Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2014 | 2 | 587--595
Tytuł artykułu

An error estimate of Gaussian Recursive Filter in 3Dvar problem

Warianty tytułu
Języki publikacji
Computational kernel of the three-dimensional variational data assimilation (3D-Var) problem is a linear system, generally solved by means of an iterative method. The most costly part of each iterative step is a matrix-vector product with a very large covariance matrix having Gaussian correlation structure. This operation may be interpreted as a Gaussian convolution, that is a very expensive numerical kernel. Recursive Filters (RFs) are a well known way to approximate the Gaussian convolution and are intensively applied in the meteorology, in the oceanography and in forecast models. In this paper, we deal with an oceanographic 3D-Var data assimilation scheme, named OceanVar, where the linear system is solved by using the Conjugate Gradient (GC) method by replacing, at each step, the Gaussian convolution with RFs. Here we give theoretical issues on the discrete convolution approximation with a first order (1st-RF) and a third order (3rd-RF) recursive filters. Numerical experiments confirm given error bounds and show the benefits, in terms of accuracy and performance, of the 3-rd RF.(original abstract)
Opis fizyczny
  • University of Naples Federico II, Italy
  • Parthenope University of Naples, Italy
  • Parthenope University of Naples, Italy
  • Centro Euro-Mediterraneo sui Cambiamenti Climatici
  • Abramowitz M., Stegun I. - Handbook of Mathematical Functions. Dover, New York, 1965.
  • Belo Pereira M., Berre L. - The use of an ensemble approach to study the background-error covariances in a global NWP model. MOn. Wea. Rev. 134, pp. 2466-2489, 2006.
  • Cabanes C., Grouazel A., von Schuckmann K., Hamon M., Turpin V., Coatanoan C., Paris F., Guinehut S., Bppne C., Ferry N., de Boyer Montgut C., Carval T., Reverding G., Puoliquen S., Traon P. Y. L. - The CORA dataset: validation and diagnostics of in-situ ocean temperature and salinity measurements. Ocean Sci 9, pp. 1-18, 2013.
  • Cuomo S., Galletti A., Giunta G. and Starace A. - Surface reconstruction from scattered point via RBF interpolation on GPU , Federated Conference on Computer Science and Information Systems (FedCSIS), 2013, pp. 433-440.
  • D' Amore L., Arcucci R., Marcellino L., Murli A. - HPC computation issues of the incremental 3D variational data assimilation scheme in OceanVarsoftware. Journal of Numerical Analysis, Industrial and Applied Mathematics, 7(3-4), pp 91-105, 2013.
  • Dahlquist G. and Bjorck A. - Numerical Methods. Prentice Hall, 573 pp. 1974.
  • Derber J., Rosati A. - A global oceanic data assimilation system. Journal of Phys. Oceanogr. 19, pp. 1333-1347, 1989.
  • Deriche R. - Separable recursive filtering for efficient multi-scale edge detection. Proc. Int. Workshop Machine Vision Machine Intelligence, Tokyo, Japan, pp 18-23, 1987
  • Dobricic S., Pinardi N. - An oceanographic three-dimensional variational data assimilation scheme. Ocean Modeling 22, pp 89-105, 2008.
  • Farina R., Cuomo S., De Michele P., Piccialli F. - A Smart GPU Implementation of an Elliptic Kernel for an Ocean Global Circulation Model, APPLIED MATHEMATICAL SCIENCES, 7 (61-64), 2013 pp.3007-3021.
  • Farina R., Dobricic S., Cuomo S. - Some numerical enhancements in a data assimilation scheme, AIP Conference Proceedings 1558, 2013, doi: 10.1063/1.4826017.
  • Farina R., Dobricic S., Storto A., Masina S., Cuomo S. - A Revised Scheme to Compute Horizontal Covariances in an Oceanographic 3D-VAR Assimilation System, CoRR, abs/1404.5756, 2014,
  • Ferry N., Barnier B., Garric G., Haines K., Masina S., Parent L., Storto A., Valdivieso M., Guinehut S., Mulet S. - NEMO: the modeling engine of global ocean reanalysis. Mercator Ocean Quaterly Newsletter 46, pp 60-66, 2012.
  • Haben S., Lawless A., Nichols N. - Conditioning and preconditioning of the variational data assimilation problem. Computers and Fluids 46, pp 252-256, 2011.
  • Haben S., Lawless A., Nichols N. - Conditioning of the 3DVar data assimilation problem. University of Reading, Dept. of Mathematics, Math Report Series 3, 2009.
  • Haglund L. - Adaptive multidimensional filtering. Linkping University, Sweden, 1992.
  • Hayden C., Purser R. - Recursive filter objective analysis of meteorological field: applications to NESDIS operational processing. Journal of Applied Meteorology 34, pp 3-15, 1995.
  • Lorenc A. C. - Development of an operational variational assimilation scheme. Journal of the Meteorological Society of Japan 75, pp 339-346, 1997.
  • Lorenc A. C. - Iterative analysis using covariance functions and filters. Quartely Journal of the Royal Meteorological Society 1-118, pp 569-591, 1992.
  • Madec G., Imbard M. - A global ocean mesh to overcome the north pole singularity. Clim. Dynamic 12, pp 381-388, 1996.
  • Purser R. J., Wu W. -S., Parish D. F., Roberts N. M. - Numerical aspects of the application of recursive filters to variational statistical analysis. Part II: spatially inhomogeneous and anisotropic covariances. Monthly Weather Review 131, pp 1524-1535, 2003.
  • Storto A., Dobricic S., Masina S., Pietro P. D. - Assimilating along-track altimetric observations through local hydrostatic adjustments in a global ocean reanalysis system. Mon. Wea. Rev. 139, pp 738-754, 2011.
  • Vliet L. J. van, Verbeek P. W. - Estimators for orientation and anisotropy in digitized images. Proc. ASCI'95, Heijen (Netherlands), pp 442-450, 1995.
  • Vliet L. V., Young I., Verbeek P. - Recursive Gaussian derivative filters. International Conference Recognition, pp 509-514, 1998.
  • Weaver A. T., Courtier P. - Correlation modelling on the sphere using a generalized diffusion equation. Quarterly Journal of the Royal Meteorological Society 127, pp 1815-1846, 2001.
  • Witkin A. - Scale-space filtering. Proc. Internat. Joint Conf. on Artificial Intelligence, Karlsruhe, germany, pp 1019-1021, 1983.
  • Young I. T., van Vliet L. J. - Recursive implementation of the Gaussian filter. Signal Processing 44, pp 139-151, 1995.
Typ dokumentu
Identyfikator YADDA

Zgłoszenie zostało wysłane

Zgłoszenie zostało wysłane

Musisz być zalogowany aby pisać komentarze.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.