• Aoyama, Y., and J. Nakano, 1999: RS/6000 SP: Practical MPI programming. IBM Corporation Doc., 238 pp.

  • Bull, J. M., J. Enright, X. Guo, C. Maynard, and F. Reid, 2010: Performance evaluation of mixed-mode OpenMP/MPI implementations. Int. J. Parallel Program., 38, 396417, https://doi.org/10.1007/s10766-010-0137-2.

    • Search Google Scholar
    • Export Citation
  • Byrd, R., P. Lu, J. Nocedal, and C. Zhu, 1995: A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput., 16, 11901208, https://doi.org/10.1137/0916069.

    • Search Google Scholar
    • Export Citation
  • Byrne, D., M. Münnich, I. Frenger, and N. Gruber, 2016: Mesoscale atmosphere ocean coupling enhances the transfer of wind energy into the ocean. Nat. Commun., 7, ncomms11867, https://doi.org/10.1038/ncomms11867.

    • Search Google Scholar
    • Export Citation
  • Chassignet, E., and Coauthors, 2009: US GODAE: Global ocean prediction with the Hybrid Coordinate Ocean Model (HYCOM). Oceanography, 22 (2), 6475, https://doi.org/10.5670/oceanog.2009.39.

    • Search Google Scholar
    • Export Citation
  • Cooper, M., and K. Haines, 1996: Altimetric assimilation with water property conservation. J. Geophys. Res., 101, 10591077, https://doi.org/10.1029/95JC02902.

    • Search Google Scholar
    • Export Citation
  • Courtier, P., 1997: Variational methods. J. Meteor. Soc. Japan, 75, 211218, https://doi.org/10.2151/jmsj1965.75.1B_211.

  • D’Amore, L., R. Arcucci, L. Carracciuolo, and A. Murli, 2013: DD-OceanVar: A domain decomposition fully parallel data assimilation software for the Mediterranean Forecasting System. Procedia Comput. Sci., 18, 12351244, https://doi.org/10.1016/j.procs.2013.05.290.

    • Search Google Scholar
    • Export Citation
  • D’Amore, L., R. Arcucci, L. Carracciuolo, and A. Murli, 2014: A scalable approach for variational data assimilation. J. Sci. Comput., 61, 239257, https://doi.org/10.1007/s10915-014-9824-2.

    • Search Google Scholar
    • Export Citation
  • Dobricic, S., and N. Pinardi, 2008: An oceanographic three-dimensional variational data assimilation scheme. Ocean Modell., 22, 89105, https://doi.org/10.1016/j.ocemod.2008.01.004.

    • Search Google Scholar
    • Export Citation
  • Durand, M., L. Fu, D. P. Lettenmaier, D. E. Alsdorf, E. Rodriguez, and D. Esteban-Fernandez, 2010: The Surface Water and Ocean Topography mission: Observing terrestrial surface water and oceanic submesoscale eddies. Proc. IEEE, 98, 766779, https://doi.org/10.1109/JPROC.2010.2043031.

    • Search Google Scholar
    • Export Citation
  • Early, J. J., R. M. Samelson, and D. B. Chelton, 2011: The evolution and propagation of quasigeostrophic ocean eddies. J. Phys. Oceanogr., 41, 15351555, https://doi.org/10.1175/2011JPO4601.1.

    • Search Google Scholar
    • Export Citation
  • EUMETSAT, 2008: GHRSST level 2P global skin sea surface temperature from the Advanced Very High Resolution Radiometer (AVHRR) on the MetOp-A satellite produced by EUMETSAT. PO.DAAC, accessed 10 March 2019, https://doi.org/10.5067/GHAMT-2PE01.

  • Farina, R., S. Dobricic, A. Storto, S. Masina, and S. Cuomo, 2015: A revised scheme to compute horizontal covariances in an oceanographic 3D-VAR assimilation system. J. Comput. Phys., 284, 631647, https://doi.org/10.1016/j.jcp.2015.01.003.

    • Search Google Scholar
    • Export Citation
  • Gaspari, G., and S. E. Cohn, 1999: Construction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc., 125, 723757, https://doi.org/10.1002/qj.49712555417.

    • Search Google Scholar
    • Export Citation
  • Gaube, P., D. J. McGillicuddy, and A. J. Moulin, 2019: Mesoscale eddies modulate mixed layer depth globally. Geophys. Res. Lett., 46, 15051512, https://doi.org/10.1029/2018GL080006.

    • Search Google Scholar
    • Export Citation
  • Hallberg, R., 2013: Using a resolution function to regulate parameterizations of oceanic mesoscale eddy effects. Ocean Modell., 72, 92103, https://doi.org/10.1016/j.ocemod.2013.08.007.

    • Search Google Scholar
    • Export Citation
  • Hayden, C. M., and R. J. Purser, 1995: Recursive filter objective analysis of meteorological fields: Applications to NESDIS operational processing. J. Appl. Meteor., 34, 315, https://doi.org/10.1175/1520-0450-34.1.3.

    • Search Google Scholar
    • Export Citation
  • Huang, X.-Y., and Coauthors, 2009: Four-dimensional variational data assimilation for WRF: Formulation and preliminary results. Mon. Wea. Rev., 137, 299314, https://doi.org/10.1175/2008MWR2577.1.

    • Search Google Scholar
    • Export Citation
  • Iovino, D., S. Masina, A. Storto, A. Cipollone, and V. N. Stepanov, 2016: A 1/16° eddying simulation of the global NEMO sea-ice–ocean system. Geosci. Model Dev., 9, 26652684, https://doi.org/10.5194/gmd-9-2665-2016.

    • Search Google Scholar
    • Export Citation
  • Lellouche, J.-M., and Coauthors, 2018: Recent updates to the Copernicus Marine Service global ocean monitoring and forecasting real-time 1/12° high-resolution system. Ocean Sci., 14, 10931126, https://doi.org/10.5194/os-14-1093-2018.

    • Search Google Scholar
    • Export Citation
  • Li, Z., J. C. McWilliams, K. Ide, and J. D. Farrara, 2015: A multiscale variational data assimilation scheme: Formulation and illustration. Mon. Wea. Rev., 143, 38043822, https://doi.org/10.1175/MWR-D-14-00384.1.

    • Search Google Scholar
    • Export Citation
  • Liu, Y., J. Zhu, J. She, S. Zhuang, W. Fu, and J. Gao, 2009: Assimilating temperature and salinity profile observations using an anisotropic recursive filter in a coastal ocean model. Ocean Modell., 30, 7587, https://doi.org/10.1016/j.ocemod.2009.06.005.

    • Search Google Scholar
    • Export Citation
  • Madec, G., and M. Imbard, 1996: A global ocean mesh to overcome the North Pole singularity. Climate Dyn., 12, 381388, https://doi.org/10.1007/BF00211684.

    • Search Google Scholar
    • Export Citation
  • Martin, M. J., and Coauthors, 2015: Status and future of data assimilation in operational oceanography. J. Oper. Oceanogr., 8, s28s48, https://doi.org/10.1080/1755876X.2015.1022055.

    • Search Google Scholar
    • Export Citation
  • Mirouze, I., and A. T. Weaver, 2010: Representation of correlation functions in variational assimilation using an implicit diffusion operator. Quart. J. Roy. Meteor. Soc., 136, 14211443, https://doi.org/10.1002/qj.643.

    • Search Google Scholar
    • Export Citation
  • Mirouze, I., and A. Storto, 2016: Handling boundaries with the one-dimensional first-order recursive filter. Quart. J. Roy. Meteor. Soc., 142, 24782487, https://doi.org/10.1002/qj.2840.

    • Search Google Scholar
    • Export Citation
  • Miyazawa, Y., and Coauthors, 2017: Assimilation of high-resolution sea surface temperature data into an operational nowcast/forecast system around Japan using a multi-scale three-dimensional variational scheme. Ocean Dyn., 67, 713728, https://doi.org/10.1007/s10236-017-1056-1.

    • Search Google Scholar
    • Export Citation
  • Mogensen, K., and A. W. M. Alonso Balmaseda, 2012: The NEMOVAR ocean data assimilation system as implemented in the ECMWF ocean analysis for System 4. ECMWF Tech. Memo. 668, 59 pp., https://www.ecmwf.int/sites/default/files/elibrary/2012/11174-nemovar-ocean-data-assimilation-system-implemented-ecmwf-ocean-analysis-system-4.pdf.

  • Oke, P. R., G. B. Brassington, D. A. Griffin, and A. Schiller, 2008: The Bluelink ocean data assimilation system (BODAS). Ocean Modell., 21, 4670, https://doi.org/10.1016/j.ocemod.2007.11.002.

    • Search Google Scholar
    • Export Citation
  • Pistoia, J., and Coauthors, 2017: Last improvements in the data assimilation scheme for the Mediterranean analysis and forecast system of the Copernicus Marine Service. Eighth EuroGOOS Int. Conf., Bergen, Norway, European Global Ocean Observing System, 335–342, https://www.earth-prints.org/handle/2122/12189.

  • Pujol, M.-I., G. Dibarboure, P.-Y. Le Traon, and P. Klein, 2012: Using high-resolution altimetry to observe mesoscale signals. J. Atmos. Oceanic Technol., 29, 14091416, https://doi.org/10.1175/JTECH-D-12-00032.1.

    • Search Google Scholar
    • Export Citation
  • Purser, R. J., W.-S. Wu, D. F. Parrish, and N. M. Roberts, 2003: Numerical aspects of the application of recursive filters to variational statistical analysis. Part II: Spatially inhomogeneous and anisotropic general covariances. Mon. Wea. Rev., 131, 15361548, https://doi.org/10.1175//2543.1.

    • Search Google Scholar
    • Export Citation
  • Qiu, B., S. Chen, P. Klein, H. Sasaki, and Y. Sasai, 2014: Seasonal mesoscale and submesoscale eddy variability along the North Pacific subtropical countercurrent. J. Phys. Oceanogr., 44, 30793098, https://doi.org/10.1175/JPO-D-14-0071.1.

    • Search Google Scholar
    • Export Citation
  • Rantakokko, J., 1997: Strategies for parallel variational data assimilation. Parallel Comput., 23, 20172039, https://doi.org/10.1016/S0167-8191(97)00094-X.

    • Search Google Scholar
    • Export Citation
  • Rodgers, D. P., 1985: Improvements in multiprocessor system design. Proc. 12th Annual Int. Symp. on Computer Architecture, Los Alamitos, CA, IEEE, 225–231, https://doi.org/10.1145/327070.327215.

  • Sasaki, H., P. Klein, B. Qiu, and Y. Sasai, 2014: Impact of oceanic-scale interactions on the seasonal modulation of ocean dynamics by the atmosphere. Nat. Commun., 5, 5636, https://doi.org/10.1038/ncomms6636.

    • Search Google Scholar
    • Export Citation
  • Schiller, A., and N. Smith, 2006: Bluelink: Large-to-coastal scale operational oceanography in the Southern Hemisphere. Ocean Weather Forecasting: An Integrated View of Oceanography, E. P. Chassignet, and J. Verron, Eds., Springer, 427–439, https://doi.org/10.1007/1-4020-4028-8_17.

  • Storto, A., and S. Masina, 2016: C-GLORSv5: An improved multipurpose global ocean eddy-permitting physical reanalysis. Earth Syst. Sci. Data, 8, 679696, https://doi.org/10.5194/essd-8-679-2016.

    • Search Google Scholar
    • Export Citation
  • Storto, A., S. Dobricic, S. Masina, and P. Di Pietro, 2011: Assimilating along-track altimetric observations through local hydrostatic adjustment in a global ocean variational assimilation system. Mon. Wea. Rev., 139, 738754, https://doi.org/10.1175/2010MWR3350.1.

    • Search Google Scholar
    • Export Citation
  • Storto, A., S. Masina, and S. Dobricic, 2014: Estimation and impact of nonuniform horizontal correlation length scales for global ocean physical analyses. J. Atmos. Oceanic Technol., 31, 23302349, https://doi.org/10.1175/JTECH-D-14-00042.1.

    • Search Google Scholar
    • Export Citation
  • Storto, A., S. Masina, and A. Navarra, 2016: Evaluation of the CMCC eddy-permitting global ocean physical reanalysis system (C-GLORS, 1982–2012) and its assimilation components. Quart. J. Roy. Meteor. Soc., 142, 738758, https://doi.org/10.1002/qj.2673.

    • Search Google Scholar
    • Export Citation
  • Teruzzi, A., P. Di Cerbo, G. Cossarini, E. Pascolo, and S. Salon, 2019: Parallel implementation of a data assimilation scheme for operational oceanography: The case of the MedBFM model system. Comput. Geosci., 124, 103114, https://doi.org/10.1016/j.cageo.2019.01.003.

    • Search Google Scholar
    • Export Citation
  • Tolman, L., 2002: Distributed-memory concepts in the wave model WAVEWATCH III. Parallel Comput., 28, 3552, https://doi.org/10.1016/S0167-8191(01)00130-2.

    • Search Google Scholar
    • Export Citation
  • Trémolet, Y., and F. X. Le Dimet, 1996: Parallel algorithms for variational data assimilation and coupling models. Parallel Comput., 22, 657674, https://doi.org/10.1016/0167-8191(96)00018-X.

    • Search Google Scholar
    • Export Citation
  • Volkov, D. L., T. Lee, and L.-L. Fu, 2008: Eddy-induced meridional heat transport in the ocean. Geophys. Res. Lett., 35, L20601, https://doi.org/10.1029/2008GL035490.

    • Search Google Scholar
    • Export Citation
  • Weaver, A. T., J. Vialard, and D. L. T. Anderson, 2003: Three- and four-dimensional variational assimilation with a general circulation model of the tropical Pacific Ocean. Part I: Formulation, internal diagnostics, and consistency checks. Mon. Wea. Rev., 131, 13601378, https://doi.org/10.1175/1520-0493(2003)131<1360:TAFVAW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wu, W.-S., R. J. Purser, and D. F. Parrish, 2002: Three-dimensional variational analysis with spatially inhomogeneous covariances. Mon. Wea. Rev., 130, 29052916, https://doi.org/10.1175/1520-0493(2002)130<2905:TDVAWS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Xu, C., X.-D. Shang, and R. X. Huang, 2014: Horizontal eddy energy flux in the world oceans diagnosed from altimetry data. Sci. Rep., 4, 5316, https://doi.org/10.1038/srep05316.

    • Search Google Scholar
    • Export Citation
  • Yang, C., S. Masina, and A. Storto, 2017: Historical ocean reanalyses (1900–2010) using different data assimilation strategies. Quart. J. Roy. Meteor. Soc., 143, 479493, https://doi.org/10.1002/qj.2936.

    • Search Google Scholar
    • Export Citation
  • Zhang, Z., W. Wang, and B. Qiu, 2014: Oceanic mass transport by mesoscale eddies. Science, 345, 322324, https://doi.org/10.1126/science.1252418.

    • Search Google Scholar
    • Export Citation
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Implementing a Parallel Version of a Variational Scheme in a Global Assimilation System at Eddy-Resolving Resolution

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  • 1 ODA Division, Centro Euro-Mediterraneo sui Cambiamenti Climatici, Bologna, Italy
  • 2 Centre for Maritime Research and Experimentation, La Spezia, Italy
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Abstract

Recent advances in global ocean prediction systems are fostered by the needs of accurate representation of mesoscale processes. The day-by-day realistic representation of its variability is hampered by the scarcity of observations as well as the capability of assimilation systems to correct the ocean states at the same scale. This work extends a 3DVAR system designed for oceanic applications to cope with global eddy-resolving grid and dense observational datasets in a hybridly parallelized environment. The efficiency of the parallelization is assessed in terms of both scalability and accuracy. The scalability is favored by a weak-constrained formulation of the continuity requirement among the artificial boundaries implied by the domain decomposition. The formulation forces possible boundary discontinuities to be less than a prescribed error and minimizes the parallel communication relative to standard methods. In theory, the exact solution is recovered by decreasing the boundary error toward zero. In practice, it is shown that the accuracy increases until a lower bound arises, because of the presence of the mesh and the finite accuracy of the minimizer. A twin experiment has been set up to estimate the benefit of employing an eddy-resolving grid within the assimilation step, as compared with an eddy-permitting one, while keeping the eddy-resolving grid within the forecast step. It is shown that the use of a coarser grid for data assimilation does not allow an optimal exploitation of the present remote sensing observation network. A global decrease of about 15% in the error statistics is found when assimilating dense surface observations, and no significant improvement is seen for sparser observations (in situ profilers).

Corresponding author: Andrea Cipollone, andrea.cipollone@cmcc.it

Abstract

Recent advances in global ocean prediction systems are fostered by the needs of accurate representation of mesoscale processes. The day-by-day realistic representation of its variability is hampered by the scarcity of observations as well as the capability of assimilation systems to correct the ocean states at the same scale. This work extends a 3DVAR system designed for oceanic applications to cope with global eddy-resolving grid and dense observational datasets in a hybridly parallelized environment. The efficiency of the parallelization is assessed in terms of both scalability and accuracy. The scalability is favored by a weak-constrained formulation of the continuity requirement among the artificial boundaries implied by the domain decomposition. The formulation forces possible boundary discontinuities to be less than a prescribed error and minimizes the parallel communication relative to standard methods. In theory, the exact solution is recovered by decreasing the boundary error toward zero. In practice, it is shown that the accuracy increases until a lower bound arises, because of the presence of the mesh and the finite accuracy of the minimizer. A twin experiment has been set up to estimate the benefit of employing an eddy-resolving grid within the assimilation step, as compared with an eddy-permitting one, while keeping the eddy-resolving grid within the forecast step. It is shown that the use of a coarser grid for data assimilation does not allow an optimal exploitation of the present remote sensing observation network. A global decrease of about 15% in the error statistics is found when assimilating dense surface observations, and no significant improvement is seen for sparser observations (in situ profilers).

Corresponding author: Andrea Cipollone, andrea.cipollone@cmcc.it
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