Climate and climate change: mathematical theory and numerical modeling

V. P. Dymnikov ; E. M. Volodin ; V. Ya. Galin ; A. V. Glazunov ; A. S. Gritsoun ; N. A. Dianskii ; V. N. Lykosov

Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 4, pp. 347-379.

Résumé

In the paper, a climate system model constructed on the basis of coupling models of general circulation of the atmosphere and ocean is presented. This model does not use the correction of turbulent heat fluxes on the sea surface. The method to calculate the response operator of climatic models and real climatic system to small external perturbations of forcing is described. The method is based on the use of dissipation-fluctuation relations for systems with a large number of positive Lyapunov's exponents. To illustrate the effectiveness of the proposed method, some results of constructing an approximate response operator for the atmospheric general circulation model are discussed. Numerical experiments to reproduce the present-day climate have been carried out. Climatic characteristics simulated by the coupled model are compared to the characteristics obtained from the community of models participating in the project SMIP. The coupled atmosphere and ocean model response to an increase of the atmospheric $\rm{CO}_2$ concentration is analyzed. It is found that the maximal warming about 2–3.5 К takes place in the centre of Euroasia. During the cold season this warming is expressed stronger (3–5 K) than during the warm season (1–1.5 K). Approximately one third of the cold season warming in Euroasia (1–2 K)is explained by a change of the atmospheric dynamics, namely, by an increase of the arctic oscillation index.

Bibliographie

[1] Alekseev V. V., Zalesnyi V. B., Chislennaya model krupnomasshtabnoi dinamiki okeana, Vychislitelnye protsessy i sistemy, 10, ed. G. I. Marchuk, Nauka, M., 1984 | Zbl

[2] Alekseev V. A., Volodin B. M., Galin V. Ya., Dymnikov V. P., Lykosov V. N., Modelirovanie sovremennogo klimata s pomoschyu atmosfernoi modeli IVM RAN, Preprint IVM RAN; 2086-V98, Moskva, 1998, 215 pp.

[3] Volodin E. M., Lykosov V. N., “Parametrizatsiya protsessov teplo- i vlagoobmena v sisteme rastitelnost-pochva dlya modelirovaniya obschei tsirkulyatsii atmosfery. 1. Opisanie i raschety s ispolzovaniem lokalnykh dannykh nablyudenii”, Izvestiya AN. Fizika atmosfery i okeana, 34 (1998), 453–465

[4] Galin V. Ya., “Parametrizatsiya radiatsionnykh protsessov v atmosfernoi modeli IVM”, Izvestiya AN. Fizika atmosfery i okeana, 34 (1998), 380–389

[5] Glazunov A. C., Dianskii H. A., Dymnikov V. P., “Lokalnyi i globalnyi otkliki atmosfernoi tsirkulyatsii na anomalii poverkhnostnoi temperatury okeana v srednikh shirotakh”, Izvestiya AN. Fizika atmosfery i okeana, 37 (2001), 581–600 | MR

[6] Dianskii N. A., Bagno A. V., Zalesnyi V. B., “Sigma-model globalnoi tsirkulyatsii okeana i ee chuvstvitelnost k variatsiyam napryazheniya treniya vetra”, Izvestiya AN. Fizika atmosfery i okeana, 38 (2002), 537–556

[7] Dianskii H. A., Volodin E. M., “Vosproizvedenie sovremennogo klimata s pomoschyu sovmestnoi modeli obschei tsirkulyatsii atmosfery i okeana”, Izvestiya AN. Fizika atmosfery i okeana, 38 (2002), 824–840

[8] Dymnikov V. P., Gritsun A. C., Khaoticheskie attraktory klimaticheskikh modelei, Preprint, IVM RAN, Moskva, 2000, 53 pp.

[9] Dymnikov V. P., Gritsun A. C., “Parnaya simmetriya globalnykh pokazatelei Lyapunova na attraktorakh modelei dinamiki atmosfery”, Izvestiya AN. Fizika atmosfery i okeana, 37:3 (2001), 269 | MR

[10] Dymnikov V. P., Filatov A. N., Osnovy matematicheskoi teorii klimata, VINITI, M., 1994

[11] Marchuk G. I., Metody vychislitelnoi matematiki, Nauka, M., 1980 | MR

[12] Marchuk G. I., Dymnikov V. P., Zalesnyi V. A., Lykosov V. N., Galin V. Ya., Matematicheskie modelirovanie obschei tsirkulyatsii atmosfery i okeana, Gidrometeoizdat, L., 1984

[13] Marchuk G. I., Dymnikov V. P., Zalesnyi V. A., Matematicheskie modeli v geofizicheskoi gidrodinamiki i chislennye metody ikh realizatsii, Gidrometeoizdat, L., 1987 | MR | Zbl

[14] Arakawa A., Lamb V. R., “A potential enstrophy and energy conserving scheme for shallow water equations”, Mon. Wea. Rev., 109 (1981), 18–36 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[15] Asselin R., “Frequency filter for time integrations”, Mon. Wea. Rev., 100 (1972), 487–490 | 2.3.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[16] Betts A. K., “A new convective adjustment scheme. Part I. Observational and theoretical basis”, Quart. J. Roy. Met. Soc., 112 (1986), 677–691

[17] Covey C., AchutaRao K. M., Lambert S. J., Taylor K. E., Intercomparison of present and future climates simulated by coupled ocean-atmosphere GCMs, Report PCMDI No 66, 2000

[18] Covey C., Abe-Ouchi A., etc., “The seasonal cycle in coupled ocean-atmosphere general circulation models”, Climate Dynamics, 16 (2000), 775–787 | DOI

[19] Dymnikov V., Filatov A., Mathematics of climate modeling, Birkhäuser, Boston, 1997 | MR | Zbl

[20] Gleckler P. J., Philips T. J., McCravy A., AMIP home page, Accessible online at http://www-pcmdi.llnl.gov/amip/

[21] Gritsoun A. S., Branstator G., Dymnikov V. P., “Construction of the linear response operator of an atmospheric general circulation model to small external forcing”, Russ. J. Numer. Anal. Math. Modelling, 17 (2002), 399–416 | MR | Zbl

[22] Hines C. O., “Doppler spread parameterization of gravity wave momentum deposition in the middle atmosphere. Part 2. Broad and quasimonochromatic spectra, and implementation”, J. Atm. Sol. Terr. Phys., 59 (1997), 387–400 | DOI

[23] Jerlov N., Optical oceanography, Elsevier, 1968

[24] Jones P. D., New M., Parker D. E., Martin S., Rigor I. G., “Surface air temperature and its changes over the past 150 years”, Rev. Geophys., 37 (1999), 173–199 | DOI

[25] Kalnay E., Kanamitsu M., etc., “The NCEP/NCAR 40-year reanalysis project”, Bulletin of the American Meteorological Society, 77 (1996), 437–471 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[26] Kraichnan R., “Classical fluctuation-relaxation theorem”, Phys. Rev., 113 (1959), 1181–1183 | DOI | MR

[27] Levitus S., World Ocean Atlas, CD-ROM Data Set U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Environmental Satellite Data and Information Service, National Oceanographie Data Center, Ocean Climate Laboratory, 1994

[28] Meehl G. A., Boer G. J., Covey C., Latif M., Stouffer R. J., “The Coupled Model Intercomparison Project (CMIP)”, Bull. Amer. Meteor. Soc., 81 (2000), 313–318 | 2.3.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[29] Mesinger F., Arakawa A., Numerical methods used in atmospheric models, Vol. I, GARP Publication Series, 17, JOC, Geneva; CP. Vol. 5, CH-1211, World Meteorological Organization, 1976

[30] Palmer T. N., Shutts G. J., Swinbank R., “Alleviation of a systematic westerly bias in general circulation an numerical weather prediction models through an orographic gravity wave drag parameterization”, Quart. J. Roy. Met. Soc., 112 (1986), 1001–1031 | DOI

[31] Pitcher E. J., Malone R. C., Ramanathan V., Blackmon M., Puri K., Bourke W., “January and July simulations with a spectral general cirrulation model”, J. of Atmos. Sci., 40 (1982), 580 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[32] Robert A. J., Henderson J., Turnbull C., “An implicit time integration sheme for baroclinic modes in the atmosphere”, Mon. Wea. Rev., 100 (1972), 329–335 | 2.3.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[33] Thompson D. W. J., Wallace J. M., “Annular modes in the extratropical circulation. Part I. Month-to-month variability”, J. Climate, 13 (2000), 1000–1017 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[34] Xie P., Arkin P., “Global precipitation: a 17-year monthly analysis based on gauge observations, satellite estimates and numerical model outputs”, Bull. Amer. Meteor. Soc., 78 (1997), 2539–2558 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI