# Mapping Smallholder Yield Heterogeneity at Multiple Scales in Eastern Africa
## 3 Results
### Performance of the Uncalibrated Model  
The uncalibrated model coefficients and associated R\({}^{2}\) of the regressions derived from APSIM-Maize simulations for both the B-K sub-region and the 1 AF region are listed in Tables S1 and S2. In general, using updated phenology parameters and a narrower sowing window significantly improved the R\({}^{2}\) of the regression using simulated data. (Using GCVI vs. MTCI had no effect on the calibration R\({}^{2}\) because conversions between CN and VIs were all linear.) In the B-K sub-region, the uncalibrated yield estimates, derived by applying these coefficients to the actual observations of GCVI or MTCI, were slightly worse than the calibrated model estimates (Table 4), but still captured up  
Figure 4: Performance of VIs in predicting farmer-reported yields as a function of field size for 2016. Numbers at the top of each panel show the number of fields included in each estimate. Red shaded region reports bootstrapped 95% confidence interval on the purestand-field estimates. to one-third of the variation for purestand fields with minimal size of 0.5 acre. The agreement between measured yields and uncalibrated model estimates was highest for the model built on simulations with updated phenology parameters, MTCI, Biomass\(\times\)HI estimation, and narrow sowing window. Prediction performance was mostly unsatisfying for the full survey sample (including very small and intercropped fields), except for cases when updated phenology parameter and narrow sowing window were used. For the broader 1 AF region, uncalibrated model estimates were fairly encouraging, capturing about one-third of the ground-based yield variations at the division level, and nearly half of variability at the district level (Table 4). The overall better performance at the district level was likely in part due to smaller standard error in the crop cut yields aggregation (Figure S3). Overall, models derived from pseudo training samples with MTCI and Biomass\(\times\)HI estimation had better performance, and were not affected by the width of sowing window. Surprisingly, although models derived from default phenology per se had smaller R\({}^{2}\) for training on simulations than that of models using updated phenology (Table S2), the former actually did a better job than the latter in yield estimation as measured by the adjusted R\({}^{2}\) (Table 4) and the spread of estimates (Figure 5c,d). We believe this was likely because the larger regression coefficient for \(T_{avg}\) in models with default phenology better captured the spatial gradient in temperature, which was a significant explanatory variable for yields in the 2016 growing season. Figure 5: Comparison of selected model predictions with crop cut yields. (**a**) Calibrated model with GCVI, (**b**) calibrated model with MTCI, (**c**) uncalibrated model with default phenology parameter and MTCI, and (**d**) uncalibrated model with updated phenology parameter and MTCI. Grey dashed lines indicate 1:1 line. A map of the yield estimates for the 1 AF region using the uncalibrated model derived from APSIM simulations with default phenology, MTCI, Biomass\(\times\)HI estimation, and Narrow sowing window is given in Figure 6. The spatial pattern of low-high yields matched well with the 1 AF measurements (Figure 1c) and a high spatial correlation with \(T_{avg}\) can be distinguished (Figure 1e). Importantly, the satellite estimates capture both these broad gradients as well as large amounts of yield variation at finer spatial scales within and between fields (Figure 6).