Estimating time-dependent parameters for a biological ocean model using an emulator approach

article i nfo We use a statistical emulator technique, the polynomial chaos expansion, to estimate time-dependent values for two parameters of a 3-dimensional biological ocean model. We obtain values for the phytoplankton carbon-to-chlorophyll ratio and the zooplankton grazing rate by minimizing the misfit between simulated and satellite-based surface chlorophyll. The misfit is measured by a spatially averaged, time-dependent dis- tance function. A cross-validation experiment demonstrates that the influence of outlying satellite data can be diminished by smoothing the distance function in time. The optimal values of the two parameters based on the smoothed distance function exhibit a strong time-dependence with distinct seasonal differences, without overfitting observations. Using these time-dependent parameters, we derive (hindcast) state esti- mates in two distinct ways: (1) by using the emulator-based interpolation and (2) by performing model runs with time-dependent parameters. Both approaches yield chlorophyll state estimates that agree better with the observations than model estimates with globally optimal, constant parameters. Moreover, the em- ulator approach provides us with estimates of parameter-induced model state uncertainty, which help deter- mine at what time improvement in the model simulation is possible. The time-dependence of the analyzed parameters can be motivated biologically by naturally occurring seasonal changes in the composition of the plankton community. Our results suggest that the parameter values of typical biological ocean models should be treated as time-dependent and will result in a better representation of plankton dynamics in these models. We further demonstrate that emulator techniques are valuable tools for data assimilation and for analyzing and improving biological ocean models.

[1]  R. Barlow,et al.  Pigment signatures of the phytoplankton composition in the northeastern Atlantic during the 1990 spring bloom , 1993 .

[2]  O. Knio,et al.  Propagating boundary uncertainties using polynomial expansions , 2012 .

[3]  Donald D. Lucas,et al.  Parametric sensitivity and uncertainty analysis of dimethylsulfide oxidation in the clear-sky remote marine boundary layer , 2004 .

[4]  Dongbin Xiu,et al.  The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..

[5]  K. Fennel,et al.  Quantifying biological carbon export for the northwest North Atlantic continental shelves , 2009 .

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

[7]  R. He,et al.  Numerical Investigation of the Middle Atlantic Bight Shelfbreak Frontal Circulation Using a High-Resolution Ocean Hindcast Model , 2010 .

[8]  Stephanie Dutkiewicz,et al.  Modeling diverse communities of marine microbes. , 2011, Annual review of marine science.

[9]  G. Evensen,et al.  An Ensemble Kalman Filter with a complex marine ecosystem model: hindcasting phytoplankton in the Cretan Sea , 2003 .

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

[11]  C. Merchant,et al.  Sensitivity analysis of an ocean carbon cycle model in the North Atlantic: an investigation of parameters affecting the air-sea CO 2 flux, primary production and export of detritus , 2011 .

[12]  Jonathan Rougier,et al.  Inference in ensemble experiments , 2007, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[13]  S. Doney,et al.  An intermediate complexity marine ecosystem model for the global domain , 2001 .

[14]  D. Xiu,et al.  Modeling uncertainty in flow simulations via generalized polynomial chaos , 2003 .

[15]  T. Kana,et al.  Dynamic model of phytoplankton growth and acclimation: responses of the balanced growth rate and the chlorophyll a:carbon ratio to light, nutrient-limitation and temperature , 1997 .

[16]  Sharon L. Smith,et al.  The interaction of phytoplankton, zooplankton and currents from 15 months of continuous data in the Mid-Atlantic Bight , 1994 .

[17]  Kenneth L. Denman,et al.  Modelling planktonic ecosystems: parameterizing complexity , 2003 .

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

[19]  J. O'Brien,et al.  Variational data assimilation and parameter estimation in an equatorial Pacific ocean model , 1991 .

[20]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[21]  R. Houghton,et al.  Phytoplankton growth at the shelf-break front in the Middle Atlantic, Bight , 1990 .

[22]  David M. Glover,et al.  A new coupled, one-dimensional biological-physical model for the upper ocean: Applications to the JGOFS Bermuda Atlantic Time-series Study (BATS) site , 1996 .

[23]  R. Askey,et al.  Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials , 1985 .

[24]  Richard J. Geider,et al.  A dynamic regulatory model of phytoplanktonic acclimation to light, nutrients, and temperature , 1998 .

[25]  E. Hofmann,et al.  Time series sampling and data assimilation in a simple marine ecosystem model , 1996 .

[26]  K. Denman,et al.  Low oxygen and high inorganic carbon on the Vancouver Island Shelf , 2011 .

[27]  A. T. Chan.  COMPARATIVE PHYSIOLOGICAL STUDY OF MARINE DIATOMS AND DINOFLAGELLATES IN RELATION TO IRRADIANCE AND CELL SIZE. II. RELATIONSHIP BETWEEN PHOTOSYNTHESIS, GROWTH, AND CARBON/CHLOROPHYLL a RATIO 1, 2 , 1980 .

[28]  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 .

[29]  Habib N. Najm,et al.  Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems , 2008, J. Comput. Phys..

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

[31]  A. T. Chan.  COMPARATIVE PHYSIOLOGICAL STUDY OF MARINE DIATOMS AND DINOFLAGELLATES IN RELATION TO IRRADIANCE AND CELL SIZE. I. GROWTH UNDER CONTINUOUS LIGHT 1, 2 , 1978 .

[32]  K. Fennel,et al.  Statistical validation of a 3-D bio-physical model of the western North Atlantic , 2009 .

[33]  Katja Fennel,et al.  Data assimilation with a local Ensemble Kalman Filter applied to a three-dimensional biological model of the Middle Atlantic Bight , 2012 .

[34]  John C. Warner,et al.  Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the Regional Ocean Modeling System , 2008, J. Comput. Phys..

[35]  Nicole L. Goebel,et al.  An emergent community ecosystem model applied to the California Current System , 2010 .

[36]  Hernan G. Arango,et al.  4DVAR data assimilation in the Intra-Americas Sea with the Regional Ocean Modeling System (ROMS) , 2008 .

[37]  Dale B. Haidvogel,et al.  Nitrogen cycling in the Middle Atlantic Bight: Results from a three‐dimensional model and implications for the North Atlantic nitrogen budget , 2006 .

[38]  Katja Fennel,et al.  Introduction and Assessment of Measures for Quantitative Model-Data Comparison Using Satellite Images , 2010, Remote. Sens..

[39]  K. Fennel,et al.  Interannual variability in atmospheric CO2 uptake on the northeast U.S. continental shelf , 2009 .

[40]  J. Kane.  The demography of Calanus finmarchicus (Copepoda: Calanoida) in the Middle Atlantic Bight, USA, 1977–2001 , 2005 .

[41]  Jens Schröter,et al.  Sequential weak constraint parameter estimation in an ecosystem model , 2003 .

[42]  Sallie W. Chisholm,et al.  Emergent Biogeography of Microbial Communities in a Model Ocean , 2007, Science.

[43]  George E. Karniadakis,et al.  Beyond Wiener–Askey Expansions: Handling Arbitrary PDFs , 2006, J. Sci. Comput..

[44]  Watson W. Gregg,et al.  Phytoplankton and iron: validation of a global three-dimensional ocean biogeochemical model , 2003 .

[45]  Stéphane Blain,et al.  An ecosystem model of the global ocean including Fe, Si, P colimitations , 2003 .

[46]  Katja Fennel,et al.  Sequential data assimilation applied to a physical-biological model for the Bermuda Atlantic time series station , 2010 .

[47]  N. Wiener.  The Homogeneous Chaos , 1938 .

[48]  S. Hooker,et al.  Algorithm development and validation for satellite‐derived distributions of DOC and CDOM in the U.S. Middle Atlantic Bight , 2008 .

[49]  Changsheng Chen,et al.  Plankton production in tidal fronts : A model of Georges Bank in summer , 1996 .

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

[51]  K. Fennel,et al.  Denitrification effects on air‐sea CO2 flux in the coastal ocean: Simulations for the northwest North Atlantic , 2008 .