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A Method to Generate Fully Multi-scale Optimal Interpolation by Combining Efficient Single Process Analyses, Illustrated by a Dineof Analysis Spiced with a Local Optimal Interpolation : Volume 10, Issue 5 (30/10/2014)

By Beckers, J.-m.

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Book Id: WPLBN0004020229
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File Size: Pages 18
Reproduction Date: 2015

Title: A Method to Generate Fully Multi-scale Optimal Interpolation by Combining Efficient Single Process Analyses, Illustrated by a Dineof Analysis Spiced with a Local Optimal Interpolation : Volume 10, Issue 5 (30/10/2014)  
Author: Beckers, J.-m.
Volume: Vol. 10, Issue 5
Language: English
Subject: Science, Ocean, Science
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Alvera-Azcárate, A., Tomazic, I., Barth, A., & Beckers, J. (2014). A Method to Generate Fully Multi-scale Optimal Interpolation by Combining Efficient Single Process Analyses, Illustrated by a Dineof Analysis Spiced with a Local Optimal Interpolation : Volume 10, Issue 5 (30/10/2014). Retrieved from

Description: GeoHydrodynamics and Environment Research, MARE, University of Liège, Sart-Tilman B5, 4000 Liège, Belgium. We present a method in which the optimal interpolation of multi-scale processes can be expanded 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 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 to a real situation in which we combine large-scale analysis of hourly Spinning Enhanced Visible and Infrared Imager (SEVIRI) satellite images using data interpolating empirical orthogonal functions (DINEOF) with a local optimal interpolation using a Gaussian covariance. It is 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.

A method to generate fully multi-scale optimal interpolation by combining efficient single process analyses, illustrated by a DINEOF analysis spiced with a local optimal interpolation

Beckers, J.-M. and Rixen, M.: EOF calculation and data filling from incomplete oceanographic datasets, J. Atmos. Ocean. Tech., 20, 1839–1856, 2003.; Alvera-Azcárate, A., Barth, A., Rixen, M., and Beckers, J.-M.: Reconstruction of incomplete oceanographic data sets using Empirical Orthogonal Functions. Application to the Adriatic Sea Surface Temperature, Ocean Model., 9, 325–346, doi:10.1016/j.ocemod.2004.08.001, 2005.; Alvera-Azcárate, A., Barth, A., Beckers, J.-M., and Weisberg, R. H.: Multivariate reconstruction of missing data in sea surface temperature, chlorophyll and wind satellite field, J. Geophys. Res., 112, C03008, doi:10.1029/2006JC003660, 2007.; Beckers, J.-M., Rixen, M., Brasseur, P., Brankart, J.-M., Elmoussaoui, A., Crépon, M., Herbaut, C., Martel, F., Van den Berghe, F., Mortier, L., Lascaratos, A., Drakopoulos, P., Korres, P., Pinardi, N., Masetti, E., Castellari, S., Carini, P., Tintore, J., Alvarez, A., Monserrat, S., Parrilla, D., Vautard, R., and Speich, S.: Model intercomparison in the Mediterranean. The MedMEx simulations of the seasonal cycle, J. Marine Syst., 33–34, 215–251, 2002.; Beckers, J.-M., Barth, A., and Alvera-Azcárate, A.: DINEOF reconstruction of clouded images including error maps – application to the Sea-Surface Temperature around Corsican Island, Ocean Sci., 2, 183–199, doi:10.5194/os-2-183-2006, 2006.; Bracewell, R.: The Fourier Transform and its Applications, 2nd Edn., rev., international student ed Edn., McGraw-Hill, New York, 1986.; Nardelli, B.: A Novel Approach for the High-Resolution Interpolation of In Situ Sea Surface Salinity, J. Atmos. Ocean. Tech., 29, 867–879, 2012.; Brasseur, P., Beckers, J.-M., Brankart, J.-M., and Schoenauen, R.: Seasonal temperature and salinity fields in the Mediterranean Sea: climatological analyses of a historical data set, Deep-Sea Res. Pt. I, 43, 159–192, doi:10.1016/0967-0637(96)00012-X, 1996.; Bretherton, F. P., Davis, R. E., and Fandry, C.: A technique for objective analysis and design of oceanographic instruments applied to MODE-73, Deep-Sea Res., 23, 559–582, doi:10.1016/0011-7471(76)90001-2, 1976.; Brisson, A., Le Borgne, P., and Marsouin, A.: Results of one year of preoperational production of sea surface temperatures from GOES-8, J. Atmos. Ocean. Tech., 19, 1638–1652, 2002.; Cushman-Roisin, B. and Beckers, J.-M.: Introduction to Geophysical Fluid Dynamics, Physical and Numerical Aspects, Academic Press, 2011.; Daley, R.: Atmospheric Data Analysis, Vol. 2, Cambridge University Press, 1993.; Delhomme, J.: Kriging in the hydrosciences, Adv. Water Resour., 1, 251–266, doi:10.1016/0309-1708(78)90039-8, 1978.; Donlon, C. J., Martin, M., Stark, J., Roberts-Jones, J., Fiedler, E., and Wimmer, W.: The operational sea surface temperature and sea ice analysis (OSTIA) system, Remote Sens. Environ., 116, 140–158, 2012.; Eastwood, S., Le Borgne, P., Péré, S., and Poulter, D.: Diurnal variability in sea surface temperature in the Arctic, Remote Sens. Environ., 115, 2594–2602, 2011.; EUMETSAT: Geostationary sea surface temperature product user manual, available at: (last access: 18 March 2014), 2011.; Fisher, M.: Background error covariance modelling, in: Seminar on Recent Development in Data Assimilation for Atmosphere and Ocean, 45–63, 2003.; Gandin, L. S.: Objective Analysis of Meteorological Fields, Tech. rep., Israel Program for Scientific Translations, Jerusalem, 1965.; Ganzedo, U., Alvera-Azcárate, A., Esnaola, G., Ezcurra, A., and Saenz, J.: Reconstruction of sea surface temper


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