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Radiation Transfer
March 2000
By Jean-Jacques
Morcrette
European Centre for Medium-range Weather
Forecasts, Shinfield Park, Reading Berkshire RG2 9AX, United Kingdom
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2 . The Earth's radiative balance and its implications
2.1 The need for parametrization
The need for a parametrization of the radiation transfer in a large-scale numerical model of the atmosphere stems for two reasons:
| • first, like the other physical processes (condensation, surface processes, turbulence, ...) the radiation transfer actually occurs at spatial scales much smaller than the scales (e.g., interaction with cloud droplets) explicitly resolved by the model in its treatment of the adiabatic part of the prognostic equations; |
| • second, although the theory of radiation transfer has been well known for decades, the complexity of the governing equation is such that it cannot be used starightforwardly in a large-scale model. A much more computationally efficient scheme has to be designed to account for the effect of the radiative processes. |
2.2 Global mean considerations
The importance of the radiation transfer processes for the Earth's atmosphere system is obvious: Radiation is the only way through which the Earth-atmosphere system can exchange energy with the rest of the universe. The importance of a proper representation of the radiative processes in climate modelling or weather forecasting (after a few days) comes from this simple consideration;
A zero-dimensional energy balance model describes the global annual mean equilibrium of the Earth-atmosphere system as
|
is the planetary albedo (the ratio between
reflected and incident solar energy at the top of the atmosphere, ToA),
is the "solar constant" (the flux of energy from
the Sun at the mean Sun-Earth distance), 
is the outgoing terrestrial longwave radiation, 
is the radiometric temperature of the Earth, and 
is the Stefan-Boltzmann constant (
W m-2 K-4 ). The factor 0.25 (= 1/4) arises
from the Earth intercepting solar radiation proportionally to its cross-section
and emitting terrrestrial radiation proportionally to its surface. According
to the latest available satellite measurements (ERBE, Earth Radiation Budget
Experiment, Barkstrom and
Smith, 1986) 
W m-2 and 
. Thus 
is 237 W m-2 and 
K. The discrepancy between this value and the mean climatological
surface temperature (
K) is explained by the so-called "greenhouse" effect, which will
be discussed later. Fig. 2.1 presents the various radiative streams within the atmosphere after Ramanathan (1987). Out of the 343 W m-2 of solar energy available at ToA in the 0.2 to 4
wavelength range, about 30% is reflected back to the outer
space without change of wavelength after scattering in the atmosphere and/or
reflection at the Earth's surface. There the true solar imput to the atmosphere
is about 237 W m-2. A large fraction of this reaches the surface
and is absorbed by land masses and oceans; only roughly one quarter of this
solar radiation is absorbed within the atmosphere and creates a mean heating
of about 0.6 K/day. The exact fractions being absorbed within clouds and
by the "clear" atmosphere are presently debated (Cess
et al., 1995; Ramanathan
et al., 1995; Pilewskie and Valero, 1995; Stephens,
1996) with the role of aerosols in clear sky atmosphere and of cloud inhomogeneities
recently coming to the forefront to explain this excess absorption not properly
accounted by the current generation of radiation schemes in GCMs (e.g.,
Cairns et al., 2000). Part of the solar
energy input to the surface (between 155 and 180 W m-2 depending
on how much is actually absorbed within the atmosphere) is returned to the
atmosphere by emission of terrestrial longwave radiation in the 4 to 100
wavelength range, but this emission (about 63 W m-2, difference
between 390 W m-2, the longwave upward emission of the surface
and 327 W m-2, the longwave downward emission of the atmosphere)
does not fully compensate for the solar flux into the surface. The deficit
of about 106 W m-2 is compensated by turbulent transport of latent
heat (for about 90 W m-2) and sensible heat (for about 16 W m-2)
from the surface to the atmosphere. The existence of a radiative balance
at ToA and of a radiative imbalance at the surface implies that the atmosphere
itself is a net source of terrestrial longwave radiation to compensate for
the warming by the solar heating, latent heat release and sensible heat
flux. Thus the atmosphere cools through emssion of longwave radiation by
about 1.6 K/day. In the above discussion, only the figures of the radiation budget at ToA are known with some degree of accuracy thanks to some decades of satellite measurements. Estimates of the components of the energy budget at the surface are more difficult to obtain due to the lack of global coverage by conventional observation systems and to the alrge uncertainties in the ongoing tentative determination of these quantities from satellite measurements.
2.3 Time and space variations of the solar zenith angle and their consequences
The solar zenith angle
is the angle between the vertical at a given point on the Earth and
the Sun's direction. Its cosine, 
, which is the relevant parameter for radiative computations can
be computed knowing the latitude, the longitude, the time of the year, and
the time of the day. 
influences the radiation transfer in two ways:
• the amount of energy
received at ToA is the product of the solar constant by a factor depending
on the time of the year ( ) and by  if  is positive and zero otherwise (see Fig. 2.2 ); |
• the atmospheric mass
encountered by a solar beam is proportional to  (for  ). |
Therefore, a diminishing
means not only less input at ToA but also more scattering and absorption
within the atmosphere, therefore an even smaller solar flux at the surface.
The time variations of 
are the daily cycle and the yearly aseasonal cycle, which induce
cyclic temperature variations and many specific patterns in the instantaneous
weather. But the most important factor of influence of radiation on the
weather is linked to its spece variations. Due to a better insolation of
the equatorial belt than of the polar regions, which is not compensated
by the terrestrial longwave output, the equatorial region is warmer than
the polar ones. This situation has two major consequences for the weather:
| • the same pressure layers are thicker at the equator than at the poles; since the sea level pressure is observed to be uniformly distributed due to friction in the planetary boundary layer, and according to Buys-Ballot's law, the zonal mean wind regime is of zonal westerlies, therefore the atmosphere precedes the Earth in its rotation; |
| • there is a need to transport heat from the equatorial to the polar regions. This transport is partly realized by the oceans, partly by the atmosphere, But a simple zonal circulation does not allow the atmosphere to fulfill this role and disturbances have to develop. |
These last two points clearly indicate what is required from a radiation scheme in a large-scale numerical model of the atmosphere: first a good estimate of the pole-equator radiative imbalance, second an accurate partition of the poleward transport of heat between oceans and atmosphere.
In the tropics, the mean annual net heating of about 60 W m-2 is the sum of a 320 W m-2 heating by absorption of solar radiation and a 260 W m-2 cooling by emission of longwave radiation. This net heating of only about 20% of the available solar input (the remaining 80% heat the tropical surface) is the driving force for the general circulation of the atmosphere and oceans. Therefore a 10% systematic error in the column absorbed solar radiation or in the longwave emission may potentailly translate into a factor 5 larger (i.e., 50%) change in the poleward transport of heat.
Also important is the dipole-like deposit of radiative energy in the earth-atmosphere system. As a whole, the troposphere is subject to a net radiative cooling (of about 106 W m-2, Ramanathan, 1987), whereas the surface is subject to a net radiative heating of the same amplitude. Here again a 10% systematic error in the amplitude of this dipole will directly affect the destabilization of the troposphere, i.e., the fundamental drive for the tropospheric convection.
These questions may seem mainly related to climate studies, especially those performed with coupled ocean-atmosphere models. However the previous argument is also relevant to NWP modelling. NWP models are integrated with an analysed non-interactive sea-surface temperature, which provides the right oceanic heat transport. In the past, most NWP (and climate) models were using cloudiness fixed and/or zonally averaged to get the right answer for the pole-equator radiative gradient. Nowadays, NWP and climate GCMs have interactive cloudiness and cloud-radiation processes, as early satellite observations have shown the longitudinal gradients of radiative heating to be of the same magnitude as the latitudinal gradients, due to the cloud distribution (Stephens and Webster, 1979).
Such gradients are illustrated in Figs. 2.3 to 2.6 , which present averaged over the summer 1987 (June-July-August) the different components of the radiation budget derived from ERBE measurements. Fig. 2.3 displays the total and clear-sky absorbed SW radiation whereas Fig. 2.4 presents the reflected SW radiation. The clear-sky fields obtained by retaining the data only when clouds were found to be absent from the field of view of the satellite are highly zonal over the oceans, with only the land surface albedo differing with the various land types introducing marked departures. In comparison, the total fields clearly show the impact of the cloudiness with higher albedo (smaller absorption) in the ITCZ, the Indian monsoon and over the storm track. Minimum albedo (maximum absorption) is found over the relatively clear-sky subtropics, except over the extended low-level (stratocumulus) cloud decks on the western facades of the continents (California, Peru, Namibia). Fig. 2.5 presents the total and clear-sky outgoing longwave radiation for the same months. This field also displays the impact of the clouds, this time mainly of the high-level cloudiness usually linked to convection in the ITCZ or over the Indian monsoon area. Over the equatorial Pacific, the clear-sky OLR is less zonal than its SW counterpart indicating the role of moister atmospheres over the west part than over the eastern part of the basin. Fig. 2.6 presents the shortwave and longwave cloud forcing, i.e., the difference between clear-sky and total fluxes. In the shortwave, clouds with their reflecting effect are responsible for a cooling of the atmosphere-surface system, through a decrease of the energy available for heating. On the opposite, in the longwave, clouds contribute to a heating of the atmosphere by trapping the radiation coming from the surface and the lower layers of the atmosphere and by emitting at the cold temperatures representative of the higher clouds.
Cloud-radiation interactions are now thought to be of importance not only for mesoscale phenomena (the sea breeze is the best but not the only example of intercation between radiation and surface discontinuities to create local dynamical circulations), but also for synoptic scale phenomena such as the onset of the Indian monsoon (Webster and Stephens, 1980).
Finally, some systematic errors of a NWP model can be traced back to a deficient radiation transfer parametrization and at least partially corrected by an improved representation of the cloud-radiation interactions in the model (Morcrette, 1990).
the latent heat flux (90 W m-2) and 
the sensible heat flux (16 W m-2).
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12.06.2002 |
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