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
[en] 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
Disciplines :
Earth sciences & physical geography
Author, co-author :
Beckers, Jean-Marie ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > GeoHydrodynamics and Environment Research (GHER)
Barth, Alexander ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > GeoHydrodynamics and Environment Research (GHER)
Tomazic, Igor ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > GeoHydrodynamics and Environment Research (GHER)
Alvera Azcarate, Aïda ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > GeoHydrodynamics and Environment Research (GHER)
Language :
English
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
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. and Rixen, M.: EOF calculation and data filling from incomplete oceanographic datasets, J. Atmos. Ocean. Tech., 20, 1839-1856, 2003
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
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: http://www.osi-saf.org (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 temperature by means of DINEOF: a case study during the fishing season in the Bay of Biscay, Int. J. Remote Sens., 32, 933-950, doi:10.1080/01431160903491420, 2011
Gasparini, G. and Cohn, S.: Construction of correlation functions in two and three dimensions, Q. J. Roy. Meteor. Soc., 125, 723-757, 1999
Golub, G. H. and Van Loan, C. F.: Matrix Computations, Vol. 3, JHU Press, 2012
Kalnay, E.: Atmospheric Modeling, Data Assimilation and Predictability, 1st Edn., Cambridge University Press, 2002
Kaplan, A., Kushnir, Y., and Cane, M. A.: Reduced space optimal interpolation of historical marine sea level pressure: 1854-1992, J. Climate, 13, 2987-3002, doi:10.1175/1520-0442(2000)0132.0.CO;2, 2000
Karagali, I., Høyer, J., and Hasager, C.: SST diurnal variability in the North Sea and the Baltic Sea, Remote Sens. Environ., 121, 159-170, 2012
Kawai, Y., Kawamura, H., Takahashi, S., Hosoda, K., Murakami, H., Kachi, M., and Guan, L.: Satellite-based high-resolution global optimum interpolation sea surface temperature data, J. Geophys. Res.-Oceans, 111, C06016, doi:10.1029/2005JC003313, 2006
Le Borgne, P., Roquet, H., and Merchant, C.: Estimation of sea surface temperature from the Spinning Enhanced Visible and Infrared Imager, improved using numerical weather prediction, Remote Sens. Environ., 115, 55-65, 2011
Le Borgne, P., Legendre, G., and Péré, S.: Comparison of MSG/SEVIRI and drifting buoy derived diurnal warming estimates, Remote Sens. Environ., 124, 622-626, 2012
Marullo, S., Santoleri, R., Banzon, V., Evans, R., and Guarracino, M.: A diurnal-cycle resolving sea surface temperature product for the tropical Atlantic, J. Geophys. Res.-Oceans, 115, C05011, doi:10.1029/2009JC005466, 2010
Marullo, S., Santoleri, R., Ciani, D., Borgne, P. L., Perec, S., Pinardi, N., Tonani, M., and Nardone, G.: Combining model and geostationary satellite data to reconstruct hourly SST field over the Mediterranean Sea, Remote Sens. Environ., 146, 11-23, doi:10.1016/j.rse.2013.11.001, 2014
Millot, C.: Circulation in the Western Mediterranean Sea, Oceanol. Acta, 10, 143-149, 1987
Nardelli, B.: A Novel Approach for the High-Resolution Interpolation of In Situ Sea Surface Salinity, J. Atmos. Ocean. Tech., 29, 867-879, 2012
Nardelli, B. B., Tronconi, C., Pisano, A., and Santoleri, R.: High and ultra-high resolution processing of satellite sea surface temperature data over Southern European Seas in the framework of MyOcean project, Remote Sens. Environ., 129, 1-16, doi:10.1016/j.rse.2012.10.012, 2013
Nikolaidis, A., Georgiou, G., Hadjimitsis, D., and Akylas, E.: Filling in missing sea-surface temperature satellite data over the Eastern Mediterranean sea using the DINEOF algorithm, Central European Journal of Geosciences, 6, 27-41, doi:10.2478/s13533-012-0148-1, 2014
Parrish, D. and Derber, J.: The National Meteorological Centers spectral statistical interpolation analysis system, Mon. Weather Rev., 120, 1747-1763, 1992
Reynolds, R.W. and Smith, T. M.: Improved global sea surface temperature analyses, J. Climate, 7, 929-948, 1994
Sheng, Z., Shi, H.-Q., and Ding, Y.-Z.: Missing satellite-based sea surface temperature data reconstructed by DINEOF method, Advances in Marine Science, 2, 017, ISSN: 1671-6647, 2009
Sirjacobs, D., Alvera-Azcárate, A., Barth, A., Park, Y., Nechad, B., Ruddick, K., and Beckers, J.-M.: Cloud filling of total suspended matter, chlorophyll and sea surface temperature remote sensing products by the data interpolation with empirical orthogonal functions methodology, application to the BELCOLOUR-1 database, ESA Special Publication, Vol. SP666, available at: http: //orbi.ulg.ac.be/handle/2268/6552 (last access: 18 March 2014), 2008
Stark, J. D., Donlon, C. J., Martin, M. J., and McCulloch, M. E.: OSTIA: an operational, high resolution, real time, global sea surface temperature analysis system, in: OCEANS 2007 - Europe, IEEE, 1-4, 2007
Stuart-Menteth, A. C., Robinson, I. S., and Challenor, P. G.: A global study of diurnal warming using satellite-derived sea surface temperature, J. Geophys. Res.-Oceans, 108, 3155, doi:10.1029/2002JC001534, 2003
Troupin, C., Machin, F., Ouberdous, M., Sirjacobs, D., Barth, A., and Beckers, J.-M.: High-resolution Climatology of the North-East Atlantic using Data-Interpolating Variational Analysis (DIVA), J. Geophys. Res., 115, C08005, doi:10.1029/2009JC005512, 2010
Volpe, G., Colella, S., Forneris, V., Tronconi, C., and Santoleri, R.: The Mediterranean Ocean Colour Observing System - system development and product validation, Ocean Sci., 8, 869-883, doi:10.5194/os-8-869-2012, 2012
Wang, Y. and Liu, D.: Reconstruction of satellite chlorophyll-A data using a modified DINEOF method: a case study in the Bohai and Yellow seas, China, Int. J. Remote Sens., 35, 204-217, doi:10.1080/01431161.2013.866290, 2014
Weaver, T. and Mirouze, I.: On the diffusion equation and its application to isotropic and anisotropic correlation modelling in variational assimilation, Q. J. Roy. Meteor. Soc., 139, 242-260, 2013
Young, N.: The rate of convergence of a matrix power series, Linear Algebra Appl., 35, 261-278, doi:10.1016/0024-3795(81)90278-0, 1981
