## 3 Results and Discussion
### The Spatiotemporal Changes in Vegetation Indices (2001-2020)  
Figure 5 shows the locations of climate stations, each of which stands for a particular geographic area where climate data are gathered, as well as the average values of vegetation indices over 20 years. Four vegetation indices are linked to each station: the normalized difference water index (NDWI), the soil-adjusted vegetation index (SAVI), the Enhanced Vegetation Index (EVI), and the normalized difference vegetation index (NDVI). Figure 4: The evapotranspiration, yield, and green water footprint of sugarcane for the time series from 2001 to 2020. Figure 5: Mean of the vegetation indices EVI, NDVI, SAVI, and NDWI over the time series from 2001 to 2020. The EVI values at each station vary from 0.12 to 0.25. Denser and healthier vegetation cover is generally indicated by higher EVI readings. The range of NDVI values is 0.17 to 0.42. NDVI counts the amount of vegetation and is a popular tool for evaluating the density and health of vegetation. The range of SAVI values is 0.26 to 0.64. With the adjustment of soil brightness, SAVI, a modified version of NDVI, offers a more realistic depiction of vegetation cover particularly in regions with elevated soil reflectance. The range of NDWI values is \(-\)0.07 to 0.15. The water content of vegetation can be detected and tracked using NDWI. Delineating spatial configurations, temporal developments, and relationships between the health of the vegetation and environmental characteristics such as land use, land cover, and climate are made possible by this dataset. The NDVI was measured between the years 2000 and 2005; it showed low values in the north and almost nonexistent values in the extreme north. On the other hand, it showed a strong presence that increased with distance to the extreme south (Figure 6). Figure 6: The difference in NDVI over the time series from 2001 to 2020 of White Nile State. From 2006 to 2010, there was an increasing tendency in the normalized differential vegetation index towards the southern regions, with the far south experiencing the highest density. The normalized difference vegetation index decreased between 2011 and 2015, especially in the north, with nearly nonexistent levels in the far north; in contrast, vegetation density rose as we got closer to the southern regions. Regarding the time frame from 2016 to 2020, the normalized difference vegetation index was scarce, perhaps absent in the north, but it rose as we approached the south, resulting in higher vegetation densities, likely due to heavier precipitation (Figure 6). According to [PERSON], [PERSON] [61], NDVI data are especially thought to be most helpful in arid areas or where there are significant interannual fluctuations in the vegetation status. Therefore, when the yield forecasting model was being developed, it was anticipated that NDVI would offer more information. The soil-adjusted vegetation index (SAVI) was measured between 2000 and 2005, with lower values in the northern parts and essentially no measurements in the northernmost sections (Figure 7). In contrast, the southern extremes of the White Nile district saw a significant increase in density. From 2006 to 2010, SAVI values decreased as one travelled towards northern territories that may have lacked SAVI presence, whereas SAVI levels gradually increased towards the southern regions, culminating in density at the farthest southern points (Figure 7). The period from 2011 to 2015 showed lower SAVI in the northern locations, almost nonexistent in the northernmost regions, and increasing vegetation density in the southern locations. For the years 2016 to 2020, there was a small amount of SAVI found, which may not have existed in the north. SAVI values increased in the south, especially in the extreme south, where they were linked to higher precipitation levels.