## 1 Introduction
### Background
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Genotype (G)** & **Environment (E)** & **Management (M)** \\ \hline \multicolumn{3}{c}{-Air temperature} \\ -Relative maturity/Growing degree days (GDD) to maturity & -Precipitation -Solar radiation -Solar radiation -Planting density -GDD to flowering -Soil bulk density -Fertilization -Potential kernel number per ear -Gain growth rate -Soil organic matter -Soil pH} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Examples of common G \(\times\) E \(\times\) M factors included in crop growth model simulations [2; 3]. The crop state variable retrieval uncertainty is in a large part caused by the variability in secondary factors [27; 28; 29; 30; 31; 32] that influence the remote sensing measurements, such as cultivar type, soil background, canopy structure, and inherent leaf properties; most of these secondary factors are strongly dependent on site and growth stage [33; 34; 35; 36]. Physical canopy radiative transfer models, such as PROSAIL [37], provide a theoretical model to understand the effect of the secondary factors by forward modeling the top-of-canopy reflectance spectrum from variables describing the soil background, canopy structure, and leaf properties [9]. However, inversion of canopy radiative transfer models is ill-posed [38] and requires the use of _a priori_ constraints to perform the retrievals [39; 40]. While temporal [40; 41; 42] and spatial [40; 43] constraints can be used to address the ill-posedness of the retrieval, they are not sufficiently powerful to remove the uncertainty. As a result, assumptions must be made about the canopy structure and leaf properties [40]. Unfortunately, although both canopy structure and leaf properties have a significant effect on the uncertainty of the retrieval [32], it is difficult to constrain them beyond finding appropriate ranges for the values based on land cover [44] and selecting vegetation indices with greater sensitivity to the variable of interest [32; 45; 46]. However, even though the full spectral modeling can optimize the best choice of vegetation indices for given applications, using vegetation indices in the retrievals directly still results in valuable spectral information being lost, undercutting the benefits of the possibility of using the full spectral information available with canopy radiative transfer models in the retrieval itself [47] as full-spectrum methods have shown good results in the literature [48; 49]. However, because of the lack of information available to remove the uncertainty about secondary factors, physical radiative transfer approaches have not dominated over empirical approaches, although these often do not use the full spectral information available from the sensor and lack a theoretical basis to control secondary factors [27; 28; 29]. The empirical algorithms overcome these issues by directly using training data to learn to use the \"subtle spectral features to reduce undesired effects\" [47] that make vegetation retrievals difficult. In addition, in some cases, empirical methods are also able to improve the retrievals with auxiliary information [29; 50; 51]. In empirical approaches, the uncertainty caused by the variability in secondary factors manifests as the \"one place, one time, one equation\" issue [27] where regressions between the satellite measurements and the crop state variables trained on one set of sites and times do not generalize well to another set of sites and times [27; 28]. The issue occurs because most empirical studies develop a global regression relating the satellite measurements to the crop state variables which does not account for the spatiotemporal variability in the secondary factors, although some studies have attempted to use the secondary factors to improve the retrieval [29; 50; 51]. Specifically, refs.