Brief Overview of the Global Atmosphere

Transcription

1 Brief Overview of the Global Atmosphere Images on pages 3, 5 through 9, 19, 77 through 80 and 90 are copyrighted by Academic Press, NY, The images are in a chapter entitled "Quasi-equilibrium thinking" (author is Kerry Emanuel) that appears in the book entitled General circulation model development: past, present and future. Edited by D. Randall. ISBN: Used with permission. Images on pages 21, 57-58, and 69 are copyrighted by Oxford, NY: Oxford University Press, Book title is Divine wind: the history and science of hurricanes. ISBN: Used with permission.

2 Atmospheric Composition Gas Name Chemical Formula Percent Volume Nitrogen N % Oxygen O % *Water H2O 0 to 4% Argon Ar 0.93% *Carbon Dioxide CO % Neon Ne % Helium He % *Methane CH % Hydrogen H % *Nitrous Oxide N2O % *Ozone O % * variable gases

3 See figure of Humidity Profiles -- Annual In book: Global Physical Climatology ISBN: Author: Dennis L. Hartmann Publisher: Academic Press Number of pages: 411

4 Mesopause Thermosphere Altitude (meters) Mesosphere Stratopause Stratosphere Tropopause Troposphere Temperature o C Figure by MIT OCW.

5 In book: Global Physical Climatology ISBN: Author: Dennis L. Hartmann Publisher: Academic Press Number of pages: 411 See Figure 1.6 and Figure 1.7

6

7 See figure Temperature vs Latitude In book: Global Physical Climatology ISBN: Author: Dennis L. Hartmann Publisher: Academic Press Number of pages: 411

8 See figure of seasonal variation of solar radiation In book: Global Physical Climatology ISBN: Author: Dennis L. Hartmann Publisher: Academic Press Number of pages: 411

9 In book: Global Physical Climatology ISBN: Author: Dennis L. Hartmann Publisher: Academic Press Number of pages: 411 See figure Insolation vs Latitude

10 A One-Dimensional Description of the Tropical Atmosphere

11 Mesopause Thermosphere Altitude (meters) Mesosphere Stratopause Stratosphere Tropopause Troposphere Temperature o C Figure by MIT OCW.

12 Elements of Thermal Balance: Solar Radiation Luminosity: 3.9 x J s -1 = 6.4 x 10 7 Wm -2 at top of photosphere Mean distance from earth: 1.5 x m Flux density at mean radius of earth L S 0 = π d Wm 2

13

14 Disposition of Solar Radiation:

15 Terrestrial Radiation: Effective emission temperature: S σt e 4 a p Earth: T = 255K = 18 C e Observed average surface temperature = 288K = 15 C

16 Highly Reduced Model Transparent to solar radiation Opaque to infrared radiation Blackbody emission from surface and each layer

17 Radiative Equilibrium: Top of Atmosphere: Surface: S σt = a T A 4 p = σ e T = A T S σ 0 T = σt + ( 1 a ) = 2σT s A p e 1 4 T = 2 T = 303K s e e

18 Surface temperature too large because: Real atmosphere is not opaque Heat transported by convection as well as by radiation

19 In book: Global Physical Climatology ISBN: Author: Dennis L. Hartmann Publisher: Academic Press Number of pages: 411 See diagram of Energy Balance

20 Principal Atmospheric Absorbers H 2 O: Bent triatomic, with permanent dipole moment and pure rotational bands as well as rotation-vibration transitions O 3 : Like water, but also involved in photodissociation CO 2 : No permanent dipole moment, so no pure rotational transitions, but temporary dipole during vibrational transitions Other gases: N 2 O, CH 4

21

22 Radiative Equilibrium Equilibrium state of atmosphere and surface in the absence of non-radiative enthalpy fluxes Radiative heating drives actual state toward state of radiative equilibrium

23 Extended Layer Models TOA: σt = σt T = T e 2 Middle Layer : 2σT = σt + σt = σt + σt Surface : σt = σt + σt s e s s e s 3 e 1 2 e T = T T = T e

24 Effects of emissivity<1

25 Full calculation of radiative equilibrium:

26 Problems with radiative equilibrium solution: Too hot at and near surface Too cold at a near tropopause Lapse rate of temperature too large in the troposphere (But stratosphere temperature close to observed)

27 Missing ingredient: Convection As important as radiation in transporting enthalpy in the vertical Also controls distribution of water vapor and clouds, the two most important constituents in radiative transfer

28 When is a fluid unstable to convection? Pressure and hydrostatic equilibrium Buoyancy Stability

29 Hydrostatic equilibrium: Weight : gρδxδyδz Pressure : pδxδy p + δ p δxδy ( ) dw F = MA: ρδxδyδz = gρδxδyδz δ pδxδy dt dw p = g α, α = 1 = specific volume dt z ρ

30 Pressure distribution in atmosphere at rest: RT R* Ideal gas : α =, R p m 1 p ln( p) g Hydrostatic : = = p z z RT z : H RT Isothermal case p = p0e, H = " scale height " g Earth: H~ 8 Km

31 Buoyancy: Weight : gρ δ xδyδz b Pressure : pδxδy p + δ p δxδy ( ) dw F = MA: ρbδxδyδz = gρbδ xδyδz δ pδxδy dt dw p p = g α g b but = dt z z αe dw α g b αe = B dt α e

32 Buoyancy and Entropy Specific Volume: Specific Entropy: s α = 1 ρ α = α( ps, ) Maxwell α T : = s p p s α T δα δ δs ( ) p = s = s p p s ( δα ) p g T T B = g = δ s= δs Γδs α α p z s s

33 The adiabatic lapse rate: First Law of Thermodynamics : dsrev dt d Q& α = T = cv + p dt dt dt dt d( α p) dp = cv + α dt dt dt dt dp = ( cv + R) α dt dt dt dp = cp α dt dt Adiabatic : c dt αdp = 0 p Hydrostatic : c dt + gdz = 0 ( dt ) = g Γ dz c s p p d

34 Γ= g cp Earth s atmosphere: Γ= 1K 100 m

35 Model Aircraft Measurements (Renno and Williams, 1995)

36 Radiative equilibrium is unstable in the troposphere Re-calculate equilibrium assuming that tropospheric stability is rendered neutral by convection: Radiative-Convective Equilibrium

37 Better, but still too hot at surface, too cold at tropopause

38 Above a thin boundary layer, most atmospheric convection involved phase change of water: Moist Convection

39 Moist Convection Significant heating owing to phase changes of water Redistribution of water vapor most important greenhouse gas Significant contributor to stratiform cloudiness albedo and longwave trapping

40 Water Variables Mass concentration of water vapor (specific humidity): q M HO 2 M Vapor pressure (partial pressure of water vapor): e C-C: air Saturation vapor pressure: e* e* = 6.112hPae ( T ) T + 30 Relative Humidity: H e e*

41 The Saturation Specific Ideal Gas Law: q Humidity ρv ρ = = p R* T = ρ m R* T e= ρv m mv e mp me* q* = v m p v

42 Phase Equilibria

43 Bringing Air to Saturation e = qp m m v e* = e*( T) 1. Increase q (or p) 2. Decrease e* (T)

44 When Saturation Occurs Heterogeneous Nucleation Supersaturations very small in atmosphere Drop size distribution sensitive to size distribution of cloud condensation nuclei

45

46 ICE NUCLEATION PROBLEMATIC Cloud top temperature ( o C) Figure by MIT OCW. Percentage of clouds with ice particle concentrations above detectable level

47 Precipitation Formation: Stochastic coalescence (sensitive to drop size distributions) Bergeron-Findeisen Process Strongly nonlinear function of cloud water concentration Time scale of precipitation formation ~10-30 minutes

48 Stability No simple criterion based on entropy: T p s = c ln R ln T p d p d 0 0 α = α s, ( ) T p q s = c ln R ln + L qr ln( H ) p T d p vt v 0 0 α = α d p ( s, pq, ) t

49 Virtual Temperature and Density Temperature Assume all condensed water falls at terminal velocity α = V a + V M + M + M c d v c pv = nr* T V a R* T Md = + p md M m v v,

50 m d 1 M d 1 i M m i i V RT M d a = d + p M v, ε where ε m v m d R d R* m d

51 ( q ) q V + V R T q α = = 1 t + 1 M M M p ε q RT ( ) d 1 q q t + p ε M v + Mc Mv qt, q M M a c d c a d v c c c Density temperature: ρ ρ ( q ) ε T T q + ρ 1 t α = R T d p ρ

52 Trick: Define a saturation entropy, s* : ( ) ( s*, pq, ) t s* st, pq, * α = α We can add an arbitrary function of q t to s* such that α α ( s*', p)

53

54 Stability Assessment using Tephigrams: Pressure (mb) Temperature (C)

55 Stability Assessment using Tephigrams: Convective Available Potential Energy (CAPE): CAPE p i n ( α α ) i p p e pi = p d p dp ( ) ln( ) ρ ρ R T T d p e

56 Other Stability Diagrams:

57 Air-Mass Showers:

58 See Figure 15 and 16 In Journal: Byers Braham. Journal of Meteorology 5 (1948): 71-86

59 Tropical Soundings

60 Annual Mean Kapingamoronga:

61

62

63

64

65

66

67

68 Radiative-Moist Convective Equilibrium

69 Precipitating Convection favors Widely Spaced Clouds (Bjerknes, 1938)

70 Properties: Convective updrafts widely spaced Surface enthalpy flux equal to vertically integrated radiative cooling M ct p θ θ = Q& z Precipitation = Evaporation = Radiative Cooling Radiation and convection highly interactive

71 Manabe and Strickler 1964 calculation:

72 Time (days) Precipitation (mm/day)

73

74

75

76

77 See figures on pages In book: General Circulation Model Development : Past, Present, and Future, Vol. 70 ISBN: Author: David A. Randall (Editor) Publisher: Academic Press Number of pages: 416

78

79

80

81 Recovery from mid-level specific humidity perturbation Specific humidity perturbation (g/kg), from to P (mb) Time (days)

82 T v Perturbation, from to P (mb) Time (days)

83

84 Robe and Emanuel, J. Atmos. Sci., 1996

85

86

87 Islam et al. Predictability Experiments

88

89

90 See figure on page 238 In book: General Circulation Model Development : Past, Present, and Future, Vol. 70 ISBN: Author: David A. Randall (Editor) Publisher: Academic Press Number of pages: 416

91

92 Frequency histogram of rawindsonde relative humidities from 1600 ascents at the tropical Pacific islands of Yap, Koror, Ponape and Majuro, January-May, Spencer and Braswell, Bull. Amer. Meteor. Soc., 1997.

93 The Three-Dimensional Circulation

94 What causes lateral enthalpy transport by atmosphere? 1: Large-scale, quasi-steady overturning motion in the Tropics, 2: Eddies with horizontal dimensions of ~ 3000 km in middle and high latitudes

95 Observed Characteristics of the Time Mean Tropical Atmosphere Monthly and seasonal means Zonal means

96 Objective Analysis Provides Best Guess as to the State of the Atmosphere 1. Start with First Guess Analysis 2. Ingest Data -Radiosondes -Surface Observations -Ship Reports and Buoy Observations -Aircraft Observations -Satellite Observations 3. Data Assimilation -Blend data to produce an initialized (balanced) analysis (or not...) 4. Run General Circulation Model to Obtain next First Guess -A six hour cycle is typical - Asynoptic Observations can also be assimilated.

97 Vorticity ζ = r V = v x u y Divergence D = r V = u x + v y Streamfunction 2 ψ = ζ Velocity Potential 2 χ = D

98 u ψ = ψ y Non-divergent (Rotational) Wind v ψ = ψ x u χ = χ x Divergent Wind v χ = χ y