Thermodynamics of convection in the moist atmosphere B. Legras, LMD/ENS http://www.lmd.ens.fr/legras 1 References recommanded books: - Fundamentals of Atmospheric Physics, M.L. Salby, Academic Press - Cloud dynamics, R.A. Houze, Academic Press Other more advanced books (plus avancés): - Thermodynamics of Atmospheres and Oceans, J.A. Curry & P.J. Webster - Atmospheric Convection, K.A. Emanuel, Oxford Univ. Press Papers - Bolton, The computation of equivalent potential temperature, MWR, 108, 1046- 1053, 1980 2 OUTLINE OF FIRST PART ● Introduction. Distribution of clouds and atmospheric circulation ● Atmospheric stratification. Dry air thermodynamics and stability. ● Moist unsaturated thermodynamics. Virtual temperature. Boundary layer. ● Moist air thermodynamics and the generation of clouds. ● Equivalent potential temperature and potential instability. ● Pseudo-equivalent potential temperature and conditional instability ● CAPE, CIN and ● An example of large-scale cloud parameterization ● 3 Introduction. Distribution of clouds and atmospheric circulation 4 Large-scale organisation of clouds IR false color composite image, obtained par combined data from 5 Geostationary satellites 22/09/2005 18:00TU (GOES-10 (135O), GOES-12 (75O), METEOSAT-7 (OE), METEOSAT-5 (63E), MTSAT (140E)) Cloud bands Cloud bands Cyclone Rita Clusters of convective clouds associated with mid- Cyclone Rita Clusters of convective clouds associated with mid- in the tropical region (15S – latitude in the tropical region (15S – latitude 15 N) perturbations 15 N) perturbations Subsidence zones: no Subsidence zones: no 5 Source: clouds, deserts clouds, deserts http://www.satmos.meteo.fr Distribution of relative humidity in the troposphere according to analysis of weather centers Courtesy of D. Jackson Detrainment of tropical convection Subsidence branch of the Hadley cell 6 Moistening by sloping motion associated with Rossby waves and baroclinic perturbations Wind and temperature at the tropopause Temperature minima at the tropical tropopause Subtropical jet winds associated with tropopause drop ERA-40 Atlas, 2005 B. Randell Isentropic surfaces crossing the tropopause in the subtropics Potential temperature 7 at the tropopause Cloud cover ISSCP data c comparison January-July 8 Beware of error in ERA-40 atlas. 200 HPa should be there ECMWF ERA-40 atlas Convection In the mid and high latitudes, poleward isentropic motion is accompanied by upward motion. In the tropic, vertical upward motion needs heating. 9 Development of an idealized baroclinic perturbation - - - - - = pression ―――― = température Cold front Warm front Air motion associated with a frontal system . 10 Visible channel Meteosat Water vapour channel Meteosat Although mixing and Descending dry air convective instability do occur during the development, the main ingredient is adiabatic Ascending moist baroclinic instability, air generating that is isentropic motion. clouds and 11 precipitations. Evaporative cooling Folkins et Martin, JAS, 2005 12 Cloud fraction according to GCI Cloud fraction according to CALIOP 18,5km 0.05% 0.5% Gettelman et al., JGR, 2002 However, convection hardly reaches the tropopause. Most 5% clouds detrain below 15 km. Only a very small fraction (<0,5% in all '' seasons) is reaching the tropopause. Liu and Zipser, JGR, 2005 13 Rosslow and Pearl, GRL, 2007 Fu et al, GRL, 2007 Fu et al, 2007 Atmospheric stratification Dry air thermodynamics and stability 14 Stratification and composition The atmosphere is stratified: ● Exponential decay of pressure and density from the ground to 100 km ● Several layers are distinguished from the temperature profile ● Troposphere from 0 to 12 km (18 km under the tropics) ● Stratosphere above up to 50 stratosphère km tropopause ● Mesosphere from 50 to90 km ● 90% of the mass under 20 km ● Standard density (à 1013 hPa et 273K): ρ=1,29 kg m -3 15 The troposphere and the stratosphere are separated by the tropopause 16 Composition of the atmosphere* Nitrogen N 2 0,7808 homogeneous Oxygen O 2 0,2095 homogeneous Water H 2O <0,030 highly variable Argon A 0,0093 homogeneous CO 2 385 ppmv homogeneous (quasi) Ozone O 3 10 ppmv stratosphere Methane CH 4 1,6 ppmv decay with z Nitrous oxide N 2O 350 ppbv decay with z CO 70 ppbv NO, CFC-11, CFC-12 < 0,3 ppbv *: composition is given 17 Mean molar mass M=28,96 g as volume mixing ratio Complementary note: Definition of mixing ratios The proportions of gases in the air are given as mass or volume mixing ratios. The reference is dry air (without water) with molar mass M =28,96 g and density d ρ . For a minor gas with molar mass M and density ρ, the mass mixing ratio is r = d m ρ/ρ . We may also use the volume mixing ratio defined as the ratio between the d gas partial pressure p to the dry air pressure p d, r v = p/p d. The relation between the two ratios is given by r v = r m M d/M. The volume mixing ratio indicates the proportion of minor gas as a number of molecules per molecule of dry air. When this proportion is very low, multiplicative factors are used and the mixing ratio is given in ppmv (part per million in volume ⇔ factor 10 6), ppbv (part per billion in volume ⇔ factor 10 9) or pptv (part per billion in volume ⇔ factor 10 12 ). Water only, which can reach r v=0.03 in tropical regions, is able to change significantly the air density. Other gases are in too small proportion to affect the density. Traditionally, the mass mixing ratio is used for the thermodynamic properties of moist air. Volume mixing ratios are mostly used in chemistry and transport studies. 18 The composition of the atmosphere in major components (N2, O2) varies little until 100 km. There are , however, strong variations among minor components (H2O, O3, ...) 19 Thermodynamics of dry air Ideal gas law p = ρ RT where R = 287 J kg -1 K -1 ● -1 -1 Ideal gas enthalpy H = C p T where C p = 1005 J kg K , heat capacity per unit mass at constant pressure. H depends only of the temperature ● At constant pressure, for quasi-static transform: δ Q = C p dT = dH = T dS ( S: entropy) ● More generally δ Q = T dS = dU + p d(1/ρ)- 1/ρ dp ) = C p dT - 1/ρ dp = C p dT - RT/p dp = C p (T/θ dθ where θ is the potential temperature κ θ = T(p 0/p) avec κ = R/C p=2/7 20 Hydrostatic law and stratification In the vertical, the air is essentially in hydrostatic equilibrium: by averaging over aan horizontal area of a few km 2, verical speed is of the order of a few cm/s and vertical acceleration is negligeable in front of gravity ● Hydrostatic law dp/dz + ρ g = 0 Combining with ideal gas law, we obtain dp/p = -g/RT dz and, for a uniform temperature (gross simplification, valid within 20%) T 0 = 255 K , we obtain p = p 0 exp (-z/H) with H = RT 0/g ≈ 7,4 km, hight scale . Pressure decreases by half every 5 km (because H ln(2) ≈ 5 km) 21 The vertical profile of temperature cannot be explained with simple laws. It depends on vertical mixing and heat transport and on the radiative emissions and absorption. ● At the ground, variations of 100 K but 50 K on the average between pole and equator ● Temperatures in the tropopause region are less varying but reach very small values. Very low temperatures (190 K) at the tropical tropopause and in the winter polar lower stratosphere. 22 23 Meridional distribution of the mean temperature 24 To retain ● The atmosphere until 100 km is composed of nitrogen (78%) , oxygen (21%) and argon (0,9%)in fixed quantity to which are added minor gases. The most important is water which is in highly variable concentration (from 35g/kg at the tropical in tropical regions to a few mg/kg at 100 hpa in the tropics and above in the stratosphere). ● The atmospheric ozone is concentrated at 90% in the stratosphere. It filters solar UV rays (under 290nm) and converts this energy to heat, maintaining a growing temperature profile from the tropopause to 50 km. ● The atmosphere is stratified. It is in hydrostatic equilibrium for motion averaged over horizontal domains larger than 10x10 km. Pressure and density decrease exponentially with altitude, being divided per 2 every 5 km ● Air thermodynamics is well described by the ideal gas law. ● ● The temperature decreases by about 6,5 K par km in the troposphere until the tropopause. Beyond this frontier, the temperature grows again until about 55 km. The height of the tropopause is variable with latitude. It is 6 km in polar regions, 12 km (300 hPa) at mid-latitudes and 18 km (100 hPa) in th tropical zone near the equator. The tropical tropopause temperature is very low of the order of 200K. 25 Dry air thermodynamics (cont'd) -1 -1 Ideal gas law p = ρ RT where R = 287 J kg K -1 -1 Ideal gas enthalpy H = C p T where C p = 1005 J kg K , heat capacity per unit mass at constant pressure. H depends only of the temperature At constant pressure, for quasi-static transform: δ Q = C p dT = dH = T dS ( S: entropy) More generally δ Q = T dS = dU + p d(1/ρ)- 1/ρ dp ) = C p dT - 1/ρ dp = C p dT - RT/p dp = C p (T/θ dθ where θ is the potential temperature κ θ = T(p 0/p) avec κ = R/C p (=2/7 for diatomic gas) 26 Potential temperature Convective motion is on the first approximation adiabatic and reversible (heat exchanges much slower than pressure equilibration and weak mixing). Conservation of potential temperature κ θ = T(p 0/p) with κ = R/C p 27 Dry air convective intability as a function of the atmospheric profile Temperature gradient Γ = - dT/dz Adiabatic gradient Γ' = g/Cp 1 dp We use 0=Q=C p dT − dp and g=0 dz dT −g to obtain = during adiabatic motion dz C p We assume that vertical motion of the parcel is along an adiabatic transform and we compare the new temperature T' to the local environment temperature to determine whether the air 28 is stable or unstable.