By Kuo-Nan Liou (Eds.)
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Extra resources for An Introduction to Atmospheric Radiation
5/lm are measured nearly simultaneously from the record of the spectrograph. The instrument corresponding to these measurements is called bologram. 1 Long Method Assume that the atmosphere consists of plane parallel layers. At a given sun's position, which is denoted by the solar zenith angle eo, the effective path length of the air mass is u sec eo, where u = roo p dz. 5) In this equation, 2 1 is the height of the station. Yl is the monochromatic transmissivity defined in Eq. 51),and m( =sec eo) represents the ratio of the air mass between the sun and observer and that at the local zenith distance.
The first term in the righthand side of Eq. 55) denotes the reduction of the radiant intensity due to absorption, whereas the second term represents the increase of the radiant intensity arising from blackbody emission of the material. To seek a solution for the Schwarzschild equation, we define the monochromatic optical thickness of the medium between points sand S1 as shown in Fig. 11 in the form IS! pds. 57) Eq. 55) becomes d1is) d ( ) = -Us) "L). Sl>S Upon multiplying Eq. [T(s)]. 59) Fig. 11 s o Configuration of the optical thickness.
The integral may easily be evaluated. Further, by letting lito = 27HX and utilizing Eq. 35), we find Eq. 34a) becomes equivalent to Eq. 34). Here, Ln« is the number of collisions per molecule per unit time. 10 requires the derivation ofEq. 34) from Eq. ] We note that the Lorentz line shape also can be derived from the classical theory of absorption and dispersion as shown in Appendix D. 37) where CXo is the width at the standard pressure Po and temperature To. 2 Doppler Broadening Assuming that there is no collision broadening in a highly rarefied gas, a molecule in a given quantum state radiates at frequency vo' If this molecule has a velocity component u in the line of sight (the line joining the molecule and the observer), and if v « C, the velocity of light, the frequency Vo appears shifted as seen by a stationary observer to the frequency v= vo(l ± vic).