# AOSC 621 Lesson 15 Radiative Heating/Cooling

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1 AOSC 621 Lesson 15 Radiative Heating/Cooling

2 Effect of radiation on clouds: fog 2

3 Clear-sky cooling/heating rate: longwave CO2 O3 H2O 3

4 Clear-sky heating rate: shortwave Standard atmosphere Heating due to O 3 absorption Why drop off near sfc? Implication on daily temp. cycle? 4

5 Net flux - ( 1 ) + (1) Net flux: = ( + 2 ) ( 2 ) 2 Net energy gain in a layer: E = E in - E out or a unit volume in the layer: E measured in W m 3 m or very thin layer: H d d Heating rate (H) H H d d d d If H < : cooling If H > : heating How does temperature change? Therefore the time change is: H de dt H de dt c p dt dt This yields: or a constant pressure: dt dt H c p de c p dt (usually measured in K/day) 5

6 Heating rates in the Atmosphere -LW Assume that the Earth s surface is a blackbody, and that the downward d intensity i at the top of the atmosphere is ero. Then we can write ( ) * B T t (,) dt B( (, d' d' dt (, ( ) B( d' 2 d' If we examine equation 1, the integrand can be viewed as udv u.dv in the relation d(uv)=vdu+udv and Eq 1 can be replaced by d B(T (, d B ( d' d' d' - d' T 1 (, ') d '

7 Heating rates in the Atmosphere which equals B( ) B() T (,) - and equation 1becomes ( ) B( ) d B( T d' (, d' * d B( B B() T (,) d' If we apply the same procedure to Equation 2 we get T (, d' ( ) t B(T (, db ( t d d' d' B( ) B( t ) T (, t ) t d d' T B( T d' (, d' (, d'

8 Heating rates in the Atmosphere The net flux net T B( net d (, t ) T will consist of four terms t B ( db ( (, d' t ) d' - T (, * B B() T (,) d' d'

9 Heating rates in the Atmosphere The heating rate at is defined as follows: dnet ( ) H ( ) d and will consist of four terms H ( ) dt (, d B( d' A. Exchange from below d d' t dt (, d d dt (, t ) B( t ) d * dt B B() B( d' (,) d d' B. C. D. Exchange with above Exchange with space Exchange with surface

10 Meaning of the Terms A: Exchange from below B: Exchange from above C: Cooling to space D: Exchange from surface

11 Heating rates in the Atmosphere Let s now examine the contribution that each term makes to the heating and cooling of the atmosphere. But first we must examine the sign of This term can be defined as follows: the term dt T (, T (. limit it as d for any ' greater than, T (, T (, dt d dt and will be positive because the distance from d ( ) to ' is less than from to '. Hence T is greater.

12 Heating rates in the Atmosphere By similar arguments it can be shown that for less than, dt/d will be negative Now we will examine the four terms for three classes of atmosphere. Isothermal One with a nominal lapse rate One with a temperature inversion

13 Isothermal Atmosphere or an isothermal atmosphere db/d will be ero. Hence the terms A and B are ero In an isothermal atmosphere the temperature at the surface is equal to the temperature of the atmosphere directly above the surface, hence term D is ero Term C is the only term that survives. dt/d is positive ( >) and B is positive. The sign in front of the term is negative, hence the overall term is negative cooling. Term db/d dt/d overall A - B + C + - D -

14 Heating rates in Isothermal Atmosphere The heating rate at is defined as follows: dnet ( ) H ( ) d and will consist of four terms H ( ) dt (, d B( d' A. Exchange from below d d' Nil t dt (, d d dt (, t ) B( t ) d * dt B B() B( d' (,) d d' B. C. D. Exchange with above Nil Exchange with space Cooling Exchange with surface Nil

15 Nominal lapse rate The temperature of the atmosphere decreases with, hence db/d is negative. The term dt /d is negative for A, positive for B and positive for D. The signs can be summaried as follows: Term db/d dt/d overall sign A (heating) B (cooling) C + - (cooling) D - + (heating)

16 Heating rates in the nominal atmosphere The heating rate at is defined as follows: dnet ( ) H ( ) d and will consist of four terms H ( ) dt (, d B( d' A. Exchange with below d d' warming t dt (, d d dt (, t ) B( t ) d * dt B B() B( d' (,) d d' B. C. D. Exchange with above Cooling Exchange with space Cooling Exchange with surface Warming

17 Temperature inversion Assume that is at the inversion. db/d changes sign at : Term db/d dt/d Overall sign A (cooling) B (heating) C + - (cooling) D - + (warming) Note that term A shows cooling, whereas for a nominal lapse rate it gave heating. The tendency of the atmosphere is to remove the inversion.

18 Heating rates in atmosphere of temperature inversion Temperature goes down with hheight h dnet ( ) H ( ) d and will consist of four terms H ( ) dt (, d B( d' A. Exchange from below d d' cooling t dt (, d d dt (, t ) B( t ) d * dt B B() B( d' (,) d d' B. C. D. Exchange with above warming Exchange with space cooling Exchange with surface warming

19 Profiles of clear sky upward and downward fluxes 1. Note that both the upward and downward fluxes decrease with increasing, but at different rates. 2. The upward flux decrease because the principle source of heating is the radiation from the ground, and this is attenuated with height. 3. The downward radiation fluxes increase towards the surface because the increasingly opaque atmosphere is emitting at progressively warmer temperatures.

20 Spectral contributions to the cooling rate tropical atmopshere

21 Vertical profile of total longwave cooling

23 Spectral dependence of cloud absorption actors increasing vapor absorption: Influence of cloud altitude: 23

24 Cloud absorption: dependence on particle sie 24

25 Longwave radiative cooling heating in clouds Longwave radiative effects of clouds strongest at which wavelengths? Heating/cooling inside cloud: Net energy gain in a layer: E = E in - E out Overall heating rate of entire cloud: - () + ()=B(T()) = H - ( *) = B(T( *)) + ( *) * BT * = * e * BT Draw graph of vertical profile: middle of cloud near top near bottom below cloud above cloud e Altitu ude Radiative heating 25

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