Ocean Science www.ocean-sci.net 1812-0784 1812-0792 6 1 2010 10.5194/os-6-161-2010 http://www.ocean-sci.net/6/161/2010/ http://www.ocean-sci.net/6/161/2010/os-6-161-2010.html http://www.ocean-sci.net/6/161/2010/os-6-161-2010.pdf 161 178 2010-02-04 Ensemble perturbation smoother for optimizing tidal boundary conditions by assimilation of High-Frequency radar surface currents – application to the German Bight A. Barth a.barth@ulg.ac.be A. Alvera-Azcárate K.-W. Gurgel J. Staneva A. Port J.-M. Beckers E. V. Stanev GeoHydrodynamics and Environment Research (GHER), MARE, AGO, University of Liège, Liège, Belgium National Fund for Scientific Research, Belgium Institute of Oceanography, University of Hamburg, Germany Institute for Coastal Research, GKSS Research Center, Geesthacht, Germany Institute for Chemistry and Biology of the Marine Environment (ICBM), University of Oldenburg, Germany High-Frequency (HF) radars measure the ocean surface currents at various spatial and temporal scales. These include tidal currents, wind-driven circulation, density-driven circulation and Stokes drift. Sequential assimilation methods updating the model state have been proven successful to correct the density-driven currents by assimilation of observations such as sea surface height, sea surface temperature and in-situ profiles. However, the situation is different for tides in coastal models since these are not generated within the domain, but are rather propagated inside the domain through the boundary conditions. For improving the modeled tidal variability it is therefore not sufficient to update the model state via data assimilation without updating the boundary conditions. The optimization of boundary conditions to match observations inside the domain is traditionally achieved through variational assimilation methods. In this work we present an ensemble smoother to improve the tidal boundary values so that the model represents more closely the observed currents. To create an ensemble of dynamically realistic boundary conditions, a cost function is formulated which is directly related to the probability of each boundary condition perturbation. This cost function ensures that the boundary condition perturbations are spatially smooth and that the structure of the perturbations satisfies approximately the harmonic linearized shallow water equations. Based on those perturbations an ensemble simulation is carried out using the full three-dimensional General Estuarine Ocean Model (GETM). Optimized boundary values are obtained by assimilating all observations using the covariances of the ensemble simulation. Alvera-Azcárate, A., Barth, A., Bouallègue, Z B., Rixen, M., and Beckers, J.-M.: Forecast Verification of a 3D model of the Ligurian Sea. The use of Discrete Wavelet Transforms in the skill assessment of spatial forecasts, J. Marine Syst., 65, 460–483, \doi10.1016/j.jmarsys.2005.09.015, http://hdl.handle.net/2268/4264, 2007. Amante, C. and Eakins, B W.: ETOPO1 1 Arc-Minute Global Relief Model: Procedures, Data Sources and Analysis, Tech. rep., NOAA Technical Memorandum NESDIS NGDC-24, 19~pp., 2009. Arakawa, A. and Lamb, V.: Computational design of the basic dynamical process of the UCLA general circulation model, Methods in Computational Physics, Academic Press, New York, 173–265, 1977. Barrick, D., Evans, M., and Weber, B.: Ocean surface currents mapped by radar, Science, 198, 138–144, 1977. Barth, A., Alvera-Azcárate, A., Beckers, J.-M., and Rixen, M.: Coupling a two-way nested primitive equation model and a statistical SST predictor of the Ligurian Sea via data assimilation, Ocean Modelling, 13, 255–270, \doi10.1016/j.ocemod.2006.02.003, http://hdl.handle.net/2268/4306, 2006. 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, \doi10.1016/j.ocemod.2007.06.007, http://hdl.handle.net/2268/4266, 2007. 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, \doi10.1029/2007JC004585, http://hdl.handle.net/2268/26171, 2008. Barth, A., Alvera-Azcárate, A., Beckers, J.-M., Weisberg, R. H., Vandenbulcke, L., Lenartz, F., and Rixen, M.: Dynamically constrained ensemble perturbations - application to tides on the West Florida Shelf, Ocean Sci., 5, 259–270, 2009. Bloom, S C., Takacs, L L., Silva, A. M D., and Ledvina, D.: Data assimilation using incremental analysis updates, Mon. Weather Rev., 124, 1256–1271, 1996. Burchard, H. and Bolding, K.: GETM – a general estuarine transport model. Scientific Documentation, Tech. Rep. EUR 20253 EN, European Commission, 2002. Burgers, G., van Leeuwen, P J., and Evensen, G.: Analysis scheme in the ensemble Kalman filter, Mon. Weather Rev., 126, 1719–1724, 1998. Chen, Y. and Snyder, C.: Assimilating Vortex Position with an Ensemble Kalman Filter, Mon. Weather Rev., 135, 1828–1845, 2007. Dick, S., Eckard, K., Müller-Navarra, S. H., Klein, H., and Komo, H.: The operational circulation model of BSH (BSHcmod) - model description and validation, Tech. Rep. 29, Berichte des Bundesamtes für Seeschifffahrt und Hydrographie (BSH), 49~pp., 2001. 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. Egbert, G. and Erofeeva, S.: Efficient inverse modeling of barotropic ocean tides, J. Atmos. Ocean. Tech., 19, 183–204, 2002. Emery, W J. and Thomson, R E.: Data Analysis Methods in Physical Oceanography., Pergamon, Elsevier Science Inc., New York, 634~pp., 1998. Evensen, G.: The Ensemble Kalman Filter: theoretical formulation and practical implementation, Ocean Dynam., 53, 343–367, 2003. Evensen, G.: Sampling strategies and square root analysis schemes for the EnKF, Ocean Dynam., 54, 539–560, 2004. Greenwald, T J., Hertenstein, R., and Vukićević, T.: An all-weather observational operator for radiance data assimilation with mesoscale forecast models, Mon. Weather Rev., 130, 1882–1897, 2002. Gurgel, K.-W.: Shipborne measurement of surface current fields by HF radar (extended version), L'Onde Electrique, 74, 54–59, 1994. Gurgel, K.-W., Essen, H.-H., and Kingsley, S P.: HF radars: Physical limitations and recent developments, Coastal Engineering, 37, 201–218, \doi10.1016/S0378-3839(99)00026-5, 1999. Hoteit, I., Cornuelle, B D., Kim, S Y., Forget, G., Köhl, A., and Terrill, E J.: Assessing 4D-VAR for dynamical mapping of coastal high-frequency radar in San Diego, Dynamics of Atmosphere and Oceans, 48, 175–197, \doidoi:10.1016/j.dynatmoce, 2009. Hunt, B R., Kalnay, E., Kostelich, E J., Ott, E., Patil, D J., Sauer, T., Szunyogh, I., Yorke, J A., and Zimin, A V.: Four-dimensional ensemble Kalman filtering, Tellus, 56A, 273–277, 2004. Hunt, B R., Kostelich, E J., and Szunyogh, I.: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter, Physica D, 230, 112–126, 2007. Keppenne, C L., Rienecker, M M., Kurkowski, N P., and Adamec, D A.: Ensemble Kalman filter assimilation of temperature and altimeter data with bias correction and application to seasonal prediction, Nonlinear Proc. Geoph., 12, 491–503, 2005. 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. Lettellier, T., Lyard, F., and Lefebre, F.: The new global tidal solution: FES2004, in: OceanSurface Topography Science Team Meeting, St. Petersburg, Florida, 2004. Lyard, F., Lefevre, F., Letellier, T., and Francis, O.: Modelling the global ocean tides: modern insights from FES2004, Ocean Dynam., 56, 394–415, \doi10.1007/s10236-006-0086-x, 2006. Malanotte-Rizzoli, P., Young, R E., and Haidvogel, D B.: Initialization and data assimilation experiments with a primitive equation model, Dynam. Atmos. Oceans, 13, 349–378, 1989. Mourre, B., De~Mey, P., Lyard, F., and Le~Provost, C.: Assimilation of sea level data over continental shelves: an ensemble method for the exploration of model errors due to uncertainties in bathymetry, Dynam. Atmos. Oceans, 38, 93–121, \doi10.1016/j.dynatmoce.2004.09.001, 2004. Nerger, L., Hiller, W., and Schröter, J.: A Comparison of Error Subspace Kalman Filters, Dynamic meteorology and oceanography, Tellus, 57A, 715–735, \doi10.1111/j.1600-0870.2005.00141.x, 2005. Ourmières, Y., Brankart, J.-M., Berline, L., Brasseur, P., and Verron, J.: Incremental analysis update implementation into a sequential ocean data assimilation system, J. Atmos. Ocean. Tech., 23, 1729–1744, 2006. Pawlowicz, R., Beardsley, B., and Lentz, S.: Classical Tidal Harmonic Analysis Including Error Estimates in MATLAB using T_TIDE, Comput. Geosci., 28, 929–937, 2002. Pham, D T.: Stochastic methods for sequential data assimilation in strongly nonlinear systems, Mon. Weather Rev., 129, 1194–1207, 2001. PRISMA: Prozesse im Schadstoffkreislauf Meer-Atmosphäre: Ökosystem Deutsche Bucht, BMFT-Projekt 03F0558A1 (1.1.1990–31.10.1993), Abschlussbericht, ZMK-Universität Hamburg, 1994. Rixen, M., Gac, J.-C L., Hermand, J.-P., Peggion, G., and Coelho, E.: Super-ensemble forecasts and resulting acoustic sensitivities in shallow waters, J. Marine Syst., 78, S290–S305, \doi10.1016/j.jmarsys.2009.01.013, 2009. Rémy, E., Gaillard, F., and Verron, J.: Variational assimilation of ocean tomographic data: twin experiments in a quasi-geostrophic model, Quarterly Journal of the Royal Meteorological Society, 128, 1739–1758, 2002. Sakov, P., Evensen, G., and Bertino, L.: Asynchronous data assimilation with the EnKF, Tellus, 62A, 24–29, 2010. Savcenko, R. and Bosch, W.: EOT08a – empirical ocean tide model from multi-mission satellite altimetry, Tech. rep., Deutsches Geodätisches Forschungsinstitut, ftp://ftp.dgfi.badw.de/pub/EOT08a/doc/EOTO8a.pdf, 2008. Schirmer, F., Essen, H.-H., Gurgel, K.-W., Schlick, T., and Hessner, K.: Circulation and contaminant fluxes in the North Sea, chap. Local variability of surface currents based on HF-radar measurements, Springer Verlag, 271–289, 1994. Spitz, Y H., Moisan, J R., Abbott, M R., and Richman, J G.: Data assimilation and a pelagic ecosystem model: parameterization using time series observations, J. Marine Syst., 16, 51–68, 1998. Staneva, J., Stanev, E V., Wolff, J.-O., Badewien, T H., Reuter, R., Flemming, B., Bartholomä, A., and Bolding, K.: Hydrodynamics and sediment dynamics in the German Bight, A focus on observations and numerical modelling in the East Frisian Wadden Sea, Cont. Shelf Res., 29, 302–319, 2009. Talagrand, O.: On the Damping of High-Frequency Motions in Four-Dimensional Assimilation of Meteorological Data, J. Atmos. Sci., 1571–1547, 1972. van Leeuwen, P J.: An Ensemble Smoother with Error Estimates, Mon. Weather Rev., 129, 709–728, 2001.