Moisture Transport due to Baroclinic Waves: Linear Analysis of Precipitating Quasi-Geostrophic Dynamics

Alfredo N. Wetzel 1 , Leslie M. Smith 2 , and Samuel N. Stechmann 3
  • 1 Department of Mathematics, University of Wisconsin–Madison, , Madison, USA
  • 2 Department of Mathematics & Department of Engineering Physics, University of Wisconsin–Madison, , Madison, USA
  • 3 Department of Mathematics & Department of Atmospheric and Oceanic Sciences, University of Wisconsin–Madison, , Madison, USA

Abstract

The effects of rainfall speed, VT, and meridional/vertical moisture gradients on the meridional moisture transport are examined in the context of mid-latitude baroclinic waves. These effects are investigated in an idealized model that can be solved analytically. The model is systematically derived in a precipitating quasi-geostrophic limit, starting from a moist atmospheric model with minimal representation of cloud microphysics. Single-phase dynamics are considered, with a comparison of three cases: unsaturated, saturated with VT = 0, and saturated with VT > 0. The Eady problem for linear baroclinic waves is analyzed, with modifications to incorporate moisture. As a preliminary step, the moist waves are shown to have properties consistent with prior studies, including larger growth rates and smaller spatial scales in the saturated cases in comparison to the classic dry Eady problem. Then, in addition, it is shown that the meridional moisture flux, as a function of height, has a mid-tropospheric maximum in the case of VT = 0, and a maximum in the lower troposphere or at the surface for sufficiently large values of VT. These results for different VT values are discussed in the context of meridional moisture transport in observational data.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] Robert F. Adler, George J. Huffman, Alfred Chang, Ralph Ferraro, Ping-Ping Xie, John Jaowiak, Bruno Rudolf, Udo Schneider, Scott Curtis, David Bolvin, Arnold Gruber, Joel Susskind, Philip Arkin, and Eric Nelkin. The version-2 global precipitation climatology project (GPCP) monthly precipitation analysis (1979-present). J. ydrometeor., 4(6):1147-1167, 2003. 10.1175/1525-7541(2003)004<1147:TVGPCP>2.0.CO;2.

  • [2] Peter R. Bannon. Linear development of quasi-geostrophic baroclinic disturbances with condensational heating. J. Atmos. Sci., 43(20):2261-2274, 1986. 10.1175/1520-0469(1986)043<2261:LDOQGB>2.0.CO;2.

  • [3] Karine Béranger, Bernard Barnier, Sergei Gulev, and Michel Crépon. Comparing 20 years of precipitation estimates from different sources over the world ocean. Ocean Dyn., 56(2):104-138, 2006. 10.1007/s10236-006-0065-2.

  • [4] J. G. Charney. The dynamics of long waves in a baroclinic westerly current. J. Meteor., 4(5):135-162, 1947. 10.1175/152- 0469(1947)004<0136:TDOLWI>2.0.CO;2.

  • [5] Hylke de Vries, John Methven, Thomas H. A. Frame, and Brian J. Hoskins. Baroclinic waves with parameterized effects of moisture interpreted using rossby wave components. J. Atmos. Sci., 67(9):2766-2784, 2010. 10.1175/2010JAS3410.1.

  • [6] Dale R. Durran and Joseph B. Klemp. On the effects of moisture on the Brunt-Väisälä frequency. J. Atmos. Sci., 39(10): 2152-2158, 1982. 10.1175/1520-0469(1982)039<2152:OTEOMO>2.0.CO;2.

  • [7] E. T. Eady. Long waves and cyclone waves. Tellus A, 1(3):33-52, 1949. 10.1111/j.2153-3490.1949.tb01265.x.

  • [8] Kerry A. Emanuel, Maurizio Fantini, and Alan J. Thorpe. Baroclinic instability in an environment of small stability to slantwise moist convection. Part I: Two-dimensional models. J. Atmos. Sci., 44(12):1559-1573, 1987. 10.1175/1520- 0469(1987)044<1559:BIIAEO>2.0.CO;2.

  • [9] Maurizio Fantini. Nongeostrophic corrections to the eigensolutions of a moist baroclinic instability problem. J. Atmos. Sci., 47(11):1277-1287, 1990. 10.1175/1520-0469(1990)047<1277:NCTTEO>2.0.CO;2.

  • [10] Dargan M. W. Frierson, Isaac M. Held, and Pablo Zurita-Gotor. A gray-radiation aquaplanet moist GCM. Part I: Static stability and eddy scale. J. Atmos. Sci., 63(10):2548-2566, 2006. 10.1175/JAS3753.1.

  • [11] Robert Gall. The effects of released latent heat in growing baroclinic waves. J. Atmos. Sci., 33(9):1686-1701, 1976. 10.1175/1520-0469(1976)033<1686:TEORLH>2.0.CO;2.

  • [12] Balasubramanian Govindasamy and S. T. Garner. The equilibration of short baroclinic waves. J. Atmos. Sci., 54(24):2850-2871, 1997. 10.1175/1520-0469(1997)054<2850:TEOSBW>2.0.CO;2.

  • [13] Gerardo Hernández-Dueñas, Andrew J. Majda, Leslie M. Smith, and Samuel N. Stechmann. Minimal models for precipitating turbulent convection. J. Fluid Mech., 717:576-611, 2 2013. 10.1017/jfm.2012.597.

  • [14] Gerardo Hernández-Dueñas, Leslie M. Smith, and Samuel N. Stechmann. Stability and instability criteria for idealized precipitating hydrodynamics. J. Atmos. Sci., 72(6):2379-2393, 2015. 10.1175/JAS-D-14-0317.1.

  • [15] James R. Holton and Gregory J. Hakim. An Introduction to Dynamic Meteorology. Academic Press, Boston, MA, 2013.

  • [16] Frédéric Laliberté, Tiffany Shaw, and Olivier Pauluis. Moist recirculation and water vapor transport on dry isentropes. J. Atmos. Sci., 69(3):875-890, 2012. 10.1175/JAS-D-11-0124.1.

  • [17] Julien Lambaerts, Guillaume Lapeyre, and Vladimir Zeitlin. Moist versus dry baroclinic instability in a simpliffed two-layer atmospheric modelwith condensation and latent heat release. J. Atmos. Sci., 69(4):1405-1426, 2012. 10.1175/JAS-D-11-0205.1.

  • [18] G. Lapeyre and I. M. Held. The role of moisture in the dynamics and energetics of turbulent baroclinic eddies. J. Atmos. Sci., 61(14):1693-1710, 2004. 10.1175/1520-0469(2004)061<1693:TROMIT>2.0.CO;2.

  • [19] Mankin Mak. On moist quasi-geostrophic baroclinic instability. J. Atmos. Sci., 39(9):2028-2037, 1982. 10.1175/1520- 0469(1982)039<2028:OMQGBI>2.0.CO;2.

  • [20] John Marshall and R. Alan Plumb. Atmosphere, Ocean, and Climate Dynamics: An Introductory Text. Academic Press, Boston, MA, 2007.

  • [21] Joy M. Monteiro and Jai Sukhatme. Quasi-geostrophic dynamics in the presence of moisture gradients. Quart. J. Roy. Meteor. Soc., 142(694):187-195, 2016. 10.1002/qj.2644.

  • [22] Paul A. O’Gorman. The effective static stability experienced by eddies in a moist atmosphere. J. Atmos. Sci., 68(1):75-90, 2011. 10.1175/2010JAS3537.1.

  • [23] Olivier Pauluis, Arnaud Czaja, and Robert Korty. The global atmospheric circulation on moist isentropes. Science, 321(5892): 1075-1078, 2008. 10.1126/science.1159649.

  • [24] Joseph Pedlosky. Geophysical Fluid Dynamics. Springer-Verlag, New York, NY, 1987.

  • [25] J. P. Peixoto and A. H. Oort. Physics of Climate. American Institute of Physics, New York, NY, 1992.

  • [26] R. Richiardone and F. Giusti. On the stability criterion in a saturated atmosphere. J. Atmos. Sci., 58(14):2013-2017, 2001. 10.1175/1520-0469(2001)058<2013:OTSCIA>2.0.CO;2.

  • [27] Leslie M. Smith and Samuel N. Stechmann. Precipitating quasi-geostrophic equations and potential vorticity inversion with phase changes. 2017. submitted.

  • [28] Kevin E. Trenberth and Julie M. Caron. Estimates of meridional atmosphere and ocean heat transports. J. Climate, 14(16): 3433-3443, 2001. 10.1175/1520-0442(2001)014<3433:EOMAAO>2.0.CO;2.

  • [29] Kevin E. Trenberth and David P. Stepaniak. Covariability of components of poleward atmospheric energy transports on seasonal and interannual timescales. J. Climate, 16(22):3691-3705, 2003. 10.1175/1520-0442(2003)016<3691:COCOPA>2.0.CO;2.

  • [30] G. K. Vallis. Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, Cambridge, U.K., 2006.

  • [31] Bin Wang and Albert Barcilon. Moist stability of a baroclinic zonal flow with conditionally unstable stratiffcation. J. Atmos. Sci., 43(7):705-719, 1986. 10.1175/1520-0469(1986)043<0705:MSOABZ>2.0.CO;2.

OPEN ACCESS

Journal + Issues

Search