Boundary conditions

The WRF model simulations were initialized using Final Operational Model

Global Tropospheric Reanalyzes from the National Center for Environmental Prediction (NCEP FNL). This is 6-hourly data of 1˚ × 1˚ (110 km) resolution (Kalnay et al., 1996). The boundary conditions used were for 21 days, corresponding to the study period of 20 days with an additional day to cater for model spin-up.

Rainfall observations

The Tropical Rainfall Measuring Mission (TRMM) provided observations for model validation. Observed estimates of daily and 3-hourly rainfall accumulations were obtained from TRMM 3B42 version 7. This product is a 0.25˚ × 0.25˚ (27.5 km) resolution precipitation estimate obtained by applying the Goddard Profiling Algorithm to extract rainfall estimates from a variety of passive microwave sources (Huffman et al., 2007). The dataset was downloaded from the GIOVANNI data handle (https://giovanni.gsfc.nasa.gov/giovanni/) of the National Aeronautics and Space Administration (NASA). Data for a 20-day period was used for evaluating the model performance.

Model setup and experimental design

Simulation of extreme rainfall that occurred over the LVB was done using the WRF modelling system, Advanced Research WRF (ARW) core version 3.9. It is a grid point model with a terrain—following vertical coordinate near the surface which transforms to a constant pressure at the highest level. WRF performs numerical integration on a staggered Arakawa C-grid with 3^rd order Runge-Kutta time integration (Skamarock et al., 2008). The model was setup with 27 vertical levels ending at the 50 hPa isobaric level. Three domains (Table 1 and Figure 2) of varying grid resolution were used with a superior 2-way domain interaction and 1:3 nesting ratio. The model was initialized using NCEP finalized reanalyzes starting 24 hours before the period of interest to allow time for model spin-up.

The domain setup was as follows; a coarse domain centered at 0.73˚ latitude, 22˚ longitude covering Africa to encompass large scale synoptic systems such as the Inter Tropical Convergence Zone and sub-tropical anti-cyclones; a nest domain d02, covering the Congo basin and the western region of the Indian Ocean to cater for moisture inflow from the Congo air mass and the Indian Ocean respectively; and a nest domain d03, covering LVB and Lake Victoria to cater for the influence of lake surface temperatures on rainfall in the basin. The ARW solver was used with a combination of physical parameterization (Table 2) coupled with static land-use data based on Moderate Resolution Imaging Spectroradiometer (MODIS) with 21 land-use categories (Friedl et al., 2002) and a special lake surface representation. The land-use was setup with varying resolution, the coarse domain used a 10-minute resolution while d02 and d03 used a 5-minute resolution.

To determine the model skill associated with the use of different cumulus – microphysical scheme combinations, the model setup was identical in all experiments, except for the cumulus and microphysical schemes (Table 2). Similar to Argent et al. (2015), the default parameterization settings of the WRF model were used as the control run.

To determine the effect of changing grid resolution, experiments done in set-up 1 were repeated with the inner most domain set to 4 km resolution (Set-up 2). A comparison was then done between results of experiments at 12 km resolution and experiments at 4 km resolution. Furthermore, to reveal the effect of changing domain size, a comparison was done between results of domain, d03 in set-up 1 and domain, d02 in set-up 2. Both domains were set at 12 km resolution and only differed in size.

Model validation methods

The Difference variable. (Willmott et al., 1985) described in Equation (1) was used to generate a spatial difference between the WRF output and TRMM.

Difference = Simulated − Observed (1)

Continuous scores. The Root Mean Square Error (RMSE) (Chai & Draxler, 2014) was used to determine model accuracy, and the Mean Error (ME) (Mugume et al., 2016) was used to determine model bias.

R M S E = 1 n ∑ i = 1 n ( S i − O i ) 2 (2)

M E = 1 n ∑ i = 1 n ( S i − O i ) (3)

In Equations (2) and (3), S is the simulated value, O is the observed value, and n is the total number of comparisons.

Categorical scores. The scores used were the Probability of Detection (POD) and False Alarm Ratio (FAR) described in Equations (4) and (5) respectively. POD and FAR values range from 0 to 1 and they are derived from a 2 × 2 contingency table (Table 3) described by Schaefer (1990).

P O D = A / ( A + C ) (4)

F A R = B / ( A + B ) (5)

Observed and simulated spatial rainfall patterns

Figure 3 shows the rainfall distribution from TRMM observations and the WRF model runs for the 20-day period. TRMM shows that the total rainfall amount received in LVB during this period was between 100 and 280 mm although rainfall amounts between 120 to 200 mm dominated the area and central LVB received a higher rainfall amount compared to the other 2 regions. On the contrary, all model runs generated higher rainfall amounts in the higher altitude western LVB compared to the other 2 regions. This gives evidence of the terrain-sensitive nature of the WRF model which was also reported by Mugume et al. (2017) and Ntwali et al. (2016).

The model runs also generated varying rainfall distributions when different cumulus and microphysical parameterization combinations were used. Overall, the rainfall was in the range of 10 to over 320 mm. Notably, runs done with the SBU_YLin microphysical scheme (Figure 3(e), Figure 3(h), & Figure 3(k))

generated higher rainfall amounts over LVB as compared to those done with other microphysical schemes. This rainfall disparity caused by the microphysical scheme is because they each use different techniques for predicting hydrometeor species.

The difference maps (Figure 4) show that all model runs underestimated the rainfall in the watershed closet to the lake. Also, except for the runs done with the Grell 3D cumulus scheme, the other runs overestimated rainfall in the highland areas in the southwestern corner of the basin. Of the areas in which the model runs show close agreement, the error ranged from 25 to 50 mm and very few areas had an error below 25 mm.

Observed and simulated temporal rainfall patterns

Figure 5 shows the temporal rainfall accumulation (a, c, e) and the diurnal evolution of rainfall (b, d, f) during the 20-day period for western, central and eastern LVB respectively. The temporal rainfall accumulation indicates that for western LVB, the model runs fairly simulate the rainfall amounts while for central and eastern LVB, there was a dominant underestimation of the rainfall. A further investigation into the diurnal variation (Figure 5(b), Figure 5(d), Figure 5(f)) alludes that the underestimation happens during the nocturnal hours of the day. For central LVB, the model, this is between 18:00 hrs. to 06:00 hrs. of the following day while for eastern LVB, this happens between 18:00 hrs. and 24:00 hrs.

Important to note is that TRMM observations (b, d, f) show that rainfall in the basin is mostly received at night and early in the morning. Sun et al. (2014) demonstrated that during this time, the lake is warmer than the adjacent land, favoring the occurrence of a land breeze that causes the rainfall. The WRF model, however, was unable to correctly simulate this nocturnal rainfall caused by the land breeze. As explained by Argent et al. (2015), there is insufficiency in the representation of the lake surface temperature within the model. The temperature of the lake is constantly colder than the adjacent land. This hinders the reversal of winds to blow from the land to the lake (that is, failure to generate the land breeze). The lack of nocturnal rainfall also explains why the model underestimated rainfall in central and eastern LVB. Mayor and Mesquita (2015) also acknowledged a similar failure of WRF over Cuba.

Skill scores

Table 4 summarizes the skill scores and corresponding ranks of model runs done using an inner-most domain set at 12 km resolution (Set-up 1). A one-sample t-test was used to test whether the skill scores generated by model runs E1 to E9 significantly differ from those of the control run and the results show that at a 95% level of confidence, changing the microphysical and cumulus parameterization schemes from the default significantly altered the model bias (ME, p < 0.05), detection ability (POD, p < 0.05) and proportion of false alarms (FAR, p < 0.05)

but not the accuracy (RMSE, p > 0.05). Overall, model runs done with the Grell 3D cumulus scheme showed closer proximity to the TRMM observations and specifically, model run E6 done with the Grell 3D cumulus scheme combined with the SBU_YLin microphysical scheme showed the most satisfactory skill and generated the best spatial representation of the rainfall.

Effect of model resolution on the skill scores

The 10 model runs done with the inner most domain set to 12 km (Set-up 1) were repeated with the inner most domain set to 4 km (Set-up 2) and the skill scores they generated were summarized in Table 5 along with the corresponding ranks. Model runs E4 and E6 which both use the Grell 3D cumulus scheme rank higher than the rest of the model runs.

Furthermore, the skill scores of the model runs at both resolutions were summarized in Table 6 and a paired-sample t-test was used to test the effect that changing model resolution from 12 km to 4 km has on the model skill. The results show that it significantly affected the accuracy (RMSE, p < 0.05), detection ability (POD, p < 0.05) and proportion of false alarms (FAR, p < 0.05) but did not significantly alter the model bias (ME, p > 0.05). Majority of the model runs generated lower RMSE, lower POD and higher FAR at 4 km resolution compared to the 12 km resolution. This implies that increasing the model’s resolution produced a higher accuracy, lowered the detection ability by 2% or more and increased the number of false alarms by 1% to 2%. For the Control run, E1, E2, E7 and E8, increasing the model resolution was of no additional value. It caused an undesirable increase in model bias.

Effect of domain size on the skill scores

The nature of the experimental set-up allowed for a domain-size sensitivity test to be carried out. For this, the paired-sample t-test was used to compare the skill scores generated by domain, d03 set at 12 km resolution (Set-up 1) to those of domain, d02 also set at 12 km resolution (Set-up 2). These domains only differed in size. The results (Table 7) suggest that changing the size of the domain significantly altered the model’s accuracy (RMSE, p < 0.05) and proportion of false alarms (FAR, p < 0.05). Majority of the model runs generated lower RMSE in the large domain. This increase in accuracy is because synoptic features are

better resolved in large domains. The large domain used in this test covered an approximate area of more than 15,000,000 km², making it suitable to capture large scale features such as the ITCZ which is responsible for rainfall in LVB during the March to May season. However, the large domain was disadvantaged by its large spatial coverage because it registered a higher number of false alarms.