Articles | Volume 17, issue 4
https://doi.org/10.5194/os-17-891-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/os-17-891-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
06 Jul 2021
Research article |
| 06 Jul 2021
| 06 Jul 2021
High-resolution stochastic downscaling method for ocean forecasting models and its application to the Red Sea dynamics
Georgy I. Shapiro
CORRESPONDING AUTHOR
School of Biological and Marine Sciences, University of Plymouth,
Plymouth, PL4 8AA, UK
Jose M. Gonzalez-Ondina
University of Plymouth Enterprise LTD, Plymouth, PL4 8AA, UK
Vladimir N. Belokopytov
Marine Hydrophysical Institute, Russian Academy of Sciences,
Sevastopol, 299011, Russia
Related authors
Georgy I. Shapiro and Jose M. Gonzalez-Ondina
Ocean Sci. Discuss., https://doi.org/10.5194/os-2021-77, https://doi.org/10.5194/os-2021-77, 2021
Preprint withdrawn
Short summary
Short summary
An effective method is developed for data assimilation in a high-resolution (child) ocean model in the case when the output from a coarse-resolution data-assimilating model (parent) is available. The basic idea is to assimilate data from the coarser model instead of actual observations. The method named Data Assimilation with Stochastic-Deterministic Downscaling (SDDA) does not allow the child model to drift away from reality as it is indirectly controlled by observations via the parent model.
F. Wobus, G. I. Shapiro, J. M. Huthnance, M. A. M. Maqueda, and Y. Aksenov
Ocean Sci., 9, 885–899, https://doi.org/10.5194/os-9-885-2013, https://doi.org/10.5194/os-9-885-2013, 2013
G. Shapiro, M. Luneva, J. Pickering, and D. Storkey
Ocean Sci., 9, 377–390, https://doi.org/10.5194/os-9-377-2013, https://doi.org/10.5194/os-9-377-2013, 2013
Georgy I. Shapiro and Jose M. Gonzalez-Ondina
Ocean Sci. Discuss., https://doi.org/10.5194/os-2021-77, https://doi.org/10.5194/os-2021-77, 2021
Preprint withdrawn
Short summary
Short summary
An effective method is developed for data assimilation in a high-resolution (child) ocean model in the case when the output from a coarse-resolution data-assimilating model (parent) is available. The basic idea is to assimilate data from the coarser model instead of actual observations. The method named Data Assimilation with Stochastic-Deterministic Downscaling (SDDA) does not allow the child model to drift away from reality as it is indirectly controlled by observations via the parent model.
Ivan Zavialov, Alexander Osadchiev, Roman Sedakov, Bernard Barnier, Jean-Marc Molines, and Vladimir Belokopytov
Ocean Sci., 16, 15–30, https://doi.org/10.5194/os-16-15-2020, https://doi.org/10.5194/os-16-15-2020, 2020
Short summary
Short summary
This study is focused on water exchange between the Sea of Azov and the Black Sea. The Sea of Azov is a small freshened sea that receives a large freshwater discharge and, therefore, can be regarded as a large river estuary connected by narrow Kerch Strait with the Black Sea. In this work we show that water transport through the Kerch Strait is governed by wind forcing and does not depend on the river discharge rate to the Sea of Azov on an intra-annual timescale.
F. Wobus, G. I. Shapiro, J. M. Huthnance, M. A. M. Maqueda, and Y. Aksenov
Ocean Sci., 9, 885–899, https://doi.org/10.5194/os-9-885-2013, https://doi.org/10.5194/os-9-885-2013, 2013
G. Shapiro, M. Luneva, J. Pickering, and D. Storkey
Ocean Sci., 9, 377–390, https://doi.org/10.5194/os-9-377-2013, https://doi.org/10.5194/os-9-377-2013, 2013
Cited articles
Badin, G., Williams, R. G., Holt, J. T., and Fernand, L. J.: Are mesoscale
eddies in shelf seas formed by baroclinic instability of tidal fronts?, J.
Geophys. Res., 114, C10021, https://doi.org/10.1029/2009JC005340, 2009.
Barenblatt, G. I., Seidov D. G., and Sutyrin G. G. (Eds.): Coherent structures and self-organisation
of ocean currents, edited by: Nauka, M., 198 pp., 1992.
Barth, A., Azcárate, A. A., Joassin, P., Beckers, J.-M., and Troupin, C.:
Introduction to Optimal Interpolation and Variational Analysis, SESAME
Summer School, Varna, Bulgaria, 35 pp., 2008.
Belokopytov, V. N.: Retrospective Analysis of the Black Sea Thermohaline
Fields on the Basis of Empirical Orthogonal Functions, J. Phys. Oceanogr., 25, 380–389, https://doi.org/10.22449/1573-160X-2018-5-380-3, 2018.
Beron-Vera, F. J., Hadjighasem, A., Xia, Q., Olascoaga, M. J., and Haller,
G.: Coherent Lagrangian swirls among submesoscale motions, P. Natl. Acad. Sci. USA, 116, 37, 18251–18256, 2019.
Boyer, T. P., Levitus, S., Garcia, H., Locarnini, R. A., Stephens, C., and Antonov, J.:
Objective analyses of annual, seasonal, and monthly temperature and salinity
for the world ocean on a 0.25∘ grid, Int. J. Climatol., 25,
931–945, https://doi.org/10.1002/joc.1173, 2005.
Brekelmans, R., Driessen, L., Hamers, H., and Hertog, D.: Gradient Estimation
Schemes for Noisy Functions, J. Optim. Theory Appl., 126, 529–551,
https://doi.org/10.1007/s10957-005-5496-2, 2005.
Bretherton, F. P., Davis, R. E., and Fandry, C. B.: A technique for
objective analysis and design of oceanographic experiments applied to
MODE-73, Deep-Sea Res., 23, 559–582, https://doi.org/10.1016/0011-7471(76)90001-2,
1976.
Bruciaferri, D., Shapiro, G. I., Stanichny, S., Zatsepin, A., Ezer, T., Wobus, F.,
Francis, X., and Hilton, D.: The development of a 3-D computational mesh to
improve the representation of dynamic processes: The Black Sea test case,
Ocean Model., 146, 101534, https://doi.org/10.1016/j.ocemod.2019.101534, 2019.
Bryan, K.: A numerical investigation of a nonlinear model of a wind-driven
ocean, J. Atmos. Sci., 20, 594–606, 1963.
CMEMS: Copernicus Marine Environment Monitoring Service,
available at: https://marine.copernicus.eu (last access: 6 July 2020), 2020.
Coriolis: Coriolis operational oceanography, available at: http://www.coriolis.eu.org, last access: 6 July 2020.
Cressman, G. P.: An Operational Objective Analysis System, Mon. Weather Rev.,
87, 367–374, https://doi.org/10.1175/1520-0493(1959)087<0367:AOOAS>2.0.CO;2, 1959
Crocker, R., Maksymczuk, J., Mittermaier, M., Tonani, M., and Pequignet, C.: An approach to the verification of high-resolution ocean models using spatial methods, Ocean Sci., 16, 831–845, https://doi.org/10.5194/os-16-831-2020, 2020.
Daley, R.: Atmospheric data analysis No. 2., Cambridge University Press, 457 pp.,
1993.
Dazhi, Y.: On post-processing day-ahead NWP forecasts using Kalman filtering,
Sol. Energy, 182, 179–181, 2019.
Delle Monache, L., Nipen, T., Liu, Y., Roux, G., and Stull, R.: Kalman
filter and analog schemes to postprocess numerical weather predictions,
Mon. Weather Rev., 139, 3554–3570, https://doi.org/10.1175/2011MWR3653.1, 2011.
Delrosso, D., Clementi, E., Grandi, A., Tonani, M., Oddo, P., Feruzza, G.,
and Pinardi, N.: Towards the Mediterranean forecasting system MyOcean v5:
numerical experiments results and validation, 2016, INGV Technical Report,
No. 345, ISSN 2039-7941, 2016.
Dobricic, S. and Pinardi, N.: An oceanographic three-dimensional variational
data assimilation scheme, Ocean Modell., 22, 89–105, 2008.
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, https://doi.org/10.5194/os-3-149-2007, 2007.
ECMWF, 2020: available at: https://confluence.ecmwf.int/display/FUG/12.A+Statistical+Concepts+-+Deterministic+Data#id-12.AStatisticalConceptsDeterministicData-The%C2%93%E2%80%9CDoublePenaltyEffect%C2%94%E2%80%9D, last access: 5 January 2021.
Ezer, T. and Mellor, G. L.: A generalized coordinate ocean model and a
comparison of the bottom boundary layer dynamics in terrain-following and in
z-level grids, Ocean Model., 6, 379–403, https://doi.org/10.1016/S1463-5003(03)00026-X,
2004.
Fletcher, S. J.: Data Assimilation for the Geosciences: From Theory to
Application, Elsevier, 919 pp., ISBN 0128044446, 2017.
Flor J.-B. (Ed.): Fronts, Waves and Vortices in Geophysical Flows, Lecture
Notes in Physics 805, Springer, Berlin, Heidelberg, https://doi.org/10.1007/978-3-642-11587-5, p. 52, 2010.
Fox-Kemper, B., Adcroft, A., Böning, C. W., et al.: Challenges and Prospects in Ocean Circulation
Models, Front. Mar. Sci., 6, 65 pp., https://doi.org/10.3389/fmars.2019.00065, 2019.
Frisch, U.: Turbulence: The legacy of A. N. Kolmogorov, Cambridge
University Press, 296 pp., ISBN 0-521-45103-5, 1995.
Fu, W., Zhou, G., and Wang, H.: Ocean Data Assimilation with Background Error
Covariance Derived from OGCM Outputs, Adv. Atmos. Sci., 21,
181–192, 2004.
Gandin, L. S.: The problem of optimal interpolation, Scientific papers, Main
Geophysical Observatory, 99, 67–75, 1959.
Gandin, L. S.: Objective analysis of meteorological fields, Leningrad,
Gidrometeoizdat, 287 pp., 1963.
Gandin, L. S.: Objective analysis of meteorological fields. Translated from
the Russian, Jerusalem, Israel Program for Scientific Translations, 242 pp.,
1965.
Gandin, L. S. and Kagan, R. L.: Statistical methods for meteorological data
interpretation, Leningrad, Gidrometeoizdat, 359 pp., 1976.
GEBCO, 2014: The GEBCO_2014 Grid, version 20150318, available at: https://www.gebco.net/, last access: 6 July 2020 (in Russian).
GFDL, 2020: available at: https://www.gfdl.noaa.gov/high-resolution-modeling/, last access: 6 July 2020.
Gilleland, E., Ahijevych, D., Brown, B. G., Casati, B. and Ebert, E. E.:
Intercomparison of spatial forecast verification methods, Weather Forecast,
24, 1416–1430, 2009.
Gilchrist B. and Cressman G. P.: An experiment in objective analysis, Tellus,
6, 309–318, 1954.
GODAE: OceanView: https://www.godae-oceanview.org/science/task-teams/intercomparison-and-validation-tt/ (last access: 6 July 2020), 2020.
Grigoriev, A. V., Ivanov, V. A., and Kapustina, N. A.: Correlation structure of thermohaline fields in the Black
Sea in summer season, Okeanologiya, 36, 364–369, 1996 (in Russian).
Guennebaud, G., Avery, P., Bachrach, A., et al.: available at: http://eigen.tuxfamily.org, last access: 6 July 2020.
Hollingsworth, A. and Lönnberg, P.: The statistical structure of
short-range forecast errors as determined from radiosonde data, Part 1: The
wind field, Tellus A, 38, 111–136, 1986.
Hoteit, I., Abualnaja, Y., Afzal, S., et al.: Towards an End-to-End Analysis and Prediction
System for Weather, Climate, and Marine Applications in the Red Sea,
B. Am. Meteorol. Soc., 102, 99–122, https://doi.org/10.1175/BAMS-D-19-0005.1, 2021.
Haben, S., Ward, J., Greetham, D. V., Singleton, C., and Grindrod, P.: A new
error measure for forecasts of household-level, high resolution electrical
energy consumption, Int. J. Forecast., 30, 246–256, https://doi.org/10.1016/j.ijforecast.2013.08.002, 2014.
Kolmogorov, A. N.: The Local Structure of Turbulence in Incompressible
Viscous Fluid for Very Large Reynolds' Numbers, Doklady Akademiia Nauk SSSR,
30, 301–305, 1941.
Korotaev, G. K., Oguz, T., Dorofeyev, V. L., Demyshev, S. G., Kubryakov, A. I., and Ratner, Yu. B.: Development of Black Sea nowcasting and forecasting system, Ocean Sci., 7, 629–649, https://doi.org/10.5194/os-7-629-2011, 2011.
Le Corre, M., Gula, J., and Tréguier, A.-M.: Barotropic vorticity balance of the North Atlantic subpolar gyre in an eddy-resolving model, Ocean Sci., 16, 451–468, https://doi.org/10.5194/os-16-451-2020, 2020.
Lesieur, M.: Turbulence in Fluids, Springer, Dordrecht, 558 pp., ISBN
978-1-4020-6434-0, 2008.
Lindsay, K.: A Newton–Krylov solver for fast spin-up of online ocean
tracers, Ocean Model., 109, 33–43, https://doi.org/10.1016/j.ocemod.2016.12.001, 2017.
Lorenc, A. C.: Analysis methods for numerical weather prediction, Q. J. Roy. Meteor. Soc., 112, 1177–1194, 1986.
Manasrah, R., Lass, H. U., and Fennel, W.: Circulation in the Gulf of Aqaba
(Red Sea) during Winter–Spring, J. Oceanogr., 62, 219–225, 2006.
Marshall, J. C.: Eddy-mean-flow interaction in a barotropic ocean model,
Q. J. Roy. Meteor. Soc., 110, 573–590, 1984.
Miller, R. N.: Numerical Modeling of Ocean Circulation, Cambridge University
Press, 242 pp., ISBN 978-0-521-78182-4, 2007.
Mass, C. F., Ovens, D., Westrick, K., and Colle, B. A.: Does increasing
horizontal resolution produce more skillful forecasts?, B. Am. Meteorol. Soc., 83, 407–430, https://doi.org/10.1175/1520-0477(2002)083<
0407:DIHRPM>2.3.CO;2, 2002.
Mirouze, I., Blockley, E. W., Lea , D. J., Martin, M. J., and Bell, M. J.: A
multiple length scale correlation operator for ocean data assimilation,
Tellus A, 68, 29744, https://doi.org/10.3402/tellusa.v68.29744, 2016.
Monin, A. S. and Yaglom, A. M.: Statistical Fluid Mechanics, Vol. 1,
Mechanics of Turbulence MIT Press, 782 pp., ISBN 100262130629, 1971.
Nelkin, M.: Universality and scaling in fully developed turbulence, Adv.
Phys., 43, 143–181, https://doi.org/10.1080/00018739400101485, 1994.
OSTIA, 2020: Operational Sea Surface Temperature and Sea Ice Analysis,
available at: http://ghrsst-pp.metoffice.com/ostia/, last access: 6 July 2020.
Park, S. K. and Xu, L. (Eds.): Data Assimilation for Atmospheric, Oceanic
and Hydrologic Applications (Vol. III), Springer, 592 pp.,
ISBN 103319828185, 2018.
Reichel, L. and Yu, X.: Matrix Decompositions for Tikhonov Regularization,
Electron. Trans. Numer. Anal., 43, 223–243, 2015.
2015.
Robinson, A. R. (Ed.): Eddies in marine science. Springer-Verlag Berlin
Heidelberg, 612 pp., ISBN 978-3-642-69003-7, 1983.
Rossby, C.-G.: Dynamics of Steady Ocean Currents in the Light of
Experimental Fluid Mechanics, Papers in Physical Oceanography and
Meteorology, 43 pp., 1936.
Ryabov, V. M., Burova, I. G., and Kalnickaya, M. A.: On numerical solution of systems of linear algebraic
equations with ill-conditioned matrices, Int. Res. J., 12, 13–17, 2018.
Smagorinsky, J.: General circulation experiments with the primitive
equations: 1. The basic experiment, Mon. Weather Rev., 91,
99–164, 1963.
Tabeart, J. M., Dance, S. L., Lawless, A. S., Nichols, N. K., and Waller, J. A.:
Improving the condition number of estimated covariance matrices, Tellus A, 72, 1–19, https://doi.org/10.1080/16000870.2019.1696646, 2020.
Tennekes, H. and Lumley, J. L.: A first course in turbulence MIT
Press, ISBN 978-0-262-20019-6, 1992.
Tikhonov, A. N.: On regularizsatuion of ill-conditioned problems, Doklady AN SSSR, 153, 49–52, 1963.
Tonani, M., Sykes, P., King, R. R., McConnell, N., Péquignet, A.-C., O'Dea, E., Graham, J. A., Polton, J., and Siddorn, J.: The impact of a new high-resolution ocean model on the Met Office North-West European Shelf forecasting system, Ocean Sci., 15, 1133–1158, https://doi.org/10.5194/os-15-1133-2019, 2019.
Vasquez, T.: Objective Analysis, Digital Atmosphere, Weather Graphics
Technologies, 2003, available at: http://www.weathergraphics.com/dl/daanal.pdf, last access: 6 July 2020.
Yudin, M.: Some regularities in the geopotential field, Scientific papers,
Main Geophysical Observatory, Vol. 121, 3–18, 1961.
Zhai, P. and Bower, A.: The response of the Red Sea to a strong wind jet
near the Tokar Gap in summer, J. Geophys. Res.-Oceans, 118, 422–434,
https://doi.org/10.1029/2012JC008444, 2013.
Zhan, P., Subramanian, A. C., Yao F., Kartadikaria, A. R., Guo, D., and
Hoteit, I.: The eddy kinetic energy budget in the Red Sea, J. Geophys. Res.-Oceans, 121, 4732–4747, https://doi.org/10.1002/2015JC011589, 2016.
Zingerlea, C. and Nurmib, P.: Monitoring and verifying cloud forecasts
originating from operational numerical models, Meteorol. Appl.,
15, 325–330, 2008.
Short summary
This paper presents an efficient method for high-resolution ocean modelling based on a combination of the deterministic and stochastic approaches. The method utilises mathematical tools similar to those developed for data assimilation in ocean modelling. The main difference is that instead of assimilating a relatively small number of observations, the SDD method assimilates all the data produced by a parent model. The method is applied to create an operational Stochastic Model of the Red Sea.
This paper presents an efficient method for high-resolution ocean modelling based on a...
