Modeling 3-D spatio-temporal biogeochemical processes with a forest of 1-D statistical emulators

This paper focuses on the spatio-temporal dynamical processes in lower trophic level marine ecosystems, where various sources of uncertainty make statistical modeling difficult. Such dynamical processes exhibit nonlinearity in time and potential nonstationarity in space. Planktonic organisms are microscopic, making it difficult to measure their abundance and resulting in limited data. Further, deterministic, component-based ecosystem models contain a large number of parameters, some of which can be difficult to estimate. We consider a Bayesian hierarchical framework for parameter estimation that uses an approximation to the dynamical models for computational feasibility. Specifically, we develop a computationally inexpensive first-order statistical emulator for a one-dimensional NPZD model with iron limitation. Then, we introduce a novel approach to the modeling of three-dimensional lower trophic level marine ecosystem processes, linking the one-dimensional emulators via a two-dimensional spatial field on the parameters. This methodology is used to estimate important biological parameters on the coastal Gulf of Alaska, leading to a reduction in Bayesian credible interval width compared with a nonspatial model. Copyright (c) 2012 John Wiley & Sons, Ltd.