This study used Lateral Boundary Conditions (LBCs) from the National Center for Atmospheric Research (NCAR) [17] [23]. It validated the model outputs using monthly rain-gauge data-sets from the Uganda National Meteorological Authority for the period 2006-2018. Like many climatic data-sets in developing countries, missing data were found and these were removed from the analyses. The LBCs used were obtained from the global bias-corrected climate model output data of version 1 of NCAR’s Community Earth System Model (CESM1) that participated in CMIP5 [17] [24]. These data-sets are interpolated to 26 pressure levels and are provided at six hourly intervals and at 1˚ × 1˚ horizontal resolution [23] [24]. The variables have been bias-corrected using the European Centre for Medium-Range Weather Forecasts Interim Reanalysis for fields from 1981 to 2005 [17]. The repository (https://rda.ucar.edu/datasets/ds316.1/) provides three input files, namely the Representative Concentration Pathway (RCP) future scenarios i.e. RCP4.5, RCP6.0 and RCP8.5. The study used these RCPs for the period 2006-2018.

This study was carried out over Uganda and used 28 study locations as presented using Figure 1. Uganda is located within the latitudes: 1˚29'S to 4˚12'N and the longitudes: 29˚34'E to 35˚29'E [9] [10]. It is a landlocked country found in the eastern part of equatorial Africa [10] [12]. The country is relatively flat in the central with a few highland areas; and having mountains in the East (Mt. Elgon; Mt. Moroto) and west (Mt. Rwenzori). The country is endowed with fresh water bodies, namely Lake Victoria, Albert, Kyoga, Edward, Wamala, George among others and has a good climate condusive for agriculture [4] [20] [25]. Most areas of the country receive a bimodal rainfall distribution i.e. March-May and September-November with exception of the northern region whose rainfall distribution tend to be unimodal peaking around August [9] [12] [20].

This study contends that the study carried out by Ongoma et al. [3] used GCM in the CMIP5 which were coarse i.e. largely coarse greater than 1.5˚ about 150 Km × 150 Km horizontal resolution compared to the horizontal resolution used in this study i.e. 30 km (about 0.3˚). Therefore, this study designs and runs a comparatively higher resolution validation experiment of the RCPs over Uganda and uses 28 study locations as presented in Figure 1. Additionally, the study carried out by Fotso-Nguemo et al. [27] over a comparatively similar region used gridded data-sets but this study uses observed station rainfall data-sets and uses comparatively a longer validation period i.e. 13 years (2006-2018).

This study first evaluates the performance of the RCPs in reproducing the observed climate patterns over the period 2006-2018 i.e. direct model output by running the Weather Research and Forecasting (WRF) model version 3.9 [10] [28] with boundary conditions of the three RCPs i.e. RCP4.5, RCP6.0 and RCP8.5 [17]. The direct model outputs are then bias corrected using quantile mapping (Equation (6)) to investigate any possible improvement in the performance as recommended by Sharma et al. [14], Ghimire et al. [15], Noor et al. [7], Cannon et al. [16], Monaghan et al. [17], Piani et al. [13] among others.

In running the WRF model, model the parameterization schemes used are adopted from Mugume et al. [29] and are presented using Table 1. These parameterization schemes are also used in Ingula et al. [30]. The study domain used in this study is shown using Figure 2. This study used single domain at 30 Km × 30 Km covering the equatorial Africa but analyses are carried out over Uganda shown with a red box in Figure 2.

The evaluation of the WRF model performance based on the three RCPs (RCP4.5, RCP6.0 & RCP8.5) is done using both continuous scores and categorical scores. The continuous scores comprise of the Pearson correlation coefficient, r, (Equation (1)) for assessing the relationship between observed and simulated; the relative root mean square error, RMSE (Equation (2)) and relative mean error, ME (Equation (3)) for examining the error magnitudes. The categorical skill scores, namely the accuracy (Equation (4)) are obtained from the contingency table (Table 2).

r = ∑ i = 1 n ( p i − p ¯ ) ( O i − O ¯ ) [ ( ∑ i = 1 n ( p i − p ¯ ) 2 ) ( ∑ i = 1 n ( O i − O ¯ ) 2 ) ] 0.5 (1)

R M S E = 1 n ∑ i = n n [ p i − O i L T M ] 2 (2)

M E = 1 n ∑ i = n n [ p i − O i L T M ] (3)

where: p i , O i , LTM, and n are the model predicted i^th value, observed i^th, long-term mean, and number of observations respectively. The relative root mean square error RMSE (Equation (2)) and the relative mean error, ME (Equation 3) presented in this study are as percentage of the LTM which is also used and recommended by Ongoma et al. [3]. This study used relative root mean square error and relative mean error in order to compare the performance against long-term mean.

Additionally, in this paper, the accuracy (i.e. hit rate) is defined as the proportion of hits (i.e. A₁₁, A₂₂ and A₃₃) (Table 2) to total observations. So in this paper for a given location, i, the accuracy is:

A C C i = A 11 + A 22 + A 33 n (4)

a hit is defined in this paper as, for example when model prediction is “below normal” and the observed is also “below normal” i.e. A₁₁; model prediction is “normal” and observation is “normal” i.e. A₂₂; and model prediction is “above normal” and observation is “above normal” i.e. A₃₃ as illustrated in Table 2.

The contingency table used, as presented using Table 2 is based on three cases, namely “below normal”, “normal” and “above normal”. These terms are in operational use by UNMA and are defined as captioned in Table 2. The long-term mean monthly rainfall used in the study is presented using Table 3. This study also used graphical analysis of line graphs and maps obtained using inverse distance weighting interpolation [38] and given by Equation (5).

p i * = ∑ i = 1 n     p i w i ∑ i = 1 n     w i (5)

p i * is the interpolated precipitation amount from p i neighboring stations weighted with w i and n is the total of stations used to derive p * .

A couple of methods for bias correction have been proposed which include:

scaling [7] [18]; gamma quantile mapping [7]; generalized quantile mapping [7] [16] [19]; and power transformation [7], among others. This study has adopted the generalized quantile mapping method to examine any potential improvement in the skill as simulated by the WRF model with different initial conditions based on the different RCPs (i.e. RCP4.5, RCP6.0 & RCP8.5). Quantitle mapping has been proposed by [19] and presented using Equation 6. This method is also used and promoted by [14] while assessing the changes in precipitation and temperature over the Teesta River basin in the Indian Himalayan region under climate change.

p * = p r c p × [ p o b s ¯ p r c p ¯ ] (6)

where p * is the bias corrected precipitation estimate from the model; p r c p is the direct model output without bias correction and p o b s is the observed precipitation and p o b s ¯ and p r c p ¯ are the mean values of p o b s and p r c p respectively.

The performance of RCPs on monthly, seasonal and annual time scales is presented using Figure 3 and Figure 4. These figures show the temporal simulation performance of WRF being driven by the different RCPs i.e. RCP4.5, RCP6.0 and RCP8.5 compared with the observed patterns. Figure 3 is for the monthly trends over the study period i.e. 2006-2018 and Figure 4 is for the annual (Figure 4(a) & Figure 4(b)) and seasonal trends i.e. March-May (Figure 4(c) & Figure 4(d)) and September-November (Figure 4(e) & Figure 4(f)) over the study period.

The performance of the WRF model pre-processed with different RCPs on monthly scale as presented by Figure 3 is generally poor and shows a negligible overall correlation i.e. of magnitudes less than 0.200. Some isolated overestimates are observed especially around 2016 and 2018. The results further show that the RCPs can overestimate the monthly rainfall to magnitudes in excess of about 400% for RCP8.5; RCP4.5 overestimates up to about 360% while RCP6.0 estimated up to 240% of the long-term mean. A critical analysis of Figure 3 shows that 36.7% of observed monthly rainfall were below long-term mean; 63.3% for RCP4.5; 58.3% for RCP6.0; and 57.5% for RCP8.5. This suggested that the RCPs largely underestimated monthly rainfall over the study period. It is this underestimation that resulted in a smaller overall relative anomaly of −3.956% for RCP4.5; 1.265% for RCP6.0; and 4.870% for RCP8.5. A detailed performance for each of the stations used is presented using Figure 5.

Additional analysis of annual rainfall patterns revealed that the RCPs largely underestimate annual rainfall totals (Figure 4(a)). This performance however improves slightly with bias correction (Figure 4(b)). Further analysis of the results for seasonal performance i.e. Figure 4(c) & Figure 4(d) for the March-May rainfall season reveals that generally RCP4.5 and RCP8.5 underestimated the March-May rainfall over the study period with exception of RCP6.0. A slight increasing trend of the total March-May rainfall amount is observed at about 1.93% over the period and a coefficient of variation of 2.4 is observed. Whereas RCP8.5 reasonably reproduced this trend, it had the largest variability i.e. coefficient of variation of 7.3. Additional analysis of the September-November results (Figure 4(e) & Figure 4(f)) also revealed an increasing trend of about 1.43% over the period. The performance of RCPs during this period largely overestimated the seasonal rainfall. RCP4.5 has the smallest relative anomaly i.e. 4.984 but comparatively a higher variability, i.e. 12.8. On the other hand, RCP6.0 has the highest anomaly but a comparatively smaller variability, i.e. 7.1.

The results in this study are comparable to the findings of Ongoma et al. [3] over East Africa. They evaluated 22 models under the CMIP5 and found the models to have a comparatively lower skill over East Africa while Fotso-Nguemo et al. [27] found RCP8.5 to present rainfall magnitudes comparatively lower than the Global Precipitation Climatology Center (GPCC) and Tropical Rainfall Measuring Mission (TRMM). While using RCP4.5 and RCP8.5 and 10 GCMs along with linear scaling as the bias correction method, Myo et al. [18] found that these RCPs projected fluctuating average monthly precipitation but found that annual precipitation is likely going to increase. These results are consistent with our findings which make us conclude that the 21^st century precipitation is going to be highly variable at monthly scale.

The spatial performance of WRF model driven by the three RCPs (RCP4.5, RCP6.0 & RCP8.5) considered in this study along with the bias corrected output using quantile mapping is presented using Figures 6-8. These figures are for correlation analysis (Figure 6); relative mean error (Figure 7), and relative root mean square error (Figure 8). Additional analysis is presented using Tables 4-6 which present results per study location for correlation (Table 4); relative mean error (Table 5) and relative root mean square error (Table 6).

Analysis of Figure 6 shows that nearly all the RCPs presented a weak negative correlation over most places of the country. A slight improvement with bias correction is noted over north western with RCP8.5 but largely, RCP4.5 and RCP6.0 presented a negative correction. RCP8.5 had a weak negative correlation on the western part of the country and a slight positive correction on the eastern part of the country. There seems to be no noticeable improvement with bias correction especially for RCP8.5. Additional analysis of the correlation values at specific locations (Table 4) reveals generally that RCP4.5 and RCP6.0 largely presented a negative correlation with observed rainfall i.e. RCP4.5 (17 cases out of 28 cases as negative correlation values) and RCP6.0 (19 cases out of 28 cases as negative values). Generally, these are very low scores and can not explain the variation in observed rainfall.

Additional analysis is carried out on results presented by Figure 7 which presents the spatialized relative mean errors. The results show that RCPs with no bias correction had a greater part of the country with a slight overestimate especially RCP4.5 i.e. with magnitudes 0 - 1.0 of the long-term mean. For all the RCPs, the southwestern region is underestimated. A further investigation of relative mean errors presented by the bias corrected model output (Figures 7(d)-(f)) reveals that largely areas that were originally overestimated are now underestimated. Areas that were originally underestimated have the relative mean errors slightly improved e.g. the case of south western region. Generally the relative mean error magnitudes for both bias corrected and direct model output remain comparatively small largely within −0.9 to 1.0 of the long-term mean. This is also observed from the performance at specific study locations presented using Table 5. A detailed analysis of the results presented in Table 5 reveals that bias correction had a tendency of removing the underestimation to become overestimation over most of locations i.e. 23 out of 28; 19 out of 28; and 21 out of 28 for RCPs 4.5; 6.0; and 8.5 respectively. In a related study by Ghimire et al. [15], they noted that bias correction reduces the overall error magnitudes. This is why the relative mean error appears positive on average in Table 5. This could also be the reason why the bias corrected results presented comparatively better performance in Figure 3 and Figure 4.

A further investigation of the relative magnitudes of errors compared to the long-term mean carried out using the relative root mean square error (Equation (2)) and presented using Figure 8 confirms the results presented in Figure 7. Generally, the magnitude of errors is approximately of magnitude 1.0 to 2.5 with exception of southwestern Uganda where they largely appear greater than 1.5 of the long-term mean especially over Mt. Rwenzori region. Additionally RCP6.0 and the bias corrected RCP4.5 and RCP6.0 appear to present comparatively larger error magnitudes of the north eastern region. A slight improvement in the magnitudes of relative root mean square errors over the south western region especially Mt. Rwenzori area is noted in all bias corrected RCP products. This is also confirmed by the results presented at specific locations in Table 6 which presents a slight improvement in the error magnitudes. A detailed analysis of the absolute root mean square errors in comparison to the long-term mean is presented using Table 6. A poor performance is noted over Kasese, Lira, Moroto and Mbarara (Table 6) of order of magnitude generally greater than 1.5 of the long-term mean especially the bias corrected results. Overall the results show that RCP4.5 presented a slightly better performance.

The foregoing results probably indicate that these RCPs may not be realistically valid in low latitudes. However, a study over Central Africa with the domain including Uganda, by Fotso-Nguemo et al. [27] noted that the ensemble mean of the 20 GCMs was able to reproduce the rainfall patterns exhibited by the Global Precipitation Climatology Center better than those presented by the Tropical Rainfall Measuring Mission. This suggests different performance scores of RCPs with different data-sets and thus underscores the importance of using station observations as ground truth in validation studies. Nonetheless, the RCPs fairly reproduces the temporal patterns (Figure 3 and Figure 4) albeit with an underestimation. This could suggest that future extreme events being projected by different studies under these RCPs could be underestimated and could actually be severe. To improve the performance of the RCPs, this study proposes data assimilation or review of these RCPs.

Figure 9 presents the spatialized accuracy in terms of the hit rate (accuracy) for the RCPs while Table 7 presents the hit rate levels per study location. The results generally show RCP8.5 presenting a slightly better skill than the rest. Isolated cases of above average skill are observed over the northwestern and northeastern regions. However, generally the skill is largely 20% - 50%. There was no noticeable improvement in skill with bias correction of the RCPs. In some cases over some areas, actually the skill degraded e.g. over the northeastern Uganda. This is in contrast to the findings of Ghimire et al. [15], who noted that bias correction improves the accuracy of numerical simulations. This study argues that the weak/no improvement in the performance after bias correction could be because the initial conditions used to initialize this study are already bias corrected as described by Monaghan et al. [17], and so additional bias correction is not necessary.

Further to the skill scores (Figure 9 and Table 7), the results are in agreement with Kisembe et al. [9], who noted that the climate simulations whereas they reproduce the climate variability, they present a poor skill regarding the rainfall seasons especially the March-May rainfall season over Uganda. In general, this study finds RCP8.5 to present a slightly better performance in terms of the hit rate and is thus proposed for future simulation over low latitudes including Uganda. However it is surprising to note that bias correction did not necessary improve performance and probably considers that this observation could be that because the LBCs used in this experiment are already bias corrected as explained earlier.