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See detailGeneration of analysis and consistent error fields using the Data Interpolating Variational Analysis (Diva)
Troupin, Charles ULg; Barth, Alexander ULg; Sirjacobs, Damien ULg et al

in Ocean Modelling (2012), 52-53

The Data Interpolating Variational Analysis (Diva) is a method designed to interpolate irregularly-spaced, noisy data onto any desired location, in most cases on regular grids. It is the combination of a ... [more ▼]

The Data Interpolating Variational Analysis (Diva) is a method designed to interpolate irregularly-spaced, noisy data onto any desired location, in most cases on regular grids. It is the combination of a particular methodology, based on the minimisation of a cost function, and a numerically efficient method, based on a finite-element solver. The cost function penalises the misfit between the observations and the reconstructed field, as well as the regularity or smoothness of the field. The intrinsic advantages of the method are its natural way to take into account topographic and dynamic constraints (coasts, advection, . . . ) and its capacity to handle large data sets, frequently encountered in oceanography. The method provides gridded fields in two dimensions, usually in horizontal layers. Three-dimension fields are obtained by stacking horizontal layers. In the present work, we summarize the background of the method and describe the possible methods to compute the error field associated to the analysis. In particular, we present new developments leading to a more consistent error estimation, by determining numerically the real covariance function in Diva, which is never formulated explicitly, contrarily to Optimal Interpolation. The real covariance function is obtained by two concurrent executions of Diva, the first providing the covariance for the second. With this improvement, the error field is now perfectly consistent with the inherent background covariance in all cases. A two-dimension application using salinity measurements in the Mediterranean Sea is presented. Applied on these measurements, Optimal Interpolation and Diva provided very similar gridded fields (correlation: 98.6%, RMS of the difference: 0.02). The method using the real covariance produces an error field similar to the one of OI, except in the coastal areas. [less ▲]

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See detailAdvanced Data Interpolating Variational Analysis. Application to climatological data
Troupin, Charles ULg; Sirjacobs, Damien ULg; Rixen, Michel et al

Poster (2011, April)

DIVA (Data Interpolating Variational Analysis) is a variational analysis tool designed to interpolate irregularly-spaced, noisy data onto any desired location, in most cases on regular grids. It is the ... [more ▼]

DIVA (Data Interpolating Variational Analysis) is a variational analysis tool designed to interpolate irregularly-spaced, noisy data onto any desired location, in most cases on regular grids. It is the combination of a particular methodology, based on the minimization of a functional, and a numerically efficient resolution method, based on a finite elements solver. The intrinsic advantages of DIVA are its natural way to take into account topographic and dynamic constraints (coasts, advection, ...) and its capacity to handle large data sets, frequently encountered in oceanography. In the present work, we describe various improvements to the variational analysis tool. The most significant advance is the development of a full error calculation, whilst until now, only an approximate error-field estimate was available. The key issue is the numerical determination of the real covariance function in DIVA, which is not formulated explicitly. This is solved by two concurrent executions of two DIVA, one providing the covariance for the other. The new calculation of the error field is now perfectly coherent with the inherent background covariance in all cases. The correlation length, which was previously set uniform over the computational domain, is now allowed to vary spatially. The efficiency of the tools for estimating the signal-to-noise ratio, through generalized cross-validation, has also been improved. Finally, a data quality-control method is implemented and allows one to detect possible outliers, based on statistics of the data-reconstruction misfit. The added value of these features are illustrated in the case of a large data set of salinity measured in the Mediterranean Sea. Several analyses are performed with different parameters in order to demonstrate their influence on the interpolated fields. In particular, we examine the benefits of using the parameter optimization tools and the advection constraint. The results are validated by means of a subset of data set apart for an independent validation. The corresponding errors fields are estimated using different methods and underline the role of the data coverage. [less ▲]

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See detailAssimilation of high-frequency radar currents in the Ligurian Sea
Barth, Alexander ULg; Chiggiato, Jacopo; Alvera Azcarate, Aïda ULg et al

Conference (2011, April)

The circulation in the Ligurian Sea is dominated by strong currents, namely the Western Corsican Current and the East Corsican Current, which jointly form the Northern Current. A high mesoscale activity ... [more ▼]

The circulation in the Ligurian Sea is dominated by strong currents, namely the Western Corsican Current and the East Corsican Current, which jointly form the Northern Current. A high mesoscale activity, including meanders and eddy formation, is associated to those energetic currents. The non-linear instability processes and apparently chaotic behavior of this current system make this region a challenging testbed for data assimilation. High-frequency radar surface currents have been measured by the NATO Undersea Research Centre (NURC), La Spezia, Italy from two sites at the Italian Coast (Isola Palmaria and San Rossore). Each of those sites measures the radial currents relative to the position of the radar system. This WERA system captures well the general circulation and mesoscale flow features. The present study shows an application of the assimilation of those measurements in a nested model con- figuration of the Ligurian Sea. It is assumed that the error in the model surface currents comes primarily from uncertainties in the lateral boundary conditions and surface wind fields. The objective of this study is to reduce the uncertainty in these forcing fields by data assimilation. An ensemble of 100 perturbed lateral boundary conditions and surface wind fields is created to take the uncertainty into account. Using an ensemble-smoother technique described in Barth et al, 2010 (Ocean Science) and Barth et al, 2010 (Ocean Dynamics, in press), improved estimates of the wind forcing and boundary conditions are obtained. By rerunning the model with the updated forcing fields, it is verified that the analyzed model solution is closer to the observed HF radar currents. This technique is similar to 4D-Var, but since it is based on the ensemble covariance between forcing fields and observations, it does not require the formulation of an adjoint. [less ▲]

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See detailAdvanced Data Interpolating Variational Analysis. Application to climatological data.
Troupin, Charles ULg; Sirjacobs, Damien ULg; Rixen, Michel et al

Poster (2011, March 21)

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See detailSuper-ensemble techniques applied to wave forecast: performance and limitations
Lenartz, Fabian ULg; Beckers, Jean-Marie ULg; Chiggiato, Jacopo et al

in Ocean Science (2010), 6(2), 595-604

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 ... [more ▼]

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. [less ▲]

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See detailSuper-Ensemble techniques: application to surface drift prediction
Vandenbulcke, Luc ULg; Beckers, Jean-Marie ULg; Lenartz, Fabian ULg et al

in Progress in Oceanography (2009), 82(3), 149-167

The prediction of surface drift of floating objects is an important task, with applications such as marine transport, pollutant dispersion, and search-and-rescue activities. But forecasting even the drift ... [more ▼]

The prediction of surface drift of floating objects is an important task, with applications such as marine transport, pollutant dispersion, and search-and-rescue activities. But forecasting even the drift of surface waters is very challenging, because it depends on complex interactions of currents driven by the wind, the wave field and the general prevailing circulation. Furthermore, although each of those can be forecasted by deterministic models, the latter all suffer from limitations, resulting in imperfect predictions. In the present study, we try and predict the drift of two buoys launched during the DART06 (Dynamics of the Adriatic sea in Real-Time 2006) and MREA07 (Maritime Rapid Environmental Assessment 2007) sea trials, using the so-called hyper-ensemble technique: different models are combined in order to minimize departure from independent observations during a training period; the obtained combination is then used in forecasting mode. We review and try out different hyper-ensemble techniques, such as the simple ensemble mean, least-squares weighted linear combinations, and techniques based on data assimilation, which dynamically update the model’s weights in the combination when new observations become available. We show that the latter methods alleviate the need of fixing the training length a priori, as older information is automatically discarded. When the forecast period is relatively short (12 h), the discussed methods lead to much smaller forecasting errors compared with individual models (at least three times smaller), with the dynamic methods leading to the best results. When many models are available, errors can be further reduced by removing colinearities between them by performing a principal component analysis. At the same time, this reduces the amount of weights to be determined. In complex environments when meso- and smaller scale eddy activity is strong, such as the Ligurian Sea, the skill of individual models may vary over time periods smaller than the forecasting period (e.g. when the latter is 36 h). In these cases, a simpler method such as a fixed linear combination or a simple ensemble mean may lead to the smallest forecast errors. In environments where surface currents have strong mean-kinetic energies (e.g. the Western Adriatic Current), dynamic methods can be particularly successful in predicting the drift of surface waters. In any case, the dynamic hyper-ensemble methods allow to estimate a characteristic time during which the model weights are more or less stable, which allows predicting how long the obtained combination will be valid in forecasting mode, and hence to choose which hyper-ensemble method one should use. [less ▲]

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See detailDynamically constrained ensemble perturbations - application to tides on the West Florida Shelf
Barth, Alexander ULg; Alvera Azcarate, Aïda ULg; Beckers, Jean-Marie ULg et al

in Ocean Science (2009), 5(3), 259-270

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 ... [more ▼]

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. [less ▲]

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See detailThree-dimensional analysis of oceanographic data with the software DIVA
Troupin, Charles ULg; Ouberdous, Mohamed ULg; Machín, Francisco et al

Poster (2008, April 13)

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See detailDIVA-4.2.1: presentation of the new features
Troupin, Charles ULg; Machín, Francisco; Ouberdous, Mohamed ULg et al

Poster (2008, April 03)

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See detailImplementation of hydrostatic constraint in the software DIVA: Theory and applications
Troupin, Charles ULg; Ouberdous, Mohamed ULg; Rixen, Michel et al

Poster (2008, March 31)

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See detailThree-dimensional analysis of oceanographic data with the software DIVA
Troupin, Charles ULg; Ouberdous, Mohamed ULg; Rixen, Michel et al

in Geophysical Research Abstracts (2008)

In oceanography, the process of gridding data is frequently used for various purposes, e.g. initialization of hydrodynamic models, or graphical representation of sparse data. DIVA (Data-Interpolating ... [more ▼]

In oceanography, the process of gridding data is frequently used for various purposes, e.g. initialization of hydrodynamic models, or graphical representation of sparse data. DIVA (Data-Interpolating Variational Analysis) is designed to perform such gridding tasks. It has the advantage of taking into account the intrinsic nature of oceanographic data, i.e. uncertainty in in situ measurements and anisotropy due to advection and irregular coastlines and topography. Three-dimensional reconstruction of temperature and salinity fields is achieved by stacking horizontal layers where independent analysis with DIVA are performed. Nevertheless, analysis in regions void of data may result in the presence of static instabilities between two or more consecutive layers. The method implemented in DIVA to remove such kinds of instabilities is the object of the present work. It consists of adding pseudo-data from one layer to the upper adjacent layer in order to create stable stratification in the vicinity of instabilities. Two approaches for assigning values to the pseudo data are tested: the first is called the mixing approach and aims at simulating a mixing process between two layers; the second is called the minimal perturbation, as it strives to minimise the perturbations inthe pseudo-data. A realistic application using temperature and salinity profiles in the North Atlantic is carried out and the results are compared with World Ocean Atlas climatologies. [less ▲]

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See detailDIVA: a Data Analysis Software with Generalized-Cross Validation and Quality Control
Troupin, Charles ULg; Rixen, Michel; Sirjacobs, Damien ULg et al

Poster (2007, May 19)

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See detailMultigrid state vector for data assimilation in a two-way nested model of the Ligurian Sea
Barth, Alexander ULg; Alvera Azcarate, Aïda ULg; Beckers, Jean-Marie ULg et al

in Journal of Marine Systems (2007), 65(1-4), 41-59

A system of two nested models composed by a coarse resolution model of the Mediterranean Sea, an intermediate resolution model of the Provencal Basin and a high resolution model of the Ligurian Sea is ... [more ▼]

A system of two nested models composed by a coarse resolution model of the Mediterranean Sea, an intermediate resolution model of the Provencal Basin and a high resolution model of the Ligurian Sea is coupled with a Kalman-filter based assimilation method. The state vector for the data assimilation is composed by the temperature, salinity and elevation of the three models. The forecast error is estimated by an ensemble run of 200 members by perturbing initial condition and atmospheric forcings. The 50 dominant empirical orthogonal functions (EOF) are taken as the error covariance of the model forecast. This error covariance is assumed to be constant in time. Sea surface temperature (SST) and sea surface height (SSH) are assimilated in this system. (c) 2006 Elsevier B.V. All rights reserved. [less ▲]

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See detailForecast verification of a 3D model of the Mediterranean Sea. The use of discrete wavelet transforms and EOFs in the skill assessment of spatial forecasts
Alvera Azcarate, Aïda ULg; Barth, Alexander ULg; Ben Bouallegue, Zied et al

in Journal of Marine Systems (2007), 65(1-4), 460-483

The quality assessment of a nested model system of the Mediterranean Sea is realised. The model has two zooms in the Provencal Basin and in the Ligurian Sea, realised with a two-way nesting approach. The ... [more ▼]

The quality assessment of a nested model system of the Mediterranean Sea is realised. The model has two zooms in the Provencal Basin and in the Ligurian Sea, realised with a two-way nesting approach. The experiment lasts for nine weeks, and at each week sea surface temperature (SST) and sea level anomaly are assimilated. The quality assessment of the surface temperature is done in a spatio-temporal approach, to take into account the high complexity of the SST distribution. We focus on the multi-scale nature of oceanic processes using two powerful tools for spatio-temporal analysis, wavelets and Empirical Orthogonal Functions (EOFs). We apply two-dimensional wavelets to decompose the high-resolution model and observed SST into different spatial scales. The Ligurian Sea model results are compared to observations at each of those spatial scales, with special attention on how the assimilation affects the model behaviour. We also use EOFs to assess the similarities between the Mediterranean Sea model and the observed SST. The results show that the assimilation mainly affects the model large-scale features, whereas the small scales show little or no improvement and sometimes, even a decrease in their skill. The multiresolution analysis reveals the connection between large- and small-scale errors, and how the choice of the maximum correlation length of the assimilation scheme affects the distribution of the model error among the different spatial scales. (c) 2006 Elsevier B.V. All rights reserved. [less ▲]

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See detail36th International Liege Colloquium on Ocean Dynamics - Liege, Belgium, 3-7 May, 2004 - Marine environmental monitoring and prediction - Preface
Desaubies, Yves; Rixen, Michel; Beckers, Jean-Marie ULg

in Journal of Marine Systems (2007), 65(1-4), 1-2

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See detailStudy of the combined effects of data assimilation and grid nesting in ocean models – application to the Gulf of Lions
Vandenbulcke, Luc ULg; Barth, Alexander ULg; Rixen, Michel et al

in Ocean Science (2006), 2

Modern operational ocean forecasting systems routinely use data assimilation techniques in order to take observations into account in the hydrodynamic model. Moreover, as end users require higher and ... [more ▼]

Modern operational ocean forecasting systems routinely use data assimilation techniques in order to take observations into account in the hydrodynamic model. Moreover, as end users require higher and higher resolution predictions, especially in coastal zones, it is now common to run nested models, where the coastal model gets its open-sea boundary conditions from a low-resolution global model. This configuration is used in the "Mediterranean Forecasting System: Towards environmental predictions" (MFSTEP) project. A global model covering the whole Mediterranean Sea is run weekly, performing 1 week of hindcast and a 10-day forecast. Regional models, using different codes and covering different areas, then use this forecast to implement boundary conditions. Local models in turn use the regional model forecasts for their own boundary conditions. This nested system has proven to be a viable and efficient system to achieve high-resolution weekly forecasts. However, when observations are available in some coastal zone, it remains unclear whether it is better to assimilate them in the global or local model. We perform twin experiments and assimilate observations in the global or in the local model, or in both of them together. We show that, when interested in the local models forecast and provided the global model fields are approximately correct, the best results are obtained when assimilating observations in the local model. [less ▲]

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See detailCoupling a two-way nested primitive equation model and a statistical SST predictor of the Ligurian Sea via data assimilation
Barth, Alexander ULg; Alvera Azcarate, Aïda ULg; Beckers, Jean-Marie ULg et al

in Ocean Modelling (2006), 13(3-4), 255-270

A primitive equation model and a statistical predictor are coupled by data assimilation in order to combine the strength of both approaches. In this work, the system of two-way nested models centred in ... [more ▼]

A primitive equation model and a statistical predictor are coupled by data assimilation in order to combine the strength of both approaches. In this work, the system of two-way nested models centred in the Ligurian Sea and the satellite-based ocean forecasting (SOFT) system predicting the sea surface temperature (SST) are used. The data assimilation scheme is a simplified reduced order Kalman filter based on a constant error space. The assimilation of predicted SST improves the forecast of the hydrodynamic model compared to the forecast obtained by assimilating past SST observations used by the statistical predictor. This study shows that the SST of the SOFT predictor can be used to correct atmospheric heat fluxes. Traditionally this is done by relaxing the model SST towards the climatological SST. Therefore, the assimilation of SOFT SST and climatological SST are also compared. (c) 2006 Elsevier Ltd. All rights reserved. [less ▲]

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See detailTwo-way nested model of mesoscale circulation features in the Ligurian Sea
Barth, Alexander ULg; Alvera Azcarate, Aïda ULg; Rixen, Michel et al

in Progress in Oceanography (2005), 66(2-4), 171-189

A coarse resolution primitive equation model of 1/4 degrees resolution is implemented covering the whole Mediterranea Sea. Within this grid a 1/20 degrees resolution model of the Liguro-Provencal basin ... [more ▼]

A coarse resolution primitive equation model of 1/4 degrees resolution is implemented covering the whole Mediterranea Sea. Within this grid a 1/20 degrees resolution model of the Liguro-Provencal basin and the northern part of the Tyrrhenian Sea is embedded. A third fine resolution model of 1/60 degrees is nested in the latter one and simulates the dynamics of the Ligurian Sea. Comparisons between one-way and two-way nesting in simulating the Northern Current (NC) are made. The properties of the Eastern and Western Corsican Current and the Northern Current are investigated with this nesting system. Special attention is given to the variability of the NC. Meanders and interactions with Winter Intermediate Water lenses are shown. Topographic features also lead to a highly variable NC. (c) 2005 Elsevier Ltd. All rights reserved. [less ▲]

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See detailReconstruction of incomplete oceanographic data sets using empirical orthogonal functions: application to the Adriatic Sea surface temperature
Alvera Azcarate, Aïda ULg; Barth, Alexander ULg; Rixen, Michel et al

in Ocean Modelling (2005), 9(4), 325-346

A method for the reconstruction of missing data based on an EOF decomposition has been applied to a large data set, a test case of Sea Surface Temperature satellite images of the Adriatic Sea. The EOF ... [more ▼]

A method for the reconstruction of missing data based on an EOF decomposition has been applied to a large data set, a test case of Sea Surface Temperature satellite images of the Adriatic Sea. The EOF decomposition is realised with a Lanczos method, which allows optimising computational time for large matrices. The results show that the reconstruction method leads to accurate reconstructions as well as a low cpu time when dealing with realistic cases. The method has been tested with different amounts of missing data, artificially adding clouds ranging from 40% to 80% of data loss, and then compared to the same data set with no missing data. A comparison with in situ data has also been made. These validation studies show that results are robust, even when the amount of missing data is very high. The reconstruction of the data from the Adriatic Sea shows realistic features and a reliable temperature distribution. In addition, the method is compared to an Optimal Interpolation reconstruction. The results obtained with both methods are very similar. The main difference is the computational time, which is reduced nearly 30 times with the method presented here. Once the reconstruction has been performed, the EOF decomposition is analysed to show the method's reliability, and a cold event on the Albanian coast is studied. The reconstructed data reflect the effect of wind on the Albanian coast, that led to a cold-water episode in this zone for a 6-day period. (c) 2004 Elsevier Ltd. All rights reserved. [less ▲]

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See detailA hydrographic and biochemical climatology of the Mediterranean and the Black Sea: some statistical pitfalls
Rixen, Michel; Beckers, Jean-Marie ULg; Maillard, Catherine

in Vandenberghe, E.; Brown, M.; Costello, M.J (Eds.) et al IOC Workshop Report 188 (2004)

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