Estimating complex ecological variables at high resolution in heterogeneous terrain using multivariate matching algorithms

1. Simulation models are valuable tools for estimating ecosystem structure and function under various climatic and environmental conditions and disturbance regimes, and are particularly relevant for investigating the potential impacts of climate change on ecosystems. However, because computational requirements can restrict the number of feasible simulations, they are often run at coarse scales or for representative points. These results can be difficult to use in decision-making, particularly in topographically complex regions. 2. We present methods for interpolating multivariate and time series simulation output to high resolution maps. First, we developed a method for applying k-means clustering to optimize selection of simulation sites to maximize the area represented for a given number of simulations. Then, we used multivariate matching to interpolate simulation results to high-resolution maps for the represented area. The methods rely on a user-defined set of matching variables that are assigned weights such that matched sites will be within a prescribed range for each variable. We demonstrate the methods with case studies using an individual-based plant simulation model to illustrate site selection and an ecosystem water balance simulation model for interpolation. 3. For the site-selection case study, our approach optimized the location of 200 simulation sites and accurately represented 96% of a large study area (1.12 x 106 km2) at a 30-arcsecond resolution. For the interpolation case study, we generated high-resolution (30-arcsecond) maps across 4.38 x 106 km2 of drylands in western North America from simulated sites representing a 10 x 10 km grid. Our estimates of interpolation errors using leave-one-out cross validation were low (<10% of the range of each variable). 4. Our point selection and interpolation methods provide a means of generating high-resolution maps of complex simulation output (e.g., multivariate and time-series) at scales relevant for local conservation planning and can help resolve the effects of topography that are lost in simulations at coarse scales or for representative points. These methods are flexible and allow the user to identify relevant matching criteria for an area of interest to balance quality of matching with areal coverage to enhance inference and decision-making in heterogenous terrain.