A Theory for the Response of Tropical Moist Convection to Mechanical Orographic Forcing

Quentin Nicolas aDepartment of Earth and Planetary Science, University of California, Berkeley, Berkeley, California

Search for other papers by Quentin Nicolas in
Current site
Google Scholar
PubMed
Close
https://orcid.org/0000-0002-4116-973X
and
William R. Boos aDepartment of Earth and Planetary Science, University of California, Berkeley, Berkeley, California
bClimate and Ecosystem Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California

Search for other papers by William R. Boos in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Spatial patterns of tropical rainfall are strongly influenced by mountains. Although theories for precipitation induced by convectively stable upslope ascent exist for the midlatitudes, these do not represent the interaction of moist convection with orographic forcing. Here, we present a theory for convective precipitation produced by the mechanical interaction of a tropical ridge with a basic-state horizontal wind. Deviations from this basic state are represented as the sum of a “dry” perturbation, due to the stationary orographic gravity wave, and a “moist” perturbation that carries the convective response. The moist component dynamics are subject to the weak temperature gradient approximation; they are forced by the dry mode’s influence on lower-tropospheric moisture and temperature. Analytical solutions provide estimates of the precipitation distribution, including peak precipitation, upstream extent, and rain shadow extent. The theory can be used with several degrees of complexity depending on the technique used to compute the dry mode, which can be drawn from linear mountain wave theory or full numerical simulations. To evaluate the theory, we use a set of convection-permitting simulations with a flow-perpendicular ridge in a long channel. The theory makes a good prediction for the cross-slope precipitation profile, indicating that the organization of convective rain by orography can be quantitatively understood by considering the effect of stationary orographic gravity waves on a lower-tropospheric convective quasi-equilibrium state.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Quentin Nicolas, qnicolas@berkeley.edu

Abstract

Spatial patterns of tropical rainfall are strongly influenced by mountains. Although theories for precipitation induced by convectively stable upslope ascent exist for the midlatitudes, these do not represent the interaction of moist convection with orographic forcing. Here, we present a theory for convective precipitation produced by the mechanical interaction of a tropical ridge with a basic-state horizontal wind. Deviations from this basic state are represented as the sum of a “dry” perturbation, due to the stationary orographic gravity wave, and a “moist” perturbation that carries the convective response. The moist component dynamics are subject to the weak temperature gradient approximation; they are forced by the dry mode’s influence on lower-tropospheric moisture and temperature. Analytical solutions provide estimates of the precipitation distribution, including peak precipitation, upstream extent, and rain shadow extent. The theory can be used with several degrees of complexity depending on the technique used to compute the dry mode, which can be drawn from linear mountain wave theory or full numerical simulations. To evaluate the theory, we use a set of convection-permitting simulations with a flow-perpendicular ridge in a long channel. The theory makes a good prediction for the cross-slope precipitation profile, indicating that the organization of convective rain by orography can be quantitatively understood by considering the effect of stationary orographic gravity waves on a lower-tropospheric convective quasi-equilibrium state.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Quentin Nicolas, qnicolas@berkeley.edu
Save
  • Abramowitz, M., and I. A. Stegun, 1964: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications, 1046 pp.

    • Crossref
    • Export Citation
  • Ahmed, F., Á. F. Adames, and J. D. Neelin, 2020: Deep convective adjustment of temperature and moisture. J. Atmos. Sci., 77, 21632186, https://doi.org/10.1175/JAS-D-19-0227.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Arakawa, A., and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large-scale environment, part I. J. Atmos. Sci., 31, 674701, https://doi.org/10.1175/1520-0469(1974)031<0674:IOACCE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Biasutti, M., S. E. Yuter, C. D. Burleyson, and A. H. Sobel, 2012: Very high resolution rainfall patterns measured by TRMM Precipitation Radar: Seasonal and diurnal cycles. Climate Dyn., 39, 239258, https://doi.org/10.1007/s00382-011-1146-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brown, R. G., and C. S. Bretherton, 1997: A test of the strict quasi-equilibrium theory on long time and space scales. J. Atmos. Sci., 54, 624638, https://doi.org/10.1175/1520-0469(1997)054<0624:ATOTSQ>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cannon, D. J., D. J. Kirshbaum, and S. L. Gray, 2014: A mixed-phase bulk orographic precipitation model with embedded convection. Quart. J. Roy. Meteor. Soc., 140, 19972012, https://doi.org/10.1002/qj.2269.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, S.-H., and Y.-L. Lin, 2005: Effects of moist Froude number and CAPE on a conditionally unstable flow over a mesoscale mountain ridge. J. Atmos. Sci., 62, 331350, https://doi.org/10.1175/JAS-3380.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chu, C.-M., and Y.-L. Lin, 2000: Effects of orography on the generation and propagation of mesoscale convective systems in a two-dimensional conditionally unstable flow. J. Atmos. Sci., 57, 38173837, https://doi.org/10.1175/1520-0469(2001)057<3817:EOOOTG>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Derbyshire, S. H., I. Beau, P. Bechtold, J.-Y. Grandpeix, J.-M. Piriou, J.-L. Redelsperger, and P. M. M. Soares, 2004: Sensitivity of moist convection to environmental humidity. Quart. J. Roy. Meteor. Soc., 130, 30553079, https://doi.org/10.1256/qj.03.130.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Derin, Y., and Coauthors, 2019: Evaluation of GPM-era global satellite precipitation products over multiple complex terrain regions. Remote Sens., 11, 2936, https://doi.org/10.3390/rs11242936.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Durran, D. R., 2003: Lee waves and mountain waves. Encyclopedia of Atmospheric Sciences, J. R. Holton, J. A. Curry, and J. A. Pyle, Eds., Academic Press, 1161–1170.

    • Crossref
    • Export Citation
  • Emanuel, K. A., 2007: Quasi-equilibrium dynamics of the tropical atmosphere. The Global Circulation of the Atmosphere, T. Schneider and A. H. Sobel, Eds., Princeton University Press, 186–218.

    • Crossref
    • Export Citation
  • Emanuel, K. A., J. D. Neelin, and C. S. Bretherton, 1994: On large-scale circulations in convecting atmospheres. Quart. J. Roy. Meteor. Soc., 120, 11111143, https://doi.org/10.1002/qj.49712051902.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Epifanio, C. C., and D. R. Durran, 2001: Three-dimensional effects in high-drag-state flows over long ridges. J. Atmos. Sci., 58, 10511065, https://doi.org/10.1175/1520-0469(2001)058<1051:TDEIHD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fuchs, Ž., and D. Raymond, 2002: Large-scale modes of a nonrotating atmosphere with water vapor and cloud–radiation feedbacks. J. Atmos. Sci., 59, 16691679, https://doi.org/10.1175/1520-0469(2002)059<1669:LSMOAN>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Haertel, P., W. R. Boos, and K. Straub, 2017: Origins of moist air in global Lagrangian simulations of the Madden–Julian oscillation. Atmosphere, 8, 158, https://doi.org/10.3390/atmos8090158.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 19992049, https://doi.org/10.1002/qj.3803.

  • Houze, R. A., Jr., 2012: Orographic effects on precipitating clouds. Rev. Geophys., 50, RG1001, https://doi.org/10.1029/2011RG000365.

  • Houze, R. A., Jr., K. L. Rasmussen, M. D. Zuluaga, and S. R. Brodzik, 2015: The variable nature of convection in the tropics and subtropics: A legacy of 16 years of the Tropical Rainfall Measuring Mission satellite. Rev. Geophys., 53, 9941021, https://doi.org/10.1002/2015RG000488.

    • Search Google Scholar
    • Export Citation
  • Huffman, G. J., and Coauthors, 2019: NASA Global Precipitation Measurement (GPM) Integrated Multi-satellitE Retrievals for GPM (IMERG). NASA Algorithm Theoretical Basis Doc., version 06, 38 pp.

    • Crossref
    • Export Citation
  • Iacono, M. J., J. S. Delamere, E. J. Mlawer, M. W. Shephard, S. A. Clough, and W. D. Collins, 2008: Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models. J. Geophys. Res., 113, D13103, https://doi.org/10.1029/2008JD009944.

    • Search Google Scholar
    • Export Citation
  • Janjić, Z. I., 2002: Nonsingular implementation of the Mellor–Yamada level 2.5 scheme in the NCEP Meso model. NCEP Office Note 437, 61 pp.

    • Crossref
    • Export Citation
  • Jiménez, P. A., J. Dudhia, J. F. González-Rouco, J. Navarro, J. P. Montávez, and E. García-Bustamante, 2012: A revised scheme for the WRF surface layer formulation. Mon. Wea. Rev., 140, 898918, https://doi.org/10.1175/MWR-D-11-00056.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., 2020: Numerical simulations of orographic convection across multiple gray zones. J. Atmos. Sci., 77, 33013320, https://doi.org/10.1175/JAS-D-20-0035.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., and R. B. Smith, 2009: Orographic precipitation in the tropics: Large-eddy simulations and theory. J. Atmos. Sci., 66, 25592578, https://doi.org/10.1175/2009JAS2990.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., B. Adler, N. Kalthoff, C. Barthlott, and S. Serafin, 2018: Moist orographic convection: Physical mechanisms and links to surface-exchange processes. Atmosphere, 9, 80, https://doi.org/10.3390/atmos9030080.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lalas, D. P., and F. Einaudi, 1973: On the stability of a moist atmosphere in the presence of a background wind. J. Atmos. Sci., 30, 795800, https://doi.org/10.1175/1520-0469(1973)030<0795:OTSOAM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lapeyre, G., and I. M. Held, 2004: The role of moisture in the dynamics and energetics of turbulent baroclinic eddies. J. Atmos. Sci., 61, 16931710, https://doi.org/10.1175/1520-0469(2004)061<1693:TROMIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Madden, R. A., and P. R. Julian, 1971: Detection of a 40–50 day oscillation in the zonal wind in the tropical Pacific. J. Atmos. Sci., 28, 702708, https://doi.org/10.1175/1520-0469(1971)028<0702:DOADOI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys., 20, 851875, https://doi.org/10.1029/RG020i004p00851.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miglietta, M. M., and R. Rotunno, 2009: Numerical simulations of conditionally unstable flows over a mountain ridge. J. Atmos. Sci., 66, 18651885, https://doi.org/10.1175/2009JAS2902.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miglietta, M. M., and R. Rotunno, 2012: Application of theory to simulations of observed cases of orographically forced convective rainfall. Mon. Wea. Rev., 140, 30393053, https://doi.org/10.1175/MWR-D-11-00253.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miglietta, M. M., and R. Rotunno, 2014: Numerical simulations of sheared conditionally unstable flows over a mountain ridge. J. Atmos. Sci., 71, 17471762, https://doi.org/10.1175/JAS-D-13-0297.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Neelin, J. D., and I. M. Held, 1987: Modeling tropical convergence based on the moist static energy budget. Mon. Wea. Rev., 115, 312, https://doi.org/10.1175/1520-0493(1987)115<0003:MTCBOT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Neelin, J. D., and N. Zeng, 2000: A quasi-equilibrium tropical circulation model—Formulation. J. Atmos. Sci., 57, 17411766, https://doi.org/10.1175/1520-0469(2000)057<1741:AQETCM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Neiman, P. J., M. Hughes, B. J. Moore, F. M. Ralph, and E. M. Sukovich, 2013: Sierra barrier jets, atmospheric rivers, and precipitation characteristics in Northern California: A composite perspective based on a network of wind profilers. Mon. Wea. Rev., 141, 42114233, https://doi.org/10.1175/MWR-D-13-00112.1.

    • Search Google Scholar
    • Export Citation
  • Nicolas, Q., 2022: qnicolas/orographicConvectionTheory: Initial release, version 1.0.0. Zenodo, https://doi.org/10.5281/zenodo.6578809.

  • Nie, J., W. R. Boos, and Z. Kuang, 2010: Observational evaluation of a convective quasi-equilibrium view of monsoons. J. Climate, 23, 44164428, https://doi.org/10.1175/2010JCLI3505.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Niu, G.-Y., and Coauthors, 2011: The community Noah land surface model with multiparameterization options (Noah-MP): 1. Model description and evaluation with local-scale measurements. J. Geophys. Res., 116, D12109, https://doi.org/10.1029/2010JD015139.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • O’Gorman, P. A., 2011: The effective static stability experienced by eddies in a moist atmosphere. J. Atmos. Sci., 68, 7590, https://doi.org/10.1175/2010JAS3537.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pierrehumbert, R. T., and B. Wyman, 1985: Upstream effects of mesoscale mountains. J. Atmos. Sci., 42, 9771003, https://doi.org/10.1175/1520-0469(1985)042<0977:UEOMM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Queney, P., 1948: The problem of air flow over mountains: A summary of theoretical studies. Bull. Amer. Meteor. Soc., 29, 1626, https://doi.org/10.1175/1520-0477-29.1.16.

    • Search Google Scholar
    • Export Citation
  • Ramesh, N., Q. Nicolas, and W. R. Boos, 2021: The globally coherent pattern of autumn monsoon precipitation. J. Climate, 34, 56875705, https://doi.org/10.1175/JCLI-D-20-0740.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., S. L. Sessions, A. H. Sobel, and Ž. Fuchs, 2009: The mechanics of gross moist stability. J. Adv. Model. Earth Syst., 1, (3), https://doi.org/10.3894/JAMES.2009.1.9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., Ž. Fuchs, S. Gjorgjievska, and S. Sessions, 2015: Balanced dynamics and convection in the tropical troposphere. J. Adv. Model. Earth Syst., 7, 10931116, https://doi.org/10.1002/2015MS000467.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Roe, G. H., 2005: Orographic precipitation. Annu. Rev. Earth Planet. Sci., 33, 645671, https://doi.org/10.1146/annurev.earth.33.092203.122541.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Satoh, M., B. Stevens, F. Judt, M. Khairoutdinov, S.-J. Lin, W. M. Putman, and P. Düben, 2019: Global cloud-resolving models. Curr. Climate Change Rep., 5, 172184, https://doi.org/10.1007/s40641-019-00131-0.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2019: A description of the Advanced Research WRF Model version 4. NCAR Tech. Note NCAR/TN-556+STR, 145 pp., https://doi.org/10.5065/1dfh-6p97.

  • Smith, R. B., 1979: The influence of mountains on the atmosphere. Advances in Geophysics, Vol. 21, Academic Press, 87230, https://doi.org/10.1016/S0065-2687(08)60262-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, R. B., 1989: Hydrostatic airflow over mountains. Advances in Geophysics, Vol. 31, Academic Press, 141, https://doi.org/10.1016/S0065-2687(08)60052-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, R. B., and I. Barstad, 2004: A linear theory of orographic precipitation. J. Atmos. Sci., 61, 13771391, https://doi.org/10.1175/1520-0469(2004)061<1377:ALTOOP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., J. Nilsson, and L. M. Polvani, 2001: The weak temperature gradient approximation and balanced tropical moisture waves. J. Atmos. Sci., 58, 36503665, https://doi.org/10.1175/1520-0469(2001)058<3650:TWTGAA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tan, J., C. Jakob, and T. P. Lane, 2013: On the identification of the large-scale properties of tropical convection using cloud regimes. J. Climate, 26, 66186632, https://doi.org/10.1175/JCLI-D-12-00624.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, G., P. R. Field, R. M. Rasmussen, and W. D. Hall, 2008: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part II: Implementation of a new snow parameterization. Mon. Wea. Rev., 136, 50955115, https://doi.org/10.1175/2008MWR2387.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tulich, S. N., and B. E. Mapes, 2010: Transient environmental sensitivities of explicitly simulated tropical convection. J. Atmos. Sci., 67, 923940, https://doi.org/10.1175/2009JAS3277.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, S., and A. H. Sobel, 2017: Factors controlling rain on small tropical islands: Diurnal cycle, large-scale wind speed, and topography. J. Atmos. Sci., 74, 35153532, https://doi.org/10.1175/JAS-D-16-0344.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wing, A. A., and T. W. Cronin, 2016: Self-aggregation of convection in long channel geometry. Quart. J. Roy. Meteor. Soc., 142, 115, https://doi.org/10.1002/qj.2628.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xie, S.-P., H. Xu, N. H. Saji, Y. Wang, and W. T. Liu, 2006: Role of narrow mountains in large scale organization of Asian monsoon convection. J. Climate, 19, 34203429, https://doi.org/10.1175/JCLI3777.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, Z.-L., and Coauthors, 2011: The community Noah land surface model with multiparameterization options (Noah-MP): 2. Evaluation over global river basins. J. Geophys. Res., 116, D12110, https://doi.org/10.1029/2010JD015140.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yu, J.-Y., C. Chou, and J. D. Neelin, 1998: Estimating the gross moist stability of the tropical atmosphere. J. Atmos. Sci., 55, 13541372, https://doi.org/10.1175/1520-0469(1998)055<1354:ETGMSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zhang, G., and R. B. Smith, 2018: Numerical study of physical processes controlling summer precipitation over the Western Ghats region. J. Climate, 31, 30993115, https://doi.org/10.1175/JCLI-D-17-0002.1.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 455 189 0
Full Text Views 264 124 18
PDF Downloads 293 125 18