Two-quartic tropospheric refractivity profile for correcting satellite data

Abstract

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...

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