Dynamically Constrained Ensemble Perturbations: Application to Tides on the West Florida Shelf

Abstract. A method is presented to create an ensemble of perturbations that satisfies linear dynamical constraints. A cost function is formulated defining the probability of each perturbation. It is shown that the perturbations created with this approach take the land-sea mask into account in a similar way as variational analysis techniques. The impact of the land-sea mask is illustrated with an idealized configuration of a barrier island. Perturbations with a spatially variable correlation length can be also created by this approach. The method is applied to a realistic configuration of the West Florida Shelf to create perturbations of the M2 tidal parameters for elevation and depth-averaged currents. The perturbations are weakly constrained to satisfy the linear shallow-water equations. Despite that the constraint is derived from an idealized assumption, it is shown that this approach is applicable to a non-linear and baroclinic model. The amplitude of spurious transient motions created by constrained perturbations of initial and boundary conditions is significantly lower compared to perturbing the variables independently or to using only the momentum equation to compute the velocity perturbations from the elevation

Monitoring Black Sea environmental changes from space: New products for altimetry, ocean colour and salinity. Potentialities and requirements for a dedicated in-situ observing system

21 pages, 13 figures, 2 tables, supplementary material https://www.frontiersin.org/articles/10.3389/fmars.2022.998970/full#supplementary-material.-- Data availability statement: The datasets generated for this study can be found on the web interface (http://www.eo4sibs.uliege.be/) and on Zenodo under data doi: 10.5281/zenodo.6397223 with a full documentation that include Products User Manuals (PUM) and Algorithm Theoretical Basis Document (ATBD). All these products are distributed in netCDF files Grégoire et al. (2022). SMOS SSS and CDM products are also available at https://bec.icm.csic.es/bec-ftp-service/In this paper, satellite products developed during the Earth Observation for Science and Innovation in the Black Sea (EO4SIBS) ESA project are presented. Ocean colour, sea level anomaly and sea surface salinity datasets are produced for the last decade and validated with regional in-situ observations. New data processing is tested to appropriately tackle the Black Sea’s particular configuration and geophysical characteristics. For altimetry, the full rate (20Hz) altimeter measurements from Cryosat-2 and Sentinel-3A are processed to deliver a 5Hz along-track product. This product is combined with existing 1Hz product to produce gridded datasets for the sea level anomaly, mean dynamic topography, geostrophic currents. This new set of altimetry gridded products offers a better definition of the main Black Sea current, a more accurate reconstruction and characterization of eddies structure, in particular, in coastal areas, and improves the observable wavelength by a factor of 1.6. The EO4SIBS sea surface salinity from SMOS is the first satellite product for salinity in the Black Sea. Specific data treatments are applied to remedy the issue of land-sea and radio frequency interference contamination and to adapt the dielectric constant model to the low salinity and cold waters of the Black Sea. The quality of the SMOS products is assessed and shows a significant improvement from Level-2 to Level -3 and Level-4 products. Level-4 products accuracy is 0.4-0.6 psu, a comparable value to that in the Mediterranean Sea. On average SMOS sea surface salinity is lower than salinity measured by Argo floats, with a larger error in the eastern basin. The adequacy of SMOS SSS to reproduce the spatial characteristics of the Black Sea surface salinity and, in particular, plume patterns is analyzed. For ocean colour, chlorophyll-a, turbidity and suspended particulate materials are proposed using regional calibrated algorithms and satellite data provided by OLCI sensor onboard Sentinel-3 mission. The seasonal cycle of ocean colour products is described and a water classification scheme is proposed. The development of these three types of products has suffered from important in-situ data gaps that hinder a sound calibration of the algorithms and a proper assessment of the datasets quality. We propose recommendations for improving the in-situ observing system that will support the development of satellite productsThis work has been carried out as part of the European Space Agency contract Earth Observation data For Science and Innovations in the Black Sea (EO4SIBS, ESA contract n° 4000127237/19/I-EF). MG received fundings from the Copernicus Marine Service (CMEMS), the European Union’s Horizon 2020 BRIDGE-BS project under grant agreement No. 101000240 and by the Project CE2COAST funded by ANR(FR), BELSPO (BE), FCT (PT), IZM (LV), MI (IE), MIUR (IT), Rannis (IS), and RCN (NO) through the 2019 “Joint Transnational Call on Next Generation Climate Science in Europe for Oceans” initiated by JPI Climate and JPI Oceans. The research on SMOS SSS has been also supported in part by the Spanish R&D project INTERACT (PID2020-114623RB-C31), which is funded by MCIN/AEI/10.13039/501100011033, funding from the Spanish government through the “Severo Ochoa Centre of Excellence” accreditation (CEX2019-000928-S) and the CSIC Thematic Interdisciplinary Platform TeledetectPeer reviewe

Assimilation of HF radar data in a regional model of the Ligurian Sea

SANGOM

divand

A tool for multidimensional variational analysis (divand) is presented. It allows the interpolation and analysis of observations on curvilinear orthogonal grids in an arbitrary high dimensional space by minimizing a cost function. This cost function penalizes the deviation from the observations, the deviation from a first guess and abruptly varying fields based on a given correlation length (potentially varying in space and time). Additional constraints can be added to this cost function such as an advection constraint which forces the analysed field to align with the ocean current. The method decouples naturally disconnected areas based on topography and topology. This is useful in oceanography where disconnected water masses often have different physical properties. Individual elements of the a priori and a posteriori error covariance matrix can also be computed, in particular expected error variances of the analysis. A multidimensional approach (as opposed to stacking 2-dimensional analysis) has the benefit of providing a smooth analysis in all dimensions, although the computational cost is increased. Primal (problem solved in the grid space) and dual formulations (problem solved in the observational space) are implemented using either direct solvers (based on Cholesky factorization) or iterative solvers (conjugate gradient method). In most applications the primal formulation with the direct solver is the fastest, especially if an a posteriori error estimate is needed. However, for correlated observation errors the dual formulation with an iterative solver is more efficient. The method is tested by using pseudo observations from a global model. The distribution of the observations is based on the position of the ARGO floats. The benefit of the 3-dimensional analysis (longitude, latitude and time) compared to 2-dimensional analysis (longitude and latitude) and the role of the advection constraint are highlighted. The tool divand is free software, and is distributed under the terms of the GPL license (http://modb.oce.ulg.ac.be/mediawiki/index.php/divand).PREDANTAR, EMODNET Chemistry 2, SeaDataNet I

Assimilation of HF radar in the Ligurian Sea: Spatial and Temporal scale considerations

SANGOM

Correction of inertial oscillations by assimilation of HFradar data in a model of the Ligurian Sea

peer reviewedThis article aims at analyzing if high-frequency radar observations of surface currents allow to improve model forecasts in the Ligurian Sea, where inertial oscillations are a dominant feature. An ensemble of ROMS models covering the Ligurian Sea, and nested in the Mediterranean Forecasting System, is coupled with two WERA high-frequency radars. A sensitivity study allows to determine optimal parameters for the ensemble filter. By assimilating observations in a single point, the obtained correction shows that the forecast error covariance matrix represents the inertial oscillations, as well as large- and meso-scale processes. Furthermore, it is shown that the velocity observations can correct the phase and amplitude of the inertial oscillations. Observations are shown to have a strong effect during approximately half a day, which confirms the importance of using a high temporal observation frequency. In general, data assimilation of HF radar observations leads to a skill score of about 30 % for the forecasts of surface velocity

Super-ensemble techniques applied to wave forecast: performance and limitations

Nowadays, several operational ocean wave forecasts are available for a same region. These predictions may considerably differ, and to choose the best one is generally a difficult task. The super-ensemble approach, which consists in merging different forecasts and past observations into a single multi-model prediction system, is evaluated in this study. During the DART06 campaigns organized by the NATO Undersea Research Centre, four wave forecasting systems were simultaneously run in the Adriatic Sea, and significant wave height was measured at six stations as well as along the tracks of two remote sensors. This effort provided the necessary data set to compare the skills of various multi-model combination techniques. Our results indicate that a super-ensemble based on the Kalman Filter improves the forecast skills: The bias during both the hindcast and forecast periods is reduced, and the correlation coefficient is similar to that of the best individual model. The spatial extrapolation of local results is not straightforward and requires further investigation to be properly implemented

Local assimilation of sea surface temperature and elevation in a two-way nested model of the Gulf of Lions, using a single multigrid state vector

A three fold nested model is built, covering (a) the Mediterranean Sea (resolution 1/4 degree) (b) its North-Western part (resolution 1/20 degree), and (c) the Gulf of Lions (resolution 1/100 degree). The GHER hydrodynamic model (see e.g. [1]) is used for a simulation of the springs of 1997 and 1998. As the model allows mode splitting, the timestep in each grid is 3 seconds for the barotropic modes, and 3 minutes for the baroclinic modes. ECMWF atmospheric forcings and MODB4/MEDAR climatic data are used. This simulation is run with one-directionnal and bi-directionnal nesting (i.e. without and with statevector feedback), and results are compared. The output of the 1997 and 1998 simulations (3D temperature and salinity fields, and sea surface elevation field) are then used to build 3D multivariate EOFs over the 3 grids alltogether. This guarantees perfect correlations between points from different grids, that are physically at the same location. The following twin experiment is then set up. The simulation from 1998 serves as a control run. A delayed state of this run, serves as initial conditions for the perturbed run. The first 40 EOFs are used to build a reduced-rank model errorspace. Sea surface temperature and sea surface elevation from the reference run, physically located in the Gulf of Lions, are then assimilated in the perturbed run, using a reduced-rank optimal interpolation assimilation scheme. A previous experiment showed non-physical long-range corrections (far outside the Gulf of Lions); these corrections are removed by multiplying the corrections with a radial Gaussian function centered on the corresponding observations. The multivariate statevector ensures corrections are made to temperature, salinity and sea surface elevation fields. Using the corrected fields, the geostrophic equilibrium is used to calculate corrections to the velocity field. In this above twin experiment, observations are assimilated all at once in the 3 grids since a single statevector is used. The results are compared to classic approaches where each grid has a corresponding statevector, and observations are assimilated in a single grid (or in different grids separately). Finally, ongoing research about statistical predictors is presented. Indeed, primitive equation models are too costly to evolve the errorspace in time, even when reducedrank assimilation schemes are used. Statistical methods aim to replace the hydrodynamic model by a much faster method, that would then be used to evolve in time each of the directions of the errorspace, or alternately, the members of an ensemble method. Statistical methods need to be trained on real results; they are thus first tested on the model itself rather than on the errorspace. Preliminary results are presented

Data assimilation as a tool for upscaling

In ocean and atmospheric sciences, grid nesting is a common procedure in order to achieve (very) high resolution model outputs in regions of particular interest, at an acceptable computational cost. Nesting of grids can be passive (one-way nesting) or active (two-way nesting, with feedback from the high resolution to the low resolution grid). The benefits of active nesting have been shown multiple times in the litterature (see e.g. [1]). The positive effect of the feedback is visible inside the nested grid, but also outside of it, as corrections are advected with the flow. It must be noted however that in many operationnal implementations, only passive nesting is used, usually because active nesting requires too much data exchange between models, which should then wait for each other during their run. Data assimilation techniques are also widespread in oceanic and atmospheric models. They are usually applied in order to merge observations in models, but also e.g. to merge different outputs from ensemble runs of a model, to merge outputs from different models, or to replace downscaling between nested grids (see [3]). In our work, we present an alternative to active nesting (for implementations currently using passive nesting). First, the low-resolution model is run, followed by the local model. Afterwards, the low-resolution model is run once more, assimilating outputs from the local model as pseudo-data. The benefits of this approach over simple passive nesting are shown using a twin experiment. The GHER model (see [2]) is configured with a 0.25 resolution of the Mediterranean Sea, and with a 0.05 resoluion of the North-Western part; a twin experiment is then set. The reference run uses full two-way nesting, another run uses one-way nesting, and in a third run the assimilation procedure described above is implemented.Conclusions from this experiment are that our "upscaling" has positive impacts on the forecasts, provided a fair amount of EOFs is used during (reduced-rank) assimilation cycles. Finally, the set-up of ongoing work to implement our upscaling procedure in a realistic, operationnal system (the MFS system) is presented

Application of a 3-D Super Ensemble to ocean forecast

Super Ensemble (SE) techniques have recently allowed improving the forecast of various important oceanographic parameters, such as the significant wave height, the speed of sound or the surface drift, by correcting the prediction at a single or multiple locations, where data were available during the whole training period. However, nowadays common observation systems, such as satellite imagery or drifters, do not always provide information at the exact same locations, hence it is necessary to generalize the approach in order to take benefit of every image or track available. In this study, we try and apply a SE, fed with remote sensing and gliders data, to 3-D hydrodynamic models. The basic idea on which rely the SE methods is that a certain combination of several model runs and possibly data could yield better results than just one single model, even if it has a higher temporal or spatial resolution. As the most efficient techniques are the ones using observations, they rapidly developed and increased in complexity by copying what had been done in the data assimilation community; getting from the simple ensemble mean of the model outputs to their linear combination based on a particle filter. In our present study, we have decided to use the Kalman filter (KF) as it alleviates the need of an a priori determination of the training period length, and does not require the run of a very large ensemble of members. In addition, we apply it in a 3-D framework in order to take benefit of the spatial information contained by each source of measurements. For example, satellite images of sea surface temperature (SST) are very useful to correct the value of this parameter, but depending on the structure of the water column, it can also give a precious guess of how warm or cold is the ocean at 20 m deep. In our experiment the domain of interest is the Ligurian Sea during the last week of September, when part of the set-up for the CalVal08 campaign (SiC Charles Trees) had already taken place. The data assimilated during the training of the filter are SST images from AVHRR, as well as temperature and salinity profiles from two Rutgers University gliders. The models used for the study are three nested models of NCOM, run without data assimilation. The two considered variables are the temperature and the salinity. As our method is designed to work in a multivariate way, salinity forecast can possibly be improved by observing temperature profiles. Statistics are computed for both the training and the testing periods with an independent set of data. In four test cases, we review the impact of both the nature of the assimilated data, and the formulation of the model covariance matrix. At the end, we show that, on the basis of previous model outputs from which we’ve drawn an estimate of the model covariance, RMS error of the forecast in the whole 3-D domain can be reduced by 30%, thanks to the only assimilation of satellite SST images