ALBERT

Description: In ocean general circulation models, near-surface atmospheric variables used to specify the atmospheric boundary condition remain one of the main sources of error. The objective of this research is to constrain the surface forcing function of an ocean model by sea surface temperature (SST) data assimilation. For that purpose, a set of corrections for ERAinterim (hereafter ERAi) reanalysis data is estimated for the period of 1989–2007, using a sequential assimilation method, with ensemble experiments to evaluate the impact of uncertain atmospheric forcing on the ocean state. The control vector of the assimilation method is extended to atmospheric variables to obtain monthly mean parameter corrections by assimilating monthly SST and sea surface salinity (SSS) climatological data in a low resolution global configuration of the NEMO model. In this context, the careful determination of the prior probability distribution of the parameters is an important matter. This paper demonstrates the importance of isolating the impact of forcing errors in the model to perform relevant ensemble experiments. The results obtained for every month of the period between 1989 and 2007 show that the estimated parameters produce the same kind of impact on the SST as the analysis itself. The objective is then to evaluate the long-term time series of the forcing parameters focusing on trends and mean error corrections of air–sea fluxes. Our corrections tend to equilibrate the net heat-flux balance at the global scale (highly positive in ERAi database), and to remove the potentially unrealistic negative trend (leading to ocean cooling) in the ERAi net heat flux over the whole time period. More specifically in the intertropical band, we reduce the warm bias of ERAi data by mostly modifying the latent heat flux by wind speed intensification. Consistently, when used to force the model, the corrected parameters lead to a better agreement between the mean SST produced by the model and mean SST observations over the period of 1989–2007 in the intertropical band.

Description: The objective of this paper is to investigate if the description of ocean uncertainties can be significantly improved by applying a local anamorphic transformation to each model variable, and by making the assumption of joint Gaussianity for the transformed variables, rather than for the original variables. For that purpose, it is first argued that a significant improvement can already be obtained by deriving the local transformations from a simple histogram description of the marginal distributions. Two distinctive advantages of this solution for large size applications are the conciseness and the numerical efficiency of the description. Second, various oceanographic examples are used to evaluate the effect of the resulting piecewise linear local anamorphic transformations on the spatial correlation structure. These examples include (i) stochastic ensemble descriptions of the effect of atmospheric uncertainties on the ocean mixed layer, and of wind uncertainties or parameter uncertainties on the ecosystem, and (ii) non-stochastic ensemble descriptions of forecast uncertainties in current sea ice and ecosystem pre-operational developments. The results indicate that (i) the transformation is accurate enough to faithfully preserve the correlation structure if the joint distribution is already close to Gaussian, and (ii) the transformation has the general tendency of increasing the correlation radius as soon as the spatial dependence between random variables becomes nonlinear, with the important consequence of reducing the number of degrees of freedom in the uncertainties, and thus increasing the benefit that can be expected from a given observation network.

Description: In biogeochemical models coupled to ocean circulation models, vertical mixing is an important physical process which governs the nutrient supply and the plankton residence in the euphotic layer. However, mixing is often poorly represented in numerical simulations because of approximate parameterizations of sub-grid scale turbulence, wind forcing errors and other mis-represented processes such as restratification by mesoscale eddies. Getting a sufficient knowledge of the nature and structure of these error sources is necessary to implement appropriate data assimilation methods and to evaluate their controllability by a given observation system. In this paper, Monte Carlo simulations are conducted to study mixing errors induced by approximate wind forcings in a three-dimensional coupled physical-biogeochemical model of the North Atlantic with a 1/4° horizontal resolution. An ensemble forecast involving 200 members is performed during the 1998 spring bloom, by prescribing realistic wind perturbations to generate mixing errors. It is shown that the biogeochemical response can be rather complex because of nonlinearities and threshold effects in the coupled model. In particular, the response of the surface phytoplankton depends on the region of interest and is particularly sensitive to the local stratification. We examine the robustness of the statistical relationships computed between the various physical and biogeochemical variables, and we show that significant information on the ecosystem can be obtained from observations of chlorophyll concentration or sea surface temperature. In order to improve the analysis step of sequential assimilation schemes, we propose to perform a simple nonlinear change of variables that operates separately on each state variable, by mapping their ensemble percentiles on the Gaussian percentiles. It is shown that this method is able to substantially reduce the estimation error with respect to the linear estimates computed by the Kalman filter.

Description: In the context of stand alone ocean models, the atmospheric forcing is generally computed using atmospheric parameters that are derived from atmospheric reanalysis data and/or satellite products. With such a forcing, the sea surface temperature that is simulated by the ocean model is usually significantly less accurate than the synoptic maps that can be obtained from the satellite observations. This not only penalizes the realism of the ocean long-term simulations, but also the accuracy of the reanalyses or the usefulness of the short-term operational forecasts (which are key GODAE and MERSEA objectives). In order to improve the situation, partly resulting from inaccuracies in the atmospheric forcing parameters, the purpose of this paper is to investigate a way of further adjusting the state of the atmosphere (within appropriate error bars), so that an explicit ocean model can produce a sea surface temperature that better fits the available observations. This is done by performing idealized assimilation experiments in which Mercator-Ocean reanalysis data are considered as a reference simulation describing the true state of the ocean. Synthetic observation datasets for sea surface temperature and salinity are extracted from the reanalysis to be assimilated in a low resolution global ocean model. The results of these experiments show that it is possible to compute piecewise constant parameter corrections, with predefined amplitude limitations, so that long-term free model simulations become much closer to the reanalysis data, with misfit variance typically divided by a factor 3. These results are obtained by applying a Monte Carlo method to simulate the joint parameter/state prior probability distribution. A truncated Gaussian assumption is used to avoid the most extreme and non-physical parameter corrections. The general lesson of our experiments is indeed that a careful specification of the prior information on the parameters and on their associated uncertainties is a key element in the computation of realistic parameter estimates, especially if the system is affected by other potential sources of model errors.

Description: Most of oceanographic operational centers use three-dimensional data assimilation schemes to produce reanalyses. We investigate here the benefits of a smoother, i.e. a four-dimensional formulation of statistical assimilation. A square-root sequential smoother is implemented with a tropical Atlantic Ocean circulation model. A simple twin experiment is performed to investigate its benefits, compared to its corresponding filter. Despite model's non-linearities and the various approximations used for its implementation, the smoother leads to a better estimation of the ocean state, both on statistical (i.e. mean error level) and dynamical points of view, as expected from linear theory. Smoothed states are more in phase with the dynamics of the reference state, an aspect that is nicely illustrated with the chaotic dynamics of the North Brazil Current rings. We also show that the smoother efficiency is strongly related to the filter configuration. One of the main obstacles to implement the smoother is then to accurately estimate the error covariances of the filter. Considering this, benefits of the smoother are also investigated with a configuration close to situations that can be managed by operational center systems, where covariances matrices are fixed (optimal interpolation). We define here a simplified smoother scheme, called half-fixed basis smoother, that could be implemented with current reanalysis schemes. Its main assumption is to neglect the propagation of the error covariances matrix, what leads to strongly reduce the cost of assimilation. Results illustrate the ability of this smoother to provide a solution more consistent with the dynamics, compared to the filter. The smoother is also able to produce analyses independently of the observation frequency, so the smoothed solution appears more continuous in time, especially in case of a low frenquency observation network.

Description: A realistic circulation model of the North Atlantic ocean at 0.25° resolution (NATL025 NEMO configuration) has been adapted to explicitly simulate model uncertainties. This is achieved by introducing stochastic perturbations in the equation of state to represent the effect of unresolved scales on the model dynamics. The main motivation for this work is to develop ensemble data assimilation methods, assimilating altimetric data from past missions Jason-1 and Envisat. The assimilation experiment is designed to provide a description of the uncertainty associated with the Gulf Stream circulation for years 2005/2006, focusing on frontal regions which are predominantly affected by unresolved dynamical scales. An ensemble based on such stochastic perturbations is first produced and evaluated using along-track altimetry observations. Then each ensemble member is updated by a square root algorithm based on the SEEK (singular evolutive extended Kalman) filter (Brasseur and Verron, 2006). These three elements – stochastic parameterization, ensemble simulation and 4-D observation operator – are then used together to perform a 4-D analysis of along-track altimetry over 10-day windows. Finally, the results of this experiment are objectively evaluated using the standard probabilistic approach developed for meteorological applications (Toth et al., 2003; Candille et al., 2007). The results show that the free ensemble – before starting the assimilation process – correctly reproduces the statistical variability over the Gulf Stream area: the system is then pretty reliable but not informative (null probabilistic resolution). Updating the free ensemble with altimetric data leads to a better reliability with an information gain of around 30% (for 10-day forecasts of the SSH variable). Diagnoses on fully independent data (i.e. data that are not assimilated, like temperature and salinity profiles) provide more contrasted results when the free and updated ensembles are compared.

Description: In biogeochemical models coupled to ocean circulation models, vertical mixing is an important physical process which governs the nutrient supply and the plankton residence in the euphotic layer. However, vertical mixing is often poorly represented in numerical simulations because of approximate parameterizations of sub-grid scale turbulence, wind forcing errors and other mis-represented processes such as restratification by mesoscale eddies. Getting a sufficient knowledge of the nature and structure of these errors is necessary to implement appropriate data assimilation methods and to evaluate if they can be controlled by a given observation system. In this paper, Monte Carlo simulations are conducted to study mixing errors induced by approximate wind forcings in a three-dimensional coupled physical-biogeochemical model of the North Atlantic with a 1/4° horizontal resolution. An ensemble forecast involving 200 members is performed during the 1998 spring bloom, by prescribing perturbations of the wind forcing to generate mixing errors. The biogeochemical response is shown to be rather complex because of nonlinearities and threshold effects in the coupled model. The response of the surface phytoplankton depends on the region of interest and is particularly sensitive to the local stratification. In addition, the statistical relationships computed between the various physical and biogeochemical variables reflect the signature of the non-Gaussian behaviour of the system. It is shown that significant information on the ecosystem can be retrieved from observations of chlorophyll concentration or sea surface temperature if a simple nonlinear change of variables (anamorphosis) is performed by mapping separately and locally the ensemble percentiles of the distributions of each state variable on the Gaussian percentiles. The results of idealized observational updates (performed with perfect observations and neglecting horizontal correlations) indicate that the implementation of this anamorphosis method into sequential assimilation schemes can substantially improve the accuracy of the estimation with respect to classical computations based on the Gaussian assumption.

Description: A realistic circulation model of the North Atlantic ocean at 1/4° resolution (NATL025 NEMO configuration) has been adapted to explicitly simulate model uncertainties. This is achieved by introducing stochastic perturbations in the equation of state to represent the effect of unresolved scales on the model dynamics. The main motivation for this work is to develop ensemble data assimilation methods, assimilating altimetric data from past missions JASON-1 and ENVISAT. The assimilation experiment is designed to better control the Gulf Stream circulation for years 2005/06, focusing on frontal regions which are predominantly affected by unresolved dynamical scales. An ensemble based on such stochastic perturbations is first produced and evaluated using along-track altimetry observations. The Incremental Analysis Update (IAU) scheme is applied in order to obtain an ensemble of continuous trajectories all over the 2005/06 assimilation period. These three elements – stochastic parameterization, ensemble simulation and 4-D observation operator – are then used together to perform a 4-D analysis of along-track altimetry over 10 day windows. Finally, the results of this experiment are objectively evaluated using the standard probabilistic approach developed for meteorological applications (Toth et al., 2003; Candille et al., 2007). The results show that the free ensemble – before starting the assimilation process – correctly reproduces the statistical variability over the Gulf Stream area: the system is then pretty reliable but not informative (null probabilistic resolution). Updating the free ensemble with altimetric data leads to a better reliability with an information gain around 30% (for 10 day forecasts of the SSH variable). Diagnoses on fully independent data (i.e. data that are not assimilated, like temperature and salinity profiles) provide more contrasted results when the free and updated ensembles are compared.

Description: In ocean general circulation models, near surface atmospheric variables used to specify the atmospheric remain one of the main sources of error. The objective of this research is to constrain the surface forcing function of an ocean model by Sea Surface Temperature (SST) data assimilation. For that purpose, a set of corrections for ERAinterim (hereafter ERAi) reanalysis data is estimated for the period from 1989 to 2007 using a sequential assimilation method, with ensemble experiments to evaluate the impact of uncertain atmospheric forcing on the ocean state. The control vector of the assimilation method is extended to atmospheric variables to obtain monthly mean parameter corrections by assimilating monthly SST and Sea Surface Salinity (SSS) climatological data in a low resolution global configuration of the NEMO model. In this context, the careful determination of the prior probability distribution of the parameters is an important matter. This paper demonstrates the importance of isolating the impact of forcing errors in the model to perform relevant ensemble experiments. The results obtained for every month of the period between 1989 and 2007 show that the estimated parameters produce the same kind of impact on the SST as the analysis itself. The objective is then to evaluate the long term time-series of the forcing parameters focusing on trends and mean error corrections of air-sea fluxes. Our corrections tend to equilibrate the net heat flux balance at the global scale (highly positive in ERAi database), and to remove the potentially unrealistic negative trend (leading to ocean cooling) in the ERAi net heat flux over the whole time period. More specifically in the intertropical band, we reduce the warm bias of ERAi data by mostly modifying the latent heat flux by wind velocity intensification. Consistently, when used to force the model, the corrected parameters lead to a better agreement between the mean SST produced by the model and mean SST observations over 1989–2007 in the intertropical band.

Description: Today, the routine assimilation of satellite data into operational models of the ocean circulation is mature enough to enable the production of global reanalyses describing the ocean circulation variability during the past decades. The expansion of the "reanalysis" concept from ocean physics to biogeochemistry is a timely challenge that motivates the present study. The objective of this paper is to investigate the potential benefits of assimilating satellite-estimated chlorophyll data into a basin-scale three-dimensional coupled physical-biogeochemical model of the North-Atlantic. The aim is on one hand to improve forecasts of ocean biogeochemical properties and on the other hand to define a methodology for producing data-driven climatologies based on coupled physical-biogeochemical modelling. A simplified variant of the Kalman filter is used to assimilate ocean color data during a 9 year-long period. In this frame, two experiences are carried out, with and without anamorphic transformations of the state vector variables. Data assimilation efficiency is assessed with respect to the assimilated data set, the nitrate World Ocean Atlas database and a derived climatology. Along the simulation period, the non-linear assimilation scheme clearly improves the surface chlorophyll concentrations analysis and forecast, especially in the North Atlantic bloom region. Nitrate concentration forecasts are also improved thanks to the assimilation of ocean color data while this improvement is limited to the upper layer of the water column, in agreement with recent related litterature. This feature is explained by the weak correlation taken into account by the assimilation between surface phytoplankton and nitrate concentration deeper than 50 m. The assessement of the non-linear assimilation experiments indicates that the proposed methodology provides the skeleton of an assimilative system suitable for reanalysing the ocean biogeochemistry based on ocean color data.