## 2 Materials and Methods
### Regression Tree Model Development  
The two regression tree mapping models in this study were developed using Cubist software [41] based on the methodology as described by [PERSON], et al. [11]. Cubist was used because of its use of generalized rules and widespread successful applications in the remote sensing field [5; 10; 11; 14; 18; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51]. Each regression tree model consisted of the dependent variable to be estimated and the set of independent variables. The dependent variable in this case was the weekly NEP (grams (g) of C\(\cdot\)m\({}^{-2}\)-week\({}^{-1}\)) from the study flux towers (Table S1). A potential drawback to regression tree models is a tendency of overfitting (substantial differences between test and training accuracy). These overfitting tendencies were assessed and minimized through nine model training iterations with varying data set sizes. Each training data set size was replicated nine times with different random seeds. Analysis of the GNU General Public License of Cubist [41] revealed that the ruleset (stratification for piecewise regressions and regression independent variable selection) cost function is the mean absolute difference modified by the ratio of the number of cases and the number of parameters. This weights the process towards having fewer parameters and trying to simplify the model as a whole while countering against over fitting and mitigating outlier impacts. More classical least squares approaches tend to be more sensitive to outliers than to absolute difference. The multiple regression determination for each ruleset is a classical least squares approach excluding extreme residual outliers. The models were designed to ingest a series of input spatial data and estimate the weekly mean daily cropland and grassland NEP throughout the U.S. Great Plains for 2000 to 2008 at 250 m spatial resolution. Under the ecological-based notation, NEP is defined as subtracting RE from GPP and denotes the net exchange of carbon between terrestrial ecosystems and the atmosphere where the ecosystem is the point of reference (Equation (2)). Therefore, any ecosystem that absorbs more carbon (C) than it releases would yield a positive NEP value and would be considered a C sink. Conversely, any ecosystem that releases more C than it absorbs would yield a negative NEP value and would be considered a C source. \[\text{NEP}=\left(\text{GPP}-\text{RE}\right), \tag{2}\]  
The model training process (Figure S1) begins by first spatially and temporally linking the flux tower data with the spatial datasets to create the training database for each model. To achieve this, the flux tower data were converted into point shapefiles with the accompanying weekly NEP records. Next, these points where spatially and temporally intersected with each of the input spatial datasets to extract the full set of input values at each point. Through this procedure, the flux tower point and accompanying NEP records were merged with the appropriate input spatial dataset values, creating the final training databases. The training data base used for developing the cropland NEP regression tree model contained 2225 samples of weekly NEP acquired from 15 flux tower locations over 13 years with temporal coverage varying by flux tower. Likewise, the grassland NEP regression tree model was trained on 1447 weekly samples acquired from 15 flux tower locations over 9 years. These data bases were then ingested into RuleQuest Cubist v. 2.06 data mining software [41] to construct the regression tree mapping models (Figure S1). Cubist ingests the training data bases, analyzes them for patterns and relationships between the independent and the dependent variables, and uses this information to create models consisting of numerous estimation rules in the form of multiple 'if-then-else' conditional statements. The completed models are in turn implemented on a pixel-by-pixel basis to estimate NEP, the dependent variable, based on the set of input spatial data, outputting a weekly map.