Indirect Measurements of Atmospheric Temperature Profiles From Satellites: Vi. High-Altitude Balloon Testing

Abstract

Artificial earth srttellites offer a unique opportunity t o exploit the possibility of deducing temperature profiles on a global scale from measurements of radiance in several narrow spectral intervals in A strongly absorbing band of an atmospheric gas whose mixture is uniform. In the earth's atmosphere the 4.3-micron and 15-micron bands of carbon dioxide and the 5-mm. band of oxygen may be used; only the 15-micron band is considered in detail, although the procedures are applicable to the other bands. The Woblem considered is the numerical solution of the integral form of the radiative transfer equation from measurements in a finite set of spectral intervals. It is shown that, by a suitable approximation of the Planck radiance, the radiative transfer equation can be reduced to an integral equation of the first kind. After a discussion of the kernel, which is associated with the transmittance of the gas, the equation is changed to a finite set of equations which is amenable to numerical solution. The solution is limited to about six pieces of information, which may be expressed as points along the vertical profile, or as coefficients of an expansion; the limitation in information is manifest in the transmittance curves for the several spectral intervals, the errors of measurement, and the approximations employed. However, even in this limited case the formal solution of the set of equations is unstable. I n this process the amount of smoothing remains small, so that the inherent properties of the temperature profile are not affected. Several possible 351 352

Meteorology and the Supersonic Transport

“…The satellite infrared spectrometer (SIRS) aboard this spacecraft measures infrared radiation in seven wavelength intervals of the carbon dioxide absorption band at 15 microns and in the water vapor widow at wavelengths from 8 to 12 microns. From these measurements we can compute the vertical distribution of atmospheric temperature from the earth's surface, or from cloud tops, at least up to 30 kilometers, over the entire globe (24). Data have thus become available from vast areas which hitherto have not been accessible to meteorological observation, and they aid enormously in synoptic analysis.…”

inversion of radiometric measurements1

“…1 illustrate this clearly. They were calculated by Wark and Fleming (1966) to show how much the black body radiation at any altitude FIG. 1.…”

“…Dr. Wark (ESSA) described the extensive work done on what might be termed the classical approach to temperature determination, that of the linear inversion of measurements at several frequencies in the 15^ band of C02 (which is presumed to be uniformly mixed in the atmosphere). Beginning with the equation of transfer for M frequencies of measurement (Wark and Fleming, 1966), and writing the Planck black body function at the 2th frequency as a multiple of the Planck function Br(z) at a reference frequency, he obtained M integral equations involving Br(z) of the form…”

“…From the solution of (4), the vertical distribution Br(z) is obtained, from which it is a trivial matter to obtain T(z). Wark and Fleming (1966) applied this technique to calculated radiances (synthetic data) to which had been added various amounts of random error. Table 1 shows some of their results for four soundings representing tropical, midlatitude and polar conditions, as functions of the size of the error.…”

“…The possibility of inferring the distribution of atmospheric parameters from satellite measurements has been widely recognized for over a decade (see Wark and Fleming, 1966, for a historical review). The importance of this technique stems from the satellite's ability to obtain information on a regular basis over the oceans and other regions that do not report conventional measurements.…”