## 2 Materials and Methods
### Regression Tree Model Development
The validation and accuracy assessment of the Cubist regression tree NEP mapping models quantified model training accuracy and model spatial and temporal accuracy through a series of leave-one-out cross validation techniques. The cross validation method withholds a specific group of flux data (data from a particular flux tower, year, or a random sample of weekly fluxes) from model development as an independent test and the mapping model is developed from the remaining flux dataset. The cross validation approach is widely accepted [52; 53; 54; 55] and has been used in C flux mapping [5; 10; 11; 13; 18] and biomass mapping [47; 56], as well as to assess expected model performance on unseen data, identify of influential flux towers and years, and to help optimize models to minimize over fitting (using random cross validation) [19; 57; 58]. Cross validation approaches provide robust accuracy assessments from many independent withheld \"test\" data, which helps to identify and minimize over fitting or over generalization [59], and allows all of the limited flux towers to be utilized in developing the final mapping models--maximizing mapping accuracy and robustness for crop and grassland NEP. Our experience with Cubist models for mapping has indicated the potential for a substantial variation of test accuracies with different randomizations of test data or different sites or years being withheld as test [11; 51]. Cross validation techniques allow multiple independent test data sets to estimate the expected accuracies of the population of pixels to be mapped and can better quantify accuracy variability across multiple random test datasets than the classical single independent data test dataset approach. To further quantify the robustness of our flux mapping algorithms, we utilized an approach similar to the \"bias/variance tradeoff\" approach [59]. With this approach, the input variables and the maximum allowed number of committee sub-models are held constant while the various size combinations of test and training are assessed [60]. The training data size (or proportion of the total weekly flux tower observations) in this experiment was increased in 10% increments from 10% to 90% with the test datasets decreasing inversely from 90% to 10%. At each level of training dataset size, we performed nine different random seeds for test data selections (nine training dataset sizes with nine different randomizations = 81 model runs). Across the nine randomizations at each level of training dataset size, the mean absolute difference (MAD) was calculated to quantify training and test accuracies, the standard deviation of MAD quantified model stability for training and test datasets at each level of training dataset size, and the MAD difference between test and training datasets quantified model over fitting. Relationships between test accuracy and training accuracies were established as a function of training dataset size to extrapolate expected model tendencies when trained on 100% of the flux tower data (which was used for map generation). Under sampling by reference or training data relative to the space and time to be mapped is an issue in both machine learning approaches and process-based mapping models used to map carbon fluxes [5; 9; 61; 5], but the area to be mapped to number of flux tower ratios were similar in this study to other carbon flux mapping efforts [5; 13; 18].