## 2 Methods
### Ecosystem Performance Modeling
#### 2.2.2 Models  
The basic modeling approach is a regression tree EP model based on the basic hypothesis that Actual Performance is a function of site potential and weather. Site potential is the long-term GSN estimated through a regression tree driven by time invariant spatial data sets related to site condition (elevation, soils, aspect, _etc._). Once site potential is mapped, it does not vary between years and is used as a driver in the EP model to represent the combined effects of site differences on boreal forest long-term productivity, Site potential should account for most of the geographic variation and allow the weather data to address interannual variations.  
Data-driven, machine learning regression tree models were used to develop models for predicting both site potential and EP. Rule-based piecewise regression techniques were employed to model the nonlinear response of long-term average ecosystem performance and annual ecosystem performance. To maximize prediction accuracy and insure model robustness, we used multiple models each with high numbers of terminal nodes and multiple regression equations, which allowed for only the most useful variables to be used in different environmental settings. This modeling approach enables the automatic handling of interactions, since different linear regression models are used in different parts of the predictor variable space [78]. This approach often results in better prediction accuracy [79] than a single multivariate linear regression. For a detailed description of the piecewise rule-based regression tree, see [5].  
Two regression tree mapping models were constructed: (1) site potential, which represents the long-term (2000-2005) average expected performance for each site (primarily geographic variability); and (2) EP model, which included site potential as an input and employed yearly weather to address interannual variability. Site potential and EP were spatial dependent variables that can be reliably replicated through time and space [5, 80]. Stratified random sampling for the site potential model (\(n=2529\)) was done to insure near-equal representation of the model development database sample locations in low, moderate, and high productivity areas to help minimize prediction bias. The EP model included years as an additional stratification criteria (\(n=15,049\)). To focus the EP model predictions on mature boreal forests all sample points were further constrained to exclude areas that had burned in the previous 50 years. Fire perimeters were obtained from the Bureau of Land Management, Alaska Fire Service [81], and the Canada Forest Service. The relatively large model development data sets helped to insure that the models were robust to a wide range of conditions. Inputs to the site potential model included temporally static variables that characterized site conditions: soil drainage, land forms, elevation, aspect, slope, compound terrain index, surficial geology merged from two sources [82, 83], ecoregions [84], median potential evapotranspiration [85], environmental domains [85], median solar radiation [85], permafrost characteristics [86], and historical monthly climate grids for North America [87].