## 3 Results
### Satellite Retrieval and Crop Growth Model Sensitivity Analysis
In Table 5, we show the actual and theoretical, modeled versus retrieved \(|\text{r}|\) and RMSE for LAI itself and \(\Delta\)LAI for \(\Delta\) = 2 to 10. The results in Table 5 show that the actual \(|\text{r}|\) and RMSE performance of the \(\Delta\)LAI retrievals significantly outperform the theoretical performance calculated with Equations (8) and (9); for example, for \(\Delta\) = 4, which corresponds to a week of measurements, the actual \(|\text{r}|\) and RMSE values are 0.70 and 0.40, while the theoretical values are 0.36 and 1.46, respectively. In Figure 7, we present the \(|\text{r}|\) correlation of the MODIS EVI2 measurements versus modeled \(\Delta\)LUE\({}_{\text{Canopy}}\) at different levels of smoothing and values of \(\Delta\). The results in Figure 7 show that the \(|\text{r}|\) MODIS EVI2/\(\Delta\)LUE\({}_{\text{Canopy}}\) correlation strongly depends on the level of smoothing and the value of \(\Delta\); however, high \(|\text{r}|\) values may be obtained when smoothing is performed at \(\Delta\) values above 5. Figure 6: (**a–c**) Retrieved versus HM Modeled \(\Delta\)LAI at \(\Delta\) = 3, 6, 9; (**d**) Retrieved versus HM Modeled LAI. The colorbars represents the number of points at each marker on the scatter plot. Only days with modeled \(\mathrm{LUE_{Canopy}}\) greater than zero are included in Figures 6 and 7 and Table 5. In addition, for consistency with Figure 2, the small number of days which have less than 95% of the underlying measured GPP time series available are not included in Figure 7.  
In addition to comparison of modeled values (from the Mead, Nebraska sites) in Figure 7, \(\Delta\mathrm{LUE_{Canopy}}\) retrievals are compared against the actual \(\Delta\mathrm{LUE_{Canopy}}\) measurements at all sites in the FLUX dataset. The performance against all the actual \(\Delta\mathrm{LUE_{Canopy}}\) data is shown in Figures 8 and 9, while the site-by-site performance is shown in Figures S1-S10 in the Supplementary Materials. Figures 8 and 9 and Figures S1-S10 show that the actual \(\Delta\mathrm{LUE_{Canopy}}\) is retrieved with a performance at or above the theoretical performance assuming independence of retrieval error with respect to time and the relationship holds at most, but not all, sites. Poor performance at some sites, as seen in Figures S1-S10, may be explained by the large pixel size of MODIS (500 m), which can cause significant noise in the measurement of the daily time series depending on the size of the field and the inhomogeneity of the area surrounding the field [97; 98]. Specifically, the mixed-pixel effect causes \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\(\Delta\) **(Days)**} & \multirow{2}{*}{\(|\mathbf{r}|\)**-Modeled v Retrieved**} & \multirow{2}{*}{\(|\mathbf{r}|\)**-Modeled v Retrieved**} & \multirow{2}{*}{**RMSE-Modeled v Retrieved**} & \multirow{2}{*}{**RMSE-Modeled v Retrieved**} & \\  & & & & & \\ \hline
2 & 0.52 & 0.13 & 0.17 & 1.46 & 2429 \\
3 & 0.64 & 0.25 & 0.29 & 1.46 & 2429 \\
4 & 0.70 & 0.36 & 0.40 & 1.46 & 2429 \\
5 & 0.75 & 0.45 & 0.50 & 1.46 & 2429 \\
6 & 0.78 & 0.53 & 0.59 & 1.46 & 2429 \\
7 & 0.81 & 0.59 & 0.68 & 1.46 & 2429 \\
8 & 0.83 & 0.65 & 0.76 & 1.46 & 2429 \\
9 & 0.85 & 0.69 & 0.84 & 1.46 & 2429 \\
10 & 0.87 & 0.73 & 0.91 & 1.46 & 2429 \\ Value Itself (no delta) & 0.92 & 0.88 & 1.04 & 1.03 & 2429 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of HM modeled versus retrieved, actual and theoretical \(|\mathbf{r}|\) and RMSE for the retrieval of \(\Delta\)LAI and LAI at different values of \(\Delta\). Figure 7: \(|\mathbf{r}|\) correlation of the MODIS EVI2 measurements versus HM modeled \(\Delta\mathrm{LUE_{Canopy}}\) at different levels of smoothing and values of \(\Delta\). N = 2359.  
the signatures of neighboring pixels to be blended and it makes it difficult to separate the time-series of individual crops, especially if spring and winter crops are grown nearby [97], as is the case at some of the sites where poor performance is observed.