Whatever happened to superrotation?

Journal of Atmospheric and Solar-Terrestrial Physics 64 (2002) 1351–1360www.elsevier.com/locate/jastp

Whatever happened to superrotation?

H. Rishbeth ∗

Department of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK

Abstract

In the 1960s, it was deduced from observations of satellite orbits that the thermosphere rotates about 20% faster than theEarth; i.e., there is a prevailing west-to-east wind of order 100 m s−1. In the seventies, this ‘superrotation’ was explained asa consequence of the day-to-night variation of ion-drag at low latitudes, caused by the strong nighttime polarization 8eldsgenerated by the F-layer dynamo. In the eighties, satellite-borne instruments measured prevailing zonal winds of only 20–30 m s−1 at low latitudes. In the 1990s, global coupled thermosphere–ionosphere models indicate similar prevailing windspeeds. Can all these be reconciled?

The paper brie;y reviews the observations and the theory, discussing the essentials of the ion-drag explanation of superrota-tion. It is now clear that the local time variation of neutral air pressure is not the simple day=night variation that was assumedin the early F-layer dynamo calculations. The present-day thermospheric models can account for a prevailing west-to-eastwind of 30–40 m s−1 at the magnetic equator, agreeing reasonably well with the wind measurements; the discrepancy withthe satellite orbital data has been reduced but not eliminated. c© 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Thermosphere rotation; Equatorial ionosphere

1. Introduction

This paper discusses some electrodynamic aspects of theionospheric F2-layer at equatorial latitudes, starting fromthe equation of motion of the neutral air. In the early in-vestigation of the F-layer dynamo and resulting polarization8elds (Rishbeth, 1971), a major objective was to explain‘superrotation’, the net eastward motion of the thermospherethat had been deduced from progressive changes in the or-bital inclination of arti8cial satellites (King-Hele, 1964). Al-though the picture regarding superrotation has changed, thecoupling of the E-layer and F-layer dynamos and the associ-ated polarization 8elds play an important role in low-latitudethermospheric dynamics. The results from satellite orbitaldata and from in-situ measurements from spacecraft, and thecon;ict between them, are reviewed in Section 2.

The subsequent sections present the relevant ideas ofionospheric dynamics. Section 3 discusses the E-layer andF-layer dynamos; Section 4 presents the wind equation that

∗ Tel.: +44(0)2380-592048; fax: +44(0)2380-593910.E-mail address: [email protected] (H. Rishbeth).

governs thermospheric winds, with calculations of prevail-ing zonal winds and superrotation obtained from simpli8edcalculations. Section 5 considers results obtained fromglobal thermosphere–ionosphere computational models, andcompares them with the observations described in Section2. Section 6 deals with variations of nighttime E-layerelectron density, which aDect the F-layer electric 8elds.Section 7 contains further discussion and conclusions.

2. Observations of superrotation and prevailing zonalwinds

2.1. Superrotation deduced from satellite orbits

From observations of the orbits of arti8cial satellites,which revealed small but consistent changes of orbital in-clination, King-Hele (1964) deduced that the thermosphererotates 10–20% faster than the Earth, and expressed his re-sults in terms of a ‘superrotation ratio’ � of 1.1–1.2. In otherwords, the thermosphere has a net west-to-east motion orprevailing wind 〈Ux〉, related to � by the equation

�= 1 + 〈Ux〉=((RE + h)� cos �); (1)

1364-6826/02/$ - see front matter c© 2002 Elsevier Science Ltd. All rights reserved.PII: S1364 -6826(02)00097 -4

1352 H. Rishbeth / Journal of Atmospheric and Solar-Terrestrial Physics 64 (2002) 1351–1360

Fig. 1. The superrotation ratio � as derived from observations ofsatellite orbits, based on the data of King-Hele (1971), showinga typical error bar of ±0:1. A few points have larger (±0:15) orsmaller error bars (±0:05).

where RE and � are the Earth’s radius and angular velocity.The Earth’s rotational speed varies with geographical lati-tude � and height h as shown in Eq. (1), being 454 m s−1

at ground level at the equator. In some papers on superro-tation, the rotational speed is taken to be 400 m s−1 whichcorresponds to latitude 34◦ at heights of 200–300 km; inthis case � = 1:1 implies a west-to-east prevailing wind of40 m s−1. Fig. 1 shows results from King-Hele (1971).

To summarize the theory: a satellite’s inclination i can bechanged by a drag force acting perpendicular to its orbitalplane, while a drag force acting tangentially to the orbitdecreases the orbital period T . Over a long period of time(much longer than any tumbling period of the satellite, andexcept for some oddly shaped satellites), the ratio of thelateral and tangential drag forces should be constant. It canbe shown that, as an approximate relation applicable to manyorbits,

Hi=HT = 13� sin i cos2!; (2)

where ! is the argument of perigee, the angular distancemeasured around the orbit between perigee and the equa-tor crossing. The full equation is much more complicatedthough, in many cases, the complicating factors are approx-imately 1 so Eq. (2) may be taken to be reasonably accu-rate for present purposes. The changes are small: a typicalsatellite in a high-inclination near-circular orbit, initially at

700 km height, changes its inclination by the order of 0:1◦

during its lifetime. Nevertheless, orbits can be determinedwith great precision and, with due allowance for gravita-tional eDects and solar radiation pressure, the deduced valuesof � have typical error bars of ±0:1. From observations ofnumerous satellites over a period of 30 years, King-Hele andco-workers built up a picture of how this eastward rotationvaries with latitude, local time, and geomagnetic activity.According to results from many satellites, summarized byKing-Hele and Walker (1977, 1988) and King-Hele (1992):

(i) Superrotation at heights of 150–250 km is greatest(max. �≈1:4) at local times 18–24 LT, whereas at 04–12 LT there is subrotation (� = 0:6–0.8). The 24-haverage of � is 1.1–1.3 at 150–350 km, decreasing toabout 0.8 at 500 km.

(ii) The superrotation is slightly greater for satellites withinclinations around 25◦ (�=1:2–1.5) than for satelliteswith inclinations of 35–55◦ (� = 0:8–1.3). It variesconsiderably from one satellite to another.

(iii) There is no systematic variation of�with solar 10:7 cmradio ;ux, which is used to represent solar activity.

2.2. E2ect of meridional winds

It has sometimes been suggested that the satellite orbitalperturbations, attributed to mean zonal thermospheric winds,might instead be due to meridional winds. A steady merid-ional wind can aDect orbital inclination, according to anequation similar to Eq. (2), viz.

Hi=HT ≈ − 13� cos i cos!; (3)

where the parameter � is de8ned similarly to �, but fora uniform meridional wind. As in Eq. (2), the full equa-tion contains several complicated factors. King-Hele (1966)showed that, unlike the eDect of a zonal wind which steadilybuilds up because of the factor cos2! in Eq. (2), the eDectof a meridional wind cancels out over a complete rotation ofperigee, in which ! goes through a full cycle. This may takesome months, and Straus and Ching (1974) did numericalsimulations that showed appreciable eDects on inclinationover shorter periods.

A prevailing meridional wind can only exist if it is partof a three-dimensional circulation, balanced by return ;owat a diDerent level (which might be at heights below thesatellite orbits). According to contemporary thermosphericmodels, summer-to-winter prevailing winds do exist at sol-stice, but they are only about 25 m s−1 or � ≈ 0:05. Beingweaker than the zonal winds deduced from the orbital anal-ysis, meridional winds seem unlikely to account for the ob-served changes of inclination. Away from solstice, a typicalsatellite in a day=night orbit encounters alternating north-ward and southward winds which, according to King-HeleandWalker (1983), produce rapid cancellation of any merid-ional eDect. In defence of the satellite analysis, King-Heleand Walker (1983) examine several cases, and conclude

H. Rishbeth / Journal of Atmospheric and Solar-Terrestrial Physics 64 (2002) 1351–1360 1353

Fig. 2. Plot of zonal west-to-east wind vs local time at the equatorialtrough at heights of about 300 km, from DE-2 data for 1981=1982(full curve) (data kindly supplied by R. Raghavarao). The horizon-tal dashed line shows the 24-h average of +34 m s−1. The crossesrepresent the steady-state wind computed from Eq. (14) and (15),using the MSIS model to derive the pressure gradients (see text),the 24-hour average of 19 m s−1 being shown by the horizontaldotted line.

that the orbital method is sound except in some unlikelysituations.

2.3. Results from in situ measurements of winds

In sharp contrast to the results of the satellite orbital anal-ysis, measurements of zonal winds by the DE-2 Wind andTemperature Experiment (Wharton et al., 1984), at heightsof about 300–450 km, yield a prevailing eastward wind ofmerely 19 m s−1 (4% superrotation) in equatorial latitudes,with a similar subrotation at middle latitudes. The exampleshown in Fig. 2 (R. Raghavarao, private communication,2000) gives a prevailing wind of 34 m s−1 which corre-sponds to 7% superrotation. Furthermore, Wharton et al.noted that these results agree with the zonal winds deducedfrom their eDect on the orbits of balloon satellites at heightsof 350–675 km (Slowey, 1975). Slowey’s six results, eachrepresenting a period of a few months within the years1963–1971, may broadly be summarized thus: eastwardwinds of 100 and 200 m s−1 in evening hours (19–21 LT),westward winds of 100 m s−1 in morning hours (07 LT),and small winds in daytime hours (09 LT and 15 LT).These agree reasonably well with the satellite orbital resultsof King-Hele and Walker (1983) for equivalent local times.Wharton et al. (1984) found that their data agree with thesmaller values of the superrotation shown by King-Hele andWalker (1983), but not with the larger values which tendto have larger error bars. Furthermore, Fejer et al. (1985)found good agreement between the average zonal plasmadrifts measured at Jicamarca and the zonal winds publishedby Wharton et al. (1984).

Further analysis of the DE-2 dataset by Raghavarao et al.(1998) gives prevailing zonal winds of about 30 m s−1 in the

F2-layer ‘equatorial trough’, and 20 m s−1 at the F2-layer‘crests’ about 20◦ north and south of the magnetic equa-tor. The weaker winds at the ‘crests’ are attributed to theincreased ion-drag due to the larger electron density.

A more recent study by McLandress et al. (1996), usingdata from the UARS and WINDII satellites, gives westwardmean zonal winds at 200 km of 40 m s−1 at the equator,both at equinox and at solstice; in neither season does theequatorial value stand out from those at neighbouring lati-tudes. This height is 100 km or more lower than that of theDE-2 data, so the results are not directly comparable.

Comparing Section 2.1 with the above reveals a discrep-ancy between the orbital inclination analysis and the in situmeasurements. So does superrotation exist in the Earth’sthermosphere at all, at least at middle and low latitudes?If not, the observational phenomenon that once seemed tobe attributable to the F-layer dynamo has all but vanished.What went wrong?

3. Ionospheric dynamos and electric polarization �elds

3.1. E-layer and F-layer dynamos

The dynamo action in the ionosphere occurs because, inresponse to neutral air winds in the presence of the geo-magnetic 8eld, positive ions and electrons (drift velocitiesVi and Ve) move in diDerent directions, essentially becauseof their very diDerent gyrofrequency=collision frequency ra-tios. The diDerential motion produces a current density

j = Ne(Vi − Ve); (4)

where −e is the electron charge and N is the concentrationof electrons or ions (which may be taken as equal). ThediDerences in direction between ion and electron drift veloc-ities are greatest in the dynamo region at 100–130 km (theregion below 100 km is quite unimportant in this matter,because of its small electron density). Above 150 km, in theF-layer, the vectors Vi and Ve are almost equal in magnitudeand the angle between their directions is small. Nevertheless,the height-integrated F-layer current is quite appreciable.

Eq. (4) is not as straightforward as it looks. Not onlydo Vi and Ve depend on the gyrofrequency=collision fre-quency ratios, which are rapidly height-varying, but also theions and electrons are driven both by the neutral air windU and also by the electric polarization 8eld E that is set upby the resulting charge separation, in accordance with Pois-son’s equation. Magnetospheric sources (particularly duringmagnetic disturbance) and electrical processes in the loweratmosphere, such as thunderstorms, also contribute to thepolarization 8eld in the ionosphere. Whatever their source,the currents and 8elds continually adjust themselves suchthat j is divergence-free and E is curl-free, both to a veryhigh degree of accuracy. The subject is fraught with com-plexity, so it is not surprising that many simpli8cations andcompromises are made in modelling the system.


Fig. 3. Sketch of the F-layer dynamo (after Rishbeth, 1997), looking eastward at the magnetic equator; the west-to-east neutral air wind inthe F-layer blows into the diagram. The two curves are lines of force of the geomagnetic 8eld. The winds drive ions perpendicular to the8eld lines, the electrical circuit being closed by currents ;owing parallel to the magnetic 8eld lines and horizontal currents in the E-layer.

The E-layer and F-layer dynamos are coupled viathe highly conducting 8eld lines (Fig. 3). Because thegyrofrequency=collision frequency ratios in the E and Flayers are very diDerent, the dynamos behave diDerently.The E-layer dynamo is essentially a voltage generator, de-livering a voltage UE × B. The F-layer dynamo resemblesa current generator, delivering a current as given by Eq.(4); but the voltage it develops is small by day becausethe highly conducting E-layer provides an easy return pathwhich short-circuits the F-layer dynamo. At night, nearlyall the E-layer plasma recombines, and the E-layer conduc-tivity falls to a level at which the F-layer dynamo becomesopen-circuited, so that it develops a voltage that approxi-mates to the full dynamo voltage UF × B. More discussionmay be found in the textbook by Kelley (1989) and sev-eral papers (e.g., Rishbeth, 1971, 1977, 1997, Crain et al.,1993a, b). Section 4.2 returns to the consequences of thisshort-circuiting and open-circuiting.

3.2. Which dynamo?

Which dynamo is dominant, at any given magnetic lati-tude, depends on the height-integrated Pedersen conductiv-ity. Although the conductivity per ion pair is always fargreater in the E-layer than in the F-layer, what counts is theintegrated conductivity along a magnetic 8eld line, whichdepends on the electron density distribution.

During the day the electrical conductivity of the E-layergreatly exceeds that of the F-layer, and the daytime E-layerdynamo makes by far the major contribution to the globalionospheric current. However, conditions are diDerentwithin about ±20◦ of the magnetic dip equator, where the8eld lines cross the magnetic equator at apex heights of lessthan about 1000 km. Within ±8◦ of the magnetic equator,the 8eld lines do not enter the F-layer, so the E-layer dy-namo is not magnetically linked to the F-layer and is mainly

driven by E-layer winds. This zone contains the equato-rial electrojet, which does not seem to play any particularrole in E-layer=F-layer coupling. SuNce it to say that theelectrojet current is due to a large vertical polarization 8eldwhich arises in the special circumstances of the equatorialgeometry; this polarization 8eld acts to nullify the geomag-netic constraint on ion and electron motions, thus creatingthe large eDective ‘Cowling’ conductivity (see textbooks).

In the intervening magnetic latitudes, between about(±)12◦ and 20◦, the magnetic 8eld lines cross the equatorat apex heights of 300–800 km. Because of their long pathlength in the equatorial F-layer, these 8eld lines have agreater integrated Pedersen conductivity (�P), so a givenhorizontal wind generates a greater current than is the casefor 8eld lines at lower and higher latitudes. As pointedout by Crain et al. (1993a), the F-layer dynamo drives thesystem because, in this latitude range, it makes the majorcontribution to the 8eld-integrated Pedersen conductivity,in that∫

F�P ds¿

∫E�P ds: (5)

Here, the ‘E’ integration (ds) extends along a 8eld line be-low 150 km and the ‘F’ integration extends from 150 kmto the equatorial apex of the 8eld line. Crain et al. (1993a)show that this inequality holds very well at night (when thesymbol � is appropriate) and is also valid by day, exceptperhaps at solar minimum. If one reckons the ‘strength’ ofthe dynamo in terms of the induced electric 8eld, the con-ductivity integrals in Eq. (5) are weighted by the wind speedblowing across the magnetic 8eld, and the inequality is mod-i8ed to∫

F�PUF ds¿

∫E�PUE ds: (6)

Since in general UF¿UE, this tips the balance even furtherin favour of the F-layer dynamo. Anderson and Mendillo


Fig. 4. Average west-to-east ion drifts at Jicamarca at equinox for low, moderate and high solar 10:7 cm ;uxes (Fejer et al., 1991).

(1983) showed that the mean zonal drift velocity of theplasma is given by the weighted mean

〈VF〉=∫F�PUFB ds

/∫F�P ds; (7)

where 〈〉 represents a zonal average over local time, whichfor present purposes may be taken as an average over longi-tude. Eccles (1998) has investigated how this drift is relatedto the requirements that curlE=0 and that div j=0, the for-mer appearing to be the major factor. Note incidentally thatthe zonal mean of the electric 8eld 〈Ex〉 must be zero; oth-erwise, the electric potential would not be uniquely de8ned.

3.3. Drifts due to the low-latitude polarization 7elds

The polarization 8elds produced by the F-layer dynamodrive fast eastward drifts at night, as observed at Jicamarca,especially before midnight (Fig. 4). The daytime westwarddrift is slower, so the plasma superrotates whether or notthe air does so. The large upward velocity at sunset, the‘pre-reversal enhancement’ which is greatest at solar max-imum, and a corresponding but smaller ‘downward bump’sometimes seen around sunrise, seem well explained interms of the zonal electric 8eld Ex that appears at the duskand dawn terminator. It may be thought of as an ‘edgeeDect’ in the large nighttime polarization 8eld, resultingfrom the curl-free nature of the 8eld. See Eccles (1998).

Fig. 4 shows that the eastward drift in the evening sec-tor, and therefore the vertical electric 8eld, increases withincreasing solar activity (Fejer et al., 1991). Since the east-ward Vx (and the consequentUx) in evening hours contributea large part of the total superrotation, there is a con;ict withthe satellite drag observations, which do not show a system-atic dependence of superrotation � on solar activity (point(iii) of Section 2.1).

4. Zonal winds in the thermosphere

4.1. The general equation of motion of the neutral air

The horizontal pressure gradients in the thermospheredrive horizontal winds, and the wind velocity U depends onthe Coriolis force due to the Earth’s rotation (angular veloc-ity &), the molecular viscosity of the air, and the ‘ion-drag’due to collisions between air molecules and the ions. Theplasma drift velocity V may be taken to be the ion velocitybecause the electrons play a negligible part in the momen-tum equation. The equation of motion is

dU=dt = F − 2& × U + KN (V − U) + (�=�)∇2U; (8)

where

dU=dt = @U=@t + (U:∇)U: (9)

As written, Eq. (8) applies in the horizontal direction only,as gravity is omitted (being almost precisely balanced bythe vertical pressure-gradient force). The vector F denotesthe force per unit mass due to the horizontal gradient of theneutral air pressure; it is

F = (1=�)∇horizp: (10)

In these equations, � is the air density, � the coeNcient ofmolecular viscosity, K the collision parameter (rate coef-8cient for ion-neutral collisions) and KN the neutral-ioncollision frequency. Besides these terms, a term denotingtidal eDects may be added, or else incorporated in thepressure-gradient term (as here). Viscosity is important inthe F-layer because it tends to smooth out the vertical vari-ation of wind velocity, though computations suggest that itdoes not remove the vertical variation entirely.

Ion-drag exists because the ions, being constrained by thegeomagnetic 8eld, cannot move freely with the wind. Thereis no ion-drag term unless the plasma drift velocity V diDersfrom the neutral-air wind U. Eq. (8) shows that, if the ions


are set in motion by electromagnetic forces, ion-drag thenacts on the neutral air as a driving force given byKN (V−U).

4.2. The simpli7ed zonal wind equation

Now consider the equation for the zonal wind Ux, derivedfrom Eq. (8). Near the equator (so no Coriolis term), omit-ting also the tidal and viscosity terms but retaining the prin-cipal part of the nonlinear advection term, Eq. (8) reducesto

dUx=dt ≡ @Ux=@t + Ux@Ux=@x = Fx + KN (Vx − Ux): (11)

With a simple picture of maximum thermospheric tempera-ture and pressure in the late afternoon, and minimum shortlybefore sunrise, the pressure-gradient force Fx and hence thewind Ux are directed east-to-west for most of the day andwest-to-east for most of the night. As mentioned in Sec-tion 3.1 above, the F-layer dynamo is by day short-circuitedby the E-layer, so that it drives electric current but buildsup little polarization 8eld. With the large daytime electrondensity, ion-drag is strong. At night the F-layer dynamois open-circuited, and builds up a strong upward polariza-tion 8eld that moves the plasma rapidly eastward. This isLenz’s law, with the electric 8eld tending to oppose itscause, namely the diDerential eastward velocity (Ux − Vx).The consequent reduction in ion-drag in Eq. (11) enablesthe eastward wind to blow faster than the westward daytimewind, giving a net eastward motion. The polarization ratio

� = (Vx=Ux) (12)

is a measure of the eDectiveness of the F-layer dynamo inbuilding up a polarization 8eld (Rishbeth, 1971). Thus,�=1if the F-layer dynamo is fully open-circuited with a totallyinsulating E-layer, and therefore most eDective, this beingthe idealized extreme nighttime case; and�=0 if the F-layerdynamo is fully short-circuited by a perfectly conductingE-layer, and therefore ineDective, this being the idealizedextreme daytime case. By its alternating short-circuiting andinsulating eDects, the E-layer acts as a kind of ‘ratchet’ thatpermits the plasma to move freely at night, when the drift ismainly eastward; but locks it to the 8eld lines by day, whenthe drift is mainly westward. This suggests that � and thesuperrotation � should peak at heights near the apex of the8eld lines for which the inequality (5) is greatest.

Calculations based on Eq. (11) with a simple day=nightpressure variation gave a mean eastward wind 〈U 〉 ofabout 50 m s−1 at the equator (Rishbeth, 1971). This initialresult was supported by Heelis et al. (1974), whose calcu-lations were based on the empirical model atmosphere ofJacchia (1965) with an experimentally determined tem-perature distribution. For a range of assumed conditions,Heelis et al. (1974) obtained mean eastward winds of 70–110 m s−1 which correspond to superrotation of 15–22%at the equator. They also found that the addition of a tidaleast-west ion velocity, produced by the E-layer dynamo,makes very little diDerence to the deduced �, so to that

extent the E-layer and F-layer dynamo 8elds may be re-garded as independent. Note that, strictly speaking, in Eq.(12) Vx is the drift due to the polarization 8eld of the F-layerdynamo only, excluding the contribution of the E-layer dy-namo.

4.3. The zonal momentum balance

Since the existence of the F-layer polarization 8elds isnot in doubt, but nevertheless the wind calculations dis-agree with the DE-2 measurements, the next question is“Whatever happened to the calculations that predicted su-perrotation?” There appears to be nothing wrong with thezonal wind equation, Eq. (11), or with the reasoning thatleads to the conclusion that ion-drag is small at night. Noris the viscosity term expected to play any major part, otherthan its well-known eDect of smoothing out the F-regionwind velocity in the vertical direction. If, however, therewere a mean zonal wind at the base of the thermosphere,it would in time be transmitted to the overlying thermo-sphere. But no such west-to-east wind of 50–100 m s−1

seems to exist; on the contrary, as previously mentioned,the WINDII=HRDI dataset of McLandress et al. (1996) in-dicates that at heights of 200 km and below the prevailingzonal winds are east-to-west, implying subrotation.

The 8nger points to the local time variations of tempera-ture and pressure. Later evidence is that a ‘midnight bulge’exists in thermospheric temperature (Herrero and Spencer,1982), so the zonal pressure-gradient force Fx is not con-sistently large and eastward, as was assumed in the originalestimates of superrotation. In their examples for 1978–1981,Herrero et al. (1985) showed that the zonal pressure-gradientforce Fx decreases rapidly after sunset (18 LT) and, whilenot actually changing sign until 03 LT, becomes quite smallafter 21 LT. As a result, the nighttime eastward wind, eventhough it reaches about 200 m s−1 in the late evening around20 LT, then becomes slower and does not give a large east-ward 24-h average. Herrero et al. (1985) computed the mo-mentum balance at four times of night, by calculating theterms in a simpli8ed version of the zonal wind equation Eq.(11), and showed that the observational data satisfy theirequation quite well.

Ideally, the way forward is to compute the thermosphericwinds by a coupled thermosphere–ionosphere model withfully self-consistent electrodynamics. Results from such amodel are indeed cited in Section 5 below. But the com-plexity of such models makes it diNcult to see just whatis going on in the thermosphere=ionosphere interaction. Forthat reason, it seems worth pursuing a much simpler model,with the neutral thermospheric parameters taken from theempirical MSIS-86 model of Hedin (1987), to investigatetwo questions. First, what key features of the thermosphere–ionosphere system really determine superrotation in equa-torial latitudes (Section 4.4)? Secondly, how well does theMSIS model with realistic ionospheric data reproduce theDE-2 wind data shown in Fig. 2 (Section 4.5)?


4.4. What really determines the prevailing zonal wind?

To start with, Eq. (11) is drastically simpli8ed by keepingonly the pressure-gradient and ion-drag as driving forces,and assuming steady-state conditions. Dropping for brevitythe subscript ‘x’, the equation reduces to

d�=dt = 0 = F − KNU (1−�) = F − U=R (13)

so that

U = FR (14)

in which

R = 1=KN (1−�) (15)

is related to the reciprocal of the neutral-ion collision fre-quency. R may be thought of as a time constant for momen-tum exchange between the ions and the air.

The essentials of superrotation may be illustrated by as-suming that the ion-drag parameter takes a 8xed daytimevalue RD (06–18 LT) and a 8xed nighttime value RN

(18–06 LT), which may not be too unrealistic in the equa-torial ionosphere. In terms of its diurnal and semidiurnalcomponents (it having no prevailing component), F maybe expressed as

F(t) = F1 cos�(t − t1) + F2 cos 2�(t − t2); (16)

where the phases t1 and t2 are the local times of the peaksof diurnal and semidiurnal components (zero phase impliesmaximum eastward amplitude at midnight). Integrating Eq.(14) over 24 hours gives the prevailing wind as

〈U 〉={∫

DRDF(t) dt +

∫NRNF(t) dt

}/(1 day); (17)

where the D(ay) integration runs from 06 to 18 LT and theN(ight) integration from 18 to 06 LT. In the integration, allthe terms on the right disappear except the cosine terms inF1, giving the prevailing wind as

〈U 〉= (2F1)(RN −RD) cos�t1 (18)

Eq. (18) shows that the superrotation depends on the diurnalcomponent of the pressure-gradient force F and on its timedelay t1 with respect to a simple sinusoidal variation (Theterdiurnal and other odd components of F also contribute,but are unlikely to be large).

For a numerical illustration, the chosen time is a magnet-ically quiet day in September 1982, a month of rather highsolar activity (mean F10:7 = 167); the chosen place is Huan-cayo (12◦S, 75◦W, magnetic latitude 2◦). The MSIS-86model (Hedin, 1987) gives F1 = 0:05 m s−2 and t1 =−3:7hours (corresponding to maximum eastward driving forceat 20.3 LT, maximum westward at 08.3 LT). The chosenvalue of K is 7×10−16 m3 s−1, consistent with the value ofion-neutral collision frequency recommended by Omidvaret al. (1998). Averaging the daytime values of HuancayoNmF2 gives a value ND=16×1011 m−3; similarly for nightNN =9×1011 m−3. Assuming eNcient polarization at night

(�N = 0:8) but only weak polarization by day (�D = 0:3),the day and night ‘time constants’ are found to be

RD = 1300 s = 0:35 h (19)

RN = 8000 s = 2:2 h (20)

These times are short compared to a day, which meansthat the steady-state approximation should be reasonable.From Eq. (18) the prevailing wind is then found to be 〈U 〉=38 m s−1, which compares well with the 34 m s−1 mean ofthe DE-2 winds shown in Fig. 2.

4.5. The local time variation of zonal wind, using theMSIS model

Although the above analysis suggests that a simple modelwith empirical parameters can account for the mean zonalwind observed by the DE-2 instruments, it is not so easyto match the detailed local time variation of U (t). Thedashed curve in Fig. 2 shows the zonal wind computed fromEqs. (14) and (15), using the same F; K; ND and NN asabove and adjusting the day and night polarizations � to 8tthe data as well as possible. The calculation is for 300 kmheight, but the results are not very height-sensitive becauseboth the pressure-gradient force and the electron density areslowly-varying in the vicinity of the F2-peak.

Perusal of Fig. 2 shows the diNculties. First, a nighttimepolarization of � = 0:85 is needed to match the observedevening peak in U (t) of about 230 m s−1, but even thishigh value of � fails to reproduce the early morning east-ward winds (00–05 LT). Next, the computed U (t) showsa marked westward ‘kick’ before dawn, which is caused bythe reversal of the MSIS zonal pressure-gradient force (andis probably associated with the ‘downward bump’ of verti-cal drift velocity mentioned in Section 3.3) but is not seenin the DE-2 data. The ‘kick’ can be limited by the quitereasonable device of using an intermediate value of polar-ization at dawn and dusk, namely � = 0:65, but even soit seriously detracts from the superrotation. The computedwestward wind by day (07–14 LT) is clearly too small, evenwith a high (and probably unrealistic) daytime polarization,� = 0:5, and reverses too early around 14 LT; and lastly,the resulting prevailing wind is only 19 m s−1 (4% superro-tation). The diDerence between this value and the 38 m s−1

derived from the Fourier component approximation in Sec-tion 4.4 is attributed to the details of the pressure-gradientvariation around dawn, to which the ‘kick’ is very sensitive;the winds may well be variable and poorly determined atthis time of day.

Thus, using the steady-state model of Eqs. (14) and (15)with the MSIS pressure-gradient force, it seems impracti-cable to match both the daytime winds and the superrota-tion to the DE-2 wind data. Some features of the computedU (t) could be improved by retaining the inertial term inEq. (13), or by other re8nements such as using hourly valuesof � and taking account of viscosity, but there seems little


Table 1Jicamarca prevailing zonal wind 〈U 〉 and drift 〈V 〉 (positivewest-to-east) from TIE-GCM (m s−1), with and without theE-layer dynamo. From Fig. 2 of Richmond et al. (1992) and newresults by Fesen (private communication, 2000)

280 km 400 km

1992 model: no dynamo〈U 〉 18 3〈V 〉 0 0

1992 model: with dynamo〈U 〉 30 18〈V 〉 20 11

2000 model: with dynamo〈U 〉 41 47〈V 〉 48 42

point in introducing such complications into what would stillbe an oversimpli8ed approach. Nevertheless, these simplesteady-state calculations do illustrate the factors involved inthe ion-drag mechanism of superrotation. Why the ‘midnightbulge’ exists in the 8rst place is a diDerent question, dis-cussed for example by Raghavarao et al. (1993). It appearsto be associated with strong downward motion of the air.

5. Prevailing winds computed from coupledthermosphere–ionosphere models

An obvious further step is to use contemporaryglobal coupled thermosphere–ionosphere models, whichinclude a range of known physical processes and drivingforces.

5.1. Coupled TIE-GCM

The global system of winds and drifts in both E- andF-regions has been computed with the coupled TIE-GCMmodel, including fully self-consistent neutral air winds, elec-tric 8elds and electrodynamic drift (Richmond et al., 1992,Richmond, 1995). For Jicamarca (12◦S, 76◦W) at solarmaximum and with magnetically quiet conditions, both thezonal wind Ux and the zonal drift Vx have a positive (east-ward) maximum in the early morning, around 02–04 LT,and a westward (negative) maximum around 16 LT. Table 1shows mean values for two heights, 250 km and 400 km,the former being where the nighttime winds are strongest.According to the model, 250 km is below the nighttimeF2-layer and 400 km is near the daytime and nighttimeF2 peak. Velocities are shown both with and withoutionospheric dynamo action. In the latter case, the ionsmove only along the magnetic 8eld direction (driven bywinds and plasma diDusion), and are practically stationaryin the zonal direction; superrotation of the neutral air isvery small.

Taking values of Vx and Ux from Fig. 2 of Richmond(1995), it is found that the polarization ratio � de8ned byEq. (12) does not diDer greatly between the post-midnightperiod (�=0:5) and the afternoon period (�=0:7), and doesnot show the day=night pattern expected from the F-layerdynamo theory. Instead, it peaks around 06 LT and againaround 22 LT, in each case with �¿ 0:8. The E-layer dy-namo 8eld complicates the matter because, in the de8nitionof� in Eq. (12), Vx excludes the contribution of the E-layerdynamo. The superrotation is only 4–6%.

Results from a recent version of the TIE-GCM model,kindly supplied by C. G. Fesen and A. D. Richmond (privatecommunication, 2000) give greater winds and drifts. Thenewer calculations were made in the course of a theoreticalstudy of the evening pre-reversal enhancement of verticalion drift, a common feature of the equatorial F-layer (Fesenet al., 2000). It is found that this reversal depends particu-larly on the nighttime E-layer electron density, which has toexceed 4×109 m−3 for the drift reversal to occur. Althoughzonal winds and superrotation were not the object of theirstudy, it seems that a large pre-reversal enhancement tendsto be accompanied by large zonal drifts and winds aroundsunset, which in turn make a major contribution to superro-tation. See also Section 6.

5.2. Superrotation at midlatitudes: results from theCTIP model

Do the coupled models predict superrotation at midlati-tudes? This question has been investigated with the aid ofthe CTIP model described by Fuller-Rowell et al. (1996)and Millward et al. (1996). The computed zonal winds at45◦N and 45◦S are largely Coriolis-controlled. They are partof the strong vortices at auroral and subauroral latitudes, thedetails of which vary in a complicated way with latitude,longitude and geomagnetic activity. The prevailing zonalwinds are around 50 m s−1 at solstice, west-to-east in lo-cal winter and east-to-west in local summer, but only about20 m s−1 at equinox; since they reverse with hemisphereand season, these winds do not represent a globally aver-aged superrotation. Evaluating their eDects on satellite orbitsis complicated, but it seems quite possible that the vorticescould in;uence the orbits of satellites that reach these lat-itudes, if the perigees encounter them systematically. Thismight help to account for the diDerent values of � derivedfrom diDerent satellites, or at diDerent epochs in the lifetimeof any one satellite.

All these results lead to the conclusion that coupled mod-els, such as CTIP and TIE-GCM, predict no systematic su-perrotation in its original sense of a steady rotation of thethermosphere. The zonal winds do not blow in a consis-tent direction, but reverse with local time, being generallyeastward in the evening and westward in the morning. Atmidlatitudes the prevailing component varies with latitudeand season, but at equatorial latitudes the models do give amodest superrotation of around 5–10%.


6. The e-ect of the nighttime E-layer electron density

The polarization parameter �, introduced in Section 4.2,depends very largely on the E-layer conductivity which isproportional to the electron density NmE. Titheridge (2000)has shown that midnight NmE depends largely on ioniz-ing radiation from the night sky, which varies considerablywith latitude and season. The radiation comes partly fromthe Earth’s hydrogen geocorona, but mostly from starlightwhich has strong localized sources and is independent ofsolar activity. The modelled midnight NmE in low latitudesis greatest in March and least in September (ratio 1.6 at theequator), and is on average 25% greater at latitude 12◦Sthan at 12◦N (Fig. 12 of Titheridge, 2000).

These variations of night E-layer conductivity have atleast two consequences. The 8rst is an annual variation inthe F-layer dynamo 8elds, and therefore in superrotation,which should be greatest in September when night NmEis smallest. The second is a variation with longitude: the8elds and superrotation should be greater in the Indian thanin the South American sector, because of the way in whichthe geographic and astronomical latitude of the magneticequator varies with longitude. It so happens that the meanequatorial value of night NmE, as given by Titheridge’smodel, is approximately the same as the maximum value of4× 1011 m−3 that permits the pre-reversal enhancement ofvertical ion drift, according to the modelling study by Fesenet al. (2000); see Section 5.1.

7. Conclusion

Both the in situ measurements of thermospheric winds,and the computational thermosphere–ionosphere models,provide some support for the idea of superrotation: prevail-ing winds exist, but their patterns are very diDerent fromthe picture of uniform eastward rotation that the term su-perrotation might be taken to imply. At low latitudes, thesuperrotation is about 5–10%; it is due to the action of theF-layer dynamo, and stems from the day-night diDerence inpolarization 8eld mentioned in Section 3.1, and the phasediDerence between the resulting variation of ion-drag andthe thermally driven zonal winds (Sections 4 and 5). It is in-;uenced by the ‘midnight bulge’, but why that bulge existsis a separate question. Meridional winds may have minoreDects on the satellite orbits, but are unlikely to be a consis-tent cause of superrotation, because they generally reversewith season and are much aDected at high midlatitudes bythe vagaries of the auroral ovals. Although not the onlyfactor that aDects the operation of the F-layer dynamo, theseasonal and latitudinal variations of NmE, which controlthe nighttime polarization 8elds, are likely to be signi8cantfactors in the varied behaviour of the nighttime equatorialionosphere.

Can superrotation in the Earth’s thermosphere be pro-duced by some quite diDerent mechanism? The answer

seems to be ‘no’. The diNculty is that, alone among theterrestrial planets, the Earth possesses both a dense atmo-sphere and a strong magnetic 8eld. The ion concentrationin the terrestrial F-region is such that ion-drag plays quitea dominant role in its dynamics, being so strong that onlya mechanism that depends on ion-drag, or at least includesion-drag in its operation (such as the F-layer dynamo)can produce superrotation. This is not so on Venus, whereion-drag is essentially non-existent because of the weaknessof the planet’s magnetic 8eld, and where thermally-forcedconvection mechanisms are a likely mechanism.

Acknowledgements

This paper was partly written during my tenure of the K.R. Ramanathan Visiting Professorship at the Physical Re-search Laboratory, Ahmedabad, India. I am most gratefulto the Director and staD of PRL for their hospitality, and toR. Raghavarao for a valuable discussion. I thank Cassan-dra Fesen and Arthur Richmond for helpful discussion andfor providing recent TIE-GCM results (Section 5.1), IngoMTuller-Wodarg for providing the CTIP prevailing windsdiscussed in Section 5.2, and Joei Wroten for help withdiagrams. CTIP is a joint collaborative project between theAtmospheric Physics Laboratory of University College,London, the School of Mathematics and Statistics of theUniversity of SheNeld, and the NOAA Space EnvironmentCenter, Boulder, Colorado.

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