Planck function temperature

Consider continuous radiation with specific intensity I incident normally on a uniform slab with a source function 5 = Bv(Tex) unit volume per unit solid angle to the volume absorption coefficient Kp and is equal to the Planck function Bv of an excitation temperature Tcx obtained by force-fitting the ratio of upper to lower state atomic level populations to the Boltzmann formula, Eq. (3.4). For the interstellar medium at optical and UV wavelengths, effectively S = 0. 

A thermodynamic function, symbolized by /, equal to the negative of the Helmholtz energy divided by the absolute temperature thus, J = -AIT. The SI units are joules per kelvin. See also Planck Function Helmholtz Energy... 

Consider an enclosure of dimensions large compared with any wavelengths under consideration, which is opaque but otherwise arbitrary in shape and composition (Fig. 4.11). If the enclosure is maintained at a constant absolute temperature T, the equilibrium radiation field will be isotropic, homogeneous, and unpolarized (see Reif, 1965, p. 373 et seq. for a good discussion of equilibrium radiation in an enclosure). At any point the amount of radiant energy per unit frequency interval, confined to a unit solid angle about any direction, which crosses a unit area normal to this direction in unit time is given by the Planck function... 

ORM assumes that the atmosphere is in local thermodynamic equilibrium this means that the temperature of the Boltzmann distribution is equal to the kinetic temperature and that the source function in Eq. (4) is equal to the Planck function at the local kinetic temperature. This LTE model is expected to be valid at the lower altitudes where kinetic collisions are frequent. In the stratosphere and mesosphere excitation mechanisms such as photochemical processes and solar pumping, combined with the lower collision relaxation rates make possible that many of the vibrational levels of atmospheric constituents responsible for infrared emissions have excitation temperatures which differ from the local kinetic temperature. It has been found [18] that many C02 bands are strongly affected by non-LTE. However, since the handling of Non-LTE would severely increase the retrieval computing time, it was decided to select only microwindows that are in thermodynamic equilibrium to avoid Non-LTE calculations in the forward model. 

Figure 2 is a plot of the low resolution ETR spectrum compared with the Planck function for a blackbody with a temperature of 6000 Kelvin. The differences in the infrared, beyond 1000 nanometers are small. The larger differences in the shortwave length region are due to the absorption of radiation by the constituents of the solar composition, resulting in the "lines" observed by Fraunhofer and named after him. 

Planck function - A thermodynamic function defined by T = -GIT, where G is Gibbs energy and T thermodynamic temperature. [2]... 

Fig. 4.1.2 Lorentz lines in absorption in a homogeneous isothermal atmosphere, generated according to the model illustrated in Fig. 4.1.1. Normal viewing fi= 1) is assumed, with surface and atmospheric temperatures of Ts = 150 K and 7 = 90 K, respectively. The line width O inEq. (4.1.1) is 1 cm and the line center is at vo = 400 cm . The product xAz is 8 cm per particle, and the particle number density is assigned the four values N = 0.1, 1,20, and 500 particles per cm. Planck functions for T = 150 K and 90 K serve as limiting boundaries for the lines.

To extract h from Eq. (5.8.4), one must determine for each resolved wavenumber interval the unknown quantities r and This is conveniently achieved by measuring two known sources in addition to the object of interest. Deep space may be one convenient reference and a warm blackbody may serve as the other. In case of an isothermal instrument temperature, 5 (7]) is the Planck function corresponding... 

The responsivity includes all instmmental properties, such as the transmission characteristics of optical filters, the detector response, amplifier gain, etc. The term tiiy, Teff) is the Planck function corresponding to the effective instrument temperature. If the instrument and the detector are at the same temperature, Tj, then that temperature is the effective temperature. However, the detector and the rest of the instrument are often at different temperatures for example, the detector may... 

The simplest form a surface spectrum can take in the thermal infrared is that of a single Planck function (blackbody). In such a case the temperature of the observed surface can be inferred directly. More often, however, a weighted sum of blackbody spectra is required to obtain an acceptable fit, especially if the observed spectrum covers an extended wavenumber range. This implies an inhomogeneous thermal stmcture across the field of view, which can arise from different causes. 

The functional derivatives with respect to temperature are calculated assuming that the temperature dependence of the atmospheric transmittance is weak relative to that of the Planck function so that K can be approximated as... 

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