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

Abstract

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 © 2012 John Wiley & Sons, Ltd.

Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling

“…Noninformative prior distributions were employed for each parameter so the influence of the priors on the solution for each site was fairly weak. In a parallel Bayes' hierarchical modelling study for the same model, Leeds et al (2013) assimilated satellite chlorophyll data at nine sites using a spatial Gaussian process model for the parameters with an anisotropic correlation matrix to allow for differences between along-shelf and cross-shelf dependence. The methods employed by Leeds et al (2013) and Fiechter et al (2013) seem promising because of their potential for rigorous treatment of uncertainty.…”

“…In a parallel Bayes' hierarchical modelling study for the same model, Leeds et al (2013) assimilated satellite chlorophyll data at nine sites using a spatial Gaussian process model for the parameters with an anisotropic correlation matrix to allow for differences between along-shelf and cross-shelf dependence. The methods employed by Leeds et al (2013) and Fiechter et al (2013) seem promising because of their potential for rigorous treatment of uncertainty. However, in the absence of crossvalidation experiments, their potential for improving the predictive skill of the models is not well evaluated at present.…”

Regional Ocean Data Assimilation

“…Once the emulator is created, it can be rapidly executed and applied repeatedly to data sets that span different spatial regions or temporal periods. Emulators have been demonstrated to be efficient alternatives for parameter optimization studies in the northern Gulf of Alaska (Hooten et al 2011, Leeds et al 2013) and Mid-Atlantic Bight .…”

A statistical overview and perspectives on data assimilation for marine biogeochemical models

“…For BGC DA, this means accounting for structural uncertainty in the governing equations, and more effectively using prior information (Parslow et al , ). It is our opinion that an important direction for BGC DA is the further development of sampling‐based Bayesian approaches for DA in conjunction with novel approaches for dimension reduction (Leeds et al , ). An obvious trade‐off in the current practice of BGC DA is between using sophisticated statistical estimation methods and using complex dynamical models.…”