Editorial Type:
Article
Article Type:
Research Article

Estimation and Impact of Nonuniform Horizontal Correlation Length Scales for Global Ocean Physical Analyses

Andrea Storto Numerical Applications and Scenarios Division, Centro Euro-Mediterraneo sui Cambiamenti Climatici, Bologna, Italy

Search for other papers by Andrea Storto in
Current site
Google Scholar
PubMed Close
,
Simona Masina Numerical Applications and Scenarios Division, Centro Euro-Mediterraneo sui Cambiamenti Climatici, Bologna, Italy

Search for other papers by Simona Masina in
Current site
Google Scholar
PubMed Close
, and
Srdjan Dobricic Numerical Applications and Scenarios Division, Centro Euro-Mediterraneo sui Cambiamenti Climatici, Bologna, Italy

Search for other papers by Srdjan Dobricic in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Oct 2014
DOI:
https://doi.org/10.1175/JTECH-D-14-00042.1
Page(s):
2330–2349
Restricted access

Abstract

Optimally modeling background-error horizontal correlations is crucial in ocean data assimilation. This paper investigates the impact of releasing the assumption of uniform background-error correlations in a global ocean variational analysis system. Spatially varying horizontal correlations are introduced in the recursive filter operator, which is used for modeling horizontal covariances in the Centro Euro-Mediterraneo sui Cambiamenti Climatici (CMCC) analysis system. The horizontal correlation length scales (HCLSs) were defined on the full three-dimensional model space and computed from both a dataset of monthly anomalies with respect to the monthly climatology and through the so-called National Meteorological Center (NMC) method. Different formulas for estimating the correlation length scale are also discussed and applied to the two forecast error datasets. The new formulation is tested within a 12-yr period (2000–11) in the ½° resolution system. The comparison with the data assimilation system using uniform background-error horizontal correlations indicates the superiority of the former, especially in eddy-dominated areas. Verification skill scores report a significant reduction of RMSE, and the use of nonuniform length scales improves the representation of the eddy kinetic energy at midlatitudes, suggesting that uniform, latitude, or Rossby radius-dependent formulations are insufficient to represent the geographical variations of the background-error correlations. Furthermore, a small tuning of the globally uniform value of the length scale was found to have a small impact on the analysis system. The use of either anomalies or NMC-derived correlation length scales also has a marginal effect with respect to the use of nonuniform HCLSs. On the other hand, the application of overestimated length scales has proved to be detrimental to the analysis system in all areas and for all parameters.

Corresponding author address: Andrea Storto, Centro Euro-Mediterraneo sui Cambiamenti Climatici, Viale Aldo Moro 44, I-40127 Bologna, Italy. E-mail: andrea.storto@cmcc.it

Abstract

Optimally modeling background-error horizontal correlations is crucial in ocean data assimilation. This paper investigates the impact of releasing the assumption of uniform background-error correlations in a global ocean variational analysis system. Spatially varying horizontal correlations are introduced in the recursive filter operator, which is used for modeling horizontal covariances in the Centro Euro-Mediterraneo sui Cambiamenti Climatici (CMCC) analysis system. The horizontal correlation length scales (HCLSs) were defined on the full three-dimensional model space and computed from both a dataset of monthly anomalies with respect to the monthly climatology and through the so-called National Meteorological Center (NMC) method. Different formulas for estimating the correlation length scale are also discussed and applied to the two forecast error datasets. The new formulation is tested within a 12-yr period (2000–11) in the ½° resolution system. The comparison with the data assimilation system using uniform background-error horizontal correlations indicates the superiority of the former, especially in eddy-dominated areas. Verification skill scores report a significant reduction of RMSE, and the use of nonuniform length scales improves the representation of the eddy kinetic energy at midlatitudes, suggesting that uniform, latitude, or Rossby radius-dependent formulations are insufficient to represent the geographical variations of the background-error correlations. Furthermore, a small tuning of the globally uniform value of the length scale was found to have a small impact on the analysis system. The use of either anomalies or NMC-derived correlation length scales also has a marginal effect with respect to the use of nonuniform HCLSs. On the other hand, the application of overestimated length scales has proved to be detrimental to the analysis system in all areas and for all parameters.

Corresponding author address: Andrea Storto, Centro Euro-Mediterraneo sui Cambiamenti Climatici, Viale Aldo Moro 44, I-40127 Bologna, Italy. E-mail: andrea.storto@cmcc.it
Save
Cover Journal of Atmospheric and Oceanic Technology
Journal of Atmospheric and Oceanic Technology

  • Adani, M., Dobricic S. , and Pinardi N. , 2011: Quality assessment of a 1985–2007 Mediterranean Sea reanalysis. J. Atmos. Oceanic Technol., 28, 569–589, doi:10.1175/2010JTECHO798.1.

    • Search Google Scholar
    • Export Citation

  • Antonov, J. I., and Coauthors, 2010: Salinity. Vol. 2, World Ocean Atlas 2009, NOAA Atlas NESDIS 69, 184 pp.

  • Barker, D. M., Huang W. , Guo Y. R. , and Xiao Q. , 2004: A three-dimensional data assimilation system for use with MM5: Implementation and initial results. Mon. Wea. Rev., 132, 897–914, doi:10.1175/1520-0493(2004)132<0897:ATVDAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Bellucci, A., Masina S. , Di Pietro P. , and Navarra A. , 2007: Using temperature salinity relations in a global ocean implementation of a multivariate data assimilation scheme. Mon. Wea. Rev., 135, 3785–3807, doi:10.1175/2007MWR1821.1.

    • Search Google Scholar
    • Export Citation

  • Belo-Pereira, M., and Berre L. , 2006: The use of an ensemble approach to study the background-error covariances in a global NWP model. Mon. Wea. Rev., 134, 2466–2489, doi:10.1175/MWR3189.1.

    • Search Google Scholar
    • Export Citation

  • Bernie, D. J., Guilyardi E. , Madec G. , Slingo J. M. , and Woolnough S. J. , 2007: Impact of resolving the diurnal cycle in an ocean–atmosphere GCM. Part 1: A diurnally forced OGCM. Climate Dyn., 29, 575–590, doi:10.1007/s00382-007-0249-6.

    • Search Google Scholar
    • Export Citation

  • Berre, L., Ştefănescu S. , and Belo M. , 2006: The representation of analysis effect in three error simulation techniques. Tellus, 58A, 196–209, doi:10.1111/j.1600-0870.2006.00165.x.

    • Search Google Scholar
    • Export Citation

  • Bonjean, F., and Lagerloef G. , 2002: Diagnostic model and analysis of the surface currents in the tropical Pacific Ocean. J. Phys. Oceanogr., 32, 2938–2954, doi:10.1175/1520-0485(2002)032<2938:DMAAOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Carton, J. A., Giese B. S. , Cao X. , and Miller L. , 1996: Impact of altimeter, thermistor, and expendable bathythermograph data on retrospective analyses of the tropical Pacific Ocean. J. Geophys. Res., 101, 14 147–14 159, doi:10.1029/96JC00631.

    • Search Google Scholar
    • Export Citation

  • Carton, J. A., Chepurin G. , Cao X. , and Giese B. S. , 2000: A Simple Ocean Data Assimilation analysis of the global upper ocean 1950–95. Part I: Methodology. J. Phys. Oceanogr., 30, 294–309, doi:10.1175/1520-0485(2000)030<0294:ASODAA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Cavalieri, D. J., Parkinson C. L. , Gloersen P. , Comiso J. C. , and Zwally H. J. , 1999: Deriving long-term time series of sea ice cover from satellite passive-microwave multisensor data sets. J. Geophys. Res., 104, 15 803–15 814, doi:10.1029/1999JC900081.

    • Search Google Scholar
    • Export Citation

  • Chelton, D., Deszoeke R. , Schlax M. , El Naggar K. , and Siwertz N. , 1998: Geographical variability of the first baroclinic Rossby radius of deformation. J. Phys. Oceanogr., 28, 433–460, doi:10.1175/1520-0485(1998)028<0433:GVOTFB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Courtier, P., Thépaut J.-N. , and Hollingsworth A. , 1994: A strategy for operational implementation of 4D-Var, using an incremental approach. Quart. J. Roy. Meteor. Soc., 120, 1367–1387, doi:10.1002/qj.49712051912.

    • Search Google Scholar
    • Export Citation

  • Cummings, J. A., 2005: Operational multivariate ocean data assimilation. Quart. J. Roy. Meteor. Soc., 131, 3583–3604, doi:10.1256/qj.05.105.

    • Search Google Scholar
    • Export Citation

  • Dai, A., and Trenberth K. E. , 2002: Estimates of freshwater discharge from continents: Latitudinal and seasonal variations. J. Hydrometeor., 3, 660–687, doi:10.1175/1525-7541(2002)003<0660:EOFDFC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Daley, R., 1991: Atmospheric Data Analysis. Cambridge University Press, 457 pp.

  • Dee, D., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553–597, doi:10.1002/qj.828.

    • Search Google Scholar
    • Export Citation

  • Derber, J., and Rosati A. , 1989: A global oceanic data assimilation system. J. Phys. Oceanogr., 19, 1333–1347, doi:10.1175/1520-0485(1989)019<1333:AGODAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Dobricic, S., and Pinardi N. , 2008: An oceanographic three-dimensional assimilation scheme. Ocean Modell., 22, 89–105, doi:10.1016/j.ocemod.2008.01.004.

    • Search Google Scholar
    • Export Citation

  • Fichefet, T., and Morales Maqueda M. A. , 1997: Sensitivity of a global sea ice model to the treatment of ice thermodynamics and dynamics. J. Geophys. Res., 102, 12 609–12 646, doi:10.1029/97JC00480.

    • Search Google Scholar
    • Export Citation

  • Gaspari, G., Cohn S. , Guo J. , and Pawson S. , 2006: Construction and application of correlation functions with variable length-fields. Quart. J. Roy. Meteor. Soc., 132, 1815–1838, doi:10.1256/qj.05.08.

    • Search Google Scholar
    • Export Citation

  • Hayden, C., and Purser R. , 1995: Recursive filter objective analysis of meteorological fields: Applications to NESDIS operational processing. J. Appl. Meteor., 34, 3–15, doi:10.1175/1520-0450-34.1.3.

    • Search Google Scholar
    • Export Citation

  • Ingleby, B., and Huddleston M. , 2007: Quality control of ocean temperature and salinity profiles—Historical and real-time data. J. Mar. Syst., 65, 158–175, doi:10.1016/j.jmarsys.2005.11.019.

    • Search Google Scholar
    • Export Citation

  • Isaksen, L., Fisher M. , and Berner J. , 2007: Use of analysis ensembles in estimating flow-dependent background error variance. Proc. ECMWF Workshop on Flow-Dependent Aspects of Data Assimilation, ECMWF, Reading, United Kingdom, 37 pp. [Available online at http://old.ecmwf.int/newsevents/meetings/workshops/2007/data_assimilation/presentations/Isaksen.pdf.]

  • Large, W. G., and Yeager S. G. , 2004: Diurnal to decadal global forcing for ocean and sea-ice models: The data sets and flux climatologies. NCAR Tech. Note NCAR/TN-460+STR, 105 pp., doi:10.5065/D6KK98Q6.

  • Le Traon, P. Y., Nadal F. , and Ducet N. , 1998: An improved mapping method of multisatellite altimeter data. J. Atmos. Oceanic Technol., 15, 522–534, doi:10.1175/1520-0426(1998)015<0522:AIMMOM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Locarnini, R. A., Mishonov A. V. , Antonov J. I. , Boyer T. P. , Garcia H. E. , Baranova O. K. , Zweng M. M. , and Johnson D. R. , 2010: Temperature. Vol. 1, World Ocean Atlas 2009, NOAA Atlas NESDIS 68, 184 pp.

  • Lorenc, A., 1992: Iterative analysis using covariance functions and filters. Quart. J. Roy. Meteor. Soc., 118, 569–591, doi:10.1002/qj.49711850509.

    • Search Google Scholar
    • Export Citation

  • Madec, G., and Imbard M. , 1996: A global ocean mesh to overcome the north pole singularity. Climate Dyn., 12, 381–388, doi:10.1007/BF00211684.

    • Search Google Scholar
    • Export Citation

  • Madec, G., Delecluse P. , Imbard M. , and Lévy C. , 1998: OPA 8.1 Ocean General Circulation Model reference manual. IPSL Note du Pôle de Modélisation 11, 91 pp.

  • Meyers, G., Phillips H. , Smith N. , and Sprintall J. , 1991: Space and time scales for optimal interpolation—Tropical Pacific Ocean. Prog. Oceanogr., 28, 189–218, doi:10.1016/0079-6611(91)90008-A.

    • Search Google Scholar
    • Export Citation

  • Mirouze, I., and Weaver A. , 2010: Representation of correlation functions in variational assimilation using an implicit diffusion operator. Quart. J. Roy. Meteor. Soc., 136, 1421–1443, doi:10.1002/qj.643.

    • Search Google Scholar
    • Export Citation

  • Pannekoucke, O., Berre L. , and Desroziers G. , 2008: Background-error correlation length-scale estimates and their sampling statistics. Quart. J. Roy. Meteor. Soc., 134, 497–508, doi:10.1002/qj.212.

    • Search Google Scholar
    • Export Citation

  • Parrish, D., and Derber J. , 1992: The National Meteorological Center’s spectral statistical interpolation analysis system. Mon. Wea. Rev., 120, 1747–1763, doi:10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Pujol, M.-I., Dobricic S. , Pinardi N. , and Adani M. , 2010: Impact of multialtimeter sea level assimilation in the Mediterranean Forecasting Model. J. Atmos. Oceanic Technol., 27, 2065–2082, doi:10.1175/2010JTECHO715.1.

    • Search Google Scholar
    • Export Citation

  • Purser, R., Wu W.-S. , Parrish D. , and Roberts N. , 2003a: Numerical aspects of the application of recursive filters to variational statistical analysis. Part I: Spatially homogeneous and isotropic Gaussian covariances. Mon. Wea. Rev., 131, 1524–1535, doi:10.1175/1520-0493(2003)131<1524:NAOTAO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Purser, R., Wu W.-S. , Parrish D. , and Roberts N. , 2003b: Numerical aspects of the application of recursive filters to variational statistical analysis. Part II: Spatially inhomogeneous and anisotropic general covariances. Mon. Wea. Rev., 131, 1536–1548, doi:10.1175/2543.1.

    • Search Google Scholar
    • Export Citation

  • Raynaud, L., Berre L. , and Desroziers G. , 2011: An extended specification of flow-dependent background error variances in the Météo-France global 4D-Var system. Quart. J. Roy. Meteor. Soc., 137, 607–619, doi:10.1002/qj.795.

    • Search Google Scholar
    • Export Citation

  • Reynolds, R. W., Smith T. M. , Liu C. , Chelton D. B. , Casey K. S. , and Schlax M. G. , 2007: Daily high-resolution blended analyses for sea surface temperature. J. Climate, 20, 5473–5496, doi:10.1175/2007JCLI1824.1.

    • Search Google Scholar
    • Export Citation

  • Simmons, A., Uppala S. , Dee D. , and Kobayashi S. , 2007: ERA-Interim: New ECMWF reanalysis products from 1989 onwards. ECMWF Newsletter, No. 110, ECMWF, Reading, United Kingdom, 25–35.

  • Storto, A., and Randriamampianina R. , 2010: Ensemble variational assimilation for the representation of background error covariances in a high-latitude regional model. J. Geophys. Res., 115, D17204, doi:10.1029/2009JD013111.

    • Search Google Scholar
    • Export Citation

  • Storto, A., Dobricic S. , Masina S. , and Di Pietro P. , 2011: Assimilating along-track altimetric observations through local hydrostatic adjustments in a global ocean reanalysis system. Mon. Wea. Rev., 139, 738–754, doi:10.1175/2010MWR3350.1.

    • Search Google Scholar
    • Export Citation

  • Storto, A., Russo I. , and Masina S. , 2012: Interannual response of global ocean hindcasts to a satellite-based correction of precipitation fluxes. Ocean Sci. Discuss., 9, 611–648, doi:10.5194/osd-9-611-2012.

    • Search Google Scholar
    • Export Citation

  • Storto, A., Masina S. , and Dobricic S. , 2013: Ensemble spread-based assessment of observation impact: Application to a global ocean analysis system. Quart. J. Roy. Meteor. Soc., 139, 1842–1862, doi:10.1002/qj.2071.

    • Search Google Scholar
    • Export Citation

  • Wang, X., Barker D. M. , Snyder C. , and Hamill T. , 2008: A hybrid ETKF–3DVAR data assimilation scheme for the WRF model. Part I: Observing system simulation experiment. Mon. Wea. Rev., 136, 5116–5131, doi:10.1175/2008MWR2444.1.

    • Search Google Scholar
    • Export Citation

  • Weaver, A. T., and Courtier P. , 2001: Correlation modelling on the sphere using a generalized diffusion equation. Quart. J. Roy. Meteor. Soc., 127, 1815–1846, doi:10.1002/qj.49712757518.

    • Search Google Scholar
    • Export Citation

  • Weaver, A. T., and Mirouze I. , 2013: On the diffusion equation and its application to isotropic and anisotropic correlation modelling in variational assimilation. Quart. J. Roy. Meteor. Soc., 139, 242–260, doi:10.1002/qj.1955.

    • Search Google Scholar
    • Export Citation

  • Weaver, A. T., Deltel C. , Machu E. , Ricci S. , and Daget N. , 2005: A multivariate balance operator for variational ocean data assimilation. Quart. J. Roy. Meteor. Soc., 131, 3605–3625, doi:10.1256/qj.05.119.

    • Search Google Scholar
    • Export Citation

  • Yaremchuk, M., and Carrier M. , 2012: On the renormalization of the covariance operators. Mon. Wea. Rev., 140, 637–649, doi:10.1175/MWR-D-11-00139.1.

    • Search Google Scholar
    • Export Citation

  • Zhou, G., Fu W. , Zhu J. , and Wang H. , 2004: The impact of location-dependent correlation scales in ocean data assimilation. Geophys. Res. Lett.,31, L21306, doi:10.1029/2004GL020579.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 872 159 17
PDF Downloads 302 68 7