Monthly average rainfall data were obtained from 11 rainfall gauge stations provided by the South African weather services (SAWS) for years 1950 to 2017 ( Figure 1 ). The choice of stations was guided by the span of time series and a threshold of 10% maximum missing data for each station ( Stooksbury et al., 1999 ). Missing data were detected in all stations, with the Tygerhoek station missing most data. Above 10% of missing data can have considerable effects on the overall series ( Ahokpossi, 2019 ), especially if they occur early or late in the record ( Kang, 2013 ; Weisent et al., 2014 ). Missing data was replaced using the long-term monthly mean values (see Nsubuga et al., 2014 ). Whereas four station annual series data gaps were completed using medians. Where surrounding stations had normal annual rainfall exceeding 10%, annual series were validated using the normal ratio method, advocated by ( Singh, 1992 ) to overcome the effect of outliers. It was also important to determine the skewness and kurtosis of data series as justified in ( Kişi et al., 2018 ) for the appropriateness of the intended statistical techniques ( Machiwal & Jha, 2012 ).

Frequency analysis in climatology requires that time series be homogenous for in-depth studies of trends over time ( Kisaka et al., 2015 ; Mahmood & Jia, 2016 ). For that matter, a test of randomness using Median Crossing tested for significant differences in mean/medians while a distribution free Cumulative Summation (CUSUM) tested for unknown change in time ( CRCCH, 2005 ). The Median Crossing test revealed that, ten stations satisfied the null hypothesis “that data comes from a random process”, except for Mbulu plantation station, whose test statistic (z) was statistically significant.

A CUSUM analysis showed significant step jumps in the medians of annual rainfall to be positive at Tyghoek and Hendersen, while Hopwell, Mbulu and Manubie had negative step jumps at 0.05. The rest of the stations experienced step jumps which were not statistically significant.

Monthly series were standardized like in ( Nicholson et al., 2018 ) to establish the mean, and the extent of fluctuation in mean rainfall recorded using Coefficient of Variation (CV: see Kumaraswamy et al., 2015 ). The CV is also an index of climatic risk, that gives an insight into a likelihood of fluctuations in reservoir storage or crop yield annually ( Suleiman & Ifabiyi, 2015 ). Rainfall anomaly series were constructed using annual total values for the 11 stations and later transformed into a regional series, here referred to as catchment climatology using a procedure described in ( Nicholson, 1986 ). The validation of the catchment climatology was tested using correlation coefficients. The Henderson and Tygerhoek stations correlated at less than 0.4 to regional climatology. Like in ( Nsubuga et al., 2014 ), the two stations were omitted for the catchment climatology series construction. Other stations reflected strong correlation to the regional climatology.

These monthly and annual rainfall time series were further analyzed using descriptive statistics including finding the minimum, maximum, range, standard deviation, variance, standard error of the mean to provide a preliminary overview of data used for the study.

An interrogation of the series was also done using Rainfall Variability Index (RVI). This index is computed as the standardized rainfall departure to separate the available rainfall time series into different climatic regimes ( Ogunrinde et al., 2019 ). In addition, a Standardized Precipitation Index (SPI) in this study is applied on a normalized time series and calculated on a 3 and 6-month time scale. Definition of the index, its computation and advantages can be followed in ( Mckee et al., 1995 ; WMO, 2012 ; Arkian et al., 2018 ).

To evaluate the varying weight of monthly rainfall to the total amount of rainfall we apply the Precipitation Concentration Index (PCI: see Viola et al., 2006 ). PCI values below 10 indicate a uniform monthly rainfall distribution in the year and values from 11 to 20 denote seasonality in rainfall distribution, whilst values above 20 denote climate with substantial monthly variability in rainfall amounts ( de Luis et al., 2011 ).

Long-term trends in seasons were determined using the Mann-Kendall (MK) test statistic for summer (December-February), spring (September-November), autumn (March-May) and winter (June-August). The MK test is best suited for evaluating changes in hydrological characteristics and meteorological time series ( Gedefaw et al., 2018 ). Its advantages are elaborated in ( Zeleňáková et al., 2018 ). This MK test statistic, Kendall’s (Z) is calculated for annual, monthly, and seasonal rainfall data using the formula below.

The hypothesis, that there is no trend is rejected when the Z value is greater in absolute value than the critical value $Z_{\text{α}}$, at 0.01 and 0.05 level of significance α ( Longobardi & Villani, 2010 ).

$s={\displaystyle {\sum }_{i=1}^{n-1}{\displaystyle {\sum }_{j=i+1}^n\text{sign}\left(y_j-y_i\right)}}$

$Z\left(S\right)=\{\begin{array}{ll}\frac{S-1}{\sqrt{V\left(S\right)}},\hfill & \text{if}S>0\hfill \\ 0,\hfill & \text{if}S=0\hfill \\ \frac{S+1}{\sqrt{V\left(S\right)}},\hfill & \text{if}S<0\hfill \end{array}$

When Z > 0, it indicates an increasing (positive) trend. When Z < 0, it represents a decreasing (negative) trend. To estimate the true slope of an existing trend (as change per year) the Theil-Sen’s nonparametric method is used. The Sen’s method can be used in cases where the trend is assumed to be linear ( Gedefaw et al., 2018 ). This means that $f\left(t\right)$ in the model $x_i=f\left(t_i\right)+{\epsilon }_i$, is equal to $f\left(t\right)=Qt+B$ where Q is the slope and B is a constant (see Kişi et al., 2018 ). The procedure in MAKESENS computes the confidence interval at two different confidence levels: α = 0.01 and α = 0.05. At first, we compute $C_{\alpha }=Z_{1-\alpha /2}\sqrt{\text{VAR}\left(s\right)}$, then $Z_{1-\alpha /2}$ is obtained from the standard normal distribution. Next $M_1=\left(N-C_a\right)/2$ and $M_2=\left(N+C_a\right)/2$ are computed ( Salmi et al., 2002 ). The lower and upper limits of the confidence interval, $Q_{\min }$ and $Q_{\max }$ are the $M_1$^th largest and the $\left(M_2+1\right)$^th largest of the N ordered slope estimates $Q_i$. If M₁ is not a whole number, the lower limit is interpolated. Correspondingly, if M₂ is not a whole number the upper limit is interpolated. To obtain an estimate of B in equation the $n$ values of differences $x_i–Q{t}_i$ are calculated. The median of these values gives an estimate of B ( Drapela & Drapelova, 2011 ). The estimates for the constant B of lines of the 99% and 95% confidence intervals are calculated (see Salmi et al., 2002 ).

Table 1 gives the minimum and maximum values (Q and B) for each 99% and 95% confidence intervals and the residuals (data minus trend) are shown. Nine of the stations exhibited decreasing trends in the annual rainfall and the trends in three of them were statistically significant. It is worth noting that these three stations (Hopwell, Hotfire and Ibhikha) were located far from each other (see Figure 1 ). Overall, rainfall is decreasing at most of the stations ( Table 1 ). There are few incidences at Mbulu and Kei-Bridge stations where rainfall reflects a positive trend which is not significant. Trend for the GKRc is significantly decreasing, with a Z statistic of −2.12 at 95%. This trend with regards to Sen’s slope estimator at stations is at Q = −19.3 mm/year.

For the tested significance levels, the following symbols are used in the table: * if trend at α = 0.05 level of significance; + if trend at α = 0.1 level of significance; If the cell is blank, the significance level is greater than 0.1. Sen’s slope estimate Q: the Sen’s estimator for the true slope of linear trend; B: estimate of the constant B in model above; f (year) = Q*(year − first Year) + B for a linear trend.

Intra rainfall trends

The results of the Mann-Kendall test on monthly rainfall trends for 1950-2017, show a non-significant increase in rainfall for the months of July and August, whilst the rest of the remaining months indicate a decrease in rainfall, with the most significant decrease (a = 0.05) in March and September (see Table 1 ).

Temporal trends for the entire study period show that, three of the seasons are experiencing a decrease in rainfall, especially in autumn where the decrease is significant at (a = 0.1) with a Q = −8 mm per year ( Table 1 ; Figure 2 ). Rainfall, however, increased in winter but not significant at a level greater than a = 0.1. Overall, the seasonality trends also confirm that the Great Kei River catchment has been progressively receiving less rainfall since 1950, especially in the autumn. Therefore, this should be put into consideration for agricultural planning and drought management.

Analysis revealed that total annual rainfall during the entire study period varied between 4988 mm to 11,574 mm (mean = 7641 ± 168 mm). Also see the distribution of annual rainfall at each station in Figure 1 . The GKRc experiences a coefficient of variation (CV) of 18% indicating a less to moderate consistency of rainfall (results not shown). The higher the CV, the more variable the year-to-year rainfall of a locality is ( Schulze, 2007 ). To attain a deeper understanding of long-term distribution for seasonal and temporal rainfall variability a PCI is computed for each station.

Temporal variability in rainfall distribution at all stations had a PCI greater than 10 to +40%, suggesting a moderate to high concentrations in the distribution of rainfall (Figure not included). A higher PCI value also indicates that rainfall is more concentrated to a few rain years during the study period and vice versa ( Zhao et al., 2011 ). Higher values for temporal concentration can be a result of seasonal concentration or a random deviation from the long-term mean ( Nsubuga et al., 2014 ). This is evident at some stations (Kei-Bridge, Manubie, Mbulu, Keilands, which showed a PCI above 25%, after the 20^th year.

Rainfall experienced in the catchment is not evenly spread out throughout the year but concentrated in certain seasons, particularly in spring and summer. Evidence of variability is demonstrated for the catchment area during 1950-2017 using RVI, (see Figure 3 ). The period 1950-1960 exhibits successive dry and wet periods, while the late years were either dry or very dry ( Figure 3 ). Summarily, very wet years were 8.6%, very dry and dry periods were 34.3% and 22.8% respectively; while 34.3% were years that received normal rainfall.

A closer observation reveals a 20-year cycle, which raises interest in knowing which 20-year climatic age was wetter or drier than the other. Analysis reveals that, the years 1970-1990 were wet, while the 1990-2010 had more dry periods.

Analysis of annual total rainfall shows that 46% of the years received rain above the mean and 54% were below the mean for the catchment. It is also evident that rainfall for the catchment during 1968, 1980, 1982, 1992, was extremely very low, which was also revealed by the SPI analysis (see Figure 4 ).

To quantify the changes in seasonal rainfall at each station for the period 1950-2017, analysis for summer (Dec.-Feb.), winter (Jun.-Aug.), spring (Sep.-Nov.), autumn (Mar.-May) is derived and plotted as anomalies. Analysis shows that 36.6% of the rainfall fell in summer, 29.3% in spring, 23.4% in autumn and 10.7% in winter seasons during the study period. It indicates that the mean rainfall of the wet season (summer and spring) was twice to that of the dry season. There was desiccation of the winter rains of 1985-1995 and autumn rains of 1990-1995. The SON season has shown the highest variability associated with below average rainfall during the late 1960’s and early 1970’s. A progressive decrease in rainfall is evident especially in the autumn season.

This study establishes that rainfall during January-February contributed 25%, whilst June contributed the lowest at 2.2% to the total annual rainfall received for the catchment (Figure not shown). The ENSO effect as well as the Madden-Julian Oscillation (MJO) have a noticeable impact on the intra-annual rainfall variability along with other factors (see Fauchereau et al., 2003 ; Mackellar et al., 2014 ; Mahlalela et al., 2020 ).

A closer look into the monthly rainfall anomalies gives further insight into the distribution of rainfall. Monthly rainfall series reveal December as the month with the most above normal rainfall in the catchment. For all months, the frequency of above mean rainfall reduces from the year 2000 in the entire study period.

As observed by ( Nsubuga et al., 2014 ) areas with coefficients > 20% are also likely to have more frequent and severe droughts. Stations like Tygerhoek, Ibhikha and Mbulu had a coefficient above 20%, which necessitated an investigation about the potential occurrence of droughts in the catchment, which can affect reservoir storage and crop yield. Droughts are apparent after a long period with a shortage or without any rainfall ( Guenang & Kamga, 2014 ). To give a better representation of abnormal wetness and dryness an SPI is used. In this work, SPI is used to quantify rainfall deficits on seasonal time scales, i.e. SPI time scale of 3 and 6 months’ is shown in Figure 5 and Figure 6 .

Figure 5 shows some consistency in SPI values between seasons in 1960-1980 and 1985-1995. Spring and summer show more years of positive SPI, while winter and autumn have more years of negative SPI for the period of analysis. In the last five years of the study period, all seasons tend towards negative SPI. The winters have experienced severe to extreme drought between 1987 and 1991 in the catchment and these droughts are still consistent with a few interruptions of wetness every ten years. Droughts are apparent, specifically in summer, which is the main rainfall season for the catchment, ( Figure 5(B) ).

For water resources management and agriculture, World Meteorological Authority (WMO) recommends a longer time scale e.g., 6 months for effective indication of rainfall over distinct seasons. For example, a 6-month SPI at the end of February would give a very good indication of the amount of rainfall that has fallen during the wet season from December through February for South Africa ( Figure 6(C) ). The same SPI can inform about stream flows and reservoir levels for the region in a particular year, which is vital for water management. Figure 6

shows the time series of SPI-6 for the catchment. The catchment recorded a classified type of drought at one or more times in the 50s, 60s, 80s, 90s and 2010s. Droughts were mild in 1968 and 2016; moderate in 1952, 1955, 1966-7, 1972, 1980, 1985, 1990-93, 2001, and 2017; severe in 1981-82, and 2015 ( Figure 6 ) based on ( Mckee et al., 1995 ) drought categorization.