Skip to main content
SpringerLink
Log in

Multiple Equilibria in a Land–Atmosphere Coupled System

  • Regular Article
  • Published:
Journal of Meteorological Research Aims and scope Submit manuscript

Abstract

Many low-order modeling studies indicate that there may be multiple equilibria in the atmosphere induced by thermal and topographic forcings. However, most work uses uncoupled atmospheric model and just focuses on the multiple equilibria with distinct wave amplitude, i.e., the high- and low-index equilibria. Here, a low-order coupled land–atmosphere model is used to study the multiple equilibria with both distinct wave phase and wave amplitude. The model combines a two-layer quasi-geostrophic channel model and an energy balance model. Highly truncated spectral expansions are used and the results show that there may be two stable equilibria with distinct wave phase relative to the topography: one (the other) has a lower layer streamfunction that is nearly in (out of) phase with the topography, i.e., the lower layer ridges (troughs) are over the mountains, called ridge-type (trough-type) equilibria. The wave phase of equilibrium state depends on the direction of lower layer zonal wind and horizontal scale of the topography. The multiple wave phase equilibria associated with ridge- and trough-types originate from the orographic instability of the Hadley circulation, which is a pitch-fork bifurcation. Compared with the uncoupled model, the land–atmosphere coupled system produces more stable atmospheric flow and more ridge-type equilibrium states, particularly, these effects are primarily attributed to the longwave radiation fluxes. The upper layer streamfunctions of both ridge- and trough-type equilibria are also characterized by either a high- or low-index flow pattern. However, the multiple wave phase equilibria associated with ridge- and trough-types are more prominent than multiple wave amplitude equilibria associated with high- and low-index types in this study.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barsugli, J. J., and D. S. Battisti, 1998: The basic effects of atmosphere–ocean thermal coupling on midlatitude variability. J. Atmos. Sci., 55, 477–493, doi: 10.1175/1520-0469(1998) 055<0477:TBEOAO>2.0.CO;2.

    Article  Google Scholar 

  • Benzi, R., A. R. Hansen, and A. Sutera, 1984: On stochastic perturbation of simple blocking models. Quart. J. Roy. Meteor. Soc., 110, 393–409, doi: 10.1002/qj.49711046406.

    Article  Google Scholar 

  • Benzi, R., P. Malguzzi, A. Speranza, et al., 1986: The statistical properties of general atmospheric circulation: Observational evidence and a minimal theory of bimodality. Quart. J. Roy. Meteor. Soc., 112, 661–674, doi: 10.1002/qj.49711247306.

    Article  Google Scholar 

  • Cai, M., and M. Mak, 1987: On the multiplicity of equilibria of baroclinic waves. Tellus, 39A, 116–137, doi: 10.3402/tellusa. v39i2.11746.

    Google Scholar 

  • Cehelsky, P., and K. K. Tung, 1987: Theories of multiple equilibria and weather regimes—A critical reexamination. Part II: Baroclinic two-layer models. J. Atmos. Sci., 44, 3282–3303, doi: 10.1175/1520-0469(1987)044<3282:TOMEAW>2.0.CO; 2.

    Google Scholar 

  • Charney, J. G., and J. G. DeVore, 1979: Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci., 36, 1205–1216, doi: 10.1175/1520-0469(1979)036<1205:MFEITA>2.0.CO;2.

    Article  Google Scholar 

  • Charney, J. G., and D. M. Straus, 1980: Form-drag instability, multiple equilibria and propagating planetary waves in baroclinic, orographically forced, planetary wave systems. J. Atmos. Sci., 37, 1157–1176, doi: 10.1175/1520-0469(1980)037 <1157:FDIMEA>2.0.CO;2.

    Article  Google Scholar 

  • Christensen, C. W., and A. Wiin-Nielsen, 1996: Blocking as a wave–wave interaction. Tellus A: Dyn. Meteor. Oceanogr., 48, 254–271, doi: 10.3402/tellusa.v48i2.12059.

    Article  Google Scholar 

  • Crommelin, D. T., J. D. Opsteegh, and F. Verhulst, 2004: A mechanism for atmospheric regime behavior. J. Atmos. Sci., 61, 1406–1419, doi: 10.1175/1520-0469(2004)061<1406:AMFARB> 2.0.CO;2.

    Article  Google Scholar 

  • De Cruz, L., J. Demaeyer, and S. Vannitsem, 2016: The modular arbitrary-order ocean–atmosphere model: MAOOAM v1.0. Geosci. Model Dev., 9, 2793–2808, doi: 10.5194/gmd-9-2793-2016.

    Article  Google Scholar 

  • De Swart, H. E., 1988: Low-order spectral models of the atmospheric circulation: A survey. Acta Appl. Math., 11, 49–96, doi: 10.1007/BF00047114.

    Article  Google Scholar 

  • Dole, R. M., and N. D. Gordon, 1983: Persistent anomalies of the extratropical Northern Hemisphere wintertime circulation: Geographical distribution and regional persistence characteristics. Mon. Wea. Rev., 111, 1567–1586, doi: 10.1175/1520-0493(1983)111<1567:PAOTEN>2.0.CO;2.

    Article  Google Scholar 

  • Egger, J., 1981: Stochastically driven large-scale circulations with multiple equilibria. J. Atmos. Sci., 38, 2606–2618, doi: 10.1175/1520-0469(1981)038<2606:SDLSCW>2.0.CO;2.

    Article  Google Scholar 

  • Faranda, D., G. Masato, N. Moloney, et al., 2016: The switching between zonal and blocked mid-latitude atmospheric circulation: A dynamical system perspective. Climate Dyn., 47, 1587–1599, doi: 10.1007/s00382-015-2921-6.

    Article  Google Scholar 

  • He, Y. L., J. P. Huang, and M. X. Ji, 2014: Impact of land–sea thermal contrast on interdecadal variation in circulation and blocking. Climate Dyn., 43, 3267–3279, doi: 10.1007/s00382-014-2103-y.

    Article  Google Scholar 

  • He, Y. L., J. P. Huang, D. D. Li, et al., 2018: Comparison of the effect of land–sea thermal contrast on interdecadal variations in winter and summer blockings. Climate Dyn., 51, 1275–1294, doi: 10.1007/s00382-017-3954-9.

    Article  Google Scholar 

  • Holton, J. R., and G. J. Hakim, 2012: An Introduction to Dynamic Meteorology. 5th Ed., Academic Press, Amsterdam, 552 pp.

    Google Scholar 

  • Huang, J. P., M. X. Ji, Y. K. Xie, et al., 2016: Global semi-arid climate change over last 60 years. Climate Dyn., 46, 1131–1150, doi: 10.1007/s00382-015-2636-8.

    Google Scholar 

  • Huang, J. P., Y. K. Xie, X. D. Guan, et al., 2017a: The dynamics of the warming hiatus over the Northern Hemisphere. Climate Dyn., 48, 429–446, doi: 10.1007/s00382-016-3085-8.

    Article  Google Scholar 

  • Huang, J., Y. Li, C. Fu, et al., 2017b: Dryland climate change: Recent progress and challenges. Rev. Geophys., 55, 719–778, doi: 10.1002/2016RG000550.

    Article  Google Scholar 

  • Koo, S., and M. Ghil, 2002: Successive bifurcations in a simple model of atmospheric zonal-flow vacillation. Chaos: An Interdiscip. J. Nonlinear Sci., 12, 300–309, doi: 10.1063/1.1468249.

    Article  Google Scholar 

  • Legras, B., and M. Ghil, 1985: Persistent anomalies, blocking and variations in atmospheric predictability. J. Atmos. Sci., 42, 433–471, doi: 10.1175/1520-0469(1985)042<0433:PABAVI> 2.0.CO;2.

    Article  Google Scholar 

  • Li, J. P., and J. F. Chou, 1996: Source of atmospheric multiple equilibria. Chin. Sci. Bull., 41, 2074–2077.

    Google Scholar 

  • Li, J. P., and J. F. Chou, 1997: The effects of external forcing, dissipation and nonlinearity on the solutions of atmospheric equations. Acta Meteor. Sinica, 11, 57–65.

    Google Scholar 

  • Li, J. P., and J. X. L. Wang, 2003: A modified zonal index and its physical sense. Geophys. Res. Lett., 30, 1632, doi: 10.1029/2003GL017441.

    Google Scholar 

  • Li, J. P., and J. F. Chou, 2003: Advances in nonlinear atmospheric dynamics. Chinese J. Atmos. Sci., 27, 653–673, doi: 10.3878/j.issn.1006-9895.2003.04.15. (in Chinese)

    Google Scholar 

  • Li, M. C., and Z. X. Luo, 1983: Nonlinear mechanism of abrupt change of atmospheric circulation during June and October. Scientia Sinica (Series B), 26, 746–754.

    Google Scholar 

  • Li, S. L., and L. R. Ji, 2001: Persistent anomaly in Ural area in summer and its background circulation characteristics. Acta Meteor. Sinica, 59, 280–293, doi: 10.11676/qxxb2001.030. (in Chinese)

    Google Scholar 

  • Liu, C. J., and S. Y. Tao, 1983: Northward jumping of subtropical highs and cusp catastrophe. Scientia Sinica (Series B), 26, 1065–1074.

    Google Scholar 

  • Lindzen, R. S., 1986: Stationary planetary waves, blocking, and interannual variability. Adv. Geophys., 29, 251–273, doi: 10.1016/S0065-2687(08)60042-4.

    Article  Google Scholar 

  • Luo, Z. X., 1987: Abrupt change of flow pattern in baroclinic atmosphere forced by joint effects of diabatic heating and orography. Adv. Atmos. Sci., 4, 137–144, doi: 10.1007/BF02677060.

    Article  Google Scholar 

  • Miao, J. H., and M. F. Ding, 1985: Catastrophe theory of seasonal variation. Scientia Sinica (Series B), 28, 1079–1092.

    Google Scholar 

  • Molteni, F., 2003: Weather regimes and multiple equilibria. Encyclopedia of Atmospheric Sciences, J. R. Holton, J. Pyle, and J. A. Curry, Eds., Academic Press, Academic, 2577–2586.

    Google Scholar 

  • Monin, A. S., 1986: An Introduction to the Theory of Climate. D. Reidel Publishing Company, Dordrecht, Holland, 261 pp.

    Google Scholar 

  • Namias, J., 1950: The index cycle and its role in the general circulation. J. Meteor., 7, 130–139, doi: 10.1175/1520-0469 (1950)007<0130:TICAIR>2.0.CO;2.

    Google Scholar 

  • Nigam, S., and E. DeWeaver, 2003: Stationary waves (orographic and thermally forced). Encyclopedia of Atmospheric Sciences, J. R. Holton, J. Pyle, and J. A. Curry, Eds., Academic Press, Academic, 2121–2137.

    Book  Google Scholar 

  • Pan, J., L. R. Ji, and C. Bueh, 2009: Intraseasonal climate characteristics of the summertime persistent anomalous circulation over Eurasian middle and high latitudes. Chinese J. Atmos. Sci., 33, 300–312, doi: 10.3878/j.issn.1006-9895.2009.02.09. (in Chinese)

    Google Scholar 

  • Reinhold, B. B., and R. T. Pierrehumbert, 1982: Dynamics of weather regimes: Quasi-stationary waves and blocking. Mon. Wea. Rev., 110, 1105–1145, doi: 10.1175/1520-0493(1982)110 <1105:DOWRQS>2.0.CO;2.

    Article  Google Scholar 

  • Reinhold, B. B., and R. T. Pierrehumbert, 1985: Corrections to “Dynamics of weather regimes: Quasi-stationary waves and blocking”. Mon. Wea. Rev., 113, 2055–2056, doi: 10.1175/1520-0493(1985)113<2055:>2.0.CO;2.

    Article  Google Scholar 

  • Ren, H. L., P. Q. Zhang, J. F. Chou, et al., 2006: Large-scale lowfrequency rainfall regimes and their transition modes in summertime over China. Chin. Sci. Bull., 51, 1355–1367, doi: 10.1007/s11434-006-1355-2.

    Article  Google Scholar 

  • Rossby, C. G., 1939: Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action. J. Marine Res., 2, 38–55, doi: 10.1357/002224039806649023.

    Article  Google Scholar 

  • Smith, R. B., 1979: The influence of mountains on the atmosphere. Adv. Geophys., 21, 87–230, doi: 10.1016/S0065-2687(08) 60262–9.

    Article  Google Scholar 

  • Sura, P., 2002: Noise-induced transitions in a barotropic β-plane channel. J. Atmos. Sci., 59, 97–110, doi: 10.1175/1520-0469(2002)059<0097:NITIAB>2.0.CO;2.

    Article  Google Scholar 

  • Sutera, A., 1986: Probability density distribution of large-scale atmospheric flow. Adv. Geophys., 29, 227–249, doi: 10.1016/S0065-2687(08)60041-2.

    Article  Google Scholar 

  • Tan, G. R., H. L. Ren, H. S. Chen, et al., 2017: Detecting primary precursors of January surface air temperature anomalies in China. J. Meteor. Res., 31, 1096–1108, doi: 10.1007/s13351-017-7013-6.

    Article  Google Scholar 

  • Thompson, D. W. J., and J. M. Wallace, 2001: Regional climate impacts of the Northern Hemisphere annular mode. Science, 293, 85–89, doi: 10.1126/science.1058958.

    Article  Google Scholar 

  • Tung, K. K., and A. J. Rosenthal, 1985: Theories of multiple equilibria— A critical reexamination. Part I: Barotropic models. J. Atmos. Sci., 42, 2804–2819, doi: 10.1175/1520-0469(1985)042 <2804:TOMEAC>2.0.CO;2.

    Google Scholar 

  • Vannitsem, S., J. Demaeyer, L. De Cruz, et al., 2015: Low-frequency variability and heat transport in a low-order nonlinear coupled ocean–atmosphere model. Physica D: Nonlinear Phenomena, 309, 71–85, doi: 10.1016/j.physd.2015.07.006.

    Article  Google Scholar 

  • Yoden, S., 1983: Nonlinear interactions in a two-layer, quasi-geostrophic, low-order model with topography. Part I: Zonal flow-forced wave interactions. J. Meteor. Soc. Japan, 61, 1–38, doi: 10.2151/jmsj1965.61.1_1.

    Google Scholar 

  • Zhu, Z. X., 1985: Equilibrium states of planetary waves forced by topography and perturbation heating and blocking situation. Adv. Atmos. Sci., 2, 359–367, doi: 10.1007/BF02677252.

    Article  Google Scholar 

  • Zhu, Z. X., and B. Z. Zhu, 1982: Equilibrium states of ultra-long waves driven by non-adiabatic heating and blocking situation. Scientia Sinica (Series B), 25, 1201–1212.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory for Semi-Arid Climate Change of the Ministry of Education, College of Atmospheric Sciences, Lanzhou University, Lanzhou, 730000, China

    Dongdong Li, Yongli He, Jianping Huang, Lu Bi & Lei Ding

Authors
  1. Dongdong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongli He
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianping Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lu Bi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Lei Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianping Huang.

Additional information

Supported by the National Science Foundation of China (41521004 and 41705047), Strategic Priority Research Program of Chinese Academy of Sciences (XDA2006010301), Foundation of Key Laboratory for Semi-Arid Climate Change of the Ministry of Education in Lanzhou University from the Fundamental Research Funds for the Central Universities (lzujbky-2017-bt04), and China 111 Project (B 13045).

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, D., He, Y., Huang, J. et al. Multiple Equilibria in a Land–Atmosphere Coupled System. J Meteorol Res 32, 950–973 (2018). https://doi.org/10.1007/s13351-018-8012-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13351-018-8012-y

Key words

Search

Navigation