Loading...

PPT – Intermediate complexity models PowerPoint presentation | free to download - id: 6fd80a-YWM3N

The Adobe Flash plugin is needed to view this content

Intermediate complexity models

- Models which are like comprehensive models in

aspiration but their developers make specific

decisions to parametrize interactions so that the

models can simulate tens to hundreds of thousands

of years

1D radiative-convective models

- Greenhouse absorbers do not only affect the

surface temperature but also they modify

atmospheric temperature by their absorption and

emission. - Radiative-convective (RC) were developed to study

these effects

- RC models are one-dimensional models like the

EBMs with many vertical layers - These models resolve many layers in the

atmosphere and seek to compute atmospheric and

surface temperatures. - They can be used for sensitivity tests and they

can offer the opportunity to incorporate more

complex radiation treatments than can be afforded

in GCMs

- Suppose there are 2 layers in the atmosphere and

each layer absorbs the incident radiation on it ?

infrared optical thickness 1

- The principal absorber in the Earths atmosphere

is water vapor which is contained almost entirely

within the first few kilometers. - The 2 layers are therefore assume to be centered

at 0.5 and 3 Km. - Both layers radiate above and below as black

bodies and the ground radiates upwards

- All radiation from the planet must be absorbed by

the top layer ? - T1 Te
- The energy balance of the lower atmospheric layer

is - sT24 2sT14 2sTe4

- It can be shown that for n layers , the

temperature of layer n can be related to the

effective temperature Te by - Tn4 ttotal(n) Te4
- with ttotal(n) being the total infrared optical

thickness from the top of the atmosphere to the

layer n - In the previous case, as each layer has t 1

then ttotal(n) n.

- Surface temperature can be obtained as
- 2sT24 sTg4 sT14
- ? Tg (3Te4)1/4

The structure of global radiative-convective

models

- The RC model can be seen as a single column

containing the atmosphere and bounded beneath by

the surface - The radiation scheme is detailed and occupies the

majority of the total computation time while the

convection is accomplished by numerical

adjustment of the temperature profile at the end

of each timestep

- The atmosphere is divided into a number of layers

not necessarily of equal thickness. - Layering can be defined with respect to height or

pressure but it is more common to introduce the

non-dimensional vertical coordinate s , not to be

confused with the Stefan-Botlzmann constant) - s (p-pT)/(ps-pT)
- With p being the pressure, pT the (constant) top

of the atmosphere pressure and ps the (variable)

pressure at the Earths surface. - The top of the atmosphere has s 0 where the

surface has always s 1.

- Compared with the standard lapse rate (6.5 K/Km)

the computed radiative temperature profile is

unstable - If a small parcel of air were disturbed from a

location close to the surface it would tend to

rise because it would be warmer than the

surrounding air. Its temperature would decrease

at roughly the observed lapse rate so that at a

given height H its temperature would be higher

than that of the atmosphere and it would continue

to rise. - This air would carry energy upwards and the

resulting convection currents would mix the

atmosphere - This convective adjustment of a radiatively

produced profile is the essence of RC

- Model from CD ?

- Simple case single cloud or aerosol layer is

spread homogeneously over the surface

- 1) Part of the incident S radiation is reflected

(acS) part is absorbed (ac(1-ac)S and part is

transmitted ((1-ac)(1-ac)S)

- 2) The transmitted radiation interacts with the

surface. Part of it is absorbed

((1-ag)(1-ac)(1-ac)S), part is reflected

(ag(1-ac)(1-ac)S) which, in turn, is absorbed by

the cloud (acag(1-ac)(1-ac)S) and transmitted

((1-ac)ag(1-ac)(1-ac)S) - 3) the cloud emits as well (esTc4) as well as the

surface (sTg4) ,which is partially absorbed by

the cloud (esTg4) and transmitted ((1-e)sTg4)

- Three main assumptions have been made
- No reflection of the upwelling shortwave

radiation by the cloud - The surface emissivity has been set to 1
- The cloud/dust absorption in the infrared region

is equal to e

- When equating absorbed, emitted and reflected

radiation at each level we have - Eq. 1) S acS ag(1-ac)(1-ac)S esTc4

((1-e)sTg4) - Eq. 2) ac(1-ac)S acag(1-ac)(1-ac)S esTg4 2

esTc4 - Eq. 3) (1-ac)ag(1-ac)(1-ac)S esTc4 sTg4

- Eq. 1) S acS ag(1-ac)(1-ac)S esTc4

((1-e)sTg4) - Eq. 2) ac(1-ac)S acag(1-ac)(1-ac)S esTg4 2

esTc4 - Eq. 3) (1-ac)ag(1-ac)(1-ac)S esTc4 sTg4
- The above equations can be solved directly by

giving values for the dust/cloud shortwave

absorption, albedo, infrared emissivity and

surface albedo. - In alternative, the surface albedo term can be

eliminated leaving an expression for Tg - sTg4 ((1-ac)S)(2-ac)/(2-e)

- From sTg4 ((1-ac)S)(2-ac)/(2-e)
- Consider S 343 W/m2
- Cloudless case
- ac 0.08 (scattering by atmospheric molecules

alone), ac 0.15 and e 0.4 ? Tg 283 K - 2) Cloudy skies
- Volcanic aerosol
- ac 0.12, ac 0.18 and e 0.43 ?Tg 280 K ?

Cooling ! - Water droplet cloud
- ac 0.3, ac 0.2 and e 0.9 ?Tg 288 K ?

Warming ! - The Greenhouse effect of the cloud is greater

than the albedo effect

More on radiation

- We saw that solar radiation is absorbed and

infrared radiation is emitted, with these two

terms balancing over the globe when averaged over

a few years - We also saw that RC models pay a lot of attention

to the radiative component - Let us see how these models attack the problem

Shortwave radiation

- Shortwave incoming radiation is simply divided

into two parts, depending on wavelength, with the

division being somewhere around 0.7 0.9 mm. - The 2 wavelength regions can either be treated

identically or absorption and scattering can be

partitioned by wavelength. - Rs stands for the shortwave part where Ra stands

for the near infrared part - Rs is 65 of the total
- ? Ra is 35 of the total
- Therefore
- Rs 0.65Scosm
- Ra 0.35Scosm with m being the solar zenith

angle

Albedo

- The albedo of the clear atmosphere in the

shortwave is subject to Rayleigh scattering and

it is given by - a0 min1, 0.085-0.247log10((p0/ps)cosm))
- For overcast atmosphere the albedo for the

scattered part of the radiation is composed of

the contribution of Rayeigh scattering

(atmosphere molecules) and of Mie scattering

(water droplets). The simplest used formulation

is - aac 1-(1- a0)(1- ac)
- Where ac is the cloud albedo for both Rs and Ra

Albedo contd.

- spectral dependence must be introduced

Shortwave radiation subject to scattering

- The part of solar radiation that is assumed to be

scattered does not interact with the atmosphere. - Thus, the only contribute to which we are

interested in is the amount that reaches, and is

absorbed by, the Earths surface, given by

Clear sky

Cloudy sky

- Multiple reflections between sky and ground or

between cloud base and ground are accounted for

by the terms in the denominators - For partly cloudy conditions
- Being N the fractional cloudiness of the sky

Shortwave radiation subject to absorption

- The solar radiation subject to absorption is

distributed as heat to the various layers in the

atmosphere and to the Earths surface. - The absorption depends on upon the effective

water vapor content as well as the ozone and

carbon dioxide amounts - Generally, for cloudy skies, the absorption in a

cloud is prescribed as a function of cloud type

only

(No Transcript)

- When the sky is partially cloudy the total flux

at level I is given by - Rai NRai(1-N)Rai
- The part of the flux subject to absorption which

is actually absorbed by the ground is - Rag (1-ag)Ra4 ? clear sky
- Rag (1-ag)Ra4/(1-agac) ? cloudy
- Rag NRag(1-N)Rag

- The total solar radiation absorbed by the ground

is - Rg RagRsg

Longwave radiation

- The calculation og longwave radiation (as the

shortwave) is based on an empirical transmission

function mainly depending on the amount of water

vapor - The net longwave radition at any level can be

expressed as - F(net) F?-F?

- The upward flux at z h for a radiation at

wavelength l is - With the first term being the infrared flux

arriving at z h from the surface (z0), given

by the surface flux BlT(0) times the infrared

trasmittance of the atmosphere, tl. Bl is the

Planck function - The second term in the equation is the

contribution of the total upward flux from the

emission of infrared radiation by atmospheric

gases below the level zh.

- Note that, unlike the surface emission, the

atmospheric emission is highly wavelength

dependent, as a consequence of the selective

absorption by CO2 or H2O in certain spectral

regions

- The downward infrared flux is composed only of

atmospheric emission (as incoming infrared

radiation from space is essentially 0)

(No Transcript)

Heat balance at the ground

- Ground temperature is obtained from the heat

balance at the ground - RgF-esTg4-HL-HS stored energy
- With HL and HS being, respectively, the sensible

heat flux from the surface and the flux of latent

heat due to evaporation from the surface, and Rg

being the solar radiation absorbed by the ground

and F the downwelling longwave radiation at the

surface

Convective adjustment

- The computational scheme analyzed so far defines

a radiative temperature profile, T(z), only

determined by the vertical divergence of the net

radiative fluxes. - Globally computed averaged vertical radiative

temperature profiles for clear sky and with

either a fixed distribution of relative humidity

or a fixed distribution of absolute humidity

yields very high surface temperatures and a

temperature profile that decreases extremely

rapid with altitude - By the mid 60s, it was realized that it was

necessary to modify the unstable profiles. - This modification was termed convective

adjustment, though it is not really a

computation of convection but rather a numerical

re-adjustment

- Temperature vertical profiles when (a) the lapse

rate is 6.5 Km/K, (b) the moist adiabatic lapse

rate, (c) no convective adjustment and (d) the

U.S. standard atmosphere (1976)

- The temperature difference between vertical

layers is adjusted to the critical lapse rate

(LRc) by changing the temperature with time

according to the integrated rate of heat

addiction.

The flow continues until the atmospheric

temperature converges to a final, equilibrium

state

- An example of convergence is shown in the figure.
- The left and right figures show, respectively,

the approach to states of pure radiative (left)

and RC equilibrium (right). The solid and dashed

lines show the approach from a warm and cold

isothermal atmosphere respectively

Sensitivity experiments with RC models

- The RC model can be summarized by saying that the

vertical temperature profile of the atmosphere

plus surface system, expressed as a vertical

temperature set Ti, is calculated in a

time-stepping procedure such that - The temperature, Ti, of a given layer I, with

height z and at time tDt is a function of the

temperature of that layer at the previous time t

and the combined effects of the net radiative and

convective energy fluxes deposited at height z.

In the equation, cp is the heat capacity at

constant pressure and r is the atmospheric

density.

- There are 2 common methods of using RC models
- To gain an equilibrium solution after a

perturbation - To follow the time evolution of the radiative

fluxes immediately following a perturbation

- Sensitivity to humidity

- Readings
- McGuffie and Henderson-Sellers
- Chapter 4, pp 117 - 163