Stochastic parameterizations of biogeochemical uncertainties in a 1/4° NEMO/PISCES model for probabilistic comparisons with ocean color data☆
Introduction
Estimating the primary production and its variability in the ocean has been the subject of advanced research over the past 40 years (Marra, 2015), motivated by the need to better understand the oceanic component of the global carbon cycle as well as the interconnections between biogeochemistry and marine ecosystems. In the early nineties, first attempts to use satellite ocean color sensors for estimating phytoplankton carbon fixation were based on productivity models driven by observed concentrations of chlorophyll-a (Behrenfeld and Falkowski, 1997). During the past 25 years, ocean color satellite missions provided a unique means to monitor almost continuously the surface signature of phytoplankton distribution in the upper ocean (Wilson, 2010). The combination of ocean color observations with three-dimensional biogeochemical general circulation models (BGCMs) through integrated approaches is a more recent but promising methodology, which aims at combining model information with data in space and time in order to estimate global budgets of phytoplankton biomass and monitor its evolution for a variety of applications (Brasseur et al., 2009). However, such integrated approaches cannot be faithfully implemented as long as data sets and model solutions are not consistent statistically one with each other.
In the prospect of model-data comparisons or melding, the model reliability should be properly characterized in terms of uncertainty, or equivalently, “model error”. An appropriate description of uncertainties implies to define a correct separation between the processes that are properly resolved, poorly resolved or unresolved by the model (Brankart et al., 2015). The representation of uncertainties is intimately linked to the particular formulation of the considered biological model. Therefore, adopting an objective methodology to derive a statistical description of these model uncertainties is a major challenge for several types of scientific and operational applications (model assessment, validation, error characterization, data assimilation etc…). This is precisely the purpose of the present paper, which builds on several earlier publications that already addressed different aspects of model uncertainty based on ensemble integrations in the framework of eddy-permitting using the LOBSTER model (Béal et al., 2010, Doron et al., 2013, Fontana et al., 2013).
In Béal et al. (2010), ensemble experiments performed with perturbed wind forcings enabled to characterize how uncertainties in the physical fields could impact the biological response in a North Atlantic, eddy-permitting model configuration. Using the same configuration, Doron et al. (2013) explored how the spatial dependence between the biological model parameters could explain the misfits between the model and the Globcolour data set, and reduce the uncertainty estimates in the selected parameters. Further, Fontana et al. (2013) implemented a sequential updating scheme to assimilate SeaWiFS (Sea-viewing Wide Field-of-view Scanner) ocean color products every 10 days and reconstruct the biogeochemical state of the North Atlantic during the 1998–2006 period. Finally, these 3 studies show that ocean color data are able to contribute to the reduction of biological uncertainties.
In this study, the more complex PISCES (Pelagic Iteraction Scheme for Carbon and Ecosystem Studies) biological model (Aumont et al., 2003) coupled to NEMO is implemented in a 1/4° North Atlantic configuration. As explain in Section 2, the PISCES formulation includes two distinct phytoplankton classes and deals with five different micro and macro nutrients to modulate the growth of biomass. In order to enable consistent model-data comparisons, we propose to investigate the potential of a generic approach to simulate appropriate biogeochemical uncertainties originating from several well identified sources and we evaluate their impacts on the model solutions. Introducing stochasticity into ecosystem models was first proposed by (Dowd and Meyer, 2003), by adding white noise processed in the model equations. The concept of stochastic perturbations for model parameter or model state integration was further developed and used in model/data comparisons, estimation and data assimilation studies (e.g.,: Gregg et al., 2009, Jones et al., 2010, Mattern et al., 2010, Dowd, 2011, Jones et al., 2013, Ciavatta et al., 2014).
In this paper, our approach relies on the introduction of stochastic representations of selected model uncertainties associated with some unresolved or poorly-resolved processes in the BGCMs. Random processes are used to generate ensemble members obtained by activating the stochastic processes in a set of independent model runs. Provided the stochasticity of the model is appropriately taken into account by making ensemble simulations, one should expect some skill for uncertainty prediction, though still conditional on model structure. The analysis of the ensemble spread is performed in terms of reliability (i.e., ability in producing pdfs in agreement with the associated observed pdfs) as defined by Candille et al. (2015) using the available ocean color observations. The relevance of this approach is further discussed in the prospect of an ocean color data assimilation system for ocean monitoring and forecasting.
This paper is structured as follows: in Section 2, we present the PISCES model and the North Atlantic configuration of a coupled NEMO/PISCES deterministic simulation; in section 3, are described the stochastic parameterizations proposed to simulate model uncertainties. Section 4 is then dedicated to the impact analysis of the stochastic parameterizations. In particular we explain that the mean effect of the perturbations implies to re-tune the deterministic initial set of parameters. Finally, in Section 5, we analyze the result of a 60-member ensemble simulation. The consistency of this simulation will be assessed from statistical comparisons with ocean color SeaWIFS observations.
Section snippets
The coupled physical–biogeochemical deterministic model
In this section, we describe the coupled model and show some general characteristics of a PISCES North Atlantic deterministic simulation (detIni) which does not include yet any stochastic process. This simulation is analyzed in terms of chlorophyll structures from comparisons with SeaWIFS ocean color satellite data (for the surface representation) and an in-situ data climatology (for the vertical distribution).
Explicit simulation of biogeochemical uncertainties
In the previous section, it has been suggested that PISCES is able to include many relevant pieces of dynamical information that can be observed by the SeaWIFS ocean color satellite data. However, we also insisted on the fact that the chlorophyll distributions are still imperfect and the model is therefore very uncertain. Biogeochemical uncertainties being ubiquitous, we cannot expect to design a specific parameterization for every single source of uncertainty. We therefore propose to focus on
Joint tuning of deterministic and stochastic parameters
As already mentioned, a key objective of this study is to perform a probabilistic simulation with a sufficient level of uncertainty to be compared with ocean color images. The consistency of the simulation is therefore examined from comparisons with ocean color data (SeaWIFS), considering that each member of the simulation need to be a possible representation of the observed large scale chlorophyll distribution. In this section, we explain that the introduction of stochastic parameterizations
A 60-member probabilistic simulation
To explore the biogeochemical model response to some of the major biological uncertainties, we present here the results of a 60-member ensemble simulation. This probabilistic simulation is performed from January 2005 to December 2005 with the parameters of the simulation stoUpd described in the previous section. In this section, the objectives are to describe the effects of the stochastic parameterizations on the chlorophyll representation. Before we analyze these effects, it is worth noting
Discussion and conclusions
In this study, we assessed the statistical consistency (reliability) between the ocean color SeaWIFS data and the surface chlorophyll representations of a coupled NEMO/PISCES 60-member ensemble simulation performed with stochastic parameterizations of biogeochemical uncertainties. Starting from a first guess PISCES deterministic simulation, we showed that despite many imperfections, this deterministic simulation was able to describe the basic observed features of the large scale North Atlantic
Acknowledgments
This work has received funding from the European Community's Seventh Framework Programme FP7/2007–2013 under grant agreements 283367 (MyOcean2), H2020 633085 (MyOcean-FO) and 283580 (SANGOMA), with additional support from CNES. It is also a contribution to the CNRS/INSU/LEFE program. The calculations were performed using HPC resources from GENCI-IDRIS (grant 2015-011279). The authors are grateful to the two anonymous reviewers for their relevant and constructive comments.
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