The Vaal Basin, where the current study area is part of, has highly contributed to South Africa's water resources development especially in the Gauteng Province (Ilunga 2017). The catchment changes in the upper Vaal River are understood to be largely due to climate change, industrial, urbanisation, and agricultural land-use changes (Jury 2016;Ilunga 2017). Due to these changes, agriculture has been identified as the most vulnerable sector in the region (Remilekun et al. 2020). There is, therefore, a need to understand better the climatic variability and its associated risks in the region and the Rietspruit sub-basin (RSB), which can be achieved through local climatic data assessments.
This study aimed to analyse the homogeneity and assess trends associated with climate change and hydrometeorological variability around the RSB in South Africa. This will supplement and enhance the locally available information on climate impact within the region. The term 'climate change' was used to denote statistically significant disparity in the normal climate conditions for stations with data spanning nearly 30 years or more. In contrast, climate variability was essentially used in the current study to examine the possible short-term deviation and fluctuations in the meteorological variables from the long-term average. Hence, it has been applied to stations with short-time data, of which in this study are less than 20 years. In this research, rainfall and temperature were the selected meteorological variables because they are the main determinants for climate change (Huang et al. 2012), which eventually influences the natural availability of water in a catchment.

Study area
The surface area of the RSB is approximately 1,139 km 2 and it empties into the Loch Vaal, which is part of the Vaal Barrage. The sub-basin stretches from latitude 26°21 0 to 26°44 0 South and from longitude 27°33 0 to 27°56 0 East. The RSB surface elevation varies from 1,424 to 1,806 m above mean sea level ( Figure 1).
Traditionally, most of South Africa is endowed with the four seasons as reported by Botai et al. (2018), which are summer (December-January-February), autumn (March-April-May), winter (June-July-August), and spring (September-October-November). Rainfall in the Upper Vaal is seasonal, with most of the rains being received between October and April. Meanwhile, the highest rainfall is received in the summer months of December and January with an annual average of around 740 mm. Minimum and maximum temperatures are generally encountered in July and January, respectively, while the catchment's average annual temperature is around 15°C (du Plessis 2017).

Data sources
The study area is characterised by meteorological stations that mostly fall just outside the sub-basin boundary ( Figure 2). In this study, available data comprised of various data lengths including long-and short-term data. Based on the available data in the study area, the present study categorised data with more than 28 years as long-term which was used to assess climate change. Observations from short-term data spanning between 5 and 16 years were used to define variations in the studied meteorological parameters. The South African Weather Service and the Agricultural Research Council of South Africa provided the raw daily temperature and rainfall data for a total of seven stations, although some stations provided more or fewer parameters even though two parameters were targeted for this study. Average monthly, seasonal, and annual rainfall values were generated from the total daily rainfall values. The daily minimum and maximum temperatures were averaged separately to come up with maximum and minimum temperatures on an annual, seasonal, and monthly basis. The discharge data were sourced from South Africa's Department of Water and Sanitation. Table 1 lists the latitude, longitude, and elevation of the meteorological and discharge stations.

Data quality control and statistical analysis
A data quality control process was applied to the observed discharge, temperature, and rainfall, data before conducting the analyses. This involved filling in missing data and testing data homogeneity. Most statistical guidelines indicate that datasets with more than 10% missing data are likely to show bias in the analysis of such data (Madley-Dowd et al. 2019). In this study, daily raw rainfall and temperature datasets had missing data ranging from 0.7 to 6% and 0.6 to 5%, respectively, while the discharge station had 8% of missing data. As such, biases in data analyses were minimised because missing data were all less than 10%. Missing data were estimated using the multiple imputation method, which simulates missing data multiple times. The multiple imputation method has been successfully applied to infill hydro-meteorological data in different studies (de Carvalho et al. 2017;Sattari et al. 2017;Ekeu-wei et al. 2018). In the current study, the statistical XLSTAT software was used to generate multiple imputations, whereby five imputations were applied as suggested by Schafer & Olsen (1998).
This study employed four statistical approaches to analyse the homogeneity and trends of the hydro-climatic data around the study area. In the beginning, the absolute homogeneity tests were independently computed for each station on the monthly, seasonal, and annual data. The absolute method was used because the climatic data in the study area are randomly distributed and sparse. The identification of trend tests and their magnitudes was carried out on the homogenous data. For the data series showing statistical significance, the sequential Mann-Kendall (SQMK) test was employed to locate the probable year when the rapid change occurred. The homogeneity and trend tests and results including p-value, Kendall's tau, MK-Stat(S), MK-Z statistics, and Sen's slope were computed using the Addinsoft's XLSTAT 2020.5 and the XRealStats computer software programs. A 'trendchange' package in RStudio was used to perform the sequential Mann-Kendal test for change point analysis.

Homogeneity tests
As part of the data quality control process, four homogeneity test methods were employed to detect the inhomogeneity and most importantly validate the homogeneity in the data, thus reducing unreliability concerns. These tests were the Standard Normal Homogeneity Test (SNHT), Pettitt's test, Buishand Range test (BRT), and von Neumann ratio (VNR). The null hypothesis of data being independent, identically distributed, and homogeneous is assumed in all of the four test methods (Patakamuri et al. 2020). In contrast, the alternative hypothesis for the Pettitt, SNHT, and BRT is that there is a point (year) where data changes and that the time series is inhomogeneous. The VNR does not provide any details on the year of change because the test's alternative hypothesis hypothesises that the data distribution is not random (Wijngaard et al. 2003). Detailed explanations and mathematical equations for performing these tests are provided in Ahmed et al. (2018).

Evaluation of homogeneity test results
The classification by Wijngaard et al. (2003) for assessing the homogeneity test results was adopted in this study. Here, the data series were summarised into three categories based on how many of the four homogeneity test methods rejected the null hypothesis at a p-value of 0.05, namely 'useful', 'doubtful', and 'suspect'. Data were classified as 'useful' when it satisfied the null hypothesis of at least three out of four homogeneity tests used in the study, while data series were put in the 'doubtful' category when the null hypothesis of homogeneity was Uncorrected Proof rejected in two of the four tests. A 'suspect' category was classified when the null hypothesis at a 5% significance level was rejected in three or all of the four homogeneity tests.

Mann-Kendall test
The Mann-Kendall test (Mann 1945) is a non-parametric test used to detect trends in climate time series. It is widely used to detect monotonic (increasing or decreasing) trends and for detecting trends in time series because it is simple, robust, does not require the data to be aligned to any statistical distribution, and is flexible to outliers in the data (Meals et al. 2011). The Mann-Kendall test assumes a null hypothesis (H o ) of no monotonic trend in the data series while its alternative hypothesis (H a ) assumes that there is a presence of a monotonic trend in the time-series data. For a time series X i ¼ x 1 , x 2 , …, x n , the Mann-Kendall test statistic S is calculated using Equation (1) as follows (Patakamuri et al. 2020): where n is the number of data points, x i and x j are the data values in time series i and j ( j . i), respectively, and sign (x j À x i ) is the sign function as indicated in Equation (2): when the sample size (data points) is greater than or equivalent to 10 (n ! 10), the MK test is characterised by a standard distribution with the mean E(S) ¼ 0, while the variance Var(S) is given using Equation (3): where n is the number of data points, m is the number of tied groups, and t k denotes the number of ties of extent k. A standardised MK test statistic Z MK is then calculated as given in Equation (4): The positive Z-value indicates an increasing trend, while the negative Z-value indicates a decreasing trend. The trend is significant if Z MK is greater than the standard normal variate Z α/2 , where α% is the significance level. For a 5% significance level, a trend is significant when |Z MK | . 1.96 (Gocic & Trajkovic 2013).

Sen's slope estimator
A Sen's slope estimator (Sen 1968) is a non-parametric method for estimating the magnitude of a trend by computing the linear rate of change (slope) and the intercept. For a given time series X i ¼ x 1, x 2 , … x n , with N pairs of data, the slope is calculated using the following equation: The median of N-values of β i gives the Sen's estimator of slope β, using Equation (6): A positive β-value represents an increasing trend, while a negative β-value represents a decreasing trend over time.

Sequential Mann-Kendall test
The SQMK test proposed by Sneyers (1990) was used in this study to determine the approximate year for the beginning of a significant trend. The SQMK test is computed using ranked values, y i of the original values in analysis (x 1 , x 2 , x 3 ,…, x n ). The magnitudes of y i (i ¼ 1, 2, 3, …, n) are compared with j y ( j ¼ 1, 2, 3, …, i À 1). For each comparison, the cases where j i . y j are counted and denoted by n i . The SQMK test sets up two series, a progressive one of u(t i ) and a backward one of u 0 (t i ).
The test statistic t is then given by Equation (7): The mean and variance of the statistic are given by Equations (8) and (9) as follows: and The sequential values of statistic u(t i ) is then calculated as in Equation (10): Using the same approach of calculating the u(t i ) values from the start to the end year, the u 0 (t i ) values are calculated backward, beginning with the end year of the data series. The estimated year (time) of trend occurrence is identified by locating where the progressive u(t i ) and retrogressive u 0 (t i ) curves intersect (Tabari et al. 2015). The critical value for a 95% confidence level is +1.96 (Zarenistanak et al. 2014).

Homogeneity tests
Homogeneity tests were performed using the four test methods (i.e., Pettitt's, SNHT, BRT, and VNR) at annual, seasonal, and monthly timescales. The absolute homogeneity test was used due to the low spatial station density and the absence of many stations with long-term data in the study area. The results of each homogeneity testing method were evaluated separately at a 95% significance level. The results were then used to detect inhomogeneous periods depending on the number of tests rejecting the null hypothesis. In this study, the null hypothesis was accepted and the data were considered homogeneous when the computed p-value for each test was greater than the significance level (0.05).

Rainfall homogeneity test
An evaluation of the monthly and seasonal rainfall homogeneity test results is indicated in Table 2. The results were classified as 'useful' (U), 'doubtful' (D), and 'suspect' (S) for each station, depending on how many homogeneity tests rejected the null hypothesis. Results for the monthly data indicate that the majority of the stations have homogeneous data, which were classified as useful. Inhomogeneous data series (labelled as suspect) were observed in January, April, and November for Zuurbekom, Winford, and Vereeniging, respectively.
The seasonal time-series data were found to be inhomogeneous in autumn and spring for Vereeniging and Fochville, respectively. The rest of the seasons in the remaining stations showed homogeneous characteristics; hence, climate trends and their results can be considered as reliable.
Annual rainfall time series were also subjected to homogeneity checks, because the tests may fail to detect nonhomogeneity in the monthly and seasonal rainfall (Ahmed et al. 2018). The homogeneity test results for annual rainfall data are summarised in Table 3. Results of the tests show that six of the seven stations had homogenous data, which were labelled as 'useful'.
Meanwhile, inhomogeneous data series were detected in three of the four homogeneity tests at the Fochville station, thus classifying the data as inhomogeneous. The break (change point) in the annual time series for the Fochville climate station was found to be in the year 2015. Generally, historical information on the station's geographical position and measurement practices are useful aspects that need to be considered when analysing the homogeneity of observed climate time series. Due to the absence of such metadata information at Fochville, it is unclear on the possible cause of inhomogeneity at the station. As such, the findings from the station need to be used with caution since they may not truly reflect climatic influences.

Temperature homogeneity test
In a similar manner to rainfall data, temperature data series for the available stations were subjected to homogeneity tests at both monthly, seasonal and annual timescales and the results are indicated in Table 4. The findings indicate that the majority of the months have homogeneous data for both maximum and minimum temperatures. However, maximum temperatures for Midvaal were classified as inhomogeneous in March, April, and November, while maximum temperatures at Winford have inhomogeneous data in February, April, and May. Hence, further climate studies such as trend analyses need to be used with caution for such types of results.

Discharge homogeneity tests
Homogeneity tests for the discharge data were performed for the only available gauging station within the hydrological boundary of the study area. The obtained data for the discharge station (C2H5) run from 1953 to 2018. Results of the homogeneity tests show that p-values for all of the four tests (Pettitt, SNHT, BR, and VNR) were less than the significance level of 0.05 for both monthly, seasonal, and annual timescales, indicating that the discharge data were inhomogeneous. The findings were compared with an evaluation of the critical values results in order to confirm the observed inhomogeneities. According to Wijngaard et al. (2003), for a sample size used in the present study (n ¼ 66), at a 95% confidence level, the critical values are 235, 8.45, 1.55, and 1.54 for Pettitt, SNHT, BR, and VNR tests, respectively. The data were regarded as inhomogeneous if the critical value is lower than the estimated test statistic for each respective test. Results show that the obtained test statistic for Pettitt, SNHT, and BR tests was higher than the above-mentioned critical values in all the timescales (Table 5). Only the test statistic values from the VNR test had values lower than the critical values (1.54). This further confirms the inhomogeneity in the discharge data.
Further analysis of the mean annual discharge data shows the Pettitt test detecting a break (change in the data) in 1986, the SNHT in 1995, and the BR in 1986, as shown in Figure 3(a)-3(c). As expected from the homogeneity test results, the discharge data are associated with significant positive trends in all the months and at an annual scale. The increasing flows, which were observed even in dry season months, are unlikely to be related to natural hydrological or climatic change and variability. The possible reasons for the increasing flows could be the additional effluent from the wastewater treatment works across the study area, which eventually discharges into the surface water bodies including the Rietspruit River. Furthermore, the eastern part of the sub-basin where the Rietspruit River is located is being more urbanised, thereby changing the natural landscape and Journal of Water and Climate Change Vol 00 No 0, 11 creating more impervious surfaces. These findings are consistent with the observations made by du Plessis (2017), who pointed out that the impervious surfaces due to increased urbanisation have led to increased runoff in the Upper Vaal. Based on these findings, there is a need to separate all the effluent discharges from the measured flows at the stream gauging station in order to have only natural flows. As such, the discharge data in this study were not used for further analysis of climate trends.

Trend analysis
Annual temperature and rainfall cycles The annual cycles of rainfall and temperature for selected stations in the study area are indicated in Figure 4. The cycles were determined from the average monthly data for the respective meteorological variables. The months of December and January saw the most rainfall, with June and July having little or no rains. Meanwhile, the lowest and highest temperatures for the studied stations were detected in the June/July and December/January periods, respectively.

Rainfall pattern and trends
Rainfall in the study area is mostly concentrated during the summer months of December, January, and February. The coefficient of variation (CV) values for the annual rainfall and summer season are presented in Table 6. The highest and lowest variability was observed at Fochville and Zuuberkom climate stations at both annual and summer season timescales, respectively. CV values between 20 and 30% are considered to be moderate while CV greater than 30% is regarded to be high (Sangma et al. 2020). This indicates that the study area is characterised by intermediate and higher rainfall variability. The distribution of annual rainfall within the RSB boundary was investigated in an ArcGIS setting using the inverse distance weighting (IDW) technique. The IDW interpolation method assumes that places with observed data will have similar values to nearby places without data than those further away (Keblouti et al. 2012). From the analysis, the mean annual rainfall within the Rietspruit ranges from 629 to 709 mm ( Figure 5), demonstrating the semi-arid and dry sub-humid characteristic of the study area (Kašanin-Grubin et al. 2018). The highest rainfall is depicted in the north-western part of the study area while low rainfall values are observed in the eastern and some parts of the western side of the RSB.
The Mann-Kendall test was applied on annual, monthly, and seasonal data to detect monotonic rainfall trends at different meteorological stations. Negative and positive Sen's slopes demonstrated a decline and increase in Uncorrected Proof rainfall, respectively. In this study, temporal trend analysis to detect potential climate change largely focused on three stations, namely Barrage, Vereeniging, and Westonaria since these sites have long-term data enough to detect potential trends due to climate change. Meanwhile, short-term trends performed in other stations were  Uncorrected Proof only used to provide an insight into the natural fluctuations of rainfall within the studied years, as the data length is not adequate to provide evidence of climate change. In general, results of the rainfall trend analysis show a combination of negative and positive trends for both monthly, seasonal, and annual time series. For monthly time series, statistically significant downward trends were observed in November at Vereeniging, and in April, August, and September at Westonaria, as seen in Table 7.
Meanwhile, at Midvaal, a statistically significant upward trend was observed in September. No statistically significant trends were found in the other months. It is worth noting that statistically significant trends were detected only in months that normally receive little rainfall, as compared with the normal wet months such as December, January, and February. Hence, such statistical significance may not make a substantive difference to the overall observed annual rainfall because rainfall in the study area is seasonal, largely falling during the summer months  Uncorrected Proof (DJF). Nonetheless, if the downward rainfall trend can continue for the dry season months, it can result in a further increase of the dry season and a reduction in soil moisture during the said period. Soil moisture is an important variable as it influences the interaction between land and atmosphere (Mishra 2020), which ultimately influences short-term weather forecasts (Costa et al. 2016). Dry season soil moisture decline due to decreasing rainfall can also cause agricultural drought and affect crop production. Therefore, it is important to continue monitoring such declining trends as they can cause direct and indirect impacts on the overall water budget of the sub-basin. MK test results in the analysed stations showed no statistically significant trends on an annual timescale. However, it is important to point out that non-significant negative trends were dominant as the trends occurred in five of the seven stations. Figure 6(a)-6(c) shows the trend on annual rainfall for the three long-term data, with the decreasing slope evident in two of the three stations.
In general, the study area is characterised by the presence of insignificant increasing and decreasing rainfall trends and moderate to high intra-annual and seasonal rainfall variability. As earlier depicted, the CV for annual rainfall ranged from 23 to 25% for the long-and medium-term data and from 19 to 57% for the shortterm data. Areas having high rainfall variability tend to be more susceptible to floods and droughts (Gajbhiye et al. 2016). A series of studies in the southern Africa region have also found no significant trends in annual rainfall data, with many indicating a downward trend. Gyamfi et al. (2016) found an insignificant trend for annual rainfall in the Olifants Basin (South Africa), which is a neighbouring basin to the Upper Vaal Basin. Using data from 138 South African stations between 1910 and 2004, Kruger (2006) detected no significant changes in rainfall in a majority of the stations. Banze et al. (2018), from a review of rainfall trends in southern Africa, concluded that rainfall will both increase and decrease in the different parts of the region; however, there is still no total agreement among researchers on the magnitude of the anticipated rainfall change in the region. In contrast, Murungweni et al. (2020), from a local-scale study in Limpopo (South Africa), established that there is a non-significant decrease in the annual rainfall.
Seasonal rainfall trends exhibited a statistically significant positive trend in autumn (March-April-May) at Fochville (Table 8). Since Fochville has short-term data, such changes can only be attributed to significant seasonal fluctuations in meteorological conditions in the area. Although homogeneity test results for autumn at Fochville indicated that the data were inhomogeneous, the slope of the trend analysis shows a relatively higher magnitude of increase (27.8 mm/year) compared with other stations in the same season as pointed out in Table 8. According to Wijngaard et al. (2003), inhomogeneous data series showing marginal trend results should be considered as incorrect, while exceedingly high monotonic trends are due to climate-related variations.
Thus, the significant positive trend in autumn at Fochville could be attributed to climatic variability. Furthermore, an increasing trend in autumn rainfall at Fochville seems to signify a possible shift in the present-day rainfall patterns around the area, since the increase was much high than the summer season which traditionally receives more rainfall. However, these results are not conclusive and such changes cannot be definitively attributed to possible climate change and variability due to the available short-term data for the station. This is particularly true because the scenario was observed at only one station; therefore, the findings should be further investigated as more climate data is made available.
For the summer period, which is the main rainfall season, insignificant upward trends were dominant, occurring in five of the seven stations. These findings align with the observations by Kruger & Nxumalo (2017), where Uncorrected Proof it was noted that summer periods have insignificant increasing trends around the Gauteng Province, which covers a part of the study area. The magnitude of statistically significant trends was determined by applying Sen's slope. The results for the long-term rainfall data (Barrage, Westonaria, and Vereeniging) indicate that trends were more rapid with a higher slope at Vereeniging, which had a maximum negative decline of 2.7 mm/year in November, as indicated  The bold value indicates a significant trend.
in Figure 7. Nevertheless, the general Sen's slope values for both upward and downwards trends were not particularly high, which aligns with the observed non-significant rainfall trends.

Temperature trends
In the same way as rainfall data, the Mann-Kendall and Sen's slope estimator was used to assess the maximum and minimum temperature trends for annual, seasonal, and monthly time series. Table 9 displays the results of the monthly Mann-Kendall tests. From the analysed stations, maximum temperatures at a monthly scale were dominated by positive (upward) trends for all but one station. An exception was at Winford where downward trends were dominant. In contrast, minimum temperatures showed a combination of downward and upward trends. Furthermore, monthly time series revealed only statistically significant upward trends, with no statistically significant downward trends.
A great focus for temperature analyses in this study was at the Vereeniging climate station because it has relatively longer data for better and conclusive climate change analysis. The plots for statistically significant increasing temperature trends for Vereeniging are indicated in Figure 8. As depicted in Figure 8(a) and 8(b), maximum temperatures displayed statistically significant upward trends in October (Sen's slope, β ¼ 0.077) and in November (β ¼ 0.084). At the same Vereeniging, a significant positive trend for minimum temperature was detected in November again, with a Sen's slope of 0.078 (Figure 8(c)). The Sen's slopes for the monthly maximum and minimum temperatures at Vereeniging are shown in Figure 9, with higher values evident in October and November. Meanwhile, significant positive trends for maximum temperatures were also detected at Midvaal in March, April, and November having Sen's slopes of 0.237, 0.173, and 0.236, respectively. The higher values of Sen's slope at Midvaal could be as a result of a short data period for Midvaal; hence, the results may not reflect climatic changes.  The results of the seasonal and annual MK and Sen's slope tests for maximum and minimum temperatures are presented in Table 10. The analysed annual average temperature shows a statistically significant increasing minimum temperature at Vereeniging and maximum temperature at Midvaal. Meanwhile, the corresponding  Uncorrected Proof minimum and maximum temperatures for these stations also showed upward trends, though they were insignificant.
Seasonal average temperatures for the available data indicate statistically significant positive trends in winter (Tmin β ¼ 0.049) and spring (Tmin Sen's slope (β) ¼ 0.049) for Vereeniging and in autumn (Tmax, β ¼ 0.2) for Midvaal. In contrast, a statistically significant negative trend was detected only at Winford in autumn (Tmax, β ¼ À0.37). MacKellar et al. (2014) also reported that maximum temperatures in South Africa's central and northern areas, which includes this study area, are increasing. They noted that the strongest trends were in the autumn (MAM) and winter (JJA) seasons.

Sequential Mann-Kendall test
Indicating the probable time of change in the analysis of hydro-meteorological trends enables one to have a comprehensive understanding of the trend detection analysis (Patakamuri et al. 2020). For those stations exhibiting statistically significant monotonic trends in the time series, the SQMK test was used to identify the period for an abrupt change in the data.
The SQMK tests were only conducted on temperature data because the summer (main rain season) and annual rainfall data showed no statistically significant trends. For temperature, the major focus was the significant trends observed at Vereeniging due to its better data period, which exhibited significant positive trends for minimum temperature in November and maximum temperature in October and November. Figure 10 shows plots of the SQMK tests for the Vereeniging temperature time series. Results show that maximum temperatures in October and November generally showed similar increasing trends. Maximum temperatures in October (Figure 10(a)) and November (Figure 10(b)) showed non-significant trend development around 2002. The November temperature was characterised by a slightly erratic trend between 1999 and 2000 as the forward curve intersected with the backward curve twice between these years until another intersection around 2002 (Figure 10(b)). Hence, the main year for the development of an increasing trend for the maximum temperature at Vereeniging was identified to be around 2002, though it was insignificant.
Although the SQMK detected several other possible change points after the year 2002 as noted by the crossing of the u(t) and u 0 (t) curves, a significant increasing trend at a 95% confidence level was detected to have developed around 2015 in October and 2016 in November. This is in agreement with the drought experienced in South Africa around the 2015/2016 period, which was one of the driest periods in South Africa (Muthelo et al. 2019). The minimum temperature, which also exhibited increasing trends in November, showed that the increasing trend started in 1997 (insignificant) and the trend turned significant in 2001 (Figure 10(c)). Again, this is consistent with the drought observed in the 2001/2002 season in most parts of southern Africa, whereby South Africa was not spared (Rouault & Richard 2005;Masih et al. 2014).
The findings in this study determined the trend turning point and the potential year in which significant temperature increases began, which is important for the interpretation of climate variations. From the results, it has been established that the emergency of some drought in South Africa was associated with significant temperature increases. Since the observed droughts were in a majority of the country, it is suggested that temperature Uncorrected Proof increases observed at the studied station may have also occurred at a regional level, despite that only one main temperature station was used in this study. In general, risks to droughts are likely to intensify as temperatures keep rising, hence the need for continued monitoring of temperature trends for prediction and planning for such climate extremes like drought.

Implications of the observed meteorological trends and variability
An understanding of hydro-meteorological variability is central for better planning, management, and sustaining water resources. This is particularly true in areas experiencing rapid urbanisation and those highly vulnerable to climate change, a common characteristic in developing countries. Temperature and rainfall are considered the vital weather parameters for describing climate change, and their magnitude influences the natural water resource availability. Even though climate change impact studies should be performed in all regions, it is a necessity in urbanised areas because the negative effects of urbanisation and related anthropogenic activities may exacerbate the impacts. Hence, this study explored the changes in rainfall and temperature at annual, seasonal, and monthly scales using both the available short-and long-term data.

Uncorrected Proof
While the short-term data cannot be fully adopted for climate change analyses, the findings from such data are usually attributed to natural climatic variability. Thus, it is critical to identify and quantify the natural climatic variation to mitigate its negative effects, especially in the near term. The analysis of short-term rainfall data can give valuable guidance for managing water supplies and reducing the intensity of natural disasters including floods and droughts (Asakereh 2019). Besides, forecasts arising from the inter-annual and decadal climatic variability can help in making decisions relating to climate change risk reduction and management (Vera et al. 2010).
In the meantime, the results from stations having short-term data provide an insight into the short durational fluctuations of the selected climatic variables and they serve as a foundation for future climate change analysis, which has been lacking in the study area. These findings can be examined further as more data becomes available. Therefore, there is a need to be observant of such short-term variations for the communities to manage and ably respond to the uncertainties due to natural climate variability. This is especially true because there are cases when natural variations can conceal the impacts of human-induced climate change in both short and long terms (Martel et al. 2018).
The annual rainfall time series exhibit non-significant trends; however, downward trends are more dominant across the study area. Still, it is important to understand the economic, social, and ecological implications if the observed downward annual rainfall trend is to continue and if the decrease will be significant. This is because continued declining trends in rainfall will likely result in diminishing groundwater levels, soil moisture depletion, and ultimately a reduction in crop harvests (Meshram et al. 2017). As the downward trends are not significant based on the present data, it follows that the major concern related to rainfall in the study area is its inconsistency than its total annual amount. Erratic rainfall during the wet season complicates farming season planning and may have an impact on agricultural productivity, especially that rain-fed agriculture predominates in the study area.
Vereeniging, which has relatively longer temperature data, showed maximum temperature rising significantly in spring as well as increases in minimum temperature in winter, spring, and annual time series. The magnitude of the increase is higher for minimum temperature (0.031°C/year) than maximum temperature (0.022°C/year). Again, seasonal temperatures showed the highest increasing magnitude in winter (cold season) with a slope of 0.049°C/year, representing an increase of 1.4°C over the period 1992-2019. Similar warming trends, with an increase of nearly 1.4°C were detected in spring (SON) for maximum temperatures during the same period. The increases are consistent with the recent regional temperature trends outlined in Niang et al. (2014), whereby it was also reported that minimum temperatures are rapidly rising than maximum temperatures in the inland part of southern Africa. Findings by Huang et al. (2012) who studied long-term temperature trends across the globe also revealed that warming in semi-arid regions is escalating during the cold seasons. At the monthly scale, maximum temperature increases of about 2.2°C in October and November were detected for the period 1992-2019. Such strong warming trends were also reported by MacKellar et al. (2014), who found temperature rises of 1.5-2°C in the central and northern parts of South Africa using data from 1960 to 2010.
In this study, the intensified magnitude of temperature increase is more evident probably because the analysis has been conducted for moderately recent periods, which has seen accelerated warming (Singh et al. 2014). Such changes in temperature can be attributed to changing climate due to anthropogenic activities, associated with urban and industrial features.
The effect of rising temperatures can influence both water quantity and quality, which has the potential to enhance evapotranspiration and reduced runoff under the same rainfall conditions (Xu et al. 2020). At such a rate of temperature increases in the study area, the possibility for the development of intense drought is also expected to increase, which will ultimately increase threats related to water availability. According to Hoegh-Guldberg et al. (2018), rising temperatures above 2°C are likely to cause a noticeable increase in the risks to drought occurrences and its magnitude, mostly in southern Africa and in the Mediterranean region. Thus, the observed temperature increases can have multiplier effects on the region such as food and water security, ecosystem services, energy, and the economy at large.
The results in this study provide a basis for the need to conduct efficient climate change modelling in the study area in order to devise well-informed decisions for the management of the RSB. This is mostly true because climate change is changing the principle of stationarity in the water resources system, which focused on predicting the future based on past hydrologic events. Hence, there is a need for reliable projections to understand the extent to which water resources will be affected due to climate variability. Furthermore, as climate change adaptation measures are put into consideration, it is also important to reflect on other non-climatic elements affecting freshwater resources, for example land-use change and population increase, which can aggravate the effects of climate change. This is because anthropogenic activities and climate change are likely to remain the most important factors driving the hydrological cycle.

CONCLUSIONS
This study attempted to analyse trends for stream discharge, rainfall, and maximum and minimum temperature for the RSB in South Africa. Homogeneity tests were performed using four statistical tests to establish the reliability of the data for hydro-meteorological variability and climate change studies. The presence and magnitude of trends over time were, respectively, determined using the non-parametric Mann-Kendall test and Sen's slope estimator, while the change point analysis was performed using the SQMK test.
The monthly, seasonal, and annual time series were homogeneous from the majority of the stations. Temperature and rainfall data were more homogeneous at the annual scale; hence, the data were further used to perform trend analyses. In contrast, stream discharge showed inhomogeneity including at the annual scale, thus the data could not be used further for trend analyses before its correction. This signifies the need for performing homogeneity tests before carrying out climate data analyses. It has been suggested that streamflow is impacted by anthropogenic activities such as the discharge of effluent, hence the measured flows did not entirely reflect the natural river flows. Therefore, it is recommended that measured streamflow be separated from the flows contributed by the effluents. This is important to isolate and distinguish discharge variability due to climate change from that caused by anthropogenic activities.
From the trend analysis, at a 5% significance level, rainfall showed insignificant increasing and decreasing trends on an annual basis in all the stations. The findings also reveal that decreasing trends were dominant for annual rainfall while the summer season, the high rainfall season in the study area, was dominated by positive trends. Broadly, based on long-term data, this study showed no extensive evidence that climate change has resulted in a significant increase or decline in rainfall over the RSB. Hence, the variability of rainfall in the study area is more of a concern than the total average rainfall.
Temperature data at Vereeniging revealed that maximum temperature has significantly increased in October and November, while minimum temperature showed a significant increase in November and the winter season. Strong warming trends were detected with temperature increases of about 2.2°C in October and November. Minimum temperatures have also exhibited a significant increase, with the increase being greater during the winter season. In the absence of a significant change to the rainfall, while temperature has been significantly rising, evaporation rates are expected to rise as well. This has the potential to increase the aridity in the study area, thereby stressing the availability of both groundwater and surface water resources.
In general, this study enhances the scientific knowledge and characteristics of hydro-meteorological variables in the upper part of the Vaal Basin and largely in South Africa. The findings are important for decision making in the water and agricultural sector, but also for monitoring the impact of climate change and variability in the RSB area. Due to the limited long-term data and small network density of weather stations in the RSB, it is critical to use regional climate model data to improve forecasting and reduce uncertainty in the climatic variables. Furthermore, because the Mann-Kendall test used in this study did not account for the effects of data autocorrelation, data series autocorrelation analyses are suggested for detecting trend patterns.