This paper presents a new model for the height profile of tropospheric refractivity N and expressions derived from it for computing corrections for satellite Doppler or range data. (N ----106 (n --1), where n is the index of refraction.) The model is theoretically based on an atmosphere with constant lapse rate of temperature, as will be shown. It treats the 'dry' and 'wet' components of N separately and represents each as a fourth-degree function of height above the geoid; each component profile starts with its locally observed surface value and decreases to zero at an effective height that is different for the two components. The height parameters were obtained by a least-squares fit to observed data. A latitude dependence has been found for the 'dry' height. The model has been found capable of closely matching any local average N profile observed in a world-wide sample of locations throughout the height range of meteorological balloon data (up to 24 km); samples are shown. The corrections based on it are readily evaluated and are finite and usable at all elevation angles. Their effectiveness is evidenced by figures showing two different kinds of observed data: first, Doppler residuals for several satellite passes without and with the use of the correction; and the 'navigation' error in station-to-orbit slant range from Doppler data, again without and with the correction. The use of the correction removed obvious systematic errors. The fact that satellite Doppler data display identifiable tropospheric effects is of interest with regard to future study of the troposphere. where f is the signal frequency and c is the vacuum velocity of light, but the 'vacuum' Doppler shift is needed for computing the orbit: = -(:2) where p is the geometric slant range to the satellite. Both ionospheric and tropospheric effects must be removed from the observed Doppler to get the vacuum Doppler shift. The two-frequency method [Guier and Wei#enbach, 1960] that removes first-order ionospheric effects does not remove the effects of the troposphere, whose refractive index is independent of frequency up to approximately 15,000 Mhz. A theoretical tropospheric correction is therefore required and must be based on some model of the troposphere; the term 'troposphere' will be used here to include all the lower uncharged part of the atmosphere. An initial tropospheric model and a subsequent improvement [Hopfield, 1963,-1965], which will here be designated as model i and model 2, have been superseded by the model to be described below. ASSUMPTIONS AND REQUIREMENTS FOR A TROPOSPHERE MODEL It will be assumed, as before, that the refractive index of the troposphere is a function of 4487 ß ß ß ß •1 PROFILES USED IN DERIVING HEIGHT PARAMETERS ß ADDITIONAL PROFILES, NOT USED IN DERIVING PARAMETERS I I alii, eq• •ll ß ß ee ß ß • ß & ee ß .o e dl ß :l pa ß ß dl ß ß ß ß ßß ß 240 280 320 360 400 ß PROFILES USED IN DERIVING HEIGHT PARAMETERS ß ADDITIONAL PROFILES, NOT USED IN DERIVING PARAMETERS ß ß O -. ß ß ß , ß , '' ' '",T 01' ,v ß , ß ß O O ß 0.9 R...

Knowledge of the height integral of atmospheric refractivity (n — 1), where n is the refractive index, is essential for prediction of atmospheric range effect at any elevation angle. Observed values of the height integral for the lower, nonionized atmosphere can be obtained from weather balloon ascent data. Year‐long collections of data from widely separated locations were used to relate this integral to surface data. Although (n — 1) at any point in a dry atmosphere depends on both pressure and temperature (the ratio P/T), the height integral of the observed dry part of (n — 1) is a linear function of surface pressure only, not of temperature. This is theoretically correct since P/T is equivalent to density, and the integral of density with height yields surface pressure. By application of this finding, the equivalent height for a (theoretically justified) quartic (n — 1) model (dry part) should be found to vary directly as surface temperature; the value obtained (least‐squares fit to observed data) is 40.1 km for surface T = 0°C with a height expansion coefficient of 0.149 km per surface degree C. This would reduce the equivalent height to zero near 0° Kelvin. This theoretical model matches observed height integrals with an rms error of a few millimeters out of 2.3 meters (far less than 1%). Agreement between stations is excellent. A study of the more variable but much smaller wet part is in progress. The wet part is significant at radio but not at optical frequencies.

High dispersion spectrograms of CO-oxygen explosions in a spherical vessel have been obtained. Under conditions affording maximum contrast between the banded spectrum and the continuum, the 3Σu−—3Σg− and the 1Σg+—3Σg− transitions of the neutral oxygen molecule have been observed in emission. Additional spectroscopic information on the absorption by OH radicals in flames has been obtained.

An expression for the contribution made by tropospheric refraction to the Dop pler shift of a satellite signal is derived. It is assumed that the troposphere is horizontal ly stratified and does not vary during the time of a pass; a two-parameter quadratic expression is used as an approximation to the refractivity profile. The qualitative effect of the troposphere during any satellite pass is to steepen the slope of the Doppler shift "ersus time curve, making the tra. eking station appear slightly closer to the orbit than it a. ctually is. When Doppler data from severfll passes are used for orbit computation, the resultant effect of the troposphere in general is not zero; thus it may bias the orbit slightly, the amount depending on the geometry of the selected passes. Conversely, if the orbit is assumed to be known, the station position as detem1ined by a single satellite pa. ss may be shifted towa. rd the orbit by 50 meters or more. Such errors are not negligible if precise geodetic work is to be dOlle with satellites. The residual tropospheric error in the Doppler shift cun probably be reduced by an order of m agnitude by using a computed tropospheric correction of the type described here. Some Doppler data from observed satellite pas ses are presented in corroboration of the theory.

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