## 4 Results
### Relationship between Net Primary Production (NPP) and Precipitation  
Monthly precipitation patterns across this region are of the rains beginning in late October, reaching their peak in January, and ending in April. Precipitation for May, June, July, August, and September is less than 10 mm in total and represents the dry season on this landscape. In relation to this, the onset of the increase in NPP is in November, and it peaks in March. The lowest NPP appears in September and October, at the very end of the dry season. There is about a two-month time lag between the seasonal change of precipitation and that of NPP, representing the vegetation response to the precipitation across the landscape. We calculated MAP and mean annual NPP (the water year is represented here by the sum of monthly NPP values from September of one year into August of the next) (1982-2010) of the entire study region and extracted their pixel values using different areas defined by land cover classes. Figure 13a-c shows the scatterplots of mean annual NPP _versus_ MAP for the three savanna land cover classes. The annual NPP of tree savanna has no significant correlation with MAP (\(p=0.22\)). By contrast, the annual NPP of bush and grassland savanna are correlated positively with MAP with correlation coefficients of 0.62 (\(p<0.01\)) and 0.10 (\(p<0.01\)), respectively. The slope of the linear regression model for tree savanna is not statistically significant (Figure 13a), suggesting that annual NPP has no linear relationship with MAP. Annual NPP of bush and grassland savanna are  
Figure 12: Spatial pattern of Kendall correlation coefficient (\(\tau\)) for 1982–2010. The positive \(\tau\) value indicates an increasing trend, and _vice versa_. linearly correlated with MAP as indicated by the significant slope coefficients (Figure 13b,c). Figure 14 shows the spatial pattern of correlation between annual totals of precipitation and NPP. Generally the values of correlation decreases from south to north, implying that the linear relationship between precipitation and NPP declines as precipitation increases. The map also shows that the correlation values over grassland and bush savanna are higher than the values over tree savanna. Figure 14: The spatial pattern of correlation coefficients between annual totals of precipitation and net primary production (NPP). Figure 13: The linear relationship between mean annual precipitation (MAP) and mean annual net primary production (NPP) by land cover classes from 1982 to 2010 for (**a**) tree savanna; (**b**) bush savanna, and (**c**) grassland savanna. One important feature of the study area is the precipitation gradients across which MAP increases from south to north. We conducted linear regression analysis on different precipitation intervals of the entire study area and the three catchments (Table 2). The regression results of different precipitation intervals show that annual NPP has a significant and positive relationship with MAP when MAP is less than about 850 mm. However, the relationships are unstable when MAP is more than about 850 mm, which is characteristic of statistical insignificance or a negative regression coefficient. The results of the Okavango and Kwando catchments are similar, which are characterized by an abrupt change in the relationship between annual NPP and MAP. It should be noted that the regression results of the Zambezi catchment are uncertain, which is characterized by generally insignificant relationships between annual NPP and MAP. We applied the piecewise linear regression model to fit all pixel values from the layers of MAP and mean annual NPP (Figure 15). The piecewise linear regression is an effective tool which can be used to identify the turning points (TP) underlying the variations in mean annual NPP with MAP [37].