Fig. 1 shows the explained variance versus the PC number diagram. Based on the recommendation of North et al. (1982) on the separation of eigenvalues for the retained components, it was found that after the 10th component, the eigenvalues were typically close; and with retaining 10 components, almost all the landmasses were classified under a given sub-region so that the addition of further components only uncovers a new rainfall region that has already been delineated. By retaining 10 components, only approximately 60 percent of the total variation was captured. This was not surprising since the addition of adjacent oceans in the classification of the JFM monthly rainfall totals implies also that the complexity of the multivariate relationship in the data set might further increase. However, in line with the study aim to uncover landmasses that are spatially coherent with adjacent oceans, retaining 10 components, is at least satisfactory since the majority of the landmasses were classified.
Fig. 2 shows the sub-regions with coherent JFM rainfall totals for the 1979-2019 period. The rainfall regions in Fig. 2 were also reproduced when the analysis period was divided into two halves (not shown), however, the stability of the classification shifted for the classification done before the satellite age (i.e. before 1979), suggesting the sensitivity of the regionalization output to the quality of the input data set. From Fig. 2, there is considerable overlapping in the classification output and also some regions tend to have both high negative and positive loadings (e.g. R5); an interpretation to this is that the causal mechanism associated with positive rainfall anomaly at a given region might as well overlap, in causing negative rainfall anomaly at another region. For example, in Fig.1 a dominant positive anomaly is evident at southern African landmass while at Madagascar and northern Mozambique a weak negative anomaly can be seen; this is typically what happens during an inactive state of the Mozambique Channel Trough when rainfall is enhanced at southern African landmasses relative to Madagascar and northern Mozambique (Barimalala et al. 2019). The weak structuring of the rainfall regions is physically realistic, but the focus for further analysis will be placed more on coherent regions where positive loadings dominate on the landmasses and adjacent oceans. Also, to aid robust physical interpretability tropical and some subtropical regions will be considered since the rainfall climatology of the mid-latitudes is much more complex (e.g. the activity of cold fronts). For this reason, R7 will not be considered.
R2, R4, R6, and R8 are selected for further analysis since these sub-regions features a considerable number of grid points at the landmasses homogeneous with adjacent oceans. R2 features high positive loading dominant at some central regions of southern Africa, Mozambique Channel, and northern Agulhas current; Fig. 3 and 4 clearly show that the spatial patterns of SLP and relative vorticity anomalies play a vital role in the development of the spatial structure of R2. Also, the wind anomalies indicate enhanced convergence of moist southeast, cross-equatorial northeast, and northwest winds at the central landmasses. R4 features a positive loading dominant at Madagascar (except for the northernmost region) and the adjacent oceans to the east coast and the west coast. From Fig.3 and 4, R4 is characterized by a strong cyclonic and negative relative vorticity anomaly dominant in oceans adjacent to Madagascar; as a result, southeast and northeast winds are adjusted to westerly towards Madagascar where they converge. It is evident that the casual mechanism of R2 and R4 partly overlaps based on enhanced cyclonic activity at the east coast of Mozambique. In R6, a positive loading dominates at the west-central equatorial landmasses and parts of the tropical South Atlantic east coast. Fig. 3 shows that wind anomalies are predominantly southerly towards the equator and from Fig. 4 enhanced relative vorticity and convergence are evident at R6. Enhancement of convergence and relative vorticity during the active months of R6 is quite conceivable since enhanced convergence by the Inter-Tropical Convergence Zone is the principal mechanism that controls the tropical rainfall. R8 is similar to R4 except that in the former enhanced cyclonic activity, cyclonic relative vorticity anomaly, and the convergence of northeast and southeast anomalous winds shift towards northern Madagascar.
Anomalies of monthly JFM divergence field, relative vorticity, 2-meter temperature, rainfall totals (i.e. the predictors) were spatially averaged at local oceanic domains that are homogeneous with the landmasses in R2, R4, R6, and R8, respectively, for the 1979-2019 period; also anomalies of JFM rainfall totals were spatially averaged for the coherent landmasses (predictand) in R2, R4, R6, and R8, respectively. To uncover the statistical relationship between the JFM rainfall totals at the landmasses and oceanic domains, in addition to the underlying dynamics, correlation and regression analysis were made. Correlations that are statistically significant at a 95% confidence level are presented in Table 1, dash in the table show correlations that are not significant. For R2, Table 1 shows that variations in SLP, relative vorticity, 2-meter temperature, and divergence at the local oceanic domains that R2 landmass is coherent with, are related to the variations in rainfall anomaly at the landmasses in R2. Cyclonic circulation, cyclonic relative vorticity, lower temperature, and enhanced convergence anomalies during austral summer at the local oceanic domains are related to enhanced rainfall in R2 landmasses. The correlation coefficient between rainfall anomalies at the local oceanic domains and the landmasses at R2 was rather found to be relatively higher at a lag of 1 month compared to lag 0. In R4, variations in SLP and rainfall anomalies at the adjacent oceans are well related to rainfall anomalies at the landmasses. Cyclonic anomaly and positive rainfall anomaly at the adjacent oceans of R4 relates to enhanced rainfall at the landmasses in R4. In R6, divergence/convergence at the local oceanic domains (i.e. parts of the tropical South Atlantic east coast) is strongly related to negative/positive rainfall anomaly at the west-central equatorial landmasses. Also, cyclonic relative vorticity and positive rainfall at the local oceanic domains are equally related to enhanced rainfall at the landmasses in R6. In R8, cyclonic anomaly and positive rainfall anomaly at the concerned local oceanic domains are well related to enhanced rainfall anomaly at northern Madagascar. Table 2 shows the percentage of variability in JFM monthly rainfall at the homogeneous landmasses explained by the oceanic indices, based on linear and multiple linear regression analysis. It can be seen that relatively, the predictors jointly captured best the variations in R6 due to the high relationship between convergence anomaly at the local oceanic domains and rainfall anomaly at the west-central equatorial landmasses.
Table 3 shows the error (i.e. predicted minus observed, in absolute value), in some summary statistics for the predicted JFM monthly rainfall totals anomaly at the landmasses, using multiple linear regression and the appropriate predictors in Table 1 and 2 (i.e. those that the correlations and regressions are statistically significant). It can be seen that prediction accurately captured the long-term mean in JFM rainfall anomaly at the respective landmasses and also relatively, the distribution of JFM rainfall anomaly at the west-central equatorial landmasses (Fig. 5) is well captured using the selected predictors. Fig. 6 shows the time series for annual (JFM) rainfall anomaly averaged over the coherent landmasses for the actual and predicted values; it can be seen that generally the year to year variability of JFM rainfall anomaly averaged over the specified coherent landmasses might be predicted using the local oceanic indices, especially at the deep tropics. The mean absolute error for predicted values in R6 is 35 mm/month but higher for the other regions (i.e. within the range of 60 – 100 mm/month).