Investigating the influences of climate change on drought in a small data-scarce river catchment

Drought is an environmental disaster that causes severe and long-lasting socio-economic impacts on human systems. The impacts encompass poor crop yield and lack of water availability (Liu et al. 2020). The former is caused by agricultural drought, which begins when soil moisture available to plants drops to a level that adversely affects crop yield (Das et al. 2020; Wambura & Dietrich 2020), whereas the latter is caused by hydrological drought. Hydrological drought occurs when stream flows, reservoirs, groundwater recharge, and lake levels are affected due to a decrease in precipitation (Zhang et al. 2019). Thus, both agricultural and hydrological droughts are caused by meteorological drought, a decrease in precipitation below the normal amount for a prolonged period (Oguntunde et al. 2020; Pei et al. 2020).

Understanding the changes in meteorological drought is crucial for the development of adaptations to climate change (Sharafati et al. 2020). This is because climate change intensifies drought by influencing evaporation and rainfall. Several studies have analyzed droughts in the East Africa region (Viste et al. 2013; Hassan et al. 2014; Bayissa et al. 2015, 2018; Peter et al. 2018; Wambura 2020b; Wambura & Dietrich 2020), however, little is known about the influences of climate change on drought events in small river catchments (<10,000 km²), partly due to a lack of high-resolution climate projections. Even the recent general circulation models (GCMs) from the Coupled Model Intercomparison Project phase five (CMIP5) also have low resolutions of about 1°–4° (approximately 110–440 km). These low-resolution GCMs cannot resolve small-scale processes influenced by land-surface heterogeneities (Osima et al. 2018). Thus, downscaled projections from regional climate models (RCMs) may add value to the processes in small river catchments (Giorgi 2019). To increase applications of high-resolution climate projections in studies of regional climate events, the World Climate Research Programme developed RCMs within the Coordinated Regional Downscaling Experiment for the Africa (CORDEX-Africa) framework (Nikulin et al. 2018).

Studies have shown that the CORDEX-Africa RCMs can simulate present-day African climatology (Osima et al. 2018). They also capture the effects of the Indian Ocean Dipole and El Niño-Southern Oscillation, the drivers of a large percentage of the interannual rainfall variability in the East African region (Endris et al. 2013; Endris et al. 2019). The most widely used RCMs of the CORDEX-Africa simulations have a spatial resolution of 0.44° (CORDEX-AFR44, Osima et al. 2018; Oguntunde et al. 2020). However, RCMs of the CORDEX-Africa simulations with a spatial resolution of 0.22° (CORDEX-AFR22, Remedio et al. 2019) are currently being produced. RCMs of both the CORDEX-AFR44 and CORDEX-AFR22 simulations dynamically downscale projections of various representative concentration pathways (RCPs) of CMIP5-GCMs. Due to its fine resolution, RCMs of the CORDEX-AFR22 simulations can be more useful for climate projections in small river catchments.

Although studies have been directly using climate models in assessing the impacts of climate change (Charles et al. 2020; Homsi et al. 2020; Hosseinzadehtalaei et al. 2020), there is a need for evaluations of climate model simulations against historical climate records before their applications. This is because different climate models may lead either to model selection uncertainty if an arbitrary model is selected or to the wrong skewness of projections if models are not properly sifted. Usually, evaluations of climate models before their applications have been hindered by a lack of reliable observed records, especially in sub-Saharan Africa (Wambura 2020a). However, the recently available gridded observational datasets at the spatial resolution of 0.5° from the Climatic Research Unit (CRU) of the University of East Anglia have been widely used in filling gaps and even replacing unreliable observed data in different parts of the world (Harris et al. 2014; Mutti et al. 2020).

Since the future climate is not simply a continuation of the past climate, evaluations of climate model simulations against historical climate records do not guarantee future projections of individual climate models. Thus, a multimodel ensemble is the only way of obtaining reliable future projections. The multimodel ensemble aggregates individual projections to make a combined projection, leveraging the strengths and diversity of the constituent models. In the East African region, Endris et al. (2013) found that the ensemble mean of the CORDEX-Africa RCMs outperforms the individual models in representing rainfall.

Therefore, this study aimed to investigate the influences of climate change on meteorological drought using the ensemble of RCMs of the CORDEX-AFR22 simulations and gridded observations from the CRU datasets in a small data-scarce river catchment. In this respect, the study responded to the following questions: (i) What is the uncertainty of selecting RCM simulations? (ii) What is the skill of an RCM in simulating the historical climate in a small catchment? (iii) How good is an ensemble simulation from RCMs? (iv) What is the direction and magnitude of climate change? (v) What is the trend of drought characteristics under changing climate?

The following is the layout of the rest of the paper. Section 2 locates the study area, and describes data, pre-processes and methods. The methods involve exploring the uncertainty of climate models, testing the skills of the models, generating ensemble simulations and projecting climate change, and estimating drought characteristics under changing climate. Section 3 presents results and discussions in a sequence similar to the aforementioned methods. Finally, Section 4 concludes the findings and offers an outlook on future studies.

The rainfall regime in the catchment is unimodal with a single rainy season from November to April (Hyandye et al. 2018). The rainfall pattern is irregular, highly localized, spatially varied, and strongly correlated with altitude (Kashaigili et al. 2006). The highlands receive an average rainfall of about 1,600 mm/year, while the lowlands receive around 600 mm/year (Shu & Villholth 2012; Hyandye et al. 2018). The mean annual temperature varies from about 18 °C at high altitudes to about 22 °C in the lowlands (ibid.).

The land-surface data used in this study was a 90 m digital elevation model downloaded from the Shuttle Radar Topography Mission database (Jarvis et al. 2008). The elevation model was used for mapping the terrain of the catchment (Figure 1(c)).

The main data used in this study include historical and projected climate datasets. Due to data scarcity in the Ndembera River catchment, the gridded historical observations from the CRU TS v. 4.06 were preferred. These are time series of monthly precipitation and monthly average daily temperatures of the fourth version of the CRU datasets (Harris et al. 2020). For this study, historical monthly precipitation data and minimum and maximum air temperature data from the CRU datasets between the years 1971 and 2000 in NetCDF format were downloaded from the database of the National Center for Atmospheric Science (https://crudata.uea.ac.uk/cru/data/hrg/, last accessed on 18 January 2023).

The projected climate dataset was made up of six RCM simulations (only available at the time of analysis) from two RCMs of the CORDEX-AFR22 simulations each driven by three CMIP5-GCMs for the RCPs with 2100 radiative forcing of 2.6 and 8.5 W/m² (RCP 2.6 and RCP 8.5). The RCP 2.6 and RCP 8.5 scenarios were selected because they represent low-end and high-end climate change scenarios, respectively (Harrison et al. 2019). However, only these two scenarios have been produced by the CORDEX AFR-22 so far. The span of the projected climate dataset (1971–2098) from RCMs of the CORDEX AFR-22 simulations included the baseline data (1971–2000) and the scenario data (2010–2098) (Remedio et al. 2019). The baseline period spanned between 1971 and 2000 because CORDEX simulations are available only from 1950 and the global warming signal in the region is successfully captured using 1971–2000 as the baseline period (Osima et al. 2018).

In this study, RCMs driven by GCMs were coded using the first letter of the RCM name and the first two letters of the name of the driving GCM (Table 1). The projected monthly precipitation data and minimum and maximum air temperature data from six RCMs for both the baseline and scenario periods in NetCDF format were downloaded from the Earth System Grid Federation database (https://esgf-data.dkrz.de/, last accessed on 18 May 2022).

In exploring the uncertainty of RCMs, the quantiles of the baseline precipitation and baseline temperatures were compared with those of historical precipitation and historical temperatures in the catchment, respectively, using the Box and Whiskers plots (Han et al. 2012). The Box and Whiskers plots were selected because they are useful in showing the skewness and distribution of data using quantiles which are not affected by outliers. The Box plot represents the middle 50% of data, which lies between the 25th and 75th percentiles. The 50th percentile of data is the median. The Whiskers represent data outside the middle 50%, these data lie between the lower extreme value and 25th percentile, and between the 75th percentile and upper extreme value. The lower extreme and upper extreme values referred to here are not absolute minimum and absolute maximum, but rather deviations of 1.5 times the interquartile range from the 25th and 75th percentiles, respectively.

After exploring the uncertainty of RCMs, baseline precipitation data and baseline temperature data (i.e., minimum and maximum) from RCMs were evaluated against corresponding historical climate data in the catchment. The evaluation measured the skills of RCMs in reproducing historical climate so that the skilled RCMs could be trusted to project a realistic future. The skills were measured using the skill score (SK) method (Perkins et al. 2007). SK is the cumulative minimum value of two probability density functions (PDFs) at each binned value. It measures the common area between two PDFs. The SK method was preferred because it compares two time series across their entire probability distributions (Wambura et al. 2015).

If the baseline simulation from an RCM describes the historical climate perfectly, SK will equal one. The poor performance of the RCM has SK close to zero, with negligible overlap between PDFs. In this study, an RCM was selected if at least one of its parameters, that is, precipitation, minimum or maximum temperature, has SK greater or equal to 75% (Wambura et al. 2015). The SK method was implemented in the Python programming environment (source codes are freely available upon request).

For generating ensembles of simulations from RCMs, a regression model was preferred. This is because unlike averages (Rhee & Cho 2016), regression models developed from historical data can adjust systematic errors in projected climate simulations. In this study, the regression models selected were the gradient boosting regressor (GBR), extreme gradient boosting regressor (XGBR), and random forest regressor (RFR). These regressors were selected because of their ability to define nonlinear associations existing between dependent and independent variables, even when a linear relationship is significant (Homsi et al. 2020). They are robust supervised learning algorithms that use many decision trees for regression (Geurts et al. 2006). The GBR sequentially builds an ensemble of decision trees, in which each new tree is trained to correct errors of the previous trees (Guillen et al. 2023). The predictions of the individual trees are combined in an additive manner, gradually improving the model's accuracy. The XGBR is an advanced implementation of the gradient boosting algorithm that uses tree pruning, regularization, and parallelization techniques to improve performance (Sibindi et al. 2023). The RFR builds an ensemble of multiple independent decision trees, each of which is fitted on a random sample of the training data and uses an averaging approach to improve the accuracy of prediction and control over-fitting (Breiman 2001). In this study, the GBR, XGBR, and RFR were implemented using the Python modules called sklearn.ensemble.GradientBoostingRegressor, xgboost.XGBRegressor, and sklearn.ensemble.RandomForestRegressor, respectively (Pedregosa et al. 2011).

Before modelling, historical precipitation data and historical temperature data (i.e., minimum and maximum) and their corresponding baseline simulations from RCMs in the catchment were split into the random training (60%) and testing (40%) subsets using the Python module called sklearn.model_selection.train_test_split (Pedregosa et al. 2011). In the regression models, historical data were dependent variables, whereas baseline simulations were independent variables. The model performances were evaluated using a coefficient of determination (R²) between ensembles of baseline simulations and historical data for both training and testing subsets. The differences between R² of the training subset and R² of testing subsets (R²diff) were also evaluated. The R² was selected because it is more informative than many evaluation criteria in regression analysis (Chicco et al. 2021).

The thresholds for a satisfactory performance were R² greater than or equal to 65% and R²diff less than 10%. The R² greater than or equal to 65% was intended to overcome the underfitting that arises when a model fails to capture important patterns in the data and performs poorly on both the training and testing data (Moriasi et al. 2007; Ritter & Muñoz-Carpena 2013; Kirasich et al. 2018). Whereas the R²diff less than 10% was intended to reduce overfitting that arises when a model performs very well on the training data but poorly on the testing data (Zhu 2020). These two criteria controlled the trade-off between accuracy and generalization. Moreover, the mean absolute error (MAE) was also used to measure how close the ensembles of baseline simulations are to the historical data (Dieng et al. 2022). It quantified the average of the absolute errors between ensembles of baseline simulations and the historical data.

To reduce underfitting and overfitting, the RFRs were automatically tuned to optimize tree heights (max_depth), the number of branches (min_samples_split), and leaves (min_samples_leaf) on 1,000 trees so that they produce the highest R² greater than or equal to 65% and the lowest R²diff less than 10%. To simplify the comparison and interpretation of the performances of the three models, the optimal hyperparameters from the RFRs were also fitted in the GBRs and XGBRs, and subsequently evaluations were conducted on both training and testing subsets. The best-fitted regression models were used to predict ensembles of simulations from RCMs between the years 1971 and 2098.

Apart from ensembles of RCMs, conditional distributions of the response variables were also used to calculate the 95% prediction uncertainty (95PPU, Meinshausen 2006; Zhao et al. 2018). The 95PPU was given by 2.5th and 97.5th percentiles of a full conditional distribution of a response variable. The 95PPUs represent the dry and wet biases of RCM precipitation and the cold and warm biases of RCM temperatures. The 95PPU was preferred because it accounts for the uncertainty associated with inputs, hyperparameters, statistical model structure, and inherent variability of predicted values.

The precipitation and temperature change projections in the catchment from ensembles and biases of RCMs were measured with respect to the baseline period (1971–2000). The projected climatological periods of approximately 30 years between the years 2010 and 2098 were categorized as near-future (2010–2039), mid-future (2040–2069), and far-future (2070–2098) (Schaeffer et al. 2015; Hyandye et al. 2018). The transition period (i.e., 2001–2009) between the baseline and near-future was not considered in climate change projections. The significance of a change between the time series of the baseline and projected periods was tested using the Wilcoxon signed-rank tests (Wilcoxon 1945; Im et al. 2020). In this test, a p-value less than or equal to 5% was used to reject the null hypothesis stating that there is no significant change between the baseline and projected periods. This statistical test was performed using the Python module called scipy.stats.wilcoxon (Virtanen et al. 2020).

The estimation of drought characteristics was preceded by the calculation of drought indices, which also depended on potential evapotranspiration. So, firstly, the minimum and maximum temperatures of the ensembles and biases of RCMs for the entire period between 1971 and 2098 were used to compute potential evapotranspiration using the Hargreaves (Hg) equation because it has limited meteorological data requirements (Hargreaves & Samani 1985; Hargreaves & Allen 2003). Although the Thornthwaite equation also has limited meteorological data requirements, studies have indicated that it overestimates potential evapotranspiration in tropical regions (van der Schrier et al. 2011). On the other hand, the Penman–Monteith equation requires extensive meteorological data, although its monthly and annual potential evapotranspiration estimates are very similar to those of the Hg equation (Droogers & Allen 2002).

Then, drought indices were calculated using the standardized precipitation evapotranspiration index (SPEI) method (Beguería et al. 2014). The SPEI method was applied to the estimated potential evapotranspiration and precipitation of the ensembles and biases of RCMs for the entire period between 1971 and 2098. The SPEI method was preferred because precipitation and evapotranspiration are the largest water fluxes in catchments (Meresa et al. 2016; Wambura et al. 2017; Wambura & Dietrich 2020). In this study, SPEIs were computed at a 12-month time scale. The 12-month time scale was selected because it reflects the long-term precipitation patterns, thus, is more suitable for depicting various precipitation regimes than shorter time scales (McKee et al. 1993; WMO 2012; Spinoni et al. 2014; Pramudya & Onishi 2018; Adarsh & Reddy 2019). More details about the SPEI procedure are found in the study by Vicente-Serrano et al. (2010) and Beguería et al. (2014). In this study, both the Hg equation and SPEI algorithm were implemented using an R-programming library called SPEI (Beguería et al. 2014).

The estimation of drought characteristics was limited to the ensemble of drought indices because the upper boundary of drought indices (from warm and wet biases of RCMs) produced some undefined values. This problem of the SPEI method not producing definitive solutions for certain values in some data has been previously associated with arid areas, high altitudes, high latitudes and long periods of no precipitation (Wu et al. 2007; Beguería et al. 2014). However, due to the limited scope of this study, the problem was not explored further. Therefore, the estimation of drought characteristics from the ensemble of drought indices involved the identification of drought events followed by the computation of an average annual drought frequency (AADF), an average annual drought duration (AADD), an average annual drought severity (AADS), and an average annual drought intensity (AADI) over a climatological period, i.e., near-future, mid-future and far-future. A drought event was considered to start when SPEI equalled −1 and negative values continued for at least two months and stop when SPEI equalled 0 (Spinoni et al. 2014). AADF is the average number of drought events per year in a climatological period. AADD is the average number of months per year from all drought events identified in a climatological period. AADS is the sum of SPEI values per year from all drought events in a climatological period. AADI is the ratio of ADDS to AADD, measured in 1 per month. Similar to the classifications of standard precipitation index (McKee et al. 1993) and SPEI (Li et al. 2014, 2015), AADI values were divided into five categories, namely, no drought (AADI = 0.00), mild drought (−0.01 ≥ AADI ≥ −0.99), moderate drought (−1.00 ≥ AADI ≥ −1.49), severe drought (−1.50 ≥ AADI ≥ −1.99), and extreme drought (−2.00 ≥ AADI) (Wambura & Dietrich 2020). AADI is the most informative drought characteristic because it depends on all other drought characteristics. Methods for drought characterization under climate change were implemented in the Python programming environment (source codes are freely available upon request).

The influences of climate change on drought were evaluated by comparing changes in precipitation as well as minimum and maximum temperature against changes in drought characteristics. Changes in drought characteristics involved an increase or a decrease in future AADF, AADD, AADS, and AADI calculated from their baseline values. Both climatological and drought changes were assessed in terms of their directions and magnitudes.

The RCMs simulate the distribution of the historical precipitation reasonably well (Figure 3(a)). The distributions of both RCM baseline and historical precipitation in the catchment were skewed to high values. Exception for the baseline precipitation of C-MO and C-MP simulations, upper extreme values of the baseline precipitation of the remaining RCMs were relatively similar to that of historical precipitation (Figure 3(a)). Figure 3(a) also shows that the middle 50% of the baseline precipitation from C-MO and C-MP simulations were larger, but the rest of the RCMs had relatively similar middle 50% to that of the historical precipitation. The median values of the baseline precipitation from C-MO and R-NC simulations were more or less similar to that of historical precipitation, although in general, all RCMs showed that precipitation data were tightly clustered around low values (Figure 3(a)).

The distributions of the RCM baseline and historical maximum temperature in the catchment did not match (Figures 3(b)). The distributions of the baseline maximum temperature from C-MO, C-MP, and C-NC simulations were largely below that of the historical maximum temperature, while from R-MO, R-MP, and R-NC simulations were slightly above. Figure 3(b) shows that upper extreme values of the baseline maximum temperature from R-MO, R-MP, C-NC, and R-NC simulations were greater than that of the historical maximum temperature in the catchment. On the other hand, C-MO, C-MP, and C-NC simulations underestimated the lower extreme value of historical maximum temperature. Except for C-MP simulation, the middle 50% of the baseline maximum temperature from the rest of the RCMs were larger than that of the historical maximum temperature in the catchment (Figure 3(b)). Despite the difference in the middle 50%, the median value of the baseline maximum temperature from R-MO simulation was more or less similar to that of the historical maximum temperature. The median values of the baseline maximum temperature from the remaining RCMs were quite different from each other and from that of the historical maximum temperature.

Figure 3(c) shows that the distributions of the RCM baseline and historical minimum temperature in the catchment had some similarities. Data in the distributions were clustered around high values of the minimum temperature. The upper extreme values of the baseline minimum temperature from RCMs were relatively similar to that of the historical minimum temperature. But the lower extreme values of the baseline minimum temperature from C-MO, C-MP, and C-NC simulations were lower than those of the historical minimum temperature and other remaining RCMs. The middle 50% of the baseline minimum temperature from C-MO, C-MP, and C-NC simulations were larger than that of the historical minimum temperature in the catchment (Figure 3(b)). Likewise, the middle 50% of the baseline maximum temperature from R-MO, R-MP, and R-NC simulations were smaller than that of the historical minimum temperature. As for the medians, R-MO, R-MP, and R-NC simulations had values more or less similar to that of the historical minimum temperature, whereas the remaining RCMs underestimated the median.

In general, the CCLM5-0-15-based RCMs slightly overestimated the historical precipitation while substantially underestimating the historical maximum and minimum temperatures (Table 1, Figure 3). On the other hand, the distributions of the REMO2015-based RCMs are relatively close to historical precipitation and historical temperatures. These uncertainties confirmed the need for an ensemble approach that corrects systematic errors in RCM simulations. The following section presents the skills of the RCMs included in the ensemble.

Figures 4(a)–4(f) show that the baseline precipitation from RCMs reasonably reproduced the historical precipitation in the catchment. The performances of RCMs were satisfactory (SK ≥ 75%), although R-MO, R-MP, and R-NC simulations had higher SKs than C-MO, C-MP, and C-NC simulations. The shapes of the PDFs also show that C-MO, C-MP, and C-NC simulations overestimated the probability of low precipitation in the catchment (Figure 4(a), 4(c), 4(e)). Discrepancies between PDFs of the baseline precipitation from these RCMs and that of historical precipitation in this catchment were discernible between 50 and 230 mm of precipitation per month. This means that these RCMs have more events of low precipitation than historical precipitation. Sun et al. (2006), Perkins et al. (2007), and Olsson et al. (2015) also found that most climate models tend to overestimate the frequency of light precipitation or ‘drizzle’.

The baseline maximum temperature from RCMs poorly reproduced the historical maximum temperature in the catchment (Figure 4(g)–4(l)). However, the RCMs captured the shape of the historical minimum temperature although there was a tendency towards a horizontal shift in the PDFs. The shapes of the PDFs show that C-MO, C-MP, and C-NC simulations underestimated the probability of middle values (24.1–26.2 °C) of the historical maximum temperature in the catchment to the extent that their SKs were far below the satisfactory value (Figure 4(g), 4(i), 4(k)). The R-MO, R-MP, and R-NC simulations had relatively small underestimations of the probability of middle values of the historical maximum temperature in the catchment, which is why their performances were satisfactory (Figure 4(h), 4(j), 4(l)).

The PDFs of the baseline minimum temperature from all RCMs simulate that of the historical minimum temperature in the catchment reasonably well (Figure 4(m)–4(r)). However, the performances of C-MO, C-MP, C-NC, and R-NC simulations were satisfactory, but those of the remaining RCMs were not. The relatively low performances of R-MP and R-MO simulations were caused by their overestimation of the probability of high values of the historical minimum temperature in the catchment (Figure 4(n), 4(p)).

Although studies assert that RCM temperature is usually very stable as compared to RCM precipitation (Olsson et al. 2015; Bayissa et al. 2021; Mwabumba et al. 2022), this study found that in this catchment the former (especially its maximum values) was less stable than the latter. This might be attributed to the inability of RCMs to capture the irregular and spatially localized climate regime in this region (Kashaigili et al. 2006). The SK tests revealed that the REMO2015-based RCMs performed reasonably well in reproducing the historical precipitation, historical maximum and minimum temperatures in the catchment (cf. Figure 4(a)–4(l)). The CCLM5-0-15-based RCMs also performed reasonably well in reproducing the historical precipitation and historical minimum temperature, but poorly in reproducing the historical maximum temperature in the catchment. The poor performances of RCMs could be attributed to errors in the historical climate data (Odon et al. 2019) or failure of RCMs to reproduce the historical climate or both. In general, all RCMs had at least two satisfactory performances in reproducing the historical climate in the catchment. Therefore, all six RCMs were considered in the computation of ensembles of simulations.

Apart from the GBR, XGBR, and RFR ensembles of the baseline maximum temperature for testing subsets, the GBR, XGBR and RFR ensembles of the baseline precipitation and baseline minimum temperature had satisfactory performances (R² ≥ 65%) for both training and testing subsets. However, the R²diffs of the GBR ensembles of the baseline precipitation, baseline maximum temperature, and baseline minimum temperature were 14, 41, and 5%, respectively. Likewise, the R²diffs of the XGBR ensembles of the baseline precipitation, baseline maximum temperature, and baseline minimum temperature were 25, 47, and 10%, respectively. This means that the GBR and XGBR ensembles highly overfitted precipitation and maximum temperature data during training (R²diff ≥10%). In contrast, the R²diffs of the RFR ensembles of the baseline precipitation, baseline maximum temperature, and baseline minimum temperature were less than 10% (Figure 5). This shows that the RFR ensembles generalized the whole datasets of precipitation, maximum and minimum temperatures. Thus, only the results of the RFR ensembles are further presented and discussed.

The RFR ensembles of the baseline precipitation from RCMs show satisfactory performances for both training and testing subsets in reproducing historical precipitation in the catchment (R² > 65%, Figure 5(a)). However, during training, the RFR ensembles failed to capture some high values of historical precipitation, especially above 190 mm per month. And during both training and testing, the ensembles overestimated values below 40 mm per month in the catchment. On average, the RFR ensembles of the baseline precipitation were off by 31 and 25 mm per month from the historical data during training and testing, respectively (Figure 5(a))

The RFR ensembles of the baseline maximum temperature from RCMs show good performances for both training and testing subsets in reproducing the historical maximum temperature in the catchment (Figure 5(b)). However, the performance for the testing subset was 1% away from becoming satisfactory. This minor loss of performance for the testing subset could not be underfitting of the random forest model because the hyperparameters were exhaustively tuned. Rather, it could be errors in the baseline and/or historical maximum temperature data.

The RFR ensembles of the baseline minimum temperature from RCMs shows satisfactory performances for both training and testing subsets in reproducing historical minimum temperature in the catchment (R² > 65%, Figure 5(c)). However, the RFR ensembles of the baseline minimum temperature also failed to capture some low and high values (<10 and > 15 °C, respectively) of historical minimum temperature for both training and testing subsets. Likewise, the RFR ensembles of maximum and minimum temperatures have an average error of 1 °C during both training and testing (Figure 5(b) and 5(c)).

The RFR ensembles of the baseline precipitation, baseline maximum temperature, and baseline minimum temperature generally had reasonably good training and testing performances. So, they were then used to project ensembles and biases of changes in precipitation, maximum, and minimum temperatures in the catchment.

Figure 6(a) shows that under the RCP 2.6 scenario, the ensemble of RCMs projects a significant 4% decrease in the average annual precipitation in the catchment during the near-future and mid-future. However, during the far-future, the average annual precipitation is projected to insignificantly decrease (p-value = 0.09) by 3%. Under the RCP 8.5 scenario, the ensemble of RCMs projects an insignificant 2% decrease (p-value = 0.24) in the average annual precipitation in the catchment during the near-future and a significant 4% decrease during the mid-future and far-future. The uncertainty intervals show that under both scenarios, the dry bias of RCMs projects a very huge decrease in the average annual precipitation, especially during the mid-future and far-future (Figure 6(a)). But the wet bias of RCMs projects a relatively small decrease in the average annual precipitation only during the near-future and under the RCP 2.6 scenario.

Under the RCP 2.6 scenario, the ensemble, cold and warm biases of RCMs project significant increases in the mean annual maximum temperature in the catchment ranging from 0.3 to 0.5 °C, with the peaks expected to be reached during the mid-future (Figure 6(b)). In contrast, under the RCP 8.5 scenario, the ensemble, cold and warm biases of RCMs project a significant 0.4 °C increase in the mean annual maximum temperature during the near-future. That increase in the mean annual maximum temperature is also projected to relatively double and quadruple during the mid-future and far-future, respectively (Figure 6(b)).

Figure 6(c) shows that under the RCP 2.6 scenario, the ensemble, the cold and warm biases of RCMs also project significant increases in the mean annual minimum temperature, with peaks expected to be reached during the mid-future. Whereas, under the RCP 8.5 scenario, the ensemble, cold and warm biases of RCMs project consistent increases in the mean annual minimum temperature throughout the century without reversals at a 5% level of significance (Figure 6(c)).

In essence, both scenarios show that changes in the average annual precipitation of the dry bias of RCMs are very large and those of the wet bias of RCMs are mostly insignificant. Changes in the mean annual maximum and minimum temperatures of the cold and warm biases of RCMs are reasonable and more or less similar to those of the ensembles. Under the RCP 2.6 scenario, the ensemble of RCMs showed that between the near-future and far-future, the decrease in the average annual precipitation is projected to lessen until it becomes insignificant. Meanwhile, the mean annual maximum and minimum temperatures are projected to rise to their peaks by mid-century but drop to values slightly above the baseline values by the end-century. This rise-peak-drop of temperatures corresponds to the radiative forcing level of the RCP 2.6 scenario, which is projected to rise to 3.1 W/m² by mid-century but drops to 2.6 W/m² by the end-century (Hausfather & Peters 2020). Besides, RCP 2.6 is the likely optimistic scenario because the current policies push for the reduction of carbon dioxide, methane, and sulphur dioxide emissions to keep global warming below 2 °C relative to pre-industrial temperatures by the end of the century (Osima et al. 2018). Under the RCP 8.5 scenario, the ensemble of RCMs projects a non-monotonically decreasing trend of the average annual precipitation from the near-future to far-future. The ensemble also projects monotonically increasing trends of the mean annual maximum and minimum temperatures in the catchment during the same periods. This is the unlikely worst-case scenario because it implies that the existing climate change policies and mitigation measures will be halted or reversed (Hausfather & Peters 2020). However, the reality of future climate will depend on the current measures implemented to combat global climate change.

In the same catchment, Hyandye et al. (2018) used global CMIP5-GCMs under the RCP 8.5 scenario and found that the average annual precipitation and mean annual temperature are expected to increase by 0.4% and 1.1 °C, respectively, during the near-future. These differences in the direction of precipitation change and magnitudes of temperatures between this study and the one by Hyandye et al. (2018) could be caused by disparities in the resolutions as well as the types of climate models used. However, Hyandye et al. (2018)’s climate change projections in the catchment were not tested for their statistical significance. Since RCMs from the CORDEX-Africa framework are recent and of higher resolutions than global CMIP5-GCMs, the findings of this study might be more reliable.

Figure 7(a) shows that some dry episodes (negative peaks of ensemble drought indices) during the baseline period in the catchment were not drought events because their durations did not reach two consecutive months. Likewise, for RCP 2.6 and RCP 8.5 scenarios, some dry periods during the near-future, mid-future, and far-future are not expected to be drought events because of their short durations (Figure 7(b)–7(g)). Between the baseline period and the near-future RCP 2.6 scenario projects the same number of drought events in the catchment (cf. Figure 7(a), 7(b), Table 2). But, between the near-future and far-future RCP 2.6 scenario projects a drop in AADF in the catchment from 0.43 to 0.27 drought events and then a rise to 0.34 events (Figure 7(b), 7(d), 7(f); Table 2). This is the drop-valley-rise of drought events for the likely optimistic scenario between the near-future and far-future. On the other hand, between the baseline and near-future RCP 8.5 scenario projects a decrease in the number of drought events in the catchment (cf. Figure 7(a), 7(c), Table 2), whereas between the near-future and far-future, the RCP 8.5 scenario projects an increase in AADF in the catchment from 0.23 to 0.41 drought events through 0.33 events (Figure 7(c), 7(e), 7(g); Table 2). This is a monotonic increase in drought events for the unlikely worst-case scenario between the near-future and far-future.

For drought durations in the catchment, the RCP 2.6 scenario projects a slight increase in AADD from 3.6 months during the baseline period to 3.7 months during the near-future (Table 2). But like AADF, between the near-future and the far-future AADD is also projected to exhibit a drop-valley-rise of months of drought per year in the catchment. In contrast, the RCP 8.5 scenario is projected to exhibit a drop of AADD between the baseline period and the near-future (Table 2). Then, AADD is projected to have a monotonic increasing trend in the catchment as the climatological period shifts from the near-future to the far-future.

In terms of drought severity, the RCP 2.6 scenario projects an increase in AADS (increasing negative values) between the baseline period and the near-future in the catchment (Table 2). Then, like AADF and AADD, from the near-future towards the far-future, the RCP 2.6 scenario projects a drop-valley-rise of AADS in the catchment. For the RCP 8.5 scenario, the pattern of AADS from the baseline period to the far-future is similar to those of AADF and AADD (Table 2). A monotonic increase in AADS in the catchment is projected between the near-future and far-future. The AADS values represent the cumulative severity within a year. The following discusses drought severity per month of a drought event, that is, AADI.

During the baseline period, drought intensity in the catchment was moderate (Table 2). By using evapotranspiration data in the assessment of agricultural drought in the Kilombero basin in the southeast of the Ndembera catchment (cf. Figure 1), Wambura & Dietrich (2020) also found that a large part of this region is currently experiencing mild to moderate droughts.

The increase in AADD and AADS projected by the RCP 2.6 scenario between the baseline period and the near-future is also reflected in AADI (Table 2). The magnitude of AADI is projected to increase (increasing negative values) from −1.03 to −1.12 but drought in the catchment remains moderate. Between the near-future and far-future, drop-valley-rise patterns of AADD and AADS resulted in a rise-peak-drop pattern of AADI. This is because during the mid-future the absolute magnitude of AADD is farther away from that of AADS, whereas during the near-future and far-future, they are closer (Table 2). However, the rise and drop of AADI between the near-future and far-future are not expected to change the moderate drought condition in the catchment. Under the RCP 8.5 scenario, a decrease in AADI between the baseline period and the near-future; and the monotonic trends of AADI between the near-future and far-future are similar to those of AADD and AADS. Thus, from the baseline to the near-future drought is projected to change from moderate to mild, but from the near-future to the far-future drought in the catchment is projected to remain moderate.

According to the optimistic scenario of climate change, the projected decrease in precipitation and increase in temperature during the near-future coincide with no change in AADF, and the increase in AADD, AADS, and AADI in the catchment (Tables 2 and 3). AADI is projected to increase by an average of 0.09 per month, but drought in the catchment is projected to remain moderate like during the baseline period (Table 3). The worst-case scenario of climate change projects an insignificant change in precipitation and significant increases in temperatures in the catchment during the near-future. These temperature changes coincide with the decrease in AADF, AADD, AADS, and AADI (Tables 2 and 3). The change in AADI is projected to cause the reduction of drought in the catchment from moderate to mild.

Under the optimistic scenario of climate change, the mid-future precipitation decrease and temperature increase coincide with the decrease in AADF, AADD, and AADS, and an increase in AADI in the catchment (Tables 2 and 3). Despite the largest increase in drought intensity during the mid-future, drought in the catchment is projected to remain moderate like during the baseline period. The worst-case scenario of climate change showed that a decrease in precipitation and an increase in temperature during the mid-future coincide with the decrease in AADF and AADD and the increase in AADS and AADI in the catchment (Tables 2 and 3). But drought in the catchment is also projected to remain moderate like during the baseline period.

The optimistic scenario also showed that the temperature increase during the far-future coincides with relatively small changes (as compared with the mid-future changes) in drought characteristics in the catchment (Tables 2 and 3). That is why drought in the catchment remained moderate like during the baseline period. Under the worst-case scenario of climate change, the far-future precipitation and temperature changes coincide with a slight decrease in AADF and a substantial increase in AADD, AADS and AADI in the catchment. But drought in the catchment is not expected to change (Tables 2 and 3).

In general, climate change projections under the optimistic scenario show that temperature changes have longer influences on drought in the catchment because a significant precipitation change is projected only during the near-future and mid-future (Table 2). Moreover, between the near-future and far-future, the maximum and minimum temperatures and their changes are projected to have a rise-peak-drop pattern which is also exhibited by the magnitudes of drought intensity and their changes in the catchment (Tables 2 and 3). It can, therefore, be inferred that there are influences of precipitation and temperature changes on drought events in the catchment, but the latter has longer and more direct influences.

The climate change projections under the worst-case scenario also show that temperature changes have longer influences on drought because a significant precipitation change is projected only during the mid-future and far-future (Table 2). Additionally, between the near-future and far-future, the maximum and minimum temperatures and their changes are projected to have monotonic trends similar to that exhibited by the magnitudes of drought intensity and their changes (Tables 2 and 3). This can also be inferred that there are influences of precipitation and temperature changes on drought events in the catchment, but the latter has longer and more direct influences. By using CMIP5-GCMs under RCP 8.5 scenario in the Han River Basin (South Korea), Jehanzaib et al. (2022) also found that drought characteristics have an increasing trend with the mid-future and far-future climatological parameters. Thus, showing the influences of climate change on drought.

Despite interesting findings from this study, a lack of enough observation data within the boundary of the catchment is still a big challenge in conducting studies in small areas such as the Ndembera River catchment. In this study, only one grid point was within the catchment boundary, the rest of the grid points were several kilometres away (See Figure 2). Thus, precipitation and temperature signals from these distant grid points might have diluted local effects which are important in understanding climate change impacts in this small catchment.

Understanding the connection between drought characteristics and climate change is crucial for enhancing adaptations. By using historical climate data from the CRU datasets and climate projections from RCMs of the CORDEX-Africa framework, this study has demonstrated that the influences of climate change on drought in a small, data-scarce river catchment can be investigated. The findings show that all six RCMs used in this study have substantial uncertainty caused by disparities between their baseline simulations and historical climate data in the catchment. That is why most of them had no satisfactory skill scores for all three climate parameters, that is, precipitation, maximum temperature, and minimum temperature. However, the ensembles of the baseline precipitation, baseline maximum temperature, and baseline minimum temperature had fairly satisfactory performances in representing the historical climate in the catchment.

Under the optimistic scenario, the ensemble projections showed that a significant precipitation decrease during the near-future is projected to lessen until it becomes insignificant in the far-future. From the near-future, the maximum and minimum temperatures in the catchment are projected to significantly rise to their peaks by mid-century and then drop to values above the baseline values by the end-century. Similarly, between the near-future and far-future the magnitudes of drought intensity are also projected to have a rise-peak-drop pattern in the catchment. However, changes in drought intensity are not expected to change the current moderate drought in the catchment.

Under the worst-case scenario, the ensemble projections showed a non-monotonically decreasing trend of precipitation and monotonically increasing trends of temperatures in the catchment between the near-future and far-future. Similarly, the magnitudes of drought intensity are also projected to exhibit monotonic trends in the catchment between the near-future and far-future. During the near-future, drought is projected to change from moderate to mild, but during the mid-future and far-future drought is projected to remain moderate like during the baseline period.

Since some of precipitation changes and all temperature changes correspond to changes in drought intensity, it can, therefore, be inferred that there are influences of precipitation and temperature changes on drought events in the catchment, but the latter has longer and more direct influences. However, further studies using high-resolution observation data and climate projections are encouraged to increase our understanding of the influences of climate change on drought in small river catchments. Moreover, the use of multiple methods in drought estimation is also encouraged to obtain a more comprehensive understanding of drought conditions.

The author would like to express gratitude to the maintainers of the CRU dataset and CORDEX-Africa framework for providing reanalysis and projected climate data, respectively.

All relevant data are available from an online repository or repositories. https://crudata.uea.ac.uk/cru/data/hrg/ (CRU datasets) and https://esgf-data.dkrz.de/(CORDEX-AFR22 simulations).

The authors declare there is no conflict.