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The General Circulation of the Atmosphere and Climate Change

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The General Circulation of the Atmosphere and Climate Change 12.812: THE GENERAL CIRCULATION OF THE ATMOSPHERE AND CLIMATE CHANGE Paul O'Gorman April 9, 2010 Contents 1 Introduction 7 1.1 Lorenz's view . 7 1.2 The general circulation: 1735 (Hadley) . 7 1.3 The general circulation: 1857 (Thompson) . 7 1.4 The general circulation: 1980-2001 (ERA40) . 7 1.5 The general circulation: recent trends (1980-2005) . 8 1.6 Course aim . 8 2 Some mathematical machinery 9 2.1 Transient and Stationary eddies . 9 2.2 The Dynamical Equations . 12 2.2.1 Coordinates . 12 2.2.2 Continuity equation . 12 2.2.3 Momentum equations (in p coordinates) . 13 2.2.4 Thermodynamic equation . 14 2.2.5 Water vapor . 14 1 Contents 3 Observed mean state of the atmosphere 15 3.1 Mass . 15 3.1.1 Geopotential height at 1000 hPa . 15 3.1.2 Zonal mean SLP . 17 3.1.3 Seasonal cycle of mass . 17 3.2 Thermal structure . 18 3.2.1 Insolation: daily-mean and TOA . 18 3.2.2 Surface air temperature . 18 3.2.3 Latitude-σ plots of temperature . 18 3.2.4 Potential temperature . 21 3.2.5 Static stability . 21 3.2.6 Effects of moisture . 24 3.2.7 Moist static stability . 24 3.2.8 Meridional temperature gradient . 25 3.2.9 Temperature variability . 26 3.2.10 Theories for the thermal structure . 26 3.3 Mean state of the circulation . 26 3.3.1 Surface winds and geopotential height . 27 3.3.2 Upper-level flow . 27 3.3.3 200 hPa u (CDC) . 27 3.3.4 Latitude-σ u (era40) . 27 3.3.5 Zonal wind shear @u=@z ..................... 30 3.3.6 Mean meridional flow [v] (era40) . 30 3.3.7 Vertical motion is σ coords, [dσ=dt] (era40) . 31 3.3.8 Definition of mean meridional streamfunction . 31 3.3.9 Mean meridional streamfunction from era40 data . 32 3.3.10 Mean meridional streamfunction from era40 data . 35 3.3.11 Variability of the circulation . 35 3.3.12 Observed variability of the circulation . 37 3.3.13 Spectral decomposition . 38 3.3.14 The energy spectrum in spherical coordinates . 39 3.4 Water vapor and the hydrological cycle . 41 3.4.1 Fig. 3.16: GPCP (Global Precipitation Climatology Project) mean precipitation rate vs. latitude and longitude in mm/day 41 3.4.2 Fig. 3.17: time and zonal mean specific humidity (ERA40) . 41 3.4.3 Fig. 3.18: time and zonal mean relative humidity . 41 4 Energetics 45 4.1 Forms of energy . 45 4.1.1 Total potential energy . 45 4.1.2 Speed of sound . 46 4.1.3 Magnitude of kinetic energy . 46 4.1.4 Fig 13.3: Meridional profiles of energy components . 47 4.2 Lagrangian rates of change of energy for air parcels . 47 4.2.1 Potential . 47 2 Contents 4.2.2 Internal . 47 4.2.3 Kinetic energy . 48 4.2.4 Latent heat . 48 4.2.5 Conversion between different forms . 49 4.2.6 Total energy . 49 4.3 Observed heating rates . 50 4.3.1 Radiation . 50 4.3.2 Diabatic heating . 51 4.4 Energy budgets in Eulerian reference frame . 51 4.4.1 Sensible heat . 51 4.4.2 Latent heat . 52 4.4.3 Kinetic energy . 52 4.4.4 Total energy . 52 4.4.5 Connection to moist static energy . 53 4.4.6 Average budgets . 53 4.5 Fluxes of energy poleward . 54 4.5.1 Fig. 13.4: Transient sensible heat . 54 4.5.2 Fig. 13.5: Components of sensible heat flux vs. lat-σ . 55 4.5.3 Fig. 12.11: Latent heat flux . 55 4.5.4 Fig. 12.12 . 55 4.5.5 Fig. 13.6: Northward sensible flux vs. latitude . 55 4.5.6 Fig. 13.7: Potential energy flux . 55 4.5.7 Fig. 13.8, 13.9: Transport of kinetic energy . 55 4.5.8 Fig. 13.10, 13.11: Total energy flux . 56 4.5.9 Fig. 13.12: Divergence of the poleward energy flux . 56 4.5.10 Comparison of different components of the total energy flux . 56 4.5.11 Division into monthly and sub-monthly . 56 4.5.12 Ocean { atmosphere division . 56 4.6 Vertical transport of energy . 56 4.6.1 Fig. 13.15: annual . 57 4.6.2 Fig. 13.15: DJF and JJA . 57 5 Forcing of the zonal mean circulation 59 5.1 Introduction . 59 5.2 Basic equations in spherical coordinates (λ, φ, p; t) . 59 5.3 Eliassen-Palm flux . 60 5.3.1 An interesting special case: steady, adiabatic, non-dissipative flow ................................ 60 5.3.2 Proof of EP theorem . 61 5.3.3 Consequence: The non-acceleration theorem . 62 5.3.4 Steady (or stationary mean) motion with heat and friction . 62 5.4 Modified momentum and energy equations . 62 5.5 Forcing of the mean meridional circulation . 63 5.6 Transformed Eulerian Mean . 64 5.7 Example of EP flux diagram . 64 3 Contents 6 Available energy and the atmospheric energy cycle 67 6.1 Heat engine . 67 6.2 Available potential energy (Lorenz, 1955, 1978, 1979) . 67 6.2.1 Definition . 67 6.2.2 What properties does the reference state have? . 68 6.3 Computing AP E ............................. 69 6.3.1 Exact formula for dry AP E ................... 69 6.3.2 Approximate form: AP E in terms of pressure variance along isentropes . 70 6.3.3 AP E in terms of temperature variance on constant pressure surfaces . 71 6.3.4 What fraction of potential energy is available? . 72 6.4 Decomposing AP E into eddy and mean components . 73 6.4.1 Aside: incompressible limit of ideal gas . 74 6.4.2 Time evolution of kinetic and available potential energy . 74 6.5 Observed energy cycle . 79 6.5.1 Fig. 14.4: Contributions to AP E and KE vs. latitude . 79 6.5.2 Fig. 14.6: Contributions to energy conversions vs. latitude . 79 6.5.3 Horizontal spectral distributions of energy conversions . 79 6.5.4 Global energy cycle . 80 6.5.5 Table 14.1, Peixoto and Oort . 81 7 Entropy budget of the atmosphere 83 8 Hydrological cycle 85 8.1 Basics . 85 8.1.1 Some definitions . 85 8.1.2 Clausius-Clapeyron relation . 85 8.1.3 Some global values . 86 8.2 Observed vapor transport . 88 8.2.1 Fig. 12.7 and 12.9: Vertically integrated zonal transport of water vapor . 89 8.2.2 Fig. 12.10, 12.11: Meridional flux of water vapor . 89 8.2.3 Fig. 12.12: Seasonality of meridional water vapor fluxes . 89 8.2.4 Fig. 12.14: Vertical flux of water vapor (and condensate) . 89 8.2.5 Streamfunction for water vapor and condensate . 89 8.2.6 Distribution of E − P = r · Q . 90 8.2.7 Fig. 12.7: Streamlines vs. lat. and lon. of the water vapor flux 90 8.3 Estimates of precipitation and evaporation rates . 91 8.3.1 Precipitation . 91 8.3.2 Evaporation . 92 8.4 Note on surface energy budget . 93 8.5 Importance of upper-tropospheric water vapor . 93 8.6 Last-saturation analysis of the mean relative humidity field . 94 8.7 Water vapor budget in isentropic coordinates . 97 4 Contents 9 Angular momentum of the atmosphere 99 9.1 Conservation of angular momentum . 99 9.2 Variations in atmospheric angular momentum . 100 9.3 Surface stress and mountain torque . 101 9.4 Torques and meridional transport of angular momentum . 103 9.5 Observed angular momentum transport . 104 Bibliography 107 5 1 Introduction 1.1 Lorenz's view During the past three centuries, the prevailing ideas about the general circulation of the earth's atmosphere have evolved in a stepwise manner. Early in each step, a new theoretical idea is formulated. Late in each step, the idea gains general acceptance, but, more or less concurrently, new observations show that the idea is wrong. (Lorenz, 1983) 1.2 The general circulation: 1735 (Hadley) See sketches in Lorenz (1983) • Zonal Coriolis force • Surface easterly and westerly winds • Angular momentum balance • Equatorward drift in midlatitudes! 1.3 The general circulation: 1857 (Thompson) • Meridional Coriolis force • Indirect cell • Also Ferrel 1859 • 1900 cloud study: no upper level poleward flow in extratropics! ... more cells(!), then angular momentum and heat transport by eddies (Jeffries 1926, Starr 1948, and.
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