## 4 Results and Discussion
### Detection of Fertilizer Applications at the Field Scale
Positive feedback loops locally amplify initial differences in nutrient inputs and organic matter contents by processes that further limit plant growth and input of organic matter into the soil, such as soil crusting and soil erosion [27]. Figure 4: False color composites (NIR band seen in red color, red band in green and green band in blue) showing the plot effect on canopy development: late August GeoEye image at 2 m resolution (**a**,**b**); late August UAV image at 0.1 m resolution (**c**,**d**); a millet field with a sandy soil (**a**–**c**); and a sorghum field with a sandy-clay soils (**b**–**d**). The model used to quantify the effect of the fertilization on the NDVI relies on the assumption of independence of the observed areas (_i.e._, the DG pixels). Figure 7 shows semi-variograms based on the 10 September 2014 image when fields are at their maximum ground cover and thus feature lowest spatial autocorrelation during the growing season. Pixel values are only strongly correlated on short distances as indicated by the low nugget values and steep rise of semi-variance. Image values are more or less uncorrelated beyond 2 m for peanut, maize and sorghum fields. The influence of spatial correlation is present at larger distances for cotton and millet, but 75% of the variance is still captured within 2 m. Without accounting for the point spread function of the various instruments, the satellite multispectral pixels can be considered as mostly independent as they sample the ground at a 2 m resolution. Figure 5: Evolution of crop height (**a,b**) and ground coverage (GC) fraction (**c,d**) for fertilizer application treatments A–F for the Millet (**a–c**) and Sorghum (**b–d**) fields also shown in Figure 4.  
The overall NDVI response to fertilizer application does not mean that all differences in application amounts can be quantified accurately. It only shows that at least one of the treatments affected the NDVI response. The plant response to fertilizer application is non-linear, but the NDVI difference between treatment pairs was significant in most cases (for at least 70% of the fields, as seen in Figure 8) for the most discriminating images as indicated by the red boxplots in Figure 6. More specifically, treatments in C and D plots were discriminated in all for peanut, cotton and sorghum fields. The maize  
Figure 6: R\({}^{2}\) boxplot from the model describing the effect of the different fertilization levels on NDVI. The grey vertical strips indicate the fertilizers application window for each crop. The red boxplots correspond to the date where crop reaction to fertilization treatments is strongest. The black dots represent extreme R\({}^{2}\) values that were identified as outliers. Figure 7: Crop specific semi-variograms fitted on NDVI values extracted from the 10 September 2014 UAV imagery with about 10 cm resolution. crop again shows a larger similarity in NDVI response between the treatments, leading to a lower proportion of plots with a significant difference. In contrast to the other crops, in millet fields, the NDVI discriminated plots D and E (_i.e._, doubling the DAP dose) best. For this crop, a higher fertilizer dose was required for a significant response of the canopy reflectance. However, in poor soil fertility environment, the largest difference in NDVI was expected for plots B and C, but the strongest response in Millet was surprisingly observed for plots D-E, while other crops C-D for other crops). This likely indicates a very strong response variability within fields.