# Mapping Smallholder Yield Heterogeneity at Multiple Scales in Eastern Africa
## Materials and Methods
### Satellite Based Yield Estimation
#### 2.4.2 Multiple Avenues to Improve Performance  
One underpinning assumption of the uncalibrated approach is that APSIM can reasonably reproduce the seasonal progress of canopy N and yield. However, this assumption can often be violated as shown in several maize model intercomparison studies (e.g., [19,20]). Following our experience with tuning APSIM simulations for rainfed maize in the US Midwest [8], we tested multiple modifications throughout the simulation pipeline.  
First, we changed a few phenology parameters that control the leaf appearance and senescence to the calibrated values in [8], because simulated canopy green-up curves by the default APSIM phenology parameters were known to be too slow in the early season for modern cultivars [21]. We did not repeat the phenology calibration procedure introduced by reference [8], because it requires frequent cloud-free observations during the growing season thus currently not feasible for the study area. An example of seasonal progress of canopy N (CN) from 50 random simulations of the APSIM-Maize model with default and updated phenology parameters is given in Figure 3. Using the updated phenology advanced the green-up phase and led to more realistic flowering time by early July in 2016.  
Second, we compared the difference of using GCVI and MTCI, both of which showed superior performance compared to other VIs in our preliminary analysis, for constructing the linear regression. Following [18], the relationship between GCVI and CN content is:  
\[\text{GCVI}=0.8\times\text{CN} \tag{2}\]  
By synthesizing the relationship between MTCI and canopy chlorophyll content (R\({}^{2}\) = 0.89) from [21] and the relationship between canopy chlorophyll content and CN (R\({}^{2}\) = 0.94) from [18], we converted CN to MTCI using:  
\[\text{MTCI}=0.789\times\text{CN}+3.05 \tag{3}\]It should also be noted that MTCI from Sentinel-2 has a 20-m resolution, since the Red-edge band of Sentinel-2 has a coarser resolution than that of the NIR or visible bands (Table 1).  
Third, existing crop modeling literature (e.g., [22]) suggested that mechanistic simulations of yields by grain formation and growth often underperform simpler approaches that predict yield by multiplying simulated biomass by a constant harvest index (HI). We therefore tested two types of simulations for calibration, one that uses APSIM to directly simulate yields, and another that first uses APSIM to calculate the end-of-season harvestable biomass and then estimates yields by multiplying a constant HI (0.45 in this study). The uncertainty associated with this approach is discussed in details later.  
Finally, we tested the effect of using wide vs. narrow sowing windows when generating the representative simulations for each site. Although farmer-reported sowing dates had a wide range from March to May, the majority were within a relative narrower range of about three weeks (Figure S4). Thus, greater weight should be given to simulations from the narrower window. Based on the distribution of 1 AF reported sowing dates, we used \"15 March\", \"25 March\", \"8 April\", and \"20 April\" as the wide sowing window and \"1 April\", \"5 April\", and \"11 April\" as the narrow sowing window for the B-K sub-region; for the 1 AF region, the wide window was \"10 March\", \"25 March\", \"5 April\", and \"15 April\", and the narrow window was \"25 March\", \"5 April\", and \"12 April\".  
Figure 3: An example of seasonal progress in canopy nitrogen from 50 random simulations by the Agricultural Production Systems Simulator (APSIM)-Maize model with default (**a**) and updated (**b**) phenology parameters (e.g., leaf appearance and senescence). The clustering of simulated curves over the day of year reflects four different sowing dates used in the simulation (i.e., “15 March”, “25 March”, “8 April”, and “20 April”). The timing when cloud-free satellite imagery was available is highlighted in colored vertical lines.