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Fishers, IN, United States

Leeds W.B.,University of Chicago | Leeds W.B.,University of Missouri | Wikle C.K.,University of Missouri | Fiechter J.,University of California at Santa Cruz | And 2 more authors.
Environmetrics | Year: 2013

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. © 2012 John Wiley & Sons, Ltd.. Source

Milliff R.F.,University of Colorado at Boulder | Fiechter J.,University of California at Santa Cruz | Leeds W.B.,University of Chicago | Herbei R.,Ohio State University | And 5 more authors.
Oceanography | Year: 2013

Lower trophic level (LTL) ocean ecosystem models are important tools for understanding ocean biogeochemical variability and its role in Earth's climate system. These models are often replete with parameters that cannot be well constrained by the sparse observational data available. LTL ocean ecosystem model parameter estimation is examined from a probabilistic perspective, using a Bayesian hierarchical model (BHM), in the coastal Gulf of Alaska (CGOA) domain that benefits from ocean station observations obtained in repeated US GLOBEC cruises. Data entering the BHM include daily average SeaWiFS satellite estimates of surface chlorophyll and GLOBEC observations of nutrient and phytoplankton profiles at inner and outer shelf stations on the Seward Line. The final form of the BHM process model component is comprised of a discrete version of the Nutrient-Phytoplankton-Zooplankton-Detritus LTL ecosystem model equations augmented to address iron limitation in the CGOA (i.e., NPZDFe), and including a vertical diffusion term to constrain the timing of the phytoplankton bloom in spring. Even in the relatively data-rich GLOBEC context, parameter estimation in the BHM requires guidance from a suite of calculations in a coupled physical-biological deterministic model-the Regional Ocean Model System coupled to an NPZDFe component (ROMS-NPZDFe). ROMS-NPZDFe simulations are used to: (1) validate the BHM formulation, (2) separate BHM limitations due to sampling from those due to LTL model approximations, and (3) obtain output distributions for zooplankton grazing rate and phytoplankton nutrient uptake rate using GLOBEC and SeaWiFS data for 2001. Uncertainty is evident from the spreads in output distributions for model parameters in the BHM. Experiments driven by simulated data from ROMS-NPZDFe helped to optimize the utility of GLOBEC observations for LTL ocean ecosystem model parameter estimation, given ever-present uncertainty issues. The ROMS-NPZDFe simulations are also used to build Bayesian statistical models as surrogates for the deterministic model. Two applications are briefly described. One estimates output distributions for selected ocean ecosystem parameters while accounting for spatial variability across the GLOBEC stations in the CGOA. A second application assimilates SeaWiFS data and simulated data from a ROMS-NPZDFe control run for 2002 to estimate complete fields of surface phytoplankton concentration, with associated spatial and temporal uncertainties. © 2013 by The Oceanography Society. All rights reserved. Source

Fiechter J.,University of California at Santa Cruz | Herbei R.,Ohio State University | Leeds W.,University of Chicago | Brown J.,Principal Scientific Group | And 4 more authors.
Ecological Modelling | Year: 2013

The present study describes a state-of-the-art methodology based on an adaptive Metropolis-Hastings algorithm to facilitate efficient Bayesian sampling for realistic lower trophic level (LTL) marine ecosystem models. The main objective is to explore the ability to differentiate between biological parameters that can learn from observations and those that cannot. The Bayesian approach is applied to the northwestern coastal Gulf of Alaska region and uses both synthetic and actual (in situ and remotely sensed) observations. LTL ecosystem dynamics in the Bayesian framework are described by a process model consisting of a 1-dimensional Nutrient-Phytoplankton-Zooplankton-Detritus formulation with iron limitation (NPZDFe) and vertical mixing. The results illustrate the ability to determine parameter posterior distributions for fundamental biological rates, such as maximum phytoplankton growth or zooplankton grazing. By using various observational platforms as data stage inputs, the results also demonstrate the impact of spatial and temporal sampling on parameter posterior distributions, as well as the benefits of having concurrent measurements for two or more state variables of the process model (e.g., chlorophyll and nitrate concentrations). Extending the method to multiple parameters is non-trivial, as posterior distributions become impacted by correlated and/or disproportionate contributions for certain model parameters. Controlled experiments with "near perfect data" were useful to characterize parameter identifiability based on information content in the BHM data stage inputs, as well as to separate uncertainties due to sampling issues vs. uncertain ecosystem process interpretation. © 2013 Elsevier B.V. Source

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