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See detailWeb-based application for Data INterpolation Empirical Orthogonal Functions (DINEOF) analysis
Tomazic, Igor ULg; Alvera Azcarate, Aïda ULg; Barth, Alexander ULg et al

Poster (2014, April)

DINEOF (Data INterpolating Empirical Orthogonal Functions) is a powerful tool based on EOF decomposition developed at the University of Liege/GHER for the reconstruction of missing data in satellite ... [more ▼]

DINEOF (Data INterpolating Empirical Orthogonal Functions) is a powerful tool based on EOF decomposition developed at the University of Liege/GHER for the reconstruction of missing data in satellite datasets, as well as for the reduction of noise and detection of outliers. DINEOF is openly available as a series of Fortran routines to be compiled by the user, and as binaries (that can be run directly without any compilation) both for Windows and Linux platforms. In order to facilitate the use of DINEOF and increase the number of interested users, we developed a web-based interface for DINEOF with the necessary parameters available to run high-quality DINEOF analysis. This includes choosing variable within selected dataset, defining a domain, time range, filtering criteria based on available variables in the dataset (e.g. quality flag, satellite zenith angle …) and defining necessary DINEOF parameters. Results, including reconstructed data and calculated EOF modes will be disseminated in NetCDF format using OpenDAP and WMS server allowing easy visualisation and analysis. First, we will include several satellite datasets of sea surface temperature and chlorophyll concentration obtained from MyOcean data centre and already remapped to the regular grid (L3C). Later, based on user’s request, we plan to extend number of datasets available for reconstruction. [less ▲]

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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 detailMulti-scale optimal interpolation: application to DINEOF analysis spiced with a local optimal interpolation
Beckers, Jean-Marie ULg; Barth, Alexander ULg; Tomazic, Igor ULg et al

in Ocean Science Discussions (2014), 11

We present a method in which the optimal interpolation of multi-scale processes can be untangled into a succession of simpler interpolations. First, we prove how the optimal analysis of a superposition of ... [more ▼]

We present a method in which the optimal interpolation of multi-scale processes can be untangled into a succession of simpler interpolations. First, we prove how the optimal analysis of a superposition of two processes can be obtained by different mathematical formulations involving iterations and analysis focusing on a single process. From the 5 different mathematical equivalent formulations we then select the most efficient ones by analyzing the behavior of the different possibilities in a simple and well controlled test case. The clear guidelines deduced from this experiment are then applied in a real situation in which we combine large-scale analysis of hourly SEVIRI satellite images using DINEOF with a local optimal interpolation using a Gaussian covariance. It is 10 shown that the optimal combination indeed provides the best reconstruction and can therefore be exploited to extract the maximum amount of useful information from the original data [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 [=GMD] (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 detailDerivation of high resolution TSM data by merging geostationary and polar-orbiting satellite data in the North Sea.
Alvera Azcarate, Aïda ULg; Barth, Alexander ULg; Vanhellemont, Quinten et al

Conference (2013, September 09)

There is a need for high resolution ocean colour data, both in space and time, for a better assessment of the variability of these data and their influence in the environment, specially at shallow areas ... [more ▼]

There is a need for high resolution ocean colour data, both in space and time, for a better assessment of the variability of these data and their influence in the environment, specially at shallow areas where factors as tides and wind play a role in their dynamics. High spatial resolution is achieved by polar-orbiting satellites, but at a low temporal resolution. The opposite is true for geostationary satellites. In order to exploit the complementary nature of geostationary and polar data, a merging methodology has been developed to obtain a unique estimate of the North Sea Total Suspended Matter (TSM). The largest difficulty in developing a merging methodology is the correct estimation of the error covariance matrix, which can be specially complex for variables like TSM. In this work, the error covariance is not parametrized a priori using an analytical expression, but expressed using a truncated spatial EOF basis calculated by analysing MODIS data using DINEOF (Data INterpolating Empirical Orthogonal Functions). This EOF basis represents more realistically the complex variability of the TSM data sets than the parametric covariance used in most optimal interpolation applications. This EOF basis is subsequently used to merge MODIS and SEVIRI TSM data using an optimal interpolation approach. Results for the North Sea 2009 TSM will be shown, demonstrating the possibilities of this technique. The influence of including variables like winds or tides in the analysis, through multivariate approaches, will be assessed. [less ▲]

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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 detailDINEOF-based bias correction of SEVIRI sea surface temperature using Metop-A/AVHRR and ENVISAT/AATSR SST
Tomazic, Igor ULg; Alvera Azcarate, Aïda ULg; Barth, Alexander ULg et al

Poster (2013)

Satellite-derived sea surface temperature (SST) show inter-sensor and inter-regional differences (biases) due to their technical characteristics, multispectral algorithm limitations and the changing ... [more ▼]

Satellite-derived sea surface temperature (SST) show inter-sensor and inter-regional differences (biases) due to their technical characteristics, multispectral algorithm limitations and the changing physical properties of the measured environments. The bias correction is usually calculated as a difference between the SST measurements from two sensors where one is defined as the reference (e.g. ENVISAT/AATSR). These empirical 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 contamination sources. We present a bias correction approach based on DINEOF (Data Interpolating Empirical Orthogonal Functions) for reconstructing missing data. Two different approaches for deriving SST bias fields were used: analysing SST biases based on reconstructed SST differences or based on differences of the reconstructed SST fields. The method is applied at a large scale (European seas) and at a regional scale (e.g. Mediterranean Sea) to correct SEVIRI and Metop-A/AVHRR SST measurements using ENVISAT/AATSR as a corrector. For SEVIRI we additionally used Metop-A/AVHRR SST as a corrector to analyse the impact of ENVISAT/AATSR failure. 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). The method is also compared to the operational bias correction method at Meteo-France/CMS that uses a temporal and spatial averaging. Results show that both approaches lead to near-zero biases when compared to AATSR SST measurements, although the differences of reconstructions exhibit much higher standard deviation (> 0.6 K) compared to the reconstruction of differences (< 0.5 K). Comparison with in situ data expectedly depends on the initial comparison between AATSR and in situ SST for specific regions. [less ▲]

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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 detailReconstruction of Total Suspended Matter data over the North Sea using DINEOF: use of the Gaussian anamorphosis transformation
Alvera Azcarate, Aïda ULg; Neukermans, Griet; Barth, Alexander ULg et al

Conference (2012, May 10)

Total Suspended Matter (TSM) from the SEVIRI sensor in the North Sea will be analysed using DINEOF (Data INterpolating Empirical Orthogonal Functions), an EOFbased technique to reconstruct missing data ... [more ▼]

Total Suspended Matter (TSM) from the SEVIRI sensor in the North Sea will be analysed using DINEOF (Data INterpolating Empirical Orthogonal Functions), an EOFbased technique to reconstruct missing data. The information needed to reconstruct the missing data is computed internally based on a truncated EOF basis, so no assumptions about the statistics of the data have to be made. DINEOF uses the mean and covariance of the original data to calculate the EOF basis. If the data are normally distributed, then the probability density distribution can be completely described by their mean and the eigenvectors of the covariance matrix (the EOFs). Variables such as TSM, however, do not have a Gaussian distribution, since TSM is never smaller than zero. DINEOF typically does not take this into account. To overcome this, a logarithmic transformation is usually performed to non-Gaussian variables, although the exponential transformation needed to retrieve the original variable units after using DINEOF leads sometimes to unrealistic high values in the reconstruction. An empirical transformation, which allows to obtain a normally distributed variable based solely on the data themselves, will be applied. This procedure, called Gaussian anamorphosis, is sometimes used in data assimilation. A Gaussian anamorphosis transformation will be applied to the TSM data of the North Sea prior to their reconstruction. The high spatial and temporal dynamics of the gapfree geostationary TSM data set will be analysed, focusing on tidal dynamics and sub-daily variability. [less ▲]

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