OS Ocean Science OS Ocean Sci. 1812-0792 Copernicus Publications Göttingen, Germany 10.5194/os-4-307-2008 Sequential assimilation of multi-mission dynamical topography into a global finite-element ocean model Skachko S. 1 3 Danilov S. 1 Janjić T. 1 Schröter J. 1 Sidorenko D. 1 Savcenko R. 2 Bosch W. 2 Alfred Wegener Institute for Polar and Marine Research, Bussestrasse 24, 27570 Bremerhaven, Germany Deutsches Geodätisches Forschungsinstitut, Alfons-Goppel-Strasse 11, 80539 Munich, Germany now at: Département des Sciences de la Terre et de l'Atmosphère, Université du Québec à Montréal, C. P. 8888 Succ. Centre-ville Montréal, Québec, H3C 3P8 Canada 18 12 2008 4 4 307 318 Copyright: © 2008 S. Skachko et al. 2008 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://os.copernicus.org/articles/4/307/2008/os-4-307-2008.html The full text article is available as a PDF file from https://os.copernicus.org/articles/4/307/2008/os-4-307-2008.pdf

This study focuses on an accurate estimation of ocean circulation via assimilation of satellite measurements of ocean dynamical topography into the global finite-element ocean model (FEOM). The dynamical topography data are derived from a complex analysis of multi-mission altimetry data combined with a referenced earth geoid. The assimilation is split into two parts. First, the mean dynamic topography is adjusted. To this end an adiabatic pressure correction method is used which reduces model divergence from the real evolution. Second, a sequential assimilation technique is applied to improve the representation of thermodynamical processes by assimilating the time varying dynamic topography. A method is used according to which the temperature and salinity are updated following the vertical structure of the first baroclinic mode. It is shown that the method leads to a partially successful assimilation approach reducing the rms difference between the model and data from 16 cm to 2 cm. This improvement of the mean state is accompanied by significant improvement of temporal variability in our analysis. However, it remains suboptimal, showing a tendency in the forecast phase of returning toward a free run without data assimilation. Both the mean difference and standard deviation of the difference between the forecast and observation data are reduced as the result of assimilation.

 References Albertella, A., Savcenko, R., Bosch, W., and Rummel, R.: Dynamic ocean topography – the geodetic approach, IAPG/FESG-Schriftenreihe, Nr. 27, Institut für Astronomische und Physikalische Geodäsie, Forschungseinrichtung Satellitengeodäsie, 64 pp., ISBN (Print) 978-3-934205-26-0, ISSN 1437-8280, 2008. Bell, M., Martin, M., and Nichols, N.: Assimilation of data into an ocean model with systematic errors near the equator, Q. J. Roy Meteor. Soc., 130, 873–893, 2004. Bosch, W.: Discrete crossover analysis (DCA), IAG Symposia, Springer, Berlin, 130, 131–136, 2007. Bosch, W. and Savchenko, R.: Satellite Altimetry: Multi Mission Cross Calibration, IAG Symposia, Springer, Berlin, 130, 51–56, 2007. Carrère, K. and Lyard, F.: Modelling the barotropic response of the global ocean to atmospheric wind and pressure forcing comparisons with observations, Geophys. Res. Lett., 30(6), 1275, 2003. Cooper, M. and Haines, K.: Altimetric assimilation with water property conservation, J. Geophys. Res., 101, 1059–1077, 1996. Danilov, S., Kivman, G., and Schröter, J.: A finite-element ocean model: principles and evaluation, Ocean Model., 6, 125–150, 2004. De Mey, P. and Robinson, A.: Assimilation of altimeter eddy fields in a limited-area quasi-geostrofic model, J. Phys. Oceanogr., 17, 2280–2293, 1987. Dee, D. and da Silva, A.: Data assimilation in the presence of forecast bias, Q. J. Roy Meteor. Soc., 124, 269–295, 1998. Derber, J C.: A variational continuous assimilation technique, Mon. Weather Rev., 174, 2437–2446, 1989. Dombrowsky, E. and De Mey, P.: Continuous assimilation in an open domain of the northeast Atlantic. Part 1: Methodology and Application to AthenA88., J. Geophys. Res., 97, 9719–9731, 1992. Eden, C., Greatbatch, R., and Böning, C.: Adiabatically Correcting an Eddy-Permitting Model Using Large-Scale Hydrographic Data: Application to the Gulf Stream and the North Atlantic Current, J. Phys. Oceanogr., 34, 701–719, 2004. Fischer, M. and Latif, M.: Assimilation of temperature and sea-level observations into a primitive-equation model of the tropical Pacific, J. Marine Syst., 6, 31–46, 1995. Förste, C., Schmidt, R., Stubenvoll, R., Flechtner, F., Meyer, U., König, R., Neumayer, H., Biancale, R., Lemoine, J.-M., Bruinsma, S., Loyer, S., Barthelmes, F., and Esselborn, S.: The GeoForschungsZentrum Potsdam / Groupe de Recherche de Geodesie Spatiale stellite-only and combined gravity field models: EIGEN-GL04S1 and EIGEN-GL04C, J. Geodesy, 82, 6, 331–346, 2008. Frieland, B.: Treatment of bias recursive filtering, IEEE Trans. Autom.\ Control, AC-14, 359–367, 1969. Fu, L. and Chelton, D.: Large-scale ocean circulation, in: Sattelite Altimetry and Earth Sciences, Int. Geophys.Ser., 69, edited by: Fu, L. L. and Cazenave, A., 133–169, Academic, San Diego, Calif., 2001. Fukumori, I.: Data assimilation by models, in: Sattelite Altimetry and Earth Sciences, Int. Geophys.Ser., 69, edited by: Fu, L. L. and Cazenave, A., 237–265, Academic, San Diego, Calif., 2001. Fukumori, I., Raughunath, R., Fu, L., and Chao, Y.: Assimilation of TOPEX/Poseidon altimeter data into a global ocean circulation model: How good are the results?, J. Geophys. Res., 104, 25 647–25 665, 1999. Gavart, M. and De Mey, P.: Isopycnal EOFs in the Azores current region: a statistical tool for dynamical analysis and data assimilation, J. Phys. Oceanogr., 27, 2146–2157, 1997. Gill, A.: Atmosphere-Ocean Dynamics, 662 pp., Academic, San Diego, Calif., 1982. Gouretski, V V. and Koltermann, K P.: WOCE Global Hydrographic Climatology, 52 pp., Bundesamt für Seeschifffahrt und Hydrographie, 2004. Hernandez, F. and Schaeffer, P.: Altimeteric Mean Sea Surfaces and Gravity Anomaly maps inter-comparisons AVI-NT-011-5242-CLS, CLS Ramonville St Agne, 48 pp., 2000. Hoteit, I., Triantafyllou, G., and Korres, G.: Comparison of extended and ensemble based Kalman filters with low and high resolution primitive equation ocean models, Nonlin. Processes Geophys., 12, 755–765, 2005. Hoteit, I., Triantafyllou, G., and Korres, G.: Using low-rank ensemble Kalman filters for data assimilation with high dimensional imperfect models, Journal of Numerical Analysis, Industrial and Applied Mathematics, 2, 67–78, 2007. Ji, M. and Leetmaa, A.: Impact of data assimilation on ocean initialisation and El Niño prediction, Mon. Weather Rev., 125, 742–753, 1997. Kivman, G., Danilov, S., Fritzsch, B., Harig, S., Reick, C., Schröter, J., Seufer, V., Sidorenko, D., Staneva, J., and Wenzel, M.: Improved estimates of the oceanic circulation using the CHAMP geoid, in: Earth Observsation with CHAMP, Results from Three Years in Orbit, edited by: Reigber, C., Luehr, H., Schwintzer, P., and Wickert, J., Springer Berlin, Heidelberg, New York, 211–216, 2005. Le Traon, P. and Morrow, R.: Ocean Currents and Eddies, in Sattelite Altimetry and Earth Sciences, Int. Geophys.Ser, 69, edited by: Fu, L. L. and Cazenave, A., 171–215, Academic, San Diego, Calif., 2001. Löhner, R., Morgan, K., Peraire, J., and Vahdati, M.: Finite-element flux-corrected transport (FEM-FCT) for the Euler and Navier-Stokes equations, Int. J. Numer. Meth. Fl., 7, 1093–1109, 1987. Lyard, F., Lefevre, F., Letellier, T., and Francis, O.: Modelling the global ocean tides: modern insights from FES2004, Ocean Dynam., 56, 394–415, 2006. Menkes, C., Boulanger, J., Busalacchi, A., Vialard, J., Delecluse, P., McPhaden, M., Hackert, E., and Grima, N.: Impact of TAO vs ERS wind stresses onto simulations of the tropical Pacific Ocean during the 1993–1998 period by the OPA OGCM, in: Climate Impact of Scale Interaction for the Tropical Ocean-Atmosphere System, vol 13 of Euroclivar Workshop Report, 46–48, 1998. Nerger, L.: Parallel Filter Algorithms for Data Assimilation in Oceanography, PhD thesis, University of Bremen, Reports on Polar and Marine Research, 487, 174 pp., 2004. Nerger, L., Danilov, S., Hiller, W., and Schröter, J.: Using sea-level data to constrain a finite-element primitive-equation ocean model with a local SEIK filter, Ocean Dynam., 56, 634–649, 2006. Nerger, L., Danilov, S., Kivman, G., Hiller, W., and Schröter, J.: Data assimilation with the Ensemble Kalman Filter and the SEIK filter applied to a finite element model, J. Marine Syst., 65, 288–298, 2007. Pakanowski, R. and Philander, S.: Parametrization of vertical mixing in numerical models of tropical oceans, J. Phys. Oceanogr., 11, 1443–1451, 1981. Pham, D T.: Stochastic Methods for Sequential Data assimilation in Strongly nonlinear systems, Mon. Weather Rev., 129, 1194–1207, 2001. Rio, M.-H. and Hernandez, F.: A mean dynamic topography computed over the world ocean from altimetry, in situ measurements, and a geoid model, J. Geophys. Res., 109, C12032, 2004. Rio, M.-H., Schaeffer, P., Lemoine, J.-M., and Hernandez, F.: Estimation of the ocean Mean Dynamic Topography through the combination of altimetric data, in-situ measurements and GRACE geoid: From global to regional studies, Proceedings of the GOCINA International workshop, Luxembourg, 2005. Sheng, J., Greatbatch, R., and Wright, D.: Improving the utility of ocean circulation models through adjustment of the momentum balance, J. Geophys. Res., 106, 16 711–16 728, 2001. Stammer, D., Wunsch, C., Giering, R., Eckert, C., Heimbach, P., Marotzke, J., Adcroft, A., Hill, C., and Marshall, J.: The global ocean circulation during 1992–1997, estimated from ocean observations and a general circulation model, J. Geophys. Res., 107, C9, 3118, 2002. Stephens, J., Antonov, T., and Boyer, T.: World ocean Atlas 2001, in: NOAA Atlas NESDIS 49, edited by: Levitus, S., Temperatures, US Government Printing Office, Washington, 176, 1, 2002. Sun, C. and Watts, D.: A circumpolar gravest empirical mode for the Southern Ocean hydrography, J. Geophys. Res., 106, 2833–2855, 2001. Triantafyllou, G., Hoteit, I., and Petihakis, G.: A singular evolutive interpolated Kalman filter for efficient data assimilation in a 3-D complex physical-biogeochemical model of the Cretan Sea, J. Marine Syst., 40–41, 213–231, 2003. Wahr, J., Bryan, F., and Molenaar, M.: Time variability of the Earth's gravity field: Hydrologicaland oceanic effects and their possible detection using GRACE, J. Geophys. Res., 103(B12), 30 205–30 229, 1998. Wang, Q., Danilov, S., and Schröter, J.: Finite element ocean circulation model based on triangular prismatic elements, with application in studying the effect of topography representation, J. Geophys. Res, 113, C05015, https://doi.org/10.1029/2007JC004482, 2008. Wenzel, M., Schröter, J., and Olbers, D.: The annual cycle of the global ocean circulation as determined by 4D VAR data assimilation, Prog. Oceanogr., 48, 73–119, 2001. Yu, L. and O'Brian, J.: Variational assimilation of the wind-stress drag coefficient and the eddy-viscosity profile, J. Phys. Oceanogr., 21, 709–719, 1991.