Stochastic estimation of biogeochemical parameters from Globcolour ocean colour satellite data in a North Atlantic 3D ocean coupled physical–biogeochemical model

Abstract

Biogeochemical parameters remain a major source of uncertainty in coupled physical–biogeochemical models of the ocean. In a previous study (Doron et al., 2011), a stochastic estimation method was developed to estimate a subset of biogeochemical model parameters from surface phytoplankton observations. The concept was tested in the context of idealised twin experiments performed with a 1/4° resolution model of the North Atlantic ocean. The method was based on ensemble simulations describing the model response to parameter uncertainty. The statistical estimation process relies on nonlinear transformations of the estimated space to cope with the non-Gaussian behaviour of the resulting joint probability distribution of the model state variables and parameters. In the present study, the same method is applied to real ocean colour observations, as delivered by the sensors SeaWiFS, MERIS and MODIS embarked on the satellites OrbView-2, Envisat and Aqua respectively. The main outcome of the present experiments is a set of regionalised biogeochemical parameters. The benefit is quantitatively assessed with an objective norm of the misfits, which automatically adapts to the different ecological regions. The chlorophyll concentration simulated by the model with this set of optimally derived parameters is closer to the observations than the reference simulation using uniform values of the parameters. In addition, the interannual and seasonal robustness of the estimated parameters is tested by repeating the same analysis using ocean colour observations from several months and several years. The results show the overall consistency of the ensemble of estimated parameters, which are also compared to the results of an independent study.

Introduction

Coupled physical–biogeochemical models (CPBM) of the ocean have been the subject of major developments during the past years with the goal of delivering hindcasts of the biogeochemical state of the ocean (e.g. Brasseur et al., 2009, Ford et al., 2012), short-term forecasts or longer-term simulations in relation with climate change (IPCC, 2007). However, the capacity of these CPBMs to realistically represent the observed variability of biogeochemical marine properties is still limited by the various sources of errors that occur in the simulations as a result of imperfect descriptions of the physical environment that drives the biology and empirical parameterisations of the biogeochemical interactions. From the seminal work of Fasham et al. (1990) to present day models, (e.g. Aumont et al., 2003), a common questioning about the development of biogeochemical models is the choice of state variables (each pool representing an organic or inorganic quantity) and the deterministic relationships that govern the fluxes between these pools. There is still debate about the minimal number of variables required to represent a given process and the optimal level of complexity of the model chosen to realistically simulate basic features such as primary production (Friedrichs et al., 2007 or Kriest et al., 2010).

A number of studies performed with CPBM involve the comparison with real-world observations. A special issue of the Journal of Marine Systems (volume 76: Skill assessment for coupled biological/physical models of marine systems, 2009) was devoted to this question, describing a number of normalised tests to objectively assess the results of realistic simulations. Related to this question are the availability and quantity of data which can be used to validate model outputs. Ocean biogeochemistry can be characterised by different quantities, such as the concentration of chlorophyll a, micro and macro-nutrients, or particulate/dissolved organic/inorganic carbon/nitrogen. The main assets of in situ measurements are their accuracy and the possibility to sample the sub-surface water column at appropriate depths. However, such measurements are very sparse in space and time. Worldwide, very few sites in the open ocean are routinely monitored (e.g., on a monthly basis), whereas automatic sampling performed from floats or gliders is still a long-term prospective for biogeochemical quantities (Claustre et al., 2010). On the other hand, achieving a global coverage, repetitivity on a few days cycle and availability of the archive (more than a decade) are the main advantages of ocean colour satellite data. The main drawback is that the measurements from space are representative of surface quantities only.

The optimal combination of model results and observations is the field of data assimilation. A comprehensive review of data assimilation in CPBM is provided by Gregg (2008). A collection of studies has been performed quite recently using ocean colour data, which demonstrate the value of the assimilation concepts inherited from optimal control or estimation theory (Armstrong et al., 1995, Fontana et al., 2009, Fontana et al., 2010, Fontana et al., 2012, Ford et al., 2012, Friedrichs, 2002, Garcia-Gorriz et al., 2003, Gregg, 2008, Hemmings et al., 2003, Hemmings et al., 2004, Hu et al., 2012, Ishizaka, 1990, Korres et al., 2012, Losa et al., 2004, Mattern et al., 2012, Natvik and Evensen, 2003a, Natvik and Evensen, 2003b, Nerger and Gregg, 2007, Nerger and Gregg, 2008, Roy et al., 2012).

Very often, variational data assimilation methods are implemented with the purpose of parameter estimation. Model simulations performed after optimisation are expected to yield better agreement with the measured data. Other studies that rely on sequential methods such as the Kalman filter, aim at a better control of the model trajectory and/or biogeochemical parameters.

In a recent paper, Doron et al. (2011) proposed an ensemble approach to objectively estimate a subset of biogeochemical parameters using ocean colour observations. In that paper, three key biogeochemical model parameters were identified to have the strongest impact on the chlorophyll a concentrations. Assuming independent parameter uncertainties for the different ecological provinces of the North Atlantic basin, Monte Carlo experiments were carried out to explore the model sensitivity to the uncertain model parameters. More precisely, an ensemble of 200 one-month simulations was performed during the spring bloom, to describe the joint probability distribution of the model state and model parameters. This probability distribution was observed to non-Gaussian, so that the linear observational update formulas of the Kalman filter were not directly applicable. For this reason, a nonlinear transformation (anamorphosis) was introduced to restore the Gaussianity of the marginal probability distribution for every model state variable and every uncertain parameter. With this upgraded description of the prior probability distribution, parameter corrections were computed from synthetic observations of the phytoplankton concentration (in the context of twin experiments). The nonlinear transformation has proved to be a key ingredient to obtain reliable estimates of the uncertain parameters in the various ecological provinces of the North Atlantic (each one with a specific non-Gaussian behaviour).

The twin experiments of Doron et al. (2011) provided an idealised framework where the only error source lies in the parameter values while all other elements are perfectly controlled. However, the error sources in real-world simulations may have different origins: the model initial conditions, the probability distribution function of the parameters, the physical forcings, or even observation errors being possibly the largest. Therefore, in a realistic case where real world observations are assimilated, the assumptions that were necessary to develop the method are not strictly valid anymore. For all these reasons, a real challenge in using a biogeochemical parameter estimation method with real ocean colour observations is to reduce the uncertainty in the biogeochemical parameters of CPBM and to objectively quantify the spread of the posterior distribution.

In this context, the objective of the present paper is to investigate to what extent the estimation method described in Doron et al. (2011) can be implemented to obtain realistic corrections of a few biogeochemical parameters using real ocean colour observations. The present paper is structured as follows: Sections 2 and 3 present the coupled model, the ocean colour data and the parameter estimation method. Section 4 describes the results of the experiments and provides an assessment of the estimated parameters. In particular, the optimised parameters are compared to a regional set of biogeochemical parameters obtained in the frame of an independent approach (Losa et al., 2004). A summary, conclusions and future research lines are proposed in Section 5.