A question of scale: modeling biomass, gain and mortality distributions of a tropical forest

Abstract

Describing the heterogeneous structure of forests is often challenging. One possibility is to analyze forest biomass in different plots and to derive plot-based frequency distributions. However, these frequency distributions depend on the plot size and thus are scale dependent. This study provides insights about transferring them between scales. Understanding the effects of scale on distributions of biomass is particularly important for comparing information from different sources such as inventories, remote sensing and modeling, all of which can operate at different spatial resolutions. Reliable methods to compare results of vegetation models at a grid scale with field data collected at smaller scales are still missing. The scaling of biomass and variables, which determine the forest biomass, was investigated for a tropical forest in Panama. Based on field inventory data from Barro Colorado Island, spanning 50 ha over 30 years, the distributions of aboveground biomass, biomass gain and mortality were derived at different spatial resolutions, ranging from 10 to 100 m. Methods for fitting parametric distribution functions were compared. Further, it was tested under which assumptions about the distributions a simple stochastic simulation forest model could best reproduce observed biomass distributions at all scales. Also, an analytical forest model for calculating biomass distributions at equilibrium and assuming mortality as a white shot noise process was tested. Scaling exponents of about 0.47 were found for the standard deviations of the biomass and gain distributions, while mortality showed a different scaling relationship with an exponent of 0.3. Lognormal and gamma distribution functions fitted with the moment matching estimation method allowed for consistent parameter transfers between scales. Both forest models (stochastic simulation and analytical solution) were able to reproduce observed biomass distributions across scales, when combined with the derived scaling relationships. The study demonstrates a way of how to approach the scaling problem in model-data comparisons by providing a transfer relationship. Further research is needed for a better understanding of the mechanisms that shape the frequency distributions at the different scales.