Analysis of Rainfall, Wind Speed and Streamflow Trends and Their Relationships in the Klip River Catchment, Alfred Duma Municipality, South Africa

Streams are important to both people and the environment, and their flow can be impacted by climate change factors such as rainfall and wind speed [1]. According to Camera et al. [2], climate change could have a major impact on the availability of water in the catchment area's rivers. Ramli et al. [3] stated that meteorological variables, such as rainfall, air temperature, humidity, air pressure, and wind speed, speed can be utilized to characterize climate change. Changes in rainfall, depending on its intensity, short-term or long-term rainfall can cause flooding, while long periods without rainfall can cause drought [4]. Existing literature by Pirah and Roslee [5] highlighted that climate change can increase the likelihood of floods; however, the timing of these events is uncertain and difficult to predict because of a number of variables at play. Liu et al. [6] indicated that climate change factors, such as wind speed may also influence streamflow, affecting the amounts and patterns of runoff. For instance, when the wind blows over a stream, water vapor is released into the air, converting more water particles into gaseous form, as a result, speeds up the rate of evaporation [7]. Wasko et al. [8] argued that a study of streamflow changes is essential for understanding the relationship between climate change and flooding. The Klip River is one of the major tributaries of the uThukela River and an essential water source for a large portion of Ladysmith and its surrounding area. However, policymakers, governments, and the community at large are concerned about dwindling streamflow and recurrent summer flooding [9, 10]. As a result, understanding how, where, and why streamflow changes are critical for sustainable water resource management and flood control [11]. This research aims to contribute to the existing knowledge of the rainfall, wind speed, and streamflow trends in the Klip River catchment. In addition, it addresses the question of how rainfall and wind speed affect streamflow. Over the recent past, numerous studies have been conducted to investigate the impact of climate change on streamflow in various catchments throughout the world. Back and Bretherton [12] investigated the relationships between wind speeds and precipitation in the Pacific Intertropical Convergence Zone. According to their findings, the increase in rainfall was substantially greater than the increase in evaporation produced by the increased wind speed. The study shows that there is a strong correlation between wind speed and precipitation. Abeysingha et al. [13] investigated the relationships between streamflow and rainfall at four gauging stations in the Gomti River basin of North India. The study results revealed a gradual decline in annual streamflow, which was attributed to increasing water extraction, increased temperatures, a higher population, and a significant decrease in rainfall. Bahati et al. [14] studied and analyzed the trends in rainfall and streamflow in the Mukono and Buibwe districts of Uganda's River Ssezibwa Catchment. The study results indicated that annual average rainfall decreased, whereas annual average streamflow increased. The increase in streamflow has been attributed to a change in land use/land cover. Lawin et al. [15] investigated the effects of observed changes in rainfall, temperature, and wind speed in Rwegura and Imbo catchment, Burundi. During the study period, rainfall showed a decreasing trend, whereas temperature and wind speed revealed increasing trends. Environmental deterioration caused by global climate change and population growth has been attributed to wind speed. Another similar study was conducted by Malede et al. [16], who studied the existing relationships between rainfall and streamflow trends, as well as potential drivers of streamflow variability in the Birr River catchment, Ethiopia. The study concluded that changes in streamflow without significant changes in rainfall may have been caused by other factors. Zhong et al. [17] investigated the pattern of streamflow and its attributions in China's Yellow River. During the study period, the runoff and rainfall results showed a decreasing trend. During the study period, the results of runoff and rainfall showed a declining trend. The study linked the decrease in streamflow to human activity. Zhao et al. [18] investigated the impact of climate variability and human activities on Streamflow in the Wanquan River Basin along the East Coast of Hainan Island in Southern China. Furthermore, trends of decreasing rainfall and increasing potential evapotranspiration were discovered. The study findings revealed that the annual streamflow reduces as the watershed's temperature rises. The study concluded that the relative impact of climate change was greater than that of human activities. Krishnan et al. [19] investigated the effect of climate change on evaporation rates in the Limbang River Basin of Sarawak, Malaysia. The results revealed an overall increasing trend in monthly evaporation rates. The study concluded that changes in rainfall, wind speed, and air temperature have a substantial impact on the study area's increasing rate of evaporation. Duethmann et al. [20] investigated the effect of changes in rainfall and temperature on the streamflow patterns of the Tarim River, Central Asia. The study's findings demonstrated that changes in temperature and rainfall caused an increase in streamflow. Despite numerous studies conducted on the trends in hydro-climatic variables such as rainfall, temperature, and evaporation, few studies have examined the trend in rainfall, wind speed, and their relationship with the trend in streamflow. Furthermore, this research question has not been addressed in the study area. Therefore, this study aimed at analyzing the monthly, seasonal, and annual trends of rainfall, streamflow, and wind speed, as well as the relationships between the trends of rainfall and wind speed and streamflow.

The Mann-Kendall (MK) test was used to determine the trends in rainfall, wind speed, and streamflow at the Klip River catchment. Numerous studies have utilized the MK test to detect trends in hydrological or climatological data such as wind speed, streamflow, and temperature [23, 24]. The MK test has the advantage of being appropriate for both non-monotonic and monotonic trends, as well as being simple and robust enough to deal with values below maximum detection and missing values [10, 25]. In the MK test, both the detection test statistics “S” and normalized test (Z) statistics can be achieved [21]. In Eq. (1), the MK test begins with the estimation of the test statistic, S.

$S=\sum_{i=1}^{N-1} \sum_{j=i+1}^N \operatorname{Sgn}\left(X_j-X_i\right)$    (1)

where, N represents the number of data points and X_i is the actual time for a time series of i = 1, 2, 3… N. Assuming (X_j-X_i) =θ, the value of Sgn (θ) is calculated using Eq. (2).

$\operatorname{Sgn}\left(X_j-X_i\right)=\left\{\begin{array}{cll}1 & \text { if } & \left(X_j-X_i\right)>\theta \\ 0 & \text { if } & \left(X_j-X_i\right)=\theta \\ -1 & \text { if } & \left(X_j-X_i\right)<\theta\end{array}\right.$    (2)

If the data points are greater or equal to 10, the S statistic will follow the normal distribution. Meanwhile, the mean of E(S) = 0 and the variance are calculated using Eq. (3), taking t_k as the ties of the sample time series.

$\operatorname{Var}(S)=\frac{N(N-1)(2 N+5)-\sum_{k=1}^N\quad t_k\left(t_k-1\right)\left(2 t_k+5\right)}{18}$      (3)

Here, the normalized statistics (Z) is estimated using Eq. (4), where Z falls in a normal distribution with a positive Z representing an increasing trend while a negative Z representing a decreasing trend.

$Z=\left\{\begin{array}{lll}\frac{S-1}{\sqrt{\operatorname{Var}(S)}} & \text { if } & S>0 \\ 0 & \text { if } & S=0 \\ \frac{S-1}{\sqrt{\operatorname{Var}(S)}} & \text { if } & S<0\end{array}\right.$    (4)

Sen’s slope estimator

In order to estimate the true slope, Sen used a non-parametric [16]. This method is used to detect the magnitude of the trend and is estimated using Eq. (5). The slope is the real-time slope of the curve in the figure, which can be expressed in the differential form of horizontal and vertical coordinates, which is more accurate.

$T=\frac{X_j-X_k}{j-k}$    (5)

Here, X_j and X_k represents the data values in j and k where j > k. Hence, the slope of each observation is estimated using Eq. (6). Whereas the median is calculated from N observations of the Sen’s Slope using Eq. (7).

$Q=Q_{\frac{N+1}{2}} \quad$ if $N$ is odd    (6)

$Q=\left(\frac{1}{2}\right) Q\left[\frac{N}{2}\right]+Q \quad$ if $N\left[\frac{N+2}{2}\right]$ if $N$ is even   （7）

Here, N which represents slope observations is shown as odd numbers, whereas the Q which represents Sen’s Estimator is calculated as Qmed $=\frac{N+1}{2}$, whereas, the Slope estimate for the even observations is calculated as Qmed $=\left[\left(\frac{N}{2}\right)+\left(\frac{N+2}{2}\right)\right] / 2$. In order to achieve the non-parametric slope test, the two-sided test is achieved at 100(1 – α) % of the confidence interval. Therefore, positive or negative Q_i is achieved as an upward (increasing) or downward (decreasing) trend [21, 26].

The study's objective was to identify and analyse existing relationships between rainfall, wind speed and streamflow trends in the Klip River catchment. The Mann-Kendall statistical test was used to investigate the relationship between monthly, seasonal and annual trends. Results of this study revealed a combination of decreasing and increasing trends in both streamflow and wind speed trend in the majority of months, while rainfall had an equal combination of both increasing and decreasing trends throughout the year. The average annual rainfall significantly decreased by -3.05 mm, streamflow had a minor decrease of -1.39 m³/s, while wind speed significantly increased by 3.68 m/s. On a monthly scale, streamflow decreased by 0.43 m³/s in January, 0.60 m³/s in February, and 0.48 m³/s in March. January rainfall slightly increased by 0.73 mm, while February and March rainfall decreased by 0.83 mm and 2.76 mm, respectively. Wind speed increased across all four seasons, with average wind speeds ranging from 2.06 to 3.05 m/s. On the basis of these results, the study can conclude that rainfall rather than wind speed has a better relationship with streamflow, meaning that each factor may influence the others. These results would be helpful to decision-makers and hydrologists in the planning and management of flooding in the study area. Finally, it is recommended that a study be conducted on the entire local hydrological responses in the Klip River catchment.