[en] A method is presented to create an ensemble of perturbations that satisfies linear dynamical constraints. A cost function is formulated defining the probability of each perturbation. It is shown that the perturbations created with this approach take the land-sea mask into account in a similar way as variational analysis techniques. The impact of the land-sea mask is illustrated with an idealized configuration of a barrier island. Perturbations with a spatially variable correlation length can be also created by this approach. The method is applied to a realistic configuration of the West Florida Shelf to create perturbations of the M2 tidal parameters for elevation and depth-averaged currents. The perturbations are weakly constrained to satisfy the linear shallow-water equations. Despite that the constraint is derived from an idealized assumption, it is shown that this approach is applicable to a non-linear and baroclinic model. The amplitude of spurious transient motions created by constrained perturbations of initial and boundary conditions is significantly lower compared to perturbing the variables independently or to using only the momentum equation to compute the velocity perturbations from the elevation.
Disciplines :
Earth sciences & physical geography
Author, co-author :
Barth, Alexander ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Océanographie physique
Alvera Azcarate, Aïda ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > GeoHydrodynamics and Environment Research (GHER)
Beckers, Jean-Marie ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Océanographie physique
Weisberg, R. H.; University of South Florida > College of Marine Science > Ocean Circulation Group
Vandenbulcke, Luc ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Océanographie physique
Lenartz, Fabian ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Département d'astrophys., géophysique et océanographie (AGO)
Rixen, Michel; NATO Undersea Research Centre
Language :
English
Title :
Dynamically constrained ensemble perturbations - application to tides on the West Florida Shelf
Alvera-Azcárate, A., Barth, A., Beckers, J., 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.
Arakawa, A. and Lamb, V.: A potential enstrophy and energy conserving scheme for the shallow water equations, Mon. Weather Rev., 109, 18-36, 1981.
Barth, A., Alvera-Azcárate, A., Beckers, J.-M., Rixen, M., and Vandenbulcke, L.: Multigrid state vector for data assimilation in a two-way nested model of the Ligurian Sea, J. Mar. Syst., 65, 41-59, doi:10.1016/j. jmarsys.2005.07.006, 2007a.
Barth, A., Beckers, J.-M., Alvera-Azcárate, A., and Weisberg, R. H.: Filtering inertia-gravity waves from the initial conditions of the linear shallow water equations, Ocean Modelling, 19, 204-218, doi:10.1016/j.ocemod. 2007.06.007, 2007b.
Barth, A., Alvera-Azcárate, A., and Weisberg, R. H.: Benefit of nesting a regional model into a large-scale ocean model instead of climatology. Application to the West Florida Shelf, Cont. Shelf Res., 28, 561-573, doi:10.1016/j.csr.2007.11.004, 2008a.
Barth, A., Alvera-Azcárate, A., and Weisberg, R. H.: A nested model study of the Loop Current generated variability and its impact on the West Florida Shelf, J. Geophys. Res., 113, C05009, doi:10.1029/2007JC004492, 2008b.
Barth, A., Alvera-Azcárate, A., and Weisberg, R. H.: Assimilation of high-frequency radar currents in a nested model of the West Florida Shelf, J. Geophys. Res., 113, C08033, doi: 10.1029/2007JC004585, 2008c.
Beckers, J.-M. and Rixen, M.: EOF calculation and data filling from incomplete oceanographic datasets, J. Atmos. Ocean. Technol., 20, 1839-1856, 2003.
Brankart, J.-M. and Brasseur, P.: Optimal analysis of in situ data in the Western Mediterranean using statistics and cross-validation., J. Atmos. Ocean. Technol., 13, 477-491, 1996.
Brankart, J.-M., Testut, C.-E., Brasseur, P., and Verron, J.: Implementation of a multivariate data assimilation scheme for isopycnic coordinate ocean models: application to a 1993-1996 hindcast of the North Atlantic Ocean circulation, J. Geophys. Res., 108, 3074, doi:10.1029/ 2001JC001198, 2003.
Brasseur, P.: A Variational Inverse Method for the Reconstruction of General Circulation Fields in the Northern Bering Sea., J. Geophys. Res., 96, 4891-4907, 1991.
Brasseur, P.: Reconstitution de champs d'observations océanographiques par le Modèle Variationnel Inverse: Méthodologie et Applications., Ph.D. thesis, Université de Liège, Collection des publications, Sciences appliquées, 1994.
Brasseur, P., Beckers, J.-M., Brankart, J.-M., and Schoenauen, R.: Seasonal Temperature and Salinity Fields in the Mediterranean Sea: Climatological Analyses of an Historical Data Set., Deep-Sea Res., 43, 159-192, 1996.
Chassignet, E. P., Hurlburt, H. E., Smedstad, O. M., Halliwell, G. R., Hogan, P. J., Wallcraft, A. J., Baraille, R., and Bleck, R.: The HYCOM (HYbrid Coordinate Ocean Model) Data Assimilative System, J. Mar. Syst., 65, 60-83, 2007.
Clarke, A. J.: Tidal Hydrogynamics, chap. The dynamics of barotropic tides over the continental shelf and slope (review), John Wiley and Sons, 1991.
Davis, T. A.: A column pre-ordering strategy for the unsymmetricpattern multifrontal method, ACM Transactions on Mathematical Software, 30, 165-195, 2004a.
Davis, T. A.: Algorithm 832: UMFPACK, an unsymmetric-pattern multifrontal method, ACM Transactions on Mathematical Software, 30, 196-199, 2004b.
Dee, D.: Simplification of the Kalman filter for meteorological data assimilation, Q. J. Roy. Meteor. Soc., 117, 365-384, 1991.
Dobricic, S., Pinardi, N., Adani, M., Tonani, M., Fratianni, C., Bonazzi, A., and Fernandez, V.: Daily oceanographic analyses by Mediterranean Forecasting System at the basin scale, Ocean Sci., 3, 149-157, 2007, http://www.ocean-sci.net/3/149/2007/.
Egbert, G. and Erofeeva, S.: Efficient inverse modeling of barotropic ocean tides, J, Atmos. Oceanic Technol., 19, 183-204, 2002.
Egbert, G., Bennett, A., and Foreman, M.: TOPEX/POSEIDON tides estimated using a global inverse model, J. Geophys. Res., 99, 24821-24852, 1994.
Evensen, G.: The Ensemble Kalman Filter: theoretical formulation and practical implementation, Ocean Dynam., 53, 343-367, 2003.
Fukumori, I.: A partitioned Kalman filter and smoother, Mon. Weather Rev., 130, 1370-1383, 2002.
He, R. and Weisberg, R. H.: Tides on the West Florida Shelf, J. Phys. Ocean., 32, 3455-3473, 2002.
Kalnay, E.: Atmospheric Modeling, Data Assimilation and Predictability, Cambridge University Press, 1 edn., 2002.
Lehoucq, R. B., Sorensen, D. C., and Yang, C.: ARPACK user's guide: solution of large scale eigenvalue problems with implicity restarted Arnoldi methods, Computational and Applied Mathematics, Rice University, http://www.caam.rice.edu/software/ARPACK/, 1997.
Lermusiaux, P., C.-S., C., Gwawarkiewicz, G., Abbot, P., Robinson, A., Miller, R., Haley, P., Leslie, W., Majumdar, S., Pang, A., and Lekien, F.: Quantifying uncertainties in ocean predictions, Oceanography, Special issue on "Advances in Computational Oceanography", 19, 90-103, 2006.
Lermusiaux, P. F. J. and Robinson, A. R.: Data assimilation via error subspace statistical estimation. Part II. Middle Atlantic Bight shelfbreak front simulations and ESSE validation., Mon. Weather Rev., 127, 1408-1432, 1999.
Pham, D. T.: Stochastic methods for sequential data assimilation in strongly nonlinear systems, Mon. Weather Rev., 129, 1194-1207, 2001.
Vallis, G. K.: Mechanisms and Parameterizations of Geostrophic Adjustment and a Variational Approach to Balanced Flow, J. Atmos. Sci., 49, 1144-1160, 1992.
Wahba, G. and Wendelberger, J.: Some new mathematical methods for variational objective analysis using splines and cross validation., Mon. Weather Rev., 108, 1122-1143, 1980.
Weaver, A. T. and Courtier, P.: Correlation modelling on the sphere using a generalized diffusion equation, Q. J. Roy. Meteor. Soc., 127, 1815-1842, 2001.
