Doreen M.C. Walker

Upper-Atmosphere Zonal Winds from Satellite Orbit Analysis.

Abstract In this paper we review and interpret the values of upper-atmosphere rotation rate (zonal winds) obtained by analysing satellite orbits determined from observations. The history of the method is briefly reviewed, the basic principles are explained, objections to the method are answered, and three examples are given. Existing analyses of the atmospheric rotation rate A are critically reviewed, and, after rejecting some and revising others, we are left with 85 values. These are divided according to local time and season, to give the variation of A with height in nine situations—namely morning, evening and average local time, for summer, winter and average season. These observational results indicate that the value of Λ (in rev/day), averaged over both local time and season, increases from 1.0 at 125 km to 1.22 at 325 km and then decreases to 1.0 at 430 km and 0.82 at 600 km. The value of Λ is higher in the evening (18–24 h), with a maximum value (near 1.4) corresponding to a West-to-East wind of 150 m s −1 at heights near 300 km. The value of Λ is lower in the morning (06–12 h), with East-to-West winds of order 50 m s −1 at heights of 200–400 km. There is also a consistent seasonal variation, the values of Λ being on average 0.15 higher in winter and 0.1 lower in summer than the average seasonal value. No significant variation with solar activity is found, but there is a slight tendency for a greater rotation rate at lower latitudes for heights above 300 km. Unexpectedly, the values for the 1960s are found to be significantly higher than those for the 1970s. Finally, these observational values are compared with the theoretical global model of Fuller-Rowell and Rees: there is complete agreement on the trends, though there are some differences in the mean values.

Variations in air density from January 1972 to April 1975 at heights near 200 km

Abstract Variations in air density have been determined using the orbit of the satellite Cosmos 462, 1971-106A, which entered orbit on 3 December 1971 with an initial perigee near 230 km and inclination 65.75°, and decayed on 4 April 1975. Accurate orbits determined at 85 epochs give perigee height correct to about 200 m throughout the satellites lifetime. Using these values of perigee height and orbital decay rates from NORAD elements, 604 values of air density at half a scale height above perigee have been evaluated. These densities have been compared with values from the COSPAR International Reference Atmosphere 1972, taking account of variations due to solar activity and geomagnetic disturbances, and day-to-night variations, to reveal the residual variations in density at a series of standard heights, 245, 240, 232 and 213 km. The main residual variation is semi-annual, with maxima usually in April and October, and minima usually in January and July; but it is irregular in phase and shape. The amplitude of the semi-annual variation is remarkably constant from year to year between 1972 and 1975, and considerably greater than that given by CIRA 1972: the April/July density ratio is 1.68, not 1.32 as in CIRA; the October–November maxima are all lower than the April maxima, whereas CIRA gives the opposite; the July minima are 18% lower than the January minima, as opposed to 10% in CIRA. A standardized semi-annual density variation for the early 1970s is presented, with January minimum of 0.94, April maximum of 1.28, July minimum of 0.77 and October–November maximum of 1.22. In addition, three other recurrent variations are recognizable: in each year the density has a subsidiary minimum in May and maximum in June; there are low values in mid November and high values in late December.

Upper-atmosphere zonal winds: Variation with height and local time

Abstract The average rotation rate of the upper atmosphere can be found by analysis of the changes in the orbital inclinations of satellites, and results previously obtained have indicated that the atmospheric rotation rate appreciably exceeds the Earths rotation rate at heights between 200 and 400 km. We have examined all such results previously published in the light of current standards of accuracy: some are accepted, some revised, and some rejected as inadequate in accuracy. We also analyse a number of fresh orbits and, adding these to the accepted and revised previous results, we derive the variation of zonal wind speed with height and local time. The rotation rate (rev/day) averaged over all local times increases from near 1.0 at 150 km height to 1.3 near 350 km (corresponding to an average west-to-east wind of 120 m/s), and then decreases to 1.0 at 400 km and probably to about 0.8 at greater heights. The maximum west-to-east winds occur in the evening hours, 18–24 h local time: these evening winds increase to a maximum of about 150 m/s at heights near 350 km and decline to near zero around 600 km. In the morning, 4–12 h local time, the winds are east to west, with speeds of 50–100 m/s above 200 km. We also tentatively conclude that, at heights above 350 km, the average rotation rate is greater in equatorial latitudes (0–25°) than at higher latitudes.

Air density at heights near 150 km in 1970, from the orbit of Cosmos 316 (1969-108A)

Abstract Cosmos 316 (1969-108A) was launched on 23 December 1969 into an orbit with an initial perigee height of 154 km at an inclination of 49.5° to the equator. Being very massive, Cosmos 316 had a longer lifetime than any previous satellite with such a low initial perigee: it remained in orbit until 28 August 1970. Because of its interest for upper-atmosphere research, the satellite was intensively observed, and accurate orbits are being determined at RAE from all available observations. Using perigee heights from the RAE orbits so far computed, and decay rates from Spacetrack bulletins, 102 values of air density have been obtained, giving a detailed picture of the variations in density at heights near 150 km between 24 December 1969 and 28 August 1970. The three strongest geomagnetic storms, on 8 March, 21 April and 17 August 1970, are marked by sudden increases in density of at least 23, 15 and 24 per cent respectively. With values of density extending over eight months, it is possible for the first time to examine a complete cycle of the semi-annual variation at a height near 150 km: the values of density, when corrected to a fixed height, exhibit minima in mid January and early August; at the intervening maximum, in April, the density is 30 per cent higher than at the minima.

Upper-atmosphere rotational speed and its variation with height

Abstract The average rotational speed of the upper atmosphere can be determined by analysing the changes in the orbital inclinations of satellites. This procedure is applied to eleven new orbits to give values of Λ, the ratio of atmospheric angular velocity to the Earths angular velocity, at heights between 250 and 380 km. When these new results are combined with 21 previous values the variation of Λ with height can be determined over a much wider height range than was previously possible, namely from 200 to 400 km. It is found that Λ increases from about 1.1 at 200 km height to about 1.35 at 300 km, and about 1.45 at 400 km. This implies that the wind is, on average, from west-to-east, with its mean speed increasing from 40 m/sec at 200 km height to 180 m/sec at 400 km (for latitudes near 30°). There is no evidence that Λ varies from year to year or with solar activity.

Evaluation of 15th-order harmonics in the geopotential from analysis of resonant orbits

Satellite orbits contracting under the influence of air drag experience 15th-order resonance when the track over the Earth repeats after 15 revolutions. If the orbital decay rate is slow enough, an orbit passing through the resonance is appreciably perturbed by the effects of 15th-order harmonics in the geopotential. We have used the observed perturbations in 23 resonant orbits, at various inclinations to the equator, to determine the harmonic coefficients of order 15 and degree 15, 16, 17,... 35. Analysis of the changes in orbital inclination on the 23 orbits gives the harmonics of odd degree, while those of even degree are found from the changes in eccentricity on 16 of the orbits. The values derived are given in tables 6 and 8. The coefficients of degrees 15, 16, 17,... 23, should be more accurate than any previously obtained; their average s. d. is 1.4 x 10-9, equivalent to 1 cm in geoid height. Comparisons with comprehensive Earth models show the Goddard Earth Model 10B to be the best, and a standard deviation of about 3 x 10-9 in the GEM 10B 15th-order coefficients is indicated.

Air density at heights of 140–180 km, from analysis of the orbit of 1968-59A

Abstract The satellite 1968-59A was launched on 11 July 1968 into a polar orbit with an initial perigee height of 160 km and apogee height 1800 km. The satellite did not decay until 6 November 1968, and analysis of its orbit yields values of air density at average intervals of 2 days between July and early November, mainly at heights of 140–180 km. Separate profiles of air density vs. height are obtained for July–August and for September–October 1968, with the latter giving values of density about 10 per cent higher. This increase in density reveals the existence of the semi-annual variation in density, well known at greater heights: the maximum density in October 1968 was about 20 per cent higher than the minimum in July, for heights near 170 km. When corrected to a fixed height, the density exhibits variations that are correlated with the geomagnetic index K p . The influence of solar radiation is only of minor importance and there is no evidence of variations with latitude or between day and night. The variations in density given by 1968-59A are found to be in good agreement with results from satellites at other heights.

Evaluation of 14th-order harmonics in the geopotential

Abstract The Earths gravitational potential is now usually expressed in terms of a double series of tesseral harmonics with several hundred terms, up to order and degree at least 20. The harmonics of order 14 can be evaluated by analysing changes in satellite orbits which experience 14th-order resonance, when the track over the Earth repeats after 14 revolutions. In this paper we describe our first evaluation of individual 14th-order coefficients in the geopotential from analysis of the variations in inclination and eccentricity of satellite orbits passing through 14th-order resonance under the action of air drag. Using results from eleven satellites, we find the following values for normalized coefficients of harmonics of order 14 and degree l, Cl, 14 and Sl, 14, for l=14, 154. 22: l 109C l,14 109Sl,14 - - - 14 −38.5 ±2.9 −7.8 ±2.2 15 4.5 ±1.1 −23.8 ±0.3 16 −22.3 ±3.6 −36.0 ±3.8 17 −15.0 ±2.6 16.8 ±1.2 18 −24.0±4.9 −3.2 ±3.7 19 −1.6 ±2.8 −7.6 ±1.0 20 8.8 ±5.8 −15.4 ±4.6 21 18.2 ±3.6 −10.6 ±1.9 22 −14.5 ±8.1 9.9 ±6.4 These values provide a test of the accuracy of the 14th-order coefficients in comprehensive geoid models. Detailed comparisons with three recent models are made, showing good agreement on some coefficients and discrepancies on others.

Air density at heights near 180 km in 1968 and 1969, from the orbit of 1967-31a

Abstract The satellite 1967-31A (A.T.S. 2), launched in April 1967, was unusual in having a low perigee (180 km initially) a near-constant cross-sectional area and a lifetime of more than two years. We have analysed its orbit to obtain 212 values of air density, mainly at heights between 160 and 190 km, during 14 months of high solar activity between 4 July 1968 and 2 September 1969 (when the satellite decayed). In general the air density exhibits only a weak dependence on solar activity, but the link between density and geomagnetic disturbances is obvious throughout: the two strongest geomagnetic storms, on 1 November 1968 and 15 May 1969, are accompanied by increases in density of 30 per cent and 70 per cent respectively. When such short-term variations are ignored, the underlying trend is a semi-annual variation in density, with maxima in October–November 1968 and March 1969, and minima in July 1968, January 1969 and July–August 1969. The July minima are deeper than the January minimum, and the average density at the maxima exceeds that at the minima by 32 per cent. A profile of density vs. height between 150 and 180 km for mid-1969 is also obtained; and a detailed comparison is made with previous results from 1968-59A.

Air density at a height of 470 km between January 1967 and May 1968, from the orbit of the satellite 1966-118A

Abstract Values of air density at a height of 470 km are calculated by analysing the orbit of the satellite 1966-118A, an Agena rocket. In all, 94 values of air density are obtained at average intervals of 5 1 2 days between January 1967 and the end of May 1968. The results confirm that there was a large semi-annual variation in air density during 1967, with the maxima (centred at April 5 and November 2) exceeding the July minimum (centred at July 31) by a factor of 2.9, and exceeding the January minimum (centred at January 18) by a factor of 2.2, after correction for the effects of solar activity. In the first half of 1968 the semi-annual variation was smaller, with the maxima in October 1967 and April 1968 exceeding the minimum in January–February 1968 by a factor of about 1–6. When these results are combined with previous data obtained by Jacchia and by Cook, it appears that the amplitude of the semi-annual variation undergoes an oscillation with a period of about 33 months, with maxima in early 1959, late 1961, early 1964 and (largest of all) early 1967, and minima in early 1960, late 1962 and at the end of 1965. These variations may be linked with the oscillations in zonal stratospheric winds, for which the pattern of dates has been similar since 1963.