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See detailApproximate and Efficient Methods to Assess Error Fields in Spatial Gridding with Data Interpolating Variational Analysis (DIVA)
Beckers, Jean-Marie ULg; Barth, Alexander ULg; Troupin, Charles ULg et al

in Journal of Atmospheric & Oceanic Technology (2014), 31(2), 515-530

We present new approximate methods to provide error fields for the spatial analysis tool Diva. It is first shown how to replace the costly analysis of a large number of covariance functions by a single ... [more ▼]

We present new approximate methods to provide error fields for the spatial analysis tool Diva. It is first shown how to replace the costly analysis of a large number of covariance functions by a single analysis for quick error computations. Then another method is presented where the error is only calculated in a small number of locations and from there the spatial error field itself interpolated by the analysis tool. The efficiency of the methods is illustrated on simple schematic test cases and a real application in the Mediterranean Sea. These examples show that with these methods one has the possibility for quick masking of regions void of sufficient data and the production of "exact" error fields at reasonable cost. The error-calculation methods can also be generalized for use with other analysis methods such as 3D-Var and are therefore potentially interesting for other implementations. [less ▲]

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See detailUntangling spatial and temporal trends in the variability of the Black Sea Cold Intermediate Layer and mixed Layer Depth using the DIVA detrending procedure
Capet, Arthur ULg; Troupin, Charles ULg; Cartensen, Jacob et al

in Ocean Dynamics (2014), 64(3), 315-324

Current spatial interpolation products may be biased by uneven distribution of measurements in time. This manuscript presents a detrending method that recognizes and eliminates this bias. The method ... [more ▼]

Current spatial interpolation products may be biased by uneven distribution of measurements in time. This manuscript presents a detrending method that recognizes and eliminates this bias. The method estimates temporal trend components in addition to the spatial structure and has been implemented within the Data Interpolating Variational Analysis (DIVA) analysis tool. The assets of this new detrending method are illustrated by producing monthly and annual climatologies of two vertical properties of the Black Sea while recognizing their seasonal and interannual variabilities : the mixed layer depth, and the cold content of its Cold Intermediate Layer (CIL). The temporal trends, given as by-products of the method, are used to analyze the seasonal and interannual variability of these variables over the past decades (1955-2011). In particular, the CIL interannual variability is related to the cumulated winter air temperature anomalies, explaining 88\% of its variation. [less ▲]

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See detaildivand-1.0: n-dimensional variational data analysis for ocean observations
Barth, Alexander ULg; Beckers, Jean-Marie ULg; Troupin, Charles ULg et al

in Geoscientific Model Development (2014), 7

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 ... [more ▼]

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). [less ▲]

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See detailInterpolation of SLA Using the Data-Interpolating Variational Analysis in the Coastal Area of the NW Mediterranean Sea
Troupin, Charles ULg; Barth, Alexander ULg; Beckers, Jean-Marie ULg et al

Poster (2013, October 07)

The spatial interpolation of along-track Sea-Level Anomalies (SLA) data to produce gridded map has numerous applications in oceanography (model validation, data assimilation, eddy tracking, ...). Optimal ... [more ▼]

The spatial interpolation of along-track Sea-Level Anomalies (SLA) data to produce gridded map has numerous applications in oceanography (model validation, data assimilation, eddy tracking, ...). Optimal Interpolation (OI) is often the preferred method for this task, as it leads to the lowest expected error and provides an error field associated to the analyzed field. However, the method suffers from limitations such as the numerical cost (due to the inversion of covariance matrices) as well as the isotropic covariance function, generally employed in altimetry. The Data-Interpolating Variational Analysis (DIVA) is a gridding method based on the minimization of a cost function using a finite-element technique. The cost function penalizes the departures from observations, the smoothness of the gridded field and physical constraints (advection, diffusion, ...). It has been shown that DIVA and OI are equivalent (provided some assumptions on the covariances are made), the main difference is that in DIVA, the covariance function is not explicitly formulated. The technique has been previously applied for the creation of regional hydrographic climatologies, which required the processing of a large number of data points. In this work we present the application and adaptation of Diva to the analysis of SLA in the Mediterranean Sea and the production of weekly maps of SLA in this region. The peculiarities of SLA along-track data are addressed: • number of observations: the finite-element technique coupled to improvements in the matrix inversion (parallel or iterative solvers) lead to a decrease of the computational time, meaning that sub-sampling of the initial data set is not required. • quality of the different missions: the weight attributed to each data point can be easily set according to the satellite that provided the observations, so that different measurement noise variances are considered. • spatial correlation scale: it varies spatially in the domain according to the value of the Rossby radius of deformation. • long-wavelength errors: each data point is associated a class, and a detrending technique allows the determination of the trend for each class, leading to a reduction of the inconsistencies between missions. • anisotropy of physical coastal features: a pseudo-velocity field derived from regional bathymetry enhances the correlations along the main currents. Particular attention will be paid to the influence of this constraint in the coastal area. The analysis and error fields obtained over the Mediterranean Sea are compared with the available gridded products from AVISO. Different ways to compute the error field are compared. The impact of the use of multiple missions to prepare the gridded fields is also examined. In situ measurements from an intensive multi-sensor experiment carried out north of the Balearic Islands in May 2009 serve to assess the quality of the gridded fields in the coastal area. [less ▲]

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See detailWP8 and WP9 developments: Data-Interpolating Variational Analysis (Diva) developments
Troupin, Charles ULg; Barth, Alexander ULg; Ouberdous, Mohamed et al

Conference (2013, September 27)

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See detailApplication of the Data-Interpolating Variational Analysis (DIVA) to sea-level anomaly measurements in the Mediterranean Sea
Troupin, Charles ULg; Barth, Alexander ULg; Beckers, Jean-Marie ULg et al

Poster (2013, September 23)

In ocean sciences, numerous techniques are available for the spatial interpolation of in situ data. These techniques mainly differ in the mathematical formulation and the numerical efficiency. Among them ... [more ▼]

In ocean sciences, numerous techniques are available for the spatial interpolation of in situ data. These techniques mainly differ in the mathematical formulation and the numerical efficiency. Among them, DIVA, which is based on the minimization of a cost function using a finite-element technique (figure 1). The cost function penalizes the departure from observations, the smoothness or regularity of the gridded field and can also include physical constraints. The technique is particularly adapted for the creation of climatologies, which required a large to several regional seas or part of the ocean to generate hydrographic climatologies. Sea-level anomalies (SLA) can be deduced from satellite-borne altimeters. The measurements are characterized by a high spatial resolution along the satellite tracks, but often a large distance between neighbour tracks. This implies the use of simultaneous altimetry missions for the construction of gridded maps. An along-track long wave-length error (correlated noise, e.g. due to orbit, residual tidal correction or inverse barometer errors) also affects the measurement and has to be taken into account in the interpolation. In this work we present the application and adaptation of Diva to the analysis of SLA in the Mediterranean Sea and the production of weekly maps of SLA in this region. Determination of the parameters The two main parameters that determines an analysis with DIVA are the correlation length (L) and the signal-to-noise ratio (SNR). Because of the particular spatial distribution of the measurements, the tools implemented in Diva for the analysis parameter determination tend to underestimate L and overestimate SNR, leading to noisy analysis (the observation constraint dominates the regularity constraint). Some adaptations of the tools are necessary to solve this issue. Numerical cost Because of the large number of observations to be processed (in comparison with in situ measurements on a similar period), the interpolation method employed is expected to be numerically efficient. Improvements in the implementation of Diva further improved the numerical performance of the method, especially thanks to the use of a parallel solver for the matrix inversion. The performance of finite-element mesh generator was also enhanced, so that interpolation of a data set of more than 1 million data points on a 100-by-100 grid can be performed in a few minutes on a personal laptop. Analysis and error field The analysis and error fields obtained over the Mediterranean Sea are compared with the available gridded products from AVISO. Different ways to compute the error field are compared. The impact of the use of multiple missions to prepare the gridded fields is also examined. [less ▲]

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See detailRecent methods for Data Interpolation: DINEOF and DIVA
Troupin, Charles ULg

Scientific conference (2013, January 31)

Detailed reference viewed: 61 (5 ULg)
See detailEstimating Inter-Sensor Sea Surface Temperature Biases using DINEOF analysis
Tomazic, Igor ULg; Alvera Azcarate, Aïda ULg; Troupin, Charles ULg et al

Poster (2013)

Climate studies need long-term data sets of homogeneous quality, in order to discern trends from other physical signals present in the data and to minimise the contamination of these trends by errors in ... [more ▼]

Climate studies need long-term data sets of homogeneous quality, in order to discern trends from other physical signals present in the data and to minimise the contamination of these trends by errors in the source data. Sea surface temperature (SST), defined as one of essential climatology variables, has been increasingly used in both oceanographical and meteorological operational context where there is a constant need for more accurate measurements. Satellite-derived SST provides an indispensable dataset, with both spatially and temporally high resolutions. However, these data have errors of 0.5 K on a global scale and present inter-sensor and inter-regional differences due to their technical characteristics, algorithm limitations and the changing physical properties of the measured environments. These inter-sensor differences should be taken into account in any research involving more than one sensor (SST analysis, long term climate research . . . ). The error correction for each SST sensor is usually calculated as a difference between the SST data derived from referent sensor (e.g. ENVISAT/AATSR) and from the other sensors (SEVIRI, AVHRR, MODIS). However, these empirical difference (bias) fields show gaps due to the satellite characteristics (e.g. narrow swath in case of AATSR) and to the presence of clouds or other atmospheric contaminations. We present a methodology based on DINEOF (Data INterpolation Empirical Orthogonal Functions) to reconstruct and analyse SST biases with the aim of studying temporal and spatial variability of the SST bias fields both at a large scale (European seas) and at a regional scale (Mediterranean Sea) and to perform the necessary corrections to the original SST fields. Two different approaches were taken: by analysing SST biases based on reconstructed SST differences and based on differences of reconstructed SST fields. Corrected SST fields based on both approaches were validated against independent in situ buoy SST data or with ENVISAT/AATSR SST data for areas without in situ data (e.g. eastern Mediterranean). [less ▲]

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See detailUpwelling, filament and eddies in the Canary Current upwelling system during the CAIBEX cruise (Summer 2009)
Troupin, Charles ULg; Sangrà, Pablo; Arístegui, Javier et al

Poster (2012, November 15)

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See detailNegative wind anomalies generated a diminution of productivity of in the North Atlantic in 2010
Troupin, Charles ULg; Machín, Francisco

Poster (2012, November 14)

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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 detailAn EOF-based technique to compute merged high resolution sea surface temperature fields
Alvera Azcarate, Aïda ULg; Troupin, Charles ULg; Barth, Alexander ULg et al

Conference (2012, May 10)

High quality sea surface temperature (SST) data sets are needed for various applications, including numerical weather prediction, ocean forecasting and climate research. The coverage, resolution and ... [more ▼]

High quality sea surface temperature (SST) data sets are needed for various applications, including numerical weather prediction, ocean forecasting and climate research. The coverage, resolution and precision of individual SST satellite observations is not sufficient for these applications, therefore the merging of these complementary data sets is needed to reduce the final data set error. This is usually performed by optimal interpolation (OI).We present an extension of the capabilities of DINEOF (Data INterpolating Empirical Orthogonal Functions) to merge data from different platforms. The analysis is based on the formalism of OI, but the crucial difference is that the error covariance is not parametrized a priori using an analytical expression, but expressed using a spatial EOF basis calculated by DINEOF. This EOF basis represents more realistically the complex variability of SST data sets than the parametric covariance used in most OI applications. An example will be presented using data from a polar-orbiting satellite (AVHRR on MetOp) and a geostationary satellite (SEVIRI on MSG). The high spatial resolution of the polar-orbiting satellite and the high temporal resolution of the geostationary satellite are retained to create a very high spatial and temporal resolution field of the western Mediterranean SST. The results are validated with independent data. [less ▲]

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See detailNegative wind anomalies generated a diminution of productivity in the North Atlantic in 2010
Troupin, Charles ULg; Machín, Francis

Poster (2012, April 27)

The weakening of the wind intensity in winter 2010, related to a low NAO index, generated unseen temperature anomalies and a significant decrease of biological activity in the Canary Current upwelling ... [more ▼]

The weakening of the wind intensity in winter 2010, related to a low NAO index, generated unseen temperature anomalies and a significant decrease of biological activity in the Canary Current upwelling system. [less ▲]

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See detailReconstruction and analysis of QuikSCAT wind measurements with an EOF-based technique
Troupin, Charles ULg; Alvera Azcarate, Aïda ULg; Beckers, Jean-Marie ULg

Poster (2012, April 24)

QuikSCAT wind products are often used to provide numerical model atmospheric forcing. However, due to the configuration of the satellite swaths, gaps are frequently observed in the daily wind maps. We ... [more ▼]

QuikSCAT wind products are often used to provide numerical model atmospheric forcing. However, due to the configuration of the satellite swaths, gaps are frequently observed in the daily wind maps. We present a solution based on truncated EOF decomposition to fill these gaps. [less ▲]

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