Precipitation with its different characteristics; intensity, duration, total amount, timing, or phase (whether liquid or solid), are an essential climate variable in shaping flood hazard [3] [6] [20] [22] [23] [24]. However, due to the basin’s data scares, the relationship between climate factors and Q_MPF was established based on annual and monthly rainfalls. The correlation analysis is performed between rainfall in the rainy seasons, i.e., March to September (6 months), and flood discharge to see the impact of climate on flood events of the study area. The maximum water discharge in Wabi-Shebele River Basin moderately correlates with the total annual rainfall over the watersheds (R² = 0.314 on average; Figure 1).

Although the time lag between maximum annual precipitation and the maximum annual flood was expected more than a day for such large size and complex land formation basins, the maximum number of consecutive wet days is positively correlated with peak daily discharges. Notably, on large sub-watersheds like Wabi at Dodola Bridge and Gode stations, its relation becomes significant with a correlation value of 0.49 and 0.7. It is noticed that climate factors than other drivers significantly influence the flooding in the Wabi-Shebele basin. Moreover, the rain-bearing clouds coverage over the Wabi-Shebele River Basin is less intense than other basins like the Abay basin in Ethiopia [13]. Therefore, flood events in the Wabi-Shebele basin are highly associated with the frequency of precipitation events.

The multiple catchment characteristics identified as vital variables affecting flows [17] [25] [26] [27] are considered watershed factors. These variables include Drainage area (DA km²), Mean basin elevation (BE m), Basin slope (BS %), Basin perimeter (BP km), Basin shape factor (SF dimensionless), Drainage density (DD km/km²), Valley slope (VS m/km), and the elongation ratio (ER dimensionless). The mean peak flow (Q_MPF) in Wabi-Shebele River Basin is positively correlated with variables: DA, BP, VL, and SF, where maximum correlation with DA, BP, and VL with a correlation coefficient of 0.92, 0.93, and 0.96, respectively. It is also evident from Figure 1 above that the correlation value between flood discharge and annual rainfall increases with catchment size. Wabi watershed at Gode station has the largest catchment size showed maximum correlation value, and Robe watershed has the smallest catchment area in this study which exhibits minimum correlation value. Different studies also confirmed the impact of watersheds’ size on peak flow. Rawas and Valeo [17] indicated that mean peak flow (Q_MPF) in arid watersheds is positively correlated with drainage size.

Similarly, the study conducted by Huang [28] showed that the drainage area affects not only the flow collection but also the time to peak flow. Moreover, the soil properties, mainly the soil infiltration rate, are sensitive variables for surface runoff generation. Coarse textured soils have big well-connected spaces and allow more water to infiltrate through them quite rapidly, while fine-grained soils dominated by clay have low infiltration rates due to their smaller-sized pore spaces [29]. Soils contain a large amount of sand and silt habit forming a crust and becoming more compacted, significantly reducing the infiltration rate. The mean peak flow (Q_MPF) in Wabi-Shebele River Basin is positively correlated with variables sand and loam.

The land use and population density, and growth in the basin are considered human activity drivers for flooding [13] [22] [30]. The flood magnitude has a high positive correlation with cultivated land and population density and a strong negative correlation with forest cover.

Using variables correlation matrix

The magnitude and type of correlation among the potential flood drivers from climate, watershed, and human variables (i.e., MAR, DA, BS, VL, SF, DD, VS, ER, clay, sand, loam, forest, AGR, and PD) are estimated using the correlation matrix (Table 3) and scatter plot matrix (Figure 2). To identify significant predictors in watershed variables absolute value of correlation coefficient, R² exceeded 0.8, is selected.

MAR, the only climatic variable in the flood drivers, positively correlates with the variables with the watershed factors (BE, BS, SF, DD, VS, loam) and human factors (forest, and AGR), with maximum correlation coefficients. Either positive or negative, the analysis indicates that MAR has a strong relation with the flood indices (Q_MPF) and variables of both other factors, which push it to be one of the candidates for flood drivers in the basin. DA is correlated with BP (R² = 0.99) and VL (R² = 1.00). SF is negatively correlated with ER (R² = −0.97), and BE is significantly positively correlated with DD (R² = 0.86). Both VS and BS do not exhibit any significant correlation with any watershed characteristics. Given these, five of the main variables were selected as independent watershed variables to avoid information redundancy or multi-col-linearity problems in the multiple regression analysis: DA, SF, BE, VS, and BS. The soil and human variables (Sand, Clay, loam, forest, AGR, and PD) have less col-linearity, directly considered the member of the PCA analysis for further selection of independent variables.

Principal Component Analysis (PCA)

Principal Component Analysis (PCA) is used to see multivariate relationships between potential driving factors and mean peak flow discharge (Q_MPF). PCA is one of the multivariate statistical techniques that can deal with highly correlated variables in regression [31] [32] [33]. In this study, the PCA is further applied to select the most influential drivers among the twelve predictors (MAR, DA, SF, BE, VS, BS, Sand, Clay, loam, forest, AGR, and PD) sorted through correlation analysis to achieve uncorrelated six PCs.

The eigenvalues represent the quantity of variability in the data, and they are presented in Table 4. The first three PCs explain the maximum degree of variability of the data set with a proportion of 45%, 26%, and 19%, respectively. They indicate about 90% of the influence of the flood induces possible mange with the variables in these three PCs. Therefore the variables in the three PCs are taken to develop the multiple linear regression equations among the flood drivers and flood indices.

The coefficients in Table 5 show the linear combinations of variables that make each principal component. The absolute values near zero indicate that a variable contributes little to the PCs, whereas larger absolute values indicate variables that contribute more to the element. In the analysis, the first principal component has high negative associations with BE, VS, MAR, and forest and a high positive association with DA and sand, so this component primarily measures the basin altitude difference and land cover. The second component has

high positive associations with BS, SF, and loam, so this component primarily measures the slope and shape of the catchment. The third component has a high positive association with sand, AGR, and PD, so this component primarily measures the basin farmland and population density.

The loading plot in Figure 3 visually shows the results for the first two components. From the graph, DA and sand indicate a small angle (<90˚) from the Q_MPF line, meaning the variables positively correlated to Q_MPF. The variables: forest, PD, BE, VS, and forest indicate angles related to 180˚, meaning they are negatively correlated to Q_MPF. However, the variables: BS, SF, and loam have no significant correlation with Q_MPF in Wabi-Shebele River Basin.

A significance level (p-value) for all drivers is examined (Table 6). The selection criterion is set to p < = 0.1 in regression analysis. Based on this criterion, DA, sand, MAR, and forest are found as the significant ones to be used in the development of regression equations to estimate the Q_MPF. Therefore, Q_MPF can well be estimated from Model 3 in Table 6, where adjusted R² has the highest value and p-value is significant (<0.05). The multiple regression equation is:

Q MPF = 6.39 MAR + 0.66 DA + 0.35 sand − 0.62 forest − 19.64 (1)

In the equation, climate factor (i.e., MAR), catchment size (i.e., DA), sand coefficient, and land use cover (i.e., forest) are the most influential exploratory

factors on flood quantiles, Q_MPF in the study area. Furthermore, forest function is negatively related to Q_MPF, meaning watersheds with high forest coverage yields less flood discharge than watersheds with less forest coverage. Similarly, the relationship between flood frequency and principal drivers is examined.

For Q₅, Model 2 with only four variables of DA, BE, VS, and MAR was selected as the best model to represent Q₅ estimation. It is noticed from Table 6 that watershed characteristics are the most influential factors of flood-peak frequency at 5 and 10-year return periods. On the other side, climate and human factors are most powerful in representing Q_MPF and flood-peak frequency at 20, 50, and 100-year return periods. The regression equations that describe the relationship between influential driving factors and different return periods flood-peak flows are:

Q 5 = 1.39 MAR + 1.43 DA + 2.98 BE + 0.51 VS − 17.67 (2)

Q 10 = 1.49 DA + 2.44 BE + 0.72 VS − 0.59 sand + 11.81 (3)

Q 20 = 3.63 MAR + 0.76 DA + 0.09 AGR − 11.59 (4)

Q 50 = 8.05 MAR − 4.70 BE − 6.59 (5)

Q 100 = 8.23 MAR − 4.59 BE − 7.42 (6)

Table 6 summarizes the evaluation statistics from the regression model to MAE, NSE, RMSE, and R² based on observed and predicted flood values for all the six flood quantiles. A value close to zero is preferable for MAE as zero indicates no error in prediction. It is seen that all the MAE values for all quantiles lie between 1 and 44. The smallest value of MAE is found in the case of Q_MPF and Q₂₀ estimations. It is noted that except for Q₅ and Q₁₀₀, most flood quantiles estimations are evaluated as good values. Figure 4 shows plots of predicted quantiles over observed flood quantiles. These plots generally present a good agreement between the predicted and observed flood quantiles. Off courses in a few cases of underestimating the flood magnitude. For instance, the observed flows for Q₅ are range between 5.08 to 387.67 m³/s, while the predicted values range from 2.04 to 352 m³/s.