Estimating parameters of forest patch transition models from gap models

An algorithm to estimate the parameter values of a transition forest landscape model (MOSAIC) from a gap model (FACET) is presented here. MOSAIC is semi-Markov; it includes random distributed holding times and fixed or deterministic delays in addition to transition probabilities. FACET is a terrain-sensitive version of ZELIG, a spatially explicit gap model. For each topographic class, the input to the algorithm consists of gap model tracer files identifying the cover type of each plot through time. These cover types or states are defined a priori. The method, based on individual plots of the FACET model, requires one FACET run initialized from the “gap” cover type and follows the time history of each plot. The algorithm estimates the transition probability by counting the number of transitions between each pair of states and estimates the fixed lags and the parameters of the probability density functions of the distributed delays by recording the times at which these transitions are made. These density functions are assumed to be Erlang; its two parameters, order and rate, are estimated using a nonlinear least squares procedure. Thus, as output, the algorithm produces four matrices at each terrain class: transition probabilities, fixed delays, and the two parameters for the Erlang distributions. The algorithm is illustrated by its application to two sites, high and low elevation, from the H.J. Andrews Forest in the Oregon Cascades. This scaling-up method helps to bridge the conceptual breach between landscape- and stand-scale models. To reflect landscape heterogeneity, the algorithm can be executed repetitively for many different terrain classes. While the method developed here focuses on FACET and MOSAIC, this general approach could be extended to use other fine-scale models or other forms of meta-models.