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

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

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. &lt;br&gt;&lt;br&gt; 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&amp;deg; 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

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

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

A multiscale ocean data assimilation approach combining spatial and spectral localisation

Ocean data assimilation systems encompass a wide range of scales that are difficult to control simultaneously using partial observation networks. All scales are not observable by all observation systems, which is not easily taken into account in current ocean operational systems. The main reason for this difficulty is that the error covariance matrices are usually assumed to be local (e.g. using a localisation algorithm in ensemble data assimilation systems), so that the large-scale patterns are removed from the error statistics. To better exploit the observational information available for all scales in the assimilation systems of the Copernicus Marine Environment Monitoring Service, we investigate a new method to introduce scale separation in the assimilation scheme. The method is based on a spectral transformation of the assimilation problem and consists in carrying out the analysis with spectral localisation for the large scales and spatial localisation for the residual scales. The target is to improve the observational update of the large-scale components of the signal by an explicit observational constraint applied directly on the large scales and to restrict the use of spatial localisation to the small-scale components of the signal. To evaluate our method, twin experiments are carried out with synthetic altimetry observations (simulating the Jason tracks), assimilated in a 1/4∘ model configuration of the North Atlantic and the Nordic Seas. Results show that the transformation to the spectral domain and the spectral localisation provides consistent ensemble estimates of the state of the system (in the spectral domain or after backward transformation to the spatial domain). Combined with spatial localisation for the residual scales, the new scheme is able to provide a reliable ensemble update for all scales, with improved accuracy for the large scale; and the performance of the system can be checked explicitly and separately for all scales in the assimilation system.</p

Uncertainty and scale interactions in ocean ensembles: from seasonal forecasts to multidecadal climate predictions

The ocean plays an important role in the climate system on time‐scales of weeks to centuries. Despite improvements in ocean models, dynamical processes involving multiscale interactions remain poorly represented, leading to errors in forecasts. We present recent advances in understanding, quantifying, and representing physical and numerical sources of uncertainty in novel regional and global ocean ensembles at different horizontal resolutions. At coarse resolution, uncertainty in 21st century projections of the upper overturning cell in the Atlantic is mostly a result of buoyancy fluxes, while the uncertainty in projections of the bottom cell is driven equally by both wind and buoyancy flux uncertainty. In addition, freshwater and heat fluxes are the largest contributors to Atlantic Ocean heat content regional projections and their uncertainties, mostly as a result of uncertain ocean circulation projections. At both coarse and eddy‐permitting resolutions, unresolved stochastic temperature and salinity fluctuations can lead to significant changes in large‐scale density across the Gulf Stream front, therefore leading to major changes in large‐scale transport. These perturbations can have an impact on the ensemble spread on monthly time‐scales and subsequently interact nonlinearly with the dynamics of the flow, generating chaotic variability on multiannual time‐scales. In the Gulf Stream region, the ratio of chaotic variability to atmospheric‐forced variability in meridional heat transport is larger than 50% on time‐scales shorter than 2 years, while between 40 and 48°S the ratio exceeds 50% on on time‐scales up to 28 years. Based on these simulations, we show that air–sea interaction and ocean subgrid eddies remain an important source of error for simulating and predicting ocean circulation, sea level, and heat uptake on a range of spatial and temporal scales. We discuss how further refinement of these ensembles can help us assess the relative importance of oceanic versus atmospheric uncertainty in weather and climate

Abrupt cooling of the mediterranean levantine intermediate water at the beginning of the 1980s: Observational evidence and model simulations

The Levantine Intermediate Water (LIW) is an important water mass for the overall hydrology of the Mediterranean Sea and there are open questions connected with the possible long-term variability of its physical characteristics. This paper is dedicated to the analysis and the interpretation of the LIW long-term variations over the last 50 years. It is based on data analysis and model simulations. On the one hand, new temperature and salinity gridded data of interannual and decadal anomalies have been produced from existing historical datasets. On the other hand, a long-term primitive equation model simulation has been generated, to be compared to the observational reconstructions. Results indicate that the major feature of both datasets (observations and model) is an intense cooling of the LIW (0.24°-0.28°C at 200-m depth) at the beginning of the 1980s (winters 1981 and 1983). Around the Aegean Sea and the Cretan Arc, the amplitude of the cooling is as large as 0.4°C. The model simulations, forced by the Comprehensive Ocean-Atmosphere Data Set atmospheric fluxes, reproduce the cooling event quite faithfully. The possible processes at the origin of these interannual/decadal variations are discussed. Hypotheses are proposed and tested against observations. In particular it is shown that over the period of interest, the major part of the LIW interannual/decadal variability has been directly forced by anomalies in the surface heat budget of the Eastern Mediterranean

The general circulation in the Mediterranean Sea: a climatological approach

A significant amount of hydrographic data has been collected in the Mediterranean during this century, providing the basic ingredients needed to construct a climatological picture of the general circulation. A pooled hydrographic data set has been prepared, which currently contains over 100,000 station profiles (CTD, Nansen bottle, XBT and MET) taken in the Eastern and Western Mediterranean Sea between 1900 and 1993. Climatological analyses of temperature and salinity data are performed at seasonal and monthly scales, using a variational method and a finite element numerical technique. The variational formulation had been demonstrated to be equivalent to objective analysis, and a hybridation of the statistical and variational methods allows to compute error fields associated to the climatology. The free parameters of the scheme are determined using a cross-validation algorithm to extract the best seasonal statistics from the observed data sets. Compared to earlier climatologies, the recent analyses show significant improvements with respect to the regional scales of the general circulation gyres. In addition, several features of the general circulation are described with a better accuracy. Finally, the barotropic equations (external mode) of a free-surface, primitive equation model are integrated in time to diagnostically adjust the sea-surface elevation to the thermohaline structures. Geostrophic velocities are then computed, integrating the thermal-wind equations with the sea-surface pressure as a reference. Results of fully prognostic, three-dimensional, primitive equation models are compared with these diagnostic computations in order to identify which features of the general circulation can be captured by observations