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 © 2012 John Wiley & Sons, Ltd.

[1]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[2]  Michael Dowd,et al.  Bayesian statistical data assimilation for ecosystem models using Markov Chain Monte Carlo , 2007 .

[3]  Peter G. Challenor,et al.  A Markov chain Monte Carlo method for estimation and assimilation into models , 1997 .

[4]  M. Dowd.  A sequential Monte Carlo approach for marine ecological prediction , 2006 .

[5]  Zhengdong Lu,et al.  Fast neural network surrogates for very high dimensional physics-based models in computational oceanography , 2007, Neural Networks.

[6]  D. Menemenlis.  Inverse Modeling of the Ocean and Atmosphere , 2002 .

[7]  Eddy Campbell,et al.  Sequential data assimilation in fine-resolution models using error-subspace emulators: Theory and preliminary evaluation , 2012 .

[8]  J. Fiechter,et al.  Quantifying eddy-chlorophyll covariability in the Coastal Gulf of Alaska , 2012 .

[9]  A. Moore,et al.  A data assimilative, coupled physicalbiological model for the Coastal Gulf of Alaska , 2011 .

[10]  J. Rougier.  Efficient Emulators for Multivariate Deterministic Functions , 2008 .

[11]  Heikki Haario,et al.  Bayesian modelling of algal mass occurrences - using adaptive MCMC methods with a lake water quality model , 2007, Environ. Model. Softw..

[12]  M. Hooten,et al.  A general science-based framework for dynamical spatio-temporal models , 2010 .

[13]  Stephen G. Yeager,et al.  The global climatology of an interannually varying air–sea flux data set , 2009 .

[14]  A. OHagan,et al.  Bayesian analysis of computer code outputs: A tutorial , 2006, Reliab. Eng. Syst. Saf..

[15]  A. O'Hagan,et al.  Bayesian emulation of complex multi-output and dynamic computer models , 2010 .

[16]  Michael A. West,et al.  A dynamic modelling strategy for Bayesian computer model emulation , 2009 .

[17]  Gabriele B. Durrant,et al.  Journal of the Royal Statistical Society Series A (Statistics in Society). Special Issue on Paradata , 2013 .

[18]  Geir Evensen,et al.  An Ensemble Kalman filter with a 1-D marine ecosystem model , 2002 .

[19]  G. Evensen.  Data Assimilation: The Ensemble Kalman Filter , 2006 .

[20]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

[21]  Robert Haining,et al.  Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95 , 1993 .

[22]  Lawrence M. Murray,et al.  A Bayesian approach to state and parameter estimation in a Phytoplankton-Zooplankton model , 2010 .

[23]  A. O'Hagan,et al.  Gaussian process emulation of dynamic computer codes , 2009 .

[24]  Scott C. Doney,et al.  Assessment of skill and portability in regional marine biogeochemical models : Role of multiple planktonic groups , 2007 .

[25]  Y. Yamanaka,et al.  Interdecadal variation of the lower trophic ecosystem in the northern Pacific between 1948 and 2002, in a 3-D implementation of the NEMURO model , 2007 .

[26]  G. Evensen,et al.  Sequential Data Assimilation Techniques in Oceanography , 2003 .

[27]  C. McClain,et al.  The calibration and validation of SeaWiFS data , 2000 .

[28]  L. Mark Berliner,et al.  Combining Information Across Spatial Scales , 2005, Technometrics.

[29]  Mevin B Hooten,et al.  Models for Bounded Systems with Continuous Dynamics , 2009, Biometrics.

[30]  Thomas R. Anderson,et al.  Parameter optimisation techniques and the problem of underdetermination in marine biogeochemical models , 2010 .

[31]  D. Higdon,et al.  Computer Model Calibration Using High-Dimensional Output , 2008 .

[32]  Thomas M. Powell,et al.  Modeling iron limitation of primary production in the coastal Gulf of Alaska , 2009 .

[33]  Christopher K. Wikle,et al.  Science-based parameterizations for dynamical spatiotemporal models , 2012 .

[34]  L. Mark Berliner,et al.  Physical‐statistical modeling in geophysics , 2003 .

[35]  J. Fiechter.  Assessing marine ecosystem model properties from ensemble calculations , 2012 .

[36]  Alan E Gelfand,et al.  A Spatio-Temporal Downscaler for Output From Numerical Models , 2010, Journal of agricultural, biological, and environmental statistics.

[37]  A comparison of two lower trophic models for the California Current System , 2007 .

[38]  Christopher K. Wikle,et al.  Hierarchical Bayesian Models for Predicting The Spread of Ecological Processes , 2003 .

[39]  W. Broenkow,et al.  Vertex: phytoplankton/iron studies in the Gulf of Alaska , 1989 .

[40]  C. Nucci,et al.  On return stroke currents and remote electromagnetic fields associated with lightning strikes to tall structures: 2. Experiment and model validation , 2007 .

[41]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[42]  L. Mark Berliner,et al.  Ocean ensemble forecasting. Part I: Ensemble Mediterranean winds from a Bayesian hierarchical model , 2011 .

[43]  Andrew O. Finley,et al.  Improving Crop Model Inference Through Bayesian Melding With Spatially Varying Parameters , 2011 .

[44]  T. Patterson,et al.  Deep Sea Research Part II: Topical Studies in Oceanography , 2013 .

[45]  Dorin Drignei.  Fast Statistical Surrogates for Dynamical 3D Computer Models of Brain Tumors , 2008 .

[46]  Yasuhiro Yamanaka,et al.  NEMURO—a lower trophic level model for the North Pacific marine ecosystem , 2007 .

[47]  Peter Franks,et al.  NPZ Models of Plankton Dynamics: Their Construction, Coupling to Physics, and Application , 2002 .

[48]  Mevin B. Hooten,et al.  Assessing First-Order Emulator Inference for Physical Parameters in Nonlinear Mechanistic Models , 2011 .

[49]  Trevor Hastie,et al.  The Elements of Statistical Learning , 2001 .

[50]  António M. Baptista,et al.  Author's Personal Copy Dynamics of Atmospheres and Oceans Fast Data Assimilation Using a Nonlinear Kalman Filter and a Model Surrogate: an Application to the Columbia River Estuary , 2022 .

[51]  Montserrat Fuentes,et al.  Model Evaluation and Spatial Interpolation by Bayesian Combination of Observations with Outputs from Numerical Models , 2005, Biometrics.

[52]  Christian P. Robert,et al.  Statistics for Spatio-Temporal Data , 2014 .

[53]  L. Mark Berliner,et al.  Spatiotemporal Hierarchical Bayesian Modeling Tropical Ocean Surface Winds , 2001 .

[54]  A. Raftery,et al.  Inference for Deterministic Simulation Models: The Bayesian Melding Approach , 2000 .

[55]  T. Tyrrell.  OF ATMOSPHERES AND OCEANS , 1998 .

[56]  M. Dowd.  Estimating parameters for a stochastic dynamic marine ecological system , 2011 .

[57]  T. J. Mitchell,et al.  Bayesian Prediction of Deterministic Functions, with Applications to the Design and Analysis of Computer Experiments , 1991 .

[58]  A. O'Hagan,et al.  Quantifying uncertainty in the biospheric carbon flux for England and Wales , 2007 .

[59]  Noel A. C. Cressie,et al.  Statistics for Spatial Data: Cressie/Statistics , 1993 .

[60]  Katja Fennel,et al.  Estimating time-dependent parameters for a biological ocean model using an emulator approach , 2012 .

[61]  H. Müller,et al.  Dynamic relations for sparsely sampled Gaussian processes , 2010 .

[62]  Dave Higdon,et al.  Combining Field Data and Computer Simulations for Calibration and Prediction , 2005, SIAM J. Sci. Comput..

[63]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[64]  L. Mark Berliner,et al.  Hierarchical Bayesian Time Series Models , 1996 .

[65]  J. Andrew Royle,et al.  A Hierarchical Spatial Model for Constructing Wind Fields from Scatterometer Data in the Labrador Sea , 1999 .

[66]  Y. Yamanaka,et al.  Comparison of seasonal characteristics in biogeochemistry among the subarctic North Pacific stations described with a NEMURO-based marine ecosystem model , 2007 .

[67]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.