Optimal analysis of in situ data in the western Mediterranean using statistics and cross-validation

To study the Mediterranean general circulation, there is a constant need for reliable interpretations of available hydrological observations. Optimal data analyses (in the probabilistic point of view of objective analysis) are fulfilled using an original finite-element technique to minimize the variational principle of the spline procedure. Anyway, a prior statistical knowledge of the problem is required to adapt the optimization criterion to the purpose of this study and to the particular features of the system. The main goal of this paper is to show how the cross-validation methodology can be used to deduce statistical estimators of this information only from the dataset. The authors also give theoretical and/or numerical evidence that modified estimators-using generalized cross-validation or sampling algorithms-are interesting in the analysis optimization process. Finally, results obtained by the application of these methods to a Mediterranean historical database and their comparison with those provided by other techniques show the usefulness and the reliability of the method

Traitement des Incertitudes en Océanographie

Ce mémoire aborde le problème général du traitement des incertitudes en océanographie, en le considérant de façon transverse, tant dans le cadre du problème direct (modélisation des océans) que du problème inverse (méthodes d'assimilation de données). Les questions abordées sont en particulier les méthodes de simulations d'ensemble, avec paramétrisation stochastiques des incertitudes, et les méthodes de réduction des incertitudes par assimilation données (sous hypothèse gaussienne et non-gaussienne)

Obstacles and benefits of the implementation of a reduced-rank smoother with a high resolution model of the tropical Atlantic Ocean

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

Characterization of mixing errors in a coupled physical biogeochemical model of the North Atlantic: implications for nonlinear estimation using Gaussian anamorphosis

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. <br><br> 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

Optimal adjustment of the atmospheric forcing parameters of ocean models using sea surface temperature data assimilation

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. <br><br> 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

Comparative assimilation of Topex/poseidon and ERS altimetric data and of TAO temperature data in the tropical Pacific Ocean during 1994-1998, and the mean sea-surface height issue

International audienceFive years of Topex/Poseidon (T/P) and ERS sea level anomaly (SLA) data (1994–1998) are assimilated every 10 days into a primitive equation model of the tropical Pacific ocean. The data assimilation technique used here is a reduced-order Kalman filter derived from the Singular Evolutive Extended Kalman (SEEK) filter [J. Mar. Syst. 16(3–4) (1998) 323] with an error covariance matrix parameterised by a subset of multivariate 3D global empirical orthogonal functions (EOFs). The assimilation run is compared to the free run and to independent data from the TAO network. The impact of sea-surface height (SSH) assimilation on surface and subsurface temperature and currents is estimated in the equatorial band. In a second stage, temperature data from the TAO array are assimilated in the same conditions as in the first stage. The comparison between the results of the two assimilation experiments is made mainly with a view to gaining insights into the mean sea-surface height (MSSH) for the assimilation of altimeter data, and more generally, into the question of biases. XBT observations and TAO array data are then used to build a physically more consistent mean sea-surface height for assimilation of SLA data. Results from the assimilation of altimeter data referenced to this new MSSH show significant improvements

Toward a data assimilation system for NEMO

International audienceIn this note, we discuss the project that has been conceived and the first achievement steps that have been carried out to set up a data assimila-­ tion system associated to NEMO. Of specific interest here are applications to operational oceanography. This data assimilation system is sche-­ matically made of three subcomponents: Interface Components, Built-in Components and External Components. Several elements of this NEMO data assimilation system have already been developed by various groups in France and in Europe and several of them could be introduced in the system (the linear Tangent and Adjoint Model, TAM, is one of the most important of them as far as variational assimilation is concerned), some others will require specific developments. Finally, we introduce the SEABASS reference configuration that is proposed to be the NEMO data as-­ similation demonstrator and the experimentation and training platform for data assimilation activities with NEMO. These various thoughts take advantage of the advances and discussions that have been carried out by the NEMOASSIM working group

Ensemble analysis and forecast of ecosystem indicators in the North Atlantic using ocean colour observations and prior statistics from a stochastic NEMO–PISCES simulator

This study is anchored in the H2020 SEAMLESS project (https://www.seamlessproject.org, last access: 29 January 2024), which aims to develop ensemble assimilation methods to be implemented in Copernicus Marine Service monitoring and forecasting systems, in order to operationally estimate a set of targeted ecosystem indicators in various regions, including uncertainty estimates. In this paper, a simplified approach is introduced to perform a 4D (space–time) ensemble analysis describing the evolution of the ocean ecosystem. An example application is provided, which covers a limited time period in a limited subregion of the North Atlantic (between 31 and 21∘ W, between 44 and 50.5∘ N, between 15 March and 15 June 2019, at a 1/4∘ and a 1 d resolution). The ensemble analysis is based on prior ensemble statistics from a stochastic NEMO (Nucleus for European Modelling of the Ocean)–PISCES simulator. Ocean colour observations are used as constraints to condition the 4D prior probability distribution. As compared to classic data assimilation, the simplification comes from the decoupling between the forward simulation using the complex modelling system and the update of the 4D ensemble to account for the observation constraint. The shortcomings and possible advantages of this approach for biogeochemical applications are discussed in the paper. The results show that it is possible to produce a multivariate ensemble analysis continuous in time and consistent with the observations. Furthermore, we study how the method can be used to extrapolate analyses calculated from past observations into the future. The resulting 4D ensemble statistical forecast is shown to contain valuable information about the evolution of the ecosystem for a few days after the last observation. However, as a result of the short decorrelation timescale in the prior ensemble, the spread of the ensemble forecast increases quickly with time. Throughout the paper, a special emphasis is given to discussing the statistical reliability of the solution. Two different methods have been applied to perform this 4D statistical analysis and forecast: the analysis step of the ensemble transform Kalman filter (with domain localization) and a Monte Carlo Markov chain (MCMC) sampler (with covariance localization), both enhanced by the application of anamorphosis to the original variables. Despite being very different, the two algorithms produce very similar results, thus providing support to each other's estimates. As shown in the paper, the decoupling of the statistical analysis from the dynamical model allows us to restrict the analysis to a few selected variables and, at the same time, to produce estimates of additional ecological indicators (in our example: phenology, trophic efficiency, downward flux of particulate organic matter). This approach can easily be appended to existing operational systems to focus on dedicated users' requirements, at a small additional cost, as long as a reliable prior ensemble simulation is available. It can also serve as a baseline to compare with the dynamical ensemble forecast and as a possible substitute whenever useful.</p

Accounting for model error in strong-constraint 4DVar data assimilation

The strong constraint formulation of four-dimensional variational data assimilation (4DVar) assumes that the model used in the process perfectly describes the true dynamics of the system. However, this assumption often does not hold and the use of an erroneous model in strong constraint 4DVar can lead to a sub-optimal estimation of the initial conditions. We show how the presence of model error can be correctly accounted for in strong constraint 4D-Var by allowing for errors in both the observations and the model when considering the statistics of the innovation vector. We demonstrate that when these combined model error and observation error statistics are used in place of the standard observation error statistics in the strong constraint formulation of 4DVar, a statistically more accurate estimate of the initial state is obtained. The calculation of the combined model error and observation error statistics requires the specification of model error covariances, which in practice are often unknown. We present a method to estimate the combined statistics from innovation data that does not require explicit specification of the model error covariances. Numerical experiments using the linear advection equation and a simple nonlinear coupled model demonstrate the success of the new methods in reducing the error in the estimate of the initial state, even in the case when only the uncorrelated part of the model error is accounted for