## 3 Results
### Satellite Retrieval and Crop Growth Model Sensitivity Analysis  
We now turn to presenting the results of the crop growth model-based sensitivity analysis. First, in Figure 4, we show the RMSE of the modeled LAI with respect to the actual ground truth LAI for different simulations where three G \(\times\) M parameters (the planting date, seed GDD to maturity, and planting density) are offset by various amounts from their actual values. The results in Figure 4 allow for analysis of the effect of biases in combinations of the three G \(\times\) M parameters varied in the figures. The results show that with respect to the ground-truth there are several combinations of parameter bias which lead to LAI RMSEs below 0.7 against the ground-truth measurements, demonstrating ill-posedness in the inversion of LAI values to G \(\times\) M parameters. As expected, the situation where none of the parameters are biased (i.e., the actual G \(\times\) M parameters applied in the field, at the center of the figure), leads to a low RMSE (near 0.6), however other combinations of biases have similar RMSE. The magnitude of the error seems to be most sensitive to variations in the planting density (as seen by patterns in the variation of the performance corresponding to the frequency of the density variation); however, significant negative GDD offsets and positive planting day delays are also seen to significantly increase the error. Overall, the error is highly variable with respect to the parameter biases and many combinations of biases lead to high error (a range of LAI RMSEs from 0.6 to 1.6 is observed). This variation shows the strong sensitivity of the LAI to these three G \(\times\) M inputs and the interactions between them. In Figure 5, the sensitivity analysis from Figure 4 is reproduced with MODIS LAI retrievals instead of ground-truth LAI measurements. First, it is important to note that the analysis causes a great increase in the number of points analyzed (from N = 146 to N = 3280) and removes potential biases from a skewed distribution of growth stages as all dates are included, instead of just the dates where the ground-truth LAI measurements were taken. Secondly, the figure shows the change in modeled versus retrieved LAI error as the MODIS EVI2/LAI regression coefficients are varied. The results show the strong dependence of the error on both the regression coefficients used and the bias in the model parameters. Interestingly, although all regression coefficients show good performance for some combinations of G \(\times\) M biases, some regression coefficients show significantly less sensitivity to G \(\times\) M biases than others in terms of LAI error. For example, low regression slopes allow for low RMSE values at a limited number of G \(\times\) M bias combinations, while high regression slopes allow for low RMSE values at a significantly greater number of G \(\times\) M bias combinations. As in Figure 4, the variation in the LAI RMSE error is very sensitive to the variation of planting density, although negative GDD offsets also have a very significant effect in increasing the error. The ill-posedness of inverting the G \(\times\) M factors from the MODIS measurements is seen clearly in the figure with several combinations of biases and regression coefficients leading to similar levels of LAI error. As expected, low parameter biases (near the center of the figure) lead to low LAI RMSE values, although negatively biasing the planting density appears to allow for better matchup with the MODIS measurements over a wider range of regression coefficients.