Ionosphere

Ionospheric Electrodynamics' A Tutorial

A.D. Richmond

High Altitude Observatory, National Center for Atmospheric Research, Boulder, Colorado

J. P. Thayer

Geoscience and Engineering Center, SRI International, Menlo Park, California

This paper gives a tutorial overview of ionospheric electrodynamics, including the observed behavior of ionospheric electric fields and currents, the physics of ionospheric electrical conductivity and Ohm's law, the operation of the ionospheric wind dynamo, and the transfer of energy between the magnetosphere and the ionosphere. The ionosphere forms an important part of the magnetospheric electrodynamic system. It is a region where ion-neutral collisions cause ions and electrons to move at different velocities across magnetic field lines, thereby violating the frozen-in flux condition and resulting in significant flow of ohmic current. Ionospheric conductivity is a function of the geomagnetic field, the plasma density, and the collision rate. Neutral winds cause generation of electric current through a dynamo effect. The winds result from diurnally varying solar heating, from upward-propagating global atmospheric waves, and from the Ampere force and Joule heating resulting from the electric current flow. Electromagnetic energy flow is normally directed from the magnetosphere into the ionosphere, as can be eval- uated with the aid of Poynting's theorem, but strong thermospheric winds can sometimes reverse the direction of this energy flow.

INTRODUCTION

The ionosphere is an electrically conducting medium, and carries a substantial portion of the electrical current flowing in the Earth's space environment. It forms a critical part of the global magnetospheric current system, providing a closure path for geomagnetic-field- aligned currents that extend to the outer magnetosphere. The magnetic stresses associated with these

Magnetospheric Current Systems Geophysical Monograph 118 Copyright 2000 by the American Geophysical Union

currents result in significant momentum transfer between the ionosphere and the magnetosphere. Impor- tant amounts of electromagnetic energy are also transferred between the magnetosphere and the ionosphere by the electric fields and currents, leading to dissipation of magnetospheric energy and to heating of the upper atmosphere. The ionosphere is a region where the frozen-in flux approximation of magnetohydrodynamics breaks down, owing to collisions between charged and neutral particles. It is also the seat of current generation produced by the dynamo effect of winds in the thermosphere, at altitudes above about 90 km. Those winds are produced not only by solar heating and by upward- propagating global atmospheric waves like tides, but they are also produced through the Ampere force and

131

132 IONOSPHERIC ELECTRODYNAMICS: A TUTORIAL

Figure 1. Schematic of global ionospheric electric currents (ribbons with arrows) and electric potentials (d- and-), viewed from the day side of the Earth.

the Joule heating exerted on the medium by the current itself. There is therefore an interesting mutual coupling between the currents and the winds. This paper presents a tutorial overview of the phenomenology and physical processes associated with ionospheric electric fields and currents.

DESCRIPTION OF GLOBAL ELECTRIC

FIELDS AND CURRENTS

Figure 1 sketches the global ionospheric currents and electric potential, with the currents illustrated by ribbons and the potential with q- and-. (On global scales, the ionospheric electric field is essentially a potential field for phenomena that vary on time scales longer than a minute or so, which are the only phenomena considered in this paper.) The Earth's main magnetic field has a dominant influence on the ionospheric conductivity and on the flow of current between the magnetosphere and the ionosphere. Electric fields and currents are therefore strongly organized with respect to the geomagnetic field. For convenience, currents at high magnetic latitudes and those at middle and low latitudes

are often considered separately, although in reality the

currents and electric fields at all latitudes are coupled. Because the Sun is ultimately responsible not only for the ionospheric conductivity but also for the drivers of ionospheric currents, the patterns of electric potential and current tend to be organized in a coordinate system of magnetic local time (MLT) and magnetic latitude. As the Earth rotates, there is therefore a daily variation in the direction and strength of currents and electric fields over any given location on the ground.

At high latitudes the ionospheric currents are joined with currents flowing along geomagnetic field lines into the magnetosphere, and the electrodynamics is dom- inated by the influences of magnetospheric processes. The total current flow is on the order of 107 A. At mid-

latitudes much of the ionospheric current is generated by the ionospheric wind dynamo, which on the average produces global current vortices on the dayside of the Earth, counterclockwise in the northern hemisphere and clockwise in the southern hemisphere. The total current flow in each vortex is on the order of 105 A. The two hemispheres are electrically coupled by currents flowing along geomagnetic field lines whenever there is an im- balance in the dynamo forcing between the hemispheres. Near the magnetic equator there is a substantial inten- sification of the eastward current known as the equatorial electrojet, which is associated with the highly anisotropic conductivity of the ionosphere and the pres- ence of a nearly horizontal geomagnetic field.

There are strong electric fields at high latitudes, on the order of several tens of millivolts per meter or more, associated with the magnetospherically produced currents. On the average, these electric fields are represented by an electric potential having a high on the morning side of the polar region and a low on the evening side, with a total potential drop that ranges from 20 kV to 200 kV. Figure 2 shows a specific example of the high-latitude potential pattern in the northern hemisphere. Both the pattern and the strength of the high-latitude potential pattern have been found to depend strongly on the direction and strength of the interplanetary magnetic field (IMF).

At middle and low latitudes electric fields are con-

siderably smaller, typically a few millivolts per meter during magnetically quiet periods. Along the magnetic equator there is a potential high around dawn and a low around dusk, with a total potential drop on the order of 7 kV. At midlatitudes the MLT of the potential high and low tend to shift more toward evening and midday, respectively.

The quiet-day geomagnetic variations associated with the overhead ionospheric currents have traditionally

RICHMOND AND THAYER 133

1992 JAN 28 01:15 lyr 12

l•y• 6.1.- Bz- -6.4

/

••c PO'I•NTIAL

91 IcY

/ \

18 06

\ / /

\ / /

50 mV/m • 09

O0

Figure 2. Electric potential in the northern hemispheric polar region estimated from ion velocities measured by two Defense Meteorological Satellite Program (DMSP) spacecraft, whose data are labeled 09 and 10, as well as from numerous ground magnetometers, on 1992 January 28, at 0115 UT. The coordinates are magnetic latitude, from 50 ø to the pole, and magnetic local time, with local noon at the top. The contour interval is 10 kV, with dashed lines indicate regions where the uncertainty in the large-scale electric field exceeds 50%. The potential high and low are marked by + and-, respectively, and combine for a total potential drop of 91 kV. The measured ion velocities are multiplied here by the magnetic field strength in order to give magnitudes in units of electric field. The electric-field directions

are rotated 90 ø clockwise from the displayed vectors. From Lu et al. [1994].

been called Sq, S for solar (as opposed to a much smaller lunar magnetic variation), and q for quiet-day. At middle latitudes they have magnitudes on the order of 30 nT. The associated ionospheric currents are called the $q currents. The centers of-the current vortices seen in Figure 1 lie around 30 ø north or south magnetic latitude. The $q magnetic variations at solar maximum are nearly twice as large as at solar minimum, due primarily to increased ionospheric conductivity but also to stronger upper atmospheric winds at solar maximum. The variations under the equatorial electrojet are more than a factor of two larger than those at other stations, and are larger at equinox than at either of the solstices. The magnitudes of the variations at midlatitudes are larger in the summer than in the winter. Both the $q

currents and their associated electric fields exhibit con-

siderable day-to-day variability, even on magnetically quiet days, that is believed to be caused by day-to-day variability in the thermospheric winds that drive the ionospheric dynamo.

During magnetic storms the global ionospheric electric fields and currents and their associated magnetic variations increase in magnitude, and exhibit rapid fluc- tuations. The disturbed magnetic perturbations are associated only partly with overhead ionospheric currents, since a substantial portion comes from more distant magnetospheric currents like the ring current and field-aligned currents. Figure 3 shows an example as- sembled by Fejer [1990] of a two-day period with some disturbances. Negative excursions of the Bz component of the IMF correspond well with the periods of auroral disturbances in the AU/AL indices. The largest

18-19 JANUARY 1984 500

-500

to IMF IJ' ""

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HUANCAYO

0 - 50- -

ß

• JICAMARCA ' • '

-I- -

ß i - i - i - 1 ß ! - - i - i - , - i - J '

O0 08 16 OO 08 16 O0

IO0

U.T.

Figure 3. Interplanetary, auroral, and equatorial electrodynamic features on 1984 January 18-19. MLT is approximately UT- 5 hours. The AU/AL indices are obtained by superposing auroral-zone magnetograms. The IMF Bz component was measured by the IMP-8 spacecraft in the solar wind. The magnetogram from Huancayo, under the equatorial electrojet, is referenced to the average quiet-day variation (the smooth line). The eastward electric field over the Jicamarca incoherent-scatter radar is also referenced to

the average quiet-day variation (smooth curve). The small circles are at local midnight. From Fejer et al. [1990].


equatorial electric-field disturbances measured at Jica- marca occurred at night, between 23 UT on January 18 and 11 UT on January 19. Because the overhead ionospheric conductivity is very small at night, the nighttime electric-field disturbances do not show up on the Huancayo magnetogram, which senses rather only the effects of distant magnetospheric currents.

The ionospheric electric field E is essentially perpendicular to the geomagnetic field B, and at middle and high latitudes it is approximately constant in altitude. The electric current density J, however, varies strongly with altitude through the ionosphere. Plate 1 illustrates the height and time variations of the component of J perpendicular to B, between 100 km and 130 km altitude, for a four-hour period on 1997 March 25, measured by the Sondrestrom radar (74.2 ø magnetic latitude). Details of how the electrodynamic parameters are derived from the monostatic radar are provided by Thayer [1998a]. The electric-field vector is also shown in the inset for one particular time, along with idealized current vectors calculated at three altitudes as outlined

in the next section (the idealized current vectors are different from the measured values of J in that the former

are computed neglecting the effects of winds and height variations of electron density). When E is strong, J tends to be approximately parallel to E at high altitudes, but the two vectors tend to become more nearly perpendicular at 100 kin.

Also shown in Plate I is the Joule heating ra. te per unit volume. Joule heating can contribute significantly to the energy budget of the thermosphere at high latitudes, at times exceeding the heating produced by solar insolation [Banks, 1977]. The Joule heating rate is structured in altitude owing to the influence of height- varying winds and conductivities. It peaks around 120 km in this example, and is closely tied to the peak in current density. The rate of local thermospheric temperature change due to Joule heating is more directly related to the heating rate per unit mass, that is, to the heating rate per unit volume divided by the mass density. For example, at 125 km an estimate of the neutral temperature increase after 20 minutes of Joule heating (using a value of 1.0 x 10 -6 W m -3) is less than 100 K. At higher altitudes, say above 200 km, the temperature increase over the same time period can be many hun- dreds of kelvins. This is due to the fact that although the volumetric Joule heating rate is decreasing with in- creasing height the neutral density is decreasing more rapidly, and so less energy is needed to significantly heat the more tenuous neutral gas.

IONOSPHERIC ELECTRICAL

CONDUCTIVITY AND OHM'S LAW

In order to understand the physics of ionospheric electrodynamics, it is essential to understand the nature of ionospheric conductivity. Three elements are critical for determining the conductivity: the plasma density, the geomagnetic field, and the rate at which the charged particles collide with neutral atmospheric molecules. Figure 4a shows typical midlatitude density profiles of atmospheric neutral molecules and of charged particles; for the latter, the densities of electrons and singly-charged positive ions are essentially the same. Note that the neutral density exceeds the plasma density by several orders of magnitude at all heights. The neutral constituents and their dynamics are obviously going to have a major impact on the plasma dynamics.

Let us examine the mean motion of the charged particles in the frame of reference of the neutral gas. The main forces acting on a charged particle are the Lorentz force and the frictional forces due to collisions with

other particle species. For ions and electrons the force- balance conditions, averaged over the particle distribu- tion functions, are respectively:

N•e(E • + vi x B) - Nemib'inVi - Nemib'ie(Vi - Ve) = 0 (1)

-Nee(r' +Ve xS)-Nerfleb'enVe -]-Nerfleb'ei(Vi--Ve) -- 0

where N• is the electron density, e is the magnitude of the electron charge, mi and vi are the ion mass and bulk velocity, rn• and v• are the electron mass and velocity, lJin , lJie , Yen, and lJei are the ion-neutral, ion- electron, electron-neutral, and electron-ion collision frequencies, which are assumed to be independent of the bulk velocities, and E • is the electric field in the frame of reference of the neutral gas. In reality, the effective electron-neutral collision frequency is somewhat different for electron motions parallel or perpendicular to B.

Analysis of (1) and (2) [e.g., Richmond, 1995b] shows that parallel to B the electron velocity dominates over the ion velocity and is given to a good approximation

by eEil = + (3)

while perpendicular to B the ion and electron velocities are given to a good approximation by

ui•gtiE'• - f•b x E 2 (4) = +


5OO

4OO

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200

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, I , I I , I I, ' 10 -2 10 0 10 2 10 4 10 6 10 8

Collision Frequencies and Oyrofrequencies (s -•)

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4OO

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200

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(•)

.

,

:-

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,. ..

I I I I I

-8 10-6 10-4 10-2 10 0 Conductivities (Sm -•)

10 2 10 -5

(d)

10-4 10-3 Ion-drag coefficients (s -•)

Figure 4. Typical ionospheric parameters at 44.6øN, 2.2øE on March 21 for medium solar activity (10.7 cm radio flux of 120 x 10 -22 W cm -2 Hz-1; sunspot number 67) and low magnetic activity (Ap - 4), obtained from the 1990 International Reference Ionosphere [Bilitza, 1990] and the MSISE-90 neutral-density model [Hedin, 1991]. (a) Number densities of electrons, ions, and neutrals at noon and midnight. The altitudes of the ionospheric regions conventionally called D, E, and F are also indicated. (b) Collision frequencies v•, ve•_L (for motion perpendicular to B), and %•11 + %ill (for motion along B), and gyrofrequencies f• and f•,. Collision frequencies are from Richmond [1995b]. (c) Noontime parallel (all), Pedersen (api, and Hall (all) conductivities. (d) Ion drag coefficients apB2/p (Pedersen) and aHB2/p (Hall), and the angular rotation rate of the Earth, •.

--t2en_L•eE•L -- •e2b x E 5 (5) V_L: 2 e + where b is a unit vector in the direction of B, and where

- (6)

•e -- ½]•/T/•e (7)

are the angular gyrofrequencies of the ions and electrons, describing their gyration in the geomagnetic field.

Figure 4b shows typical noontime midlatitude profiles of the collision and gyro-frequencies for electrons and positive ions. The collision frequency of electrons with neutrals determines the mobility of electrons along B below about 200 km, while above that height collisions with ions become more important. In any case,

136 IONOSPHERIC ELECTRODYNAMICS' A TUTORIAL

130

125

120

115

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- I

- I

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t

13 14 15

UT (hours)

0.025 O. 150 0.275 0.400 0.525 0.650

JOULE HEATING RATE (uW

Current Calculations at 14:30 UT

Norlh E

J127 kl

Fast

North

• J 117k•

Norlh

Scale:

Current ...... •:> vector

25 gAm -2

E-field • 60 mVm -•

Plate 1. An example of the variations of electrodynamic parameters with height and time in the high- latitude E region, measured by the Sondrestrom incoherent-scatter radar at a resolution of 3 km in height and 5 minutes in time. The vectors are the measured horizontal current density, in/•A/m 9'. 'Northward is up and eastward is toward the right. The scalar image behind the current vectors is the volumetric Joule heating rate in/2W/m 3. The inset shows numerical calculations of the horizontal current density J at three different altitudes, corresponding to the radar electric-field measurement E at 1430 UT, accounting for changes in the ion-neutral collision frequency and the ion gyrofrequency with height, while neglecting neutral winds and using a constant electron density at all altitudes.


Altitude v d

e

160 km • i •

125km X • e Hall i Pedersen

110km • •-• e i

Figure 15. Schematic of height variations of electron (e) and ion (i) velocities, v, and of the electric current J. The magnetic field B is into the page, and the electric field E' is downward. The Pedersen component of the current is downward, and the Hall component is toward the left.

the electron mobility p•rallel to B is sufficiently large to produce a very large electrical conductivity in that direction. This large conductivity tends largely to short out any parallel electric field in the ionosphere, i.e.,

for phenomena with scale sizes perpendicular to B of about 1 km or more. In the plane perpendicular to B, the situation is very different. The geomagnetic field has a very strong influence on the charged particle motion perpendicular to the magnetic field, and therefore on the perpendicular conductivity at all altitudes above 70 km. It tends to constrain charged particles to spiral around field lines. Notice that at high altitudes, where Uin << f•i and Uenñ << f•e, (4)and (5) reduce to

E'xB

viñ-v•ñ- B2 (9) which represents the E x B (E-cross-B) drift velocity of charged particles in crossed electric and magnetic fields. Thus at high altitudes in the ionosphere the ions and electrons essentially move together in the direction perpendicular to the magnetic field. Together with the approximation (8), this leads to the condition of "frozen- in magnetic flux" at these high altitudes, whereby all charged particles on a common magnetic field line at one time remain on a common field line at all future

times. However, collisions of charged particles with neutrals break the condition of frozen-in magnetic flux, so that the charged particles along a given field line no longer move to neighboring field lines in unison. What is important in determining the degree to which charged particles are tied to magnetic field lines is the ratio of the collision frequency with neutrals to the angular gyrofrequency in the magnetic field. The electron gyrofrequency is nearly 107 tad/s, while the ion gyrofrequency is only a little over 100 tad/s, with some height de- pendence due to the varying mean molecular mass of the ions. The electron collision frequency equals the gyrofrequency around 70 km, well below heights where there is enough plasma density to carry significant current. As a consequence, the electrons are essentially tied to the magnetic field throughout the entire conducting ionosphere. For ions, collisions are relatively much more important. Even though the ion collision frequency with neutrals is about two orders of magnitude smaller than the electron-neutral collision fre-

quency, it does not decrease to the level of the ion gyrofrequency until an altitude of about 125 km. It is only above about 150 km that the ions become strongly tied to the magnetic field, and that the frozen-in flux condition is approximately valid. Below 110 km the motion of the ions is strongly coupled with that of the neutral air through collisions. The intermediate altitude range, 110- 150 km, is where the ions gain the ability to move at a velocity substantially different from either the E x B velocity or the velocity of the neutrals.

Figure 5 illustrates the variations of ion motion and electric current with altitude, in the neutral frame of reference. At all three altitudes shown, the electrons essentially move at the E x B velocity, toward the right. At 160 km the ions move nearly in that direction, but have a small component of velocity in the direction of E'. At 125 km the ion-velocity component parallel to E' becomes approximately equal to the component in the E x B direction. At 110 km the ions are nearly im- mobilized, but do still have a small velocity component nearly parallel to E'.

The electric current density J is given by

J - N•e(vi- v•). (10)

By convention, the component of J in the direction of E', in the plane perpendicular to B, is called "Pedersen" current, while the component perpendicular to both E' and B is called "Hall" current. At 150 km the velocity difference between ions and electrons is small but lies


approximately in the direction of E •, and so the resulting electric current is mainly Pedersen. At 110 km, on the other hand, the current is carried mainly by negatively charged electrons moving at the E • x B velocity, and the current is mainly Hall, flowing opposite to the electron velocity. Around 125 km the Pedersen and Hall current components are comparable.

By combining (3)-(5) with (10), we obtain an expres- sion for Ohm's law:

J - apE•_ + a•rb x E' _t_ + allEilb

.•'ee 2

me(Yen]]-• lYeill ) (12) See lJin•i lJen.J_•e

+ lJ in -[- • i Y en.L -[- • e 2 ) (13)

Nee • • ) (14) - lYe n 1

where all, ap, and a• are respectively the parallel, Ped- ersen, and Hall conductivities.

Ohm's law seems to work very well in the ionosphere for time scales considerably longer than the inverse collision and gyro-ffequencies, that is, longer than a minute or so, although the assumed linearity between J and E' may fail if the electric field becomes so large that it affects the values of the collision frequencies. Ohm•s law does not say anything about cause and effect; that is, it does not say that the electric field is the source of the current or that the current is the source of the electric

field. It merely states that the electric field and current are linearly related. If one exists then the other must also exist. Any mechanism that drives current through the medium must be accompanied by an electric field, and any mechanism that creates an electric field in the medium must be accompanied by current flow.

By appropriately defining a conductivity tensor 5, dimensioned 3 x 3, we can write Ohm's law in a more compact form:

J = 5E' (15)

The components of the conductivity tensor are shown in Figure 4c for typical noontime midlatitude conditions. The principal anisotropy of the conductivity is the very large difference between the conductivity along B and the conductivity perpendicular to B at all heights above 80 km. Although one might be tempted to conclude that this large difference would result in currents along B that were much larger than those perpendicular to B, that is not the case in the lower ionosphere. The

reason is that parallel currents cannot continue flowing into the poorly conducting lower atmosphere, and must find a continuation path that traverses magnetic field lines. The parallel and perpendicular current densities are therefore linked together, and the parallel current density is severely limited in its magnitude. As a consequence, the parallel electric field must be very small, as represented by (8). The ratio of parallel to perpendicular electric field strengths is roughly of the order of the ratio of perpendicular to parallel conductivity, typically 10 -5. Another important feature of the anisotropy of the conductivity is the changing ratio of Hall to Peder- sen conductivity with height: a H is larger below about 125 km, while ap is larger above that height. Around 100 kmaH is about 30 times larger than ap. The conductivities have a great deal of variability as the ionospheric plasma density changes, and, to a lesser extent, as the neutral density of the upper atmosphere changes. There is a large day-night difference, and also an important change with the solar cycle. There is great variability in the auroral zone, due to the irregular nature of auroral ionization by precipitating energetic particles.

At magnetic high latitudes, where geomagnetic field lines are approximately vertical, the electric field is approximately horizontal, and an electric field mapped from the magnetosphere is approximately constant with height over the few-hundred-kilometer thickness of the ionosphere. Under these conditions we can often treat the ionosphere as a thin conducting shell, with shell conductances given by the height integrals of the Pedersen and Hall conductivities. Figure 6 shows an example of the Hall conductance over the northern polar region, estimated by combining a variety of data for the auroral conductivity component, plus a model of the conductance produced by solar extreme ultraviolet radiation on the dayside of the Earth. The magnitudes of the solar and auroral contributions are roughly comparable, although the auroral component is highly variable. The Pealersen conductance tends to have a magnitude comparable with that of the Hall conductance. The ratio of Hall to Pedersen conductance in the auroral region increases with the mean energy of the ionizing auroral particles [e.g., Robinson et al., 1987].

IONOSPHERIC WIND DYNAMO

It is important to remember that Ohm's law applies to the reference frame of the material medium, in this case essentially the neutral gas that provides the ion collisions. The electric field E • has to be that measured

in this frame. If there is a wind of velocity U, then E • is


oo

Figure 6. Example of Hall conductance, in units of siemens, poleward of 50 ø magnetic latitude on 1990 March 20 at 2000 UT. Local noon is at the top. The contour interval is 2 S.

related to the electric field in the frame of reference of

the Earth, E, by the (nonrelativistic) transformation'

E'- E + U x B. (16)

On time scales longer than a minute or so E is electro- static'

E - -X7• (17)

Unlike E, the so-called "dynamo electric field" U x B is not constrained to be either a potential field or constant along B. When it is not, which is normally the case, then it cannot be canceled by E, so that E' must be non-zero and current must flow. This is the essence

of the ionospheric wind dynamo effect: the motion of the conducting medium through the geomagnetic field by winds usually leads to current generation. On time scales longer than a fraction of a second, the current must be divergence-free:

X7.J -0 (18)

Combining (15)-(18) results in a partial differential equation for •:

v. [av] - v. [au x B] (19)

With suitable boundary conditions, (19) can be solved for •, and the distributions of electric fields and cur-

rents can be determined everywhere in the ionosphere. In practice, (19) can be simplified considerably by tak- ing advantage of the fact that geomagnetic field lines are essentially equipotentials. Since ß varies only in the two spatial dimensions transverse to B, (19) can be reduced to a partial diffecential equation in only two dimensions by integrating it along field lines, all the way from one hemisphere to the other for closed field lines. When that is done, it is the field-line integrals of the transverse components of b and of bU x B that become important, rather than the height-varying values of of a and aU x B themselves. Those altitudes

that give the dominant contribution to the field-line integrals, mainly 90-200 km at day, define what is called the "dynamo region."

The appropriate boundary condition for (19) at the base of the ionosphere is that the vertical current density goes to zero, since estimates of current flow between the lower atmosphere and the ionosphere indicate that it is negligible on a global scale, if perhaps not always so locally above thunderstorms. The upper boundary condition is much more complicated, as it essentially requires knowledge of how the magnetosphere behaves and how it reacts to changes in the ionospheric conditions. Typically, modelers of the ionospheric dynamo either ignore the magnetosphere altogether, or else treat it as a simple voltage generator or current generator. However, it is possible to take into account the electrodynamic interaction between the ionosphere and the inner part of the magnetosphere in a relatively simple way by using the concept of "shielding" [e.g., South- wood, 1977]. As magnetospheric electric fields convect plasma toward or away from the Earth, gradient- curvature drifts of the modified distributions of hot

particles generate electric currents that produce field- aligned currents into and out of the ionosphere at high latitudes, the so-called "region-2" field-aligned currents. These alter the electric potential in the ionosphere and, because of the tight electrical connection with the magnetosphere, the magnetospheric electric field is also al- tered. The alteration is such that further inward or out-

ward motion of the plasma is strongly diminished. This corresponds to a weakening of the east-west electric field, so that the low-latitude boundary of the region- 2 current tends to become more nearly equipotential, and the penetration of electric field to middle and low latitudes is suppressed. The magnetospheric plasma takes several tens of minutes to redistribute after any change in the potential at the high-latitude boundary,


above 125 km Boundary ExB B• • Condition E -•' ddz

Casel -• •- I

I I

I

Case 2 • ' I I

Figure 7. Two cases of dynamo action driven by winds above 125 km. The magnetic field B is into the page. In case 1 the wind velocity U is a counterclockwise vortex, while in case 2 the horizontal wind is divergent. The assumed boundary conditions are that the vertical current density at the top and bottom of the ionosphere are zero, and that the electric potential vanishes at the horizontal boundaries. The polarization electric field is E, and the height-integrated horizontal current density is f Jdz.

so shielding is not effective for rapidly varying fields. In the steady state, the electric fields in the auroral zone do not penetrate much into midlatitudes, and an ap- proximate boundary condition that is sometimes used in dynamo modeling is to set the potential around the equatorward edge of the shielding region to zero. A slightly more sophisticated way to treat the shielding in a steady state was shown by Vasyliunas [1972] to be simply to replace the hot magnetospheric plasma by an effective Hall conductor, with a conductance many times larger than that of the ionosphere at the foot of the respective fields lines.

From inspection of (19), one might expect that in regions of the ionosphere where magnetospheric influences are relatively weak, the solution for ß will tend to yield an electric field -V• that is of the same order of magnitude as U x B. Another way of saying this is that the resultant E x B drift velocities might be expected to be on the order of magnitude of U. In fact, that expectation is not too far from reality, with a few caveats. First, the high conductivity along geomagnetic field lines tends to average the dynamo effects of winds along field lines, so that winds with vertically oscillat- ing structure tend to be ineffective in generating •lectric fields, and winds in regions of relatively low conductivity along the field line are also ineffective, like the day- time F region or the nighttime valley between the E and F regions. Second, the peculiar conditions in the lower ionosphere near the magnetic equator, where the ratio of field-line-integrated Hall to Pedersen conductivities is very large, give rise to a significant Cowling effect and a strong vertical polarization electric field that is much larger than typical magnitudes of U x B. This

vertical polarization field drives the strong horizontal Hall current of the equatorial electrojet. The peak current density in the equatorial electrojet is on the order of 10 -5 A/m 2, comparable to that in the auroral electrojets. However, the equatorial electrojet current is confined to a relatively small altitude region, so that its height-integrated value tends to be less than that of typical auroral electrojets.

Figure 7 illustrates the way that electric fields and currents respond to two different idealized forms of the wind, for a laterally bounded region with zero electric potential around the boundary, and for upper and lower boundary conditions requiring zero vertical current. The geometry is plane, with a vertically downward magnetic field. For both cases the wind exists mainly above 125 km, where the Pealersen conductivity dominates. However, the electric field that is generated extends down to lower heights, where it can drive Hall current. The first case is that of a counterclockwise

wind vortex. The dynamo electric field U x B drives Pealersen current toward the center of the vortex, which must be offset by an equal amount of outward Peal- ersen current driven by an outward polarization electric field which is immediately established. Although the Pealersen current is effectively canceled, the electric. field causes electrons to circulate counterclockwise at all

heights, which in the lower part of the dynamo region (where ion motion is impeded by collisions) gives rise to a clockwise Hall current. The resultant net height- integrated current is therefore a clockwise vortex. (Note that if the wind vortex had existed only at lower altitudes, in the Hall conductivity region, instead of at the higher altitudes, the winds would convect the ions in a counterclockwise vortex of Hall current, and the height- integrated current would be reversed.)

The second case is that of a divergent wind, which drives a non-divergent counterclockwise Pealersen current. In reality, since the Hall conductivity does not entirely vanish above 125 km, a small outward-directed Hall current will also exist, which must be offset by a small inward-directed polarization electric field and Pedersen current. However, the dominant current is just the counterclockwise wind-driven Pealersen current. In this case the generation of the electric field is weak: it is theoretically possible to have current flow with- out any significant electric field (in the Earth frame of reference).

The winds that drive the dynamo effects have a variety of sources. Figure 8 shows a model simulation of winds in the upper atmosphere driven by a combination of solar heating and upward-propagating atmospheric


9O

6O

• 3o

•- 0

• -30 -6o

-9o

9o

6o

3o

0

-30

-6o

I80-i50-120-90-60-30 0 30 60 90 i20 i50 I80

LONGITUDE

Figure 8. Temperatures (contours) and winds (arrows) at 12 UT for equinox, solar-minimum conditions, at atmospheric pressure levels of 6.8 /•Pa (approximately 300 km, top) and 2.7 mPa (approximately 125 km, bottom). Tem- peratures are expressed as departures from the global mean. Contour intervals are 20 K (top) and 12 K (bottom). The maximum wind arrows are 166 m/s (top) and 71 m/s (bottom). (Adapted from Fesen et al. [1986].)

tides from the lower atmosphere. The daily heating of the atmosphere above 100 km causes dayside expan- sion and a pressure bulge that drives winds toward the night side. These winds generally increase in strength with height through the dynamo region, so they are largest where the Pedersen conductivity dominates over the Hall conductivity. In Figure 8 the character of this wind component is clearly manifested in the upper thermosphere, at 300 km, but it is also present at lower altitudes. On the day side, the midlatitude poleward wind in the dynamo region drives westward current. A west- east polarization electric field develops in the low latitude dayside ionosphere that helps to close this midlatitude westward current and form the global $q vortices. The current driven by this wind component is supple- mented by current driven by semidiurnal tides (that is, global waves with 12-hour period) that are generated at lower atmospheric levels and propagate upward into the thermosphere. These waves have oscillatory character- istics in all three spatial dimensions as well as in time, and dominate the simulated winds at 125 km shown in

Figure 8. Their dynamo effects are more complicated

to characterize than those of the wind driven by thermospheric solar heating, but they provide a significant contribution to the $q current. Observations of tides in the lower thermosphere have revealed a large amount of variability, not only on a seasonal basis, but also on a day-to-day basis. This wind variability can be expected to contribute to the day-to-day variability observed in the $q magnetic variations.

Another driver of thermospheric winds, especially important at high latitudes, is the electric current. There are two ways that the current affects the winds: through the Ampere force (or J x B force) and through Joule heating. The Ampere force represents the sum of Lorentz forces on the ions and electrons, forces that are transfeted to the neutrals through collisions. It therefore balances the collisional force exerted by the neutrals on the ions and electrons as represented by the second terms in (1) and (2). The force per unit mass on the neutrals, or Ampere acceleration, is

1 (NemilYinV i •r- NemeVenVe), p

where p is air mass density and where, as in (1) and (2), the velocities are those with respect to the frame of reference of the neutral air. This acceleration is mainly- important above 100 km, where the ion term dominates. For this reason it is often called "ion drag." Use of (4), (5), (13), (14), (11), and (16), with some manipulation, shows that this acceleration can also be written as

JxB

crpB2 ( ExB ) P B2 U_l

crHB2 ( ExB ) •b x B2 U_L P

(20)

where Uñ is the component of U perpendicular to B. The first term on the right-hand side simultaneously accelerates the wind towards the E x B drift velocity and acts as a frictional drag; or viewed in the reference frame of the neutral air, it accelerates the wind towards the E • x B drift velocity. It is effective on a time scale determined by the inverse of the coefficient crpB2/p. The second term on the right-hand side of (20) simultaneously accelerates the wind in the direction of E and causes an acceleration perpendicular to the wind velocity that generally opposes the Coriolis acceleration associated with the Earth's rotation.

Figure 4d shows typical midlatitude profiles of the coefficients o'pB 2/p and o'HB 2/p. For reference, the


angular rotation rate of the Earth is also shown, which is representative of the Coriolis acceleration or of the time-rate-of change of a diurnally varying wind. The Pealersen coefficient eypB2/p is much more important than the Hall coefficient erHB2/p. Above 130 km it varies with height as the electron density. These day- time midlatitude profiles are also roughly representative of values in the nighttime auroral zone, though of course the actual values vary with the electron density. A value of 10 -4 s -1 represents about a 3-hour acceleration time for the wind.

At high latitudes, where the magnitude of E x B/B 2 typically exceeds that of Uñ, the Ampbre force above 125 km tends to accelerate the neutral wind towards

the E x B/B 9' velocity. Figure 9 shows an example of the influence of ion convection on the wind, taken from a numerical simulation. Figure 9a is the electric potential over the northern high latitudes, showing the assumed pattern of two-cell ion convection. Figure 9b is the steady-state wind response at 145 km altitude, with a vector scale 4 times as sensitive as that on the

left. There is a large-scale day-to-night flow, in addi- tion to an imprint of the two-cell ion-convection pattern. The convection-driven component of the wind velocity is considerably smaller than the E x B/B 9' velocity, and the pattern is turned counter-clockwise about 2 hours. This rotation is in the direction of the Earth's rotation

and corresponds roughly to the time scale for ion drag to be effective. To a large extent, that rotation also pre- vents the wind from having a chance to acce'lerate up to the ion velocity, because the direction and strength of the ion convection is continually changing.

What would now happen if we cut off the current flow between the ionosphere and the magnetosphere? These winds would continue to have a dynamo effect. With the model we can do such experiments. In Figure 9c, the neutral wind pattern of Figure 9b has been retained, while all current flow with the magnetosphere has been canceled. As in Case I of Figure 7, the wind vortices generate an electric potential that tends to cause the ions to drift with the neutrals, or more specifically, with the height-averaged neutral velocity, weighted by the Pedersen conductivity. To zeroth order, the potential has the appearance of the potential that had been imposed from the magnetosphere earlier, although the electric potential is about 25% as large, 7.5 kV vs. 30 kV, and again the pattern is rotated in the sense of Earth's rotation. This effect has been called the "flywheel" effect [Banks, 1972], since the spinning mass of the neutral atmospheric vortices tends to maintain the ion convection that originally spun it up.

The Joule heating has a different form of influence on thermospheric dynamics than does the Ampere force. Joule heating causes the air to rise and flow equatorward above 125 kin. At middle and low latitudes the

air subsides, and there is a return poleward circulation below 125 km to preserve mass continuity, though the air velocity there is much smaller, because the air is much more dense. The Coriolis force acting on the equatorward wind causes westward zonal winds to develop encircling the poles and extending to midlatitudes. For a storm lasting many hours, the westward winds continue to build up, becoming considerably stronger than the equatorward winds, and these westward winds can continue many hours after the heating subsides. The meridional circulation, on the other hand, shuts down fairly quickly after the heating stops. These westward winds can have an important influence on the ionospheric wind dynamo, an effect that has been called the "disturbance dynamo" [Blanc and Richmond, 1980].

ELECTROMAGNETIC ENERGY TRANSFER BETWEEN THE MAGNETOSPHERE AND

THE IONOSPHERE

In examining the role of the ionosphere-thermosphere system in the energy exchange with the magnetosphere at high latitudes, we need to recognize that the net current and electric field are the result of all processes oc- curring along the field line, including both ionospheric and magnetospheric influences. Separating these two contributions in terms of currents and electric field is

not feasible - measuring the winds, conductivities, and electric fields simultaneously over a range of spatial scales to evaluate the ionospheric influences at high latitudes is extremely challenging. This has led to the concept of applying Poynting's theorem to the high-latitude ionosphere. The theorem, derived from Maxwell's equa- tions, reads

4-V. +J.E-O (21) Ot 2/•0 /•0

where/•0 is the permeability of free space and c is the speed of light. A clear treatment of how Poynting's theorem can be applied to describing the electromagnetic energy flow within the magnetosphere has been given by Hill [1983]. Cowley [1991] presented a general view of electromagnetic energy exchange between the magnetosphere and ionosphere, applying a source-sink concept.

Poynting's theorem applies to all types of electromagnetic interactions, ranging from electromagnetic waves


TIEGCM ELECTRIC POTENTIAL (volts) TIECCM NEUTRAL WINDS UT - 0.OO UT - 0.00 145 km

12 12

kOC•k ll•[ kOC•k ll•[

TIEGCU ELECTRIC POTENTIAL (volts) Perira lat = 47.5 UT = O.OB

12

(c)

18 6

7o u/s 0 •

LOCAL TINE

Figure 9. Results of a simulation illustrating the "flywheel" effect for solar-minimum equinox: conditions. Contour intervals are 1000 V; vector velocity scales vary, as shown at the lower right of each plot. Electric-potential contours and E x B velocity vectors in geographic coordinates between 47.5 ø and the North Pole, at 0 UT, for a diurnally reproducible simulation with an imposed cross-polar-cap potential of 30 kV. (b) Corresponding neutral wind vectors at 145 km altitude. (c) Electric potential contours and E x B velocity vectors one time step later, after field-aligned current between the ionosphere and the outer magnetosphere has been cut off. From Richmond [1995a].


to steady-state fields. Here we consider only the energy flow associated with quasi-steady-state ionospheric fields, varying on time scales longer than about 10 minutes. For such fields the time-rate-of-change of electromagnetic energy density c9[(B 2 + E 2/c 2)/2/•o]/0t is generally negligible in comparison with the other terms in (21) between 100 km and 200 km altitude, and we can consider a balance between the convergence of E x B//•0 and the rate of electromagnetic energy transfer to the medium• J ß E. For such fields E is also essentially a potential field, as expressed by (17). E x B//•0 is often called the Poynting vector, but the Poynting vector can also be defined in other ways, as long as it has a divergence equal to the divergence of E x B/•u0. For ionospheric purposes it is convenient to represent B as the sum of the main geomagnetic field, which is given by the negative gradient of a scalar magnetic potential 1/0, and a perturbation 5B:

B - -VVo + •B (22)

Then the Poynting vector S can be defined by

ExSB S - , (•3)

/•0

since •7. (•7• x •7V0) vanishes identically. Plate 2 illustrates the geometry of the electromag-

netic fields and Poynting vector at high latitudes, where geomagnetic field lines are approximately vertical. At an altitude of 600 km, a typical height for low-Earth- orbiting (LEO) scientific spacecraft, •B is predominantly horizontal where significant field-aligned currents flow. E is also predominantly horizontal by virtue of its orthogonality with the main geomagnetic field. S is therefore predominantly vertical. At the bottom boundary of the ionosphere, where field-aligned current is absent, E and the horizontal component of •B tend to lie in roughly the same direction, and so the component of S parallel to B, $ll, tends to be considerably smaller than it is on the top side of the ionosphere. Thus there •ends to be a divergence of S through the ionosphere, which is usually negative and therefore corresponds to a dissipation of electromagnetic energy. There can also be horizontal contributions to the divergence of S, but •hey are generally much smaller than the vertical contributions. If we integrate (21) over a cylindrical volume aligned with a geomagnetic field line, as illustrated in Plate 2, and if we neglect both Sll at the bottom and the horizontal contributions to the divergence of S, then we find that

200km •.•00km • q_ J. Edz, (24) J90km

where z is altitude, and where the + (-) sign applies to the northern (southern) hemisphere. Thus spacecraft measurements of $ll can give us an estimate of the height-integrated electromagnetic energy transfer to the ionosphere [Kelley et al., 1991].

The electromagnetic energy transfer to the ionosphere/ thermosphere can be divided into two components: Joule heating and acceleration of the medium. That is, by making use of (16), we find that

J.E =J.E • +U-J xB. (25)

The first term on the right-hand side of (25) is the electromagnetic energy transfer rate in the frame of reference of the medium, and corresponds to Joule heating. Ohm's law gives it a value of •pE• + •11E•, which is always positive. The second term on the right of (25) is the scalar product of the velocity and the Ampere force, which corresponds to the feeding of kinetic energy of the medium by this force, or, if negative, to the extraction of kinetic energy from the medium. When kinetic energy is extracted, it may be converted locally to Joule heat, or it may contribute negatively to J. E, in which case it would be transferred through the Poynting vector to another ionospheric altitude or even back to the magnetosphere. Thayer [1998b] showed that the two terms on the right-hand side of (25) can be comparable in magnitude at a given height in the polar region. However, when integrated in height through the thickness of the conducting ionosphere, the second term is usually considerably smaller than the first [Lu et al., 1995; Thayer et al., 1995]. LEO spacecraft observations have shown that the Poynting vector is primarily downward throughout the high latitudes [e.g., Gary et al., 1994, 1995], which is compatible with a dominance of the Joule heating term in (25). Nonetheless, that study also found upward values of $1[ over an extended region on numerous polar passes of the Dynamics Ex- plorer spacecraft, suggesting that the second term on the right of (25) can, at times and in certain regions, dominate over the first. Modeling studies [e.g., Thayer and Vickery, 1992; Thayer et al., 1995] indicate that the winds spun up by the Ampere acceleration have a tendency to contribute to an upward $[I in cases where the large-scale electric field has rapidly decreased.

CONCLUDING REMARKS

The coupling between ionospheric electrodynamics and thermospheric dynamics, and their coupling with magnetospheric electrodynamics and with lower-atmospheric dynamics, create a rich variety of phenomena which pose an abundance of research questions to the


Satellite Measurement

600 kin-

100 kmm

t

.. I l

ß Ionosphere ",, ........... . .... •: . -

Dusk. •. Da• n ß • Magnetic field

•. Current system, J ..•

-•- Poynting vector, •S

-•-- Satellite measurement path

• Radar measurement domain ..............

Plate 2. A schematic of the "region 1" current system associated with the transfer of energy and momentum into the ionosphere. The view is looking towards the Sun over the northern hemisphere, with spacecraft and radar measurement domains depicted accordingly. Over the polar cap the magnetic field •s downward, E and the Pedersen current Jp are directed from dawn to dusk, while the Hall current J H flows into the page in this plane. The Poynting vector S is primarily downward. Typical height profiles of a p and aH are indicated over the pole. The neutral wind U•v is a response to multiple forces, and has components both in the plane and out of the plane of the figure. In the inset, 1• is a unit vector parallel to B, fi is a unit vector normal to the side of the cylindrical volume, and Sii and S•_ are the components of S parallel and perpendicular to B, respectively. This figure is a modification of Figure 7 of Cowley [1991].


scientific community. It is because of these interactions that observations of ionospheric electrodynamics can tell us a great deal about magnetospheric processes and about global atmospheric dynamics. Furthermore, the ionosphere plays an active role in the electrodynamics of the magnetosphere, and the impact of the interactive electrodynamics on the upper atmosphere can be pro- found. It is a challenge to the ionosphere-thermosphere community to try to unravel these complex plasma and neutral interactions.

Acknowledgments. We thank Gang Lu and two referees for helpful comments on an earlier draft. This work was supported by the NASA Sun-Earth Connection Theory program and by NASA grant W-19,201. The work by one of us (JPT) was partially funded by NSF Cooperative Agreement ATM-9813556 and NSF grant ATM-9714705.

REFERENCES

Banks, P.M., Magnetospheric processes and the behaviour of the neutral atmosphere, Space Res., 12, 1051-1067, 1972.

Banks, P.M., Observations of Joule and particle heating in the auroral zone, J. Atmos. Terr. Phys., 39, 179, 1977.

Bilitza, D., ed., International Reference Ionosphere 1990, NSSDC 90-22, Greenbelt, Maryland, 1990.

Blanc, M., and A.D. Richmond, The ionospheric disturbance dynamo, J. Geophys. Res., 85, 1669-1686, 1980.

Cowley, S.W.H., Acceleration and heating of space plasma: Basic concepts, Ann. Geophys., 9, 176-187, 1991.

Fejer, B.G., M.C. Kelley, C. Senior, O. de la Beaujardi•re, J.A. Holt, C.A. Tepley, R. Burnside, M.A. Abdu, J.H.A. Sobral, R.F. Woodman, Y. Kamide, and R. Lepping, Low- and mid-latitude ionospheric electric fields during the Jan- uary 1984 GISMOS campaign, J. Geophys. Res., 95, 2367-2377, 1990.

Fesen, C.G., R.E. Dickinson, and R.G. Robie, Simulation of thermospheric tides at equinox with the National Center for Atmospheric Research Thermospheric General Circu- lation Model, J. Geophys. Res., 91, 4471-4489, 1986.

Gary, J.B., R.A. Heelis, W.B. Hanson, and J.A. Slavin, Field-aligned Poynting flux observations in the high- latitude ionosphere, J. Geophys. Res., 99, 11,417-11,427, 1994.

Gary, J.B., R.A. Heelis, and J.P. Thayer, Summary of field- aligned Poynting flux observations from DE 2, Geophys. Res. Lett., 22, 1861-1864, 1995.

Hedin, A.E., Extension of the MSIS thermosphere model into the middle and lower atmosphere, J. Geophys. Res., 96, 1159, 1991.

Hill, T.W., Solar-wind magnetosphere coupling, in Solar- Terrestrial Physics, edited by R.L. Carovillano and J.M. Forbes, pp. 261-302, D. Reidel, Norwell, Mass., 1983.

Kelley, M.C., D.J. Knudsen, and J.F. Vickrey, Poynting flux measurements on a satellite: A diagnostic tool for space research, J. Geophys. Res., 96, 201-207 , 1991.

Lu, G., A.D. Richmond, B.A. Emery, P.H. Reiff, O. de la Beaujardi•re, F.J. Rich, W.F. Denig, H.W. Kroehl, L.R. Lyons, J.M. Ruohoniemi, E. Friis-Christensen, H. Opgenoorth, M.A.L. Persson, R.P. Lepping, A.S. Rodger, T. Hughes, A. McEwin, S. Dennis, R. Morris, G. Burns, and L. Tomlinson, Interhemispheric asymmetry of the high-latitude ionospheric convection pattern, J. Geophys. Res., 99, 6491-6510, 1994.

Richmond, A.D., The ionospheric wind dynamo: effects of its coupling with different atmospheric regions, in The Up- per Mesosphere and Lower Thermosphere (R. M. Johnson and T. L. Killeen, eds.), Am. Geophys. Union. Wash. DC, 49-65, 1995a.

Richmond, A.D., Ionospheric electrodynamics, in Handbook of Atmospheric Electrodynamics, Vol. II (H. Volland, ed.), CRC Press, Boca Raton, Florida, 249-290, 1995b.

Robinson, R.M., R.R. Vondrak, K. Miller, T. Dabbs, and D. Hardy, On calculating ionospheric conductances from the flux and energy of precipitating electrons, J. Geophys. Res., 92, 2565-2569, 1987.

Southwood, D.J., The role of hot plasma in magnetospheric convection, J. Geophys. Res., 82, 5512-5520, 1977.

Thayer, J.P., and J.F. Vickrey, On the contribution of the thermospheric neutral wind to high latitude energetics, Geophys. Res. Lett., 19, 265-268, 1992.

Thayer, J.P., J.F. Vickrey, R.A. Heelis, and J.B. Gary, Inter- pretation and modeling of the high-latitude electromagnetic energy flux, J. Geophys. Res., 100, 19,715-19,728, 1995.

Thayer, J.P., Height-resolved Joule heating rates in the high- latitude E region and the influence of neutral winds, J. Geophys. Res., 103, 471-487, 1998a.

Thayer, J.P., Radar measurements of the energy rates associated with the dynamic ionospheric load/generator, Geo- phys. Res. Lett., 25, 469-472, 1998b.

Vasyliunas, V.M., The interrelationship of magnetospheric processes, in Earth's Magnetosphere Processes, edited by B. M. McCormac, pp. 29-38, D. Reidel, Norwell, Mass., 1972.

A.D. Richmond, High Altitude Observatory, National Center for Atmospheric Research, 3450 Mitchell Lane, Boul- der, CO 80301. (e-mail: [email protected])

J.P. Thayer, Geoscience and Engineering Center, SRI International, 333 Ravenswood Avenue, Menlo Park, CA 94025. (e-mail: [email protected])

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