Radiation radiative equilibrium

The greenhouse effect is a natural phenomenon whereby the earth s atmosphere is more transparent to solar radiation than terrestrial infixed radiation (emitted by the earth s surface and atmosphere). Consequently, the planet s mean surface temperature is about 33 K higher than the planet s radiative equilibrium temperature (the temperature at which the earth comes into equilibrium with the energy received from the sun). 

The concept of global radiative equilibrium is useful in identifying the various factors that govern climatic variability. At radiative equilibrium, the flux of solar radiation absorbed by the planet equals the flux of infrared radiation to space. That is. 

For this purpose, a new type of "unified model atmospheres" has been developed at the Munich Observatory by R. Gabler (1986) and A. Wagner (1986) in cooperation with J. Puls, A. Pauldrach and R.P. Kudritzki. These NLTE model atmospheres are spherically extended, in radiative equilibrium, and include the density and velocity distribution of radiation driven winds. The spectra of H and He lines are then calcu-... 

We consider the non-LTE spectral formation in a spherically expanding atmosphere. The velocity field v(r) is specified in its supersonic part by the usual analytical law with the parameters y, (final velocity) and the exponent 8=1, The temperature structure is derived from the assumption of radiative equilibrium, but only approximately evaluated for the grey LTE case. The atmosphere is assumed to consist of pure helium. The model atom has a total of 28 energy levels, among these 17 levels of He I. The line radiation transfer is treated in the "comoving frame". 

Nariai and Murata (1987) solved the structure of an atmosphere in a binary system by treating the radiation from the other component explicitly in the radiative equilibrium equation. However, it is possible to treat the same problem as an example with a source term which is generated by the decay of the direct radiation from the other component. 

Since the body is in radiative equilibrium, qx(T) also expresses the spectral radiative flux emitted by the body at the wavelength X. The incident radiation q (T) comes from the black walls of the enclosure at temperature T, and the emission by the walls is not influenced by the body regardless if it is a blackbody or not. Let qxb(T) be the spectral blackbody emissive flux at temperature T. Then,... 

A zone with Qt > 0 is called a (net) radiation source, as it emits more radiation than it absorbs. A zone with Qt < 0 is a (net) radiation receiver, that absorbs more radiation than it emits. An adiabatic zone (Q = 0) with respect to the outside is known as a reradiating wall. Its temperature is such that it emits just as much radiation as it absorbs from radiation incident upon it (radiative equilibrium). 

In the centre of main-sequence stars, the radiation flux l/4nr2 can become very large, whilst up remains small. Thus the temperature gradient dlnT/dlnP required for radiative equilibrium (Eq. (30)) becomes large, and the material becomes convectively unstable. This gives rise to nuclear-driven convective cores in massive stars, and also convective zones in helium-burning stars. 

Now there is a theorem of Kirchhoff s (1859) which states that the ratio of the emissive and absorptive powers of a body depends only on the temperature of the body, and not on its nature otherwise radiative equilibrium could not exist within a cavity containing substances of different kinds. (By emissive power is meant the radiant energy emitted by the body per unit time, by absorptive power the fraction which the body absorbs of the radiant energy which falls upon it.) By a black body is meant a body with absorptive power equal to unity, i.e. a body which absorbs the whole of the radiant energy falling upon it. The radiation emitted by such a body—called black radiation —is therefore a function of the temperature alone, and it is important to know the spectral distribution of the intensity of this radiation. The following pages are devoted to the determination of the law of this intensity. 

At lower altitudes, except at the tropical tropopause and in the winter hemisphere, the stratosphere may be considered to be approximately in radiative equilibrium, while the mesosphere is very far from these conditions. The most dramatic manifestation of the importance of meridional motions for the temperature structure of the middle atmosphere occurs at the summer polar mesopause, where the temperature (about 130 K) is the lowest observed anywhere on Earth, even though the region receives substantially more solar radiation than does the winter mesopause (Box 3.2). 

The radiative equilibrium of this system needs to be set up. Only diffuse radiation that fractions are considered in accordance with the optical parameters for diffuse radiation that are to be used. The problem is relatively complex and confusing. The single steps for the derivation of the transport equations cannot be discussed explicitly. They are only explained in the corresponding diagrams (Figs 5.21 and 5.22). 

The final assumption, (6), is that of radiative equilibrium. Here, we assume that the volume absorption rate of IR radiation ial) is equal to the volume rate of emission iactB In). This was discussed in Section IV in terms of the net heating rate H, which is zero in radiative equilibrium (RE). This assumption requires that radiation alone heats or cools the atmosphere. It ignores the important process of convection, which we will include later. 

At each radius in the dust shell the grain temperature is calculated from the condition of radiative equilibria in the radiation of both the star and the other dust. Neglecting for the moment the secondary radiation, the equilibrium implies that... 

In the foregoing the flux of incident solar radiation relative to the local vertical is —fiottFo, whereas the incident solar flux averaged over a spherical planet is —jtFo/4. This implies a reduced flux ttF should replace rFo under conditions of global radiative equilibrium. If /xq =... 

These two equations state that, in each cell, the surface radiates away as much heat (right hand side) as it receives (left hand side). The term involving F on the left hand side is the solar radiation absorbed at the surface. The downwelling longwave radiation from the atmosphere is a fraction p of die energy radiated upward by the surface plus half the meridional transport D. This result is taken from a toy model of the radiative equilibrium between the atmosphere and the surface, Thorndike 1992. P is a measure of die longwave emissivity of the atmosphere. In today s atmosphere P is... 

The equation shows that the average temperature is determined by the average radiation balance . The absence of k implies that the average temperature is unaffected by poleward heat transport. The AT equation shows that the temperature contrast between the two cells is determined by the contrast in the radiation balance, softened by the poleward heat transport. Using numerical values for the parameters shows that the radiative cooling (b = 1.53 Wm K" ) and the poleward advection (k=1.75 Wm 2K ) are equally important. In other words, the meridional temperature contrast in the coupled system is about half what it would be if it were determined solely by radiative equilibrium and no advection. Figure 2 shows the solutions for Ti and T2 as functions of k. See the Table 1 for numerical values of Tj and T2, using a value of k for today s climate. 

Equation (4.87) was obtained under the assumption of strict thermodynamic equilibrium between the particle and the surrounding radiation field that is, the particle at temperature T is embedded in a radiation field characterized by the same temperature. However, we are almost invariably interested in applying (4.87) to particles that are not in thermodynamic equilibrium with the surrounding radiation. For example, if the only mechanisms for energy transfer are radiative, then a particle illuminated by the sun or another star will come to constant temperature when emission balances absorption but the particle s steady temperature will not, in general, be the same as that of the star. The validity of Kirchhoff s law for a body in a nonequilibrium environment has been the subject of some controversy. However, from the review by Baltes (1976) and the papers cited therein, it appears that questions about the validity of Kirchhoff s law are merely the result of different definitions of emission and absorption, and we are justified in using (4.87) for particles under arbitrary illumination. 

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