Simple Climate Models

Transcription

1 Simple Climate Models Lecture 3 One-dimensional (vertical) radiative-convective models Vertical atmospheric processes The vertical is the second important dimension, because there are... Stron radients (of temperature, humidity, etc) Sinificant flux diverences (zonal fluxes are lare, but their diverences are quite small) The most important vertical processes are convection lare-scale ascent & descent (subsidence) : meridional circulation small-scale turbulent overturnin & mixin (unstable stratification) radiation absorption and re-emission (some SW, but especially LW) Convection & Atmospheric lapse rates The troposphere is (on averae) just stable but there are major differences between reions of ascent (active convection) and descent (subsidence) in ascendin reions (small) : slihtly unstable mostly saturated with water vapour (condensation) lapse rates tend to moist adiabatic, i.e. Γ < 6 C/km in descendin reions (lare) : slihtly stable under-saturated (because the air has been dried out) lapse rate tends to dry adiabatic, i.e. Γ 1 C/km lare-scale averae lapse rates are actually close to 6.5 C/km everywhere (due to lateral mixin, etc)

2 Relative Humidity Hih ( 1%) in ascendin air (condensation) Low (< 6%) in descendin (dry) air over the sea, evaporation causes RH to increase rapidly (to 85%) over land, humidification depends on P-E hih in tropics, and near ± 6 latitude low around ± 3 latitude (subsidence) (which is why there are deserts there...) Overall, RH 8 ± 15 % almost everywhere (NB almost everywhere is over the sea!!) A very basic description of the atmosphere The US standard atmosphere lapse rate = -6.5 C/km RH = 75 % Ascent (and excess precipitation) near the equator (in the ITCZ) around ± 6 latitude Subsidence (and excess evaporation) near the poles around ± 3 latitude Hadley and Ferrel circulation cells Radiative equilibrium two-stream approximation, rey atmosphere Static medium (no convection etc) Enery balance, due to radiation only Partial absorption, independent of wavelenth the rey atmosphere Simple case : consider wellin and downwellin thermal infra-red only... Deduce temperature radient (and T s ) Consider optical thickness τ of many layers... See M.L. Salby (in Trenberth, 1992) also J.T. Houhton, The Physics of Atmospheres, second edition, CUP (1997)

3 Recommended proto-book A First Course in Climate : Earth and Elsewhere Volume I: Thermodynamics and radiation Volume II: Dynamics of the Atmosphere (with just enouh oceanoraphy to et by) R. T. Pierrehumbert Department of Geophysical Sciences University of Chicao Chicao, IL See also my attempt (less abstract) Simple but very useful models of the atmosphere Rad-Conv Text.pdf (on course web-site) N.B. not yet complete. where and Radiative (equilibrium) processes (1) net IR flux usin the two-stream approximation and a rey atmosphere Divide atmosphere into thin layers, of optical thickness τ = ρ a dz if ward IR flux is F F = F F = const = F ( a / ) p, and p = pressure..., and downward IR flux is F F, and at equil'm, df / dz = dn dn (net ward IR flux at TOA) τ

4 Radiative (equilibrium) processes (2) but df where ( ) df/dτ = F but alsodf F B τ /dτ = F B τ ( ), and -df /dτ = F B( τ ) ( ) = F = 2B( τ ) tot = F dτ = Fτ + const = F ( τ + 1) = 2B( τ ) F ( ) = ( τ + 1 ), and F = 2B( τ ) = F ( τ + 1) 2 tot = σt tot 4 2B τ /dτ = F B τ (black- body radiation) F dn tot tot = F dn dn Radiative (equilibrium) processes (3) But, since Also ( ) = ( τ + 1 ), B( 1) ( F + Ftot ) = F ( 1+ τ/ 2) ( τ ) = 1/ ( 1+ τ/ 2) { ε = F /F } and B( T ) = F ( τ ) = F ( 1+ τ/ 2) Since F B τ 1 = 2 F = σt 4 F 2 T 4 = T 4 = F. = σt ( 1+ τ/ 2) 4 Radiative (equilibrium) processes (4) T and τ = 2 with H H = T ( 1+ τ/ 2) 4 4 ( T /T 1) ( 1/1.254) but NB alsot T and a lapse - rate of = 1/ 4 T = 288 K, T = 33 K 6.5 K/km = 5 km 6 mbar These results are inconsistent there is a problem here... = 255 K, τ = mbar 8 mbar

5 The problem is due to Development of a near-round temperature discontinuity Which makes the temperature stratification statically unstable Causin vertical convection Which carries a sinificant heat flux So the assumptions of a static atmosphere, and heat transport by radiation only are untenable We need to allow for convection, and so need a radiative-convective model Instability of pure radiative equilibrium [H=7 km, tau=1.6, T= 15.8 C] Radiative and convective temperature profiles T(rad've) T(lapse) Temperature (de C) Pressure (atmos) The near-round temperature discontinuity

6 Convective adjustment: (time-dependent calculation) calculate radiative fluxes (diverence => heatin or coolin) date temperature profile if unstable w.r.t. chosen lapse rate apply convective mixin desired lapse rate (conserve heat, water, etc) implied convective heat flux... repeat radiative-convective equilibrium tropo-pause & (unrealistic) stratosphere Radiative-convective equilibrium (lobal averae) [H=7 km, tau=2., Ts=291 K, T= 13.8 C] 32. Corrected Radiative-convective temperature profiles T(lapse) T(rad-con) T(actual) T(rad've) Temperature (de K) Pressure (atmos) Radiative-convective equilibrium (equator) [H=7 km, tau=1.8, Ts=35 K, T= 15.5 C] 32. Corrected Radiative-convective temperature profiles T(lapse) T(rad-con) T(actual) T(rad've) Temperature (de K) Pressure (atmos)

7 Radiative-convective equilibrium (mid-latitude) [H=7 km, tau=1.8, Ts=288 K, T= 15. C] 32. Corrected Radiative-convective temperature profiles Temperature (de K) T(lapse) T(rad-con) T(actual) T(rad've) Pressure (atmos) Radiative-convective equilibrium (polar) [H=7 km, tau=1.8, Ts=247 K, T= 13.5 C] 32. Corrected Radiative-convective temperature profiles T(lapse) T(rad-con) T(actual) T(rad've) Temperature (de K) Pressure (atmos) Grey Atmosphere Radiative Convective Model 1% saturated, lapse-rate = 5 C/km [includin water-vapour/altitude relationship]

8 OLWR versus Temperature T s =31 K T s =3 K

9 T s =29 K T s =28 K T s =27 K

10 T s =26 K T s =25 K 1-D Radiative-Convective models : features Can include various radiatively active ases (water vapour, ozone, CO 2, methane etc...) better representation of stratosphere c.f. troposphere.. Allow direct estimation of GH ects (and thus climate sensitivity) Can estimate OLWR as a function of T s Can calculate troposphere heiht c.f. latitude Can include clouds : e.. if RH > RH crit 9 % specify albedo (.5) or estimate (diffuse scatterin) specify cloud heiht & depth fixed cloud top heiht, or temperature (?) several cloud layers? (how to model?)

11 1-D Radiative-Convective models : in practice Need to consider many ( 2) layers many radiatively active species (ases etc) interation over many spectral lines and bands, and over a continuum (8 to 13 µm) both UV/Visible and IR radiation Also particulate scatterin... Complex and time-consumin calculations...! Essentially = radiation code of a GCM N.B. Computational demand of radiation code may exceed that of fluid flow, in GCM s 1-D Radiative-Convective Models Overview Are valid only locally (isolated, pointwise), or as a lobal mean but the results vary with latitude/insolation latitudinal variation of tropo-pause heiht, etc but inconsistency : adjacent columns are not compatible (have different temperature profiles) So one needs to allow for lateral transports need for 2-D (meridional/vertical) models (at least)