## 1 Introduction  
### Background  
Mechanistic crop growth models temporally predict the growth of crops as a function of genotype x environment x management (G \(\times\) E \(\times\) M) factors [1]. By mechanistically modeling the effects of G \(\times\) E \(\times\) M factors and their interactions, crop growth models are able to integrate information about the properties of the seed (genotype), the decisions farmers make both at planting and within the season (management), and the variability in the weather and soil (environment). Examples of these factors in each category of G \(\times\) E \(\times\) M are shown in Table 1[2; 3]. In addition to these G \(\times\) E \(\times\) M factors, biotic stresses--such as weeds, pests, and diseases--can further limit the growth of crops and these factors are difficult to model, although some recent advances have been made [4]. Nevertheless, in highly developed cropping systems, such as the US corn belt, fields tend to be well-managed and the reduction in yield caused by unmodeled factors, such as biotic stresses, is generally 20% or less [5; 6]. As a result, mechanistic crop growth model simulations are able to provide valuable information with relatively strong predictive performance in highly developed cropping systems [6; 7]. Assimilation of remote sensing data into crop growth models can be used to reduce the uncertainty in the G \(\times\) E \(\times\) M factors (which control crop growth) via calibration [8; 9; 10; 11]. In the calibration approach to remote sensing data assimilation, the model parameters and G \(\times\) E \(\times\) M factors affecting crop growth are adjusted by reinitialization until the crop growth model output agrees with the remote sensing observation (as opposed to the updating or forcing approaches where the crop model state variables are themselves directly altered) [9]. However, uncertainty in the remote sensing retrievals of crop state variables, such as leaf area index (LAI), leads to significant challenges [9] in the calibration and determination of the G \(\times\) E \(\times\) M factors. This is because the interactions of G \(\times\) E \(\times\) M factors in crop growth models are highly non-linear and careful application of inversion techniques is required to determine input parameters from observations [12; 13]. As a result, even small uncertainties in the remote sensing retrievals can propagate into significant errors in the G \(\times\) E \(\times\) M factors determined by calibration [14]. Therefore, calibration of crop models with remote sensing data is primarily used to analyze output variables, such as yields and biomass, discarding the G \(\times\) E \(\times\) M factors determined by calibration as an intermediate step [8; 15; 16; 17; 18]. Nevertheless, improved understanding of the G \(\times\) E \(\times\) M factor variability can greatly improve our ability to use crop growth models at the regional scale [6; 19; 20] to predict into the future and answer questions about climate change [21], agricultural policies [22; 23], and yield gaps [24]. At the regional scale, G \(\times\) E \(\times\) M parameter uncertainty is even more significant due to a lack of calibration data as compared to the field-scale [1; 25]. Thus, constraints from measurements other than yield are vital for further reduction in the uncertainty [25] at this scale. Illustrating this point, ref. [25] found that the majority of the uncertainty in LAI simulations for regional simulations of Indian groundnut was parametric uncertainty, indicating the potential of reductions in the uncertainties of satellite retrievals (such as those of LAI) to significantly improve our understanding of G \(\times\) E \(\times\) M variability in calibration of regional crop models [26].