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Intermediate complexity models


Intermediate complexity models Models which are like comprehensive models in aspiration but their developers make specific decisions to parametrize interactions so ... – PowerPoint PPT presentation

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Title: Intermediate complexity models

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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Eq. 2) ac(1-ac)S acag(1-ac)(1-ac)S esTg4 2
  • Eq. 3) (1-ac)ag(1-ac)(1-ac)S esTc4 sTg4

  • Eq. 1) S acS ag(1-ac)(1-ac)S esTc4
  • Eq. 2) ac(1-ac)S acag(1-ac)(1-ac)S esTg4 2
  • 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

  • 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
  • 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

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  • 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
  • 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
  • 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

  • The downward infrared flux is composed only of
    atmospheric emission (as incoming infrared
    radiation from space is essentially 0)

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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

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

  • 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

The flow continues until the atmospheric
temperature converges to a final, equilibrium
  • 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

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