Factors influencing the intensity of magnetospheric substorms

Journal of Atmospheric and Terresfria/Physics, Printed in Great Britain.

Vol. 55, No. 8, pp. 109-I

122, 1993. 0

OfE-9169/93 $6.00+ 1993 Pergamon Press

.OO

Ltd

Factors influencing the intensity of magnetospheric substorms R. L. MCPHERRON*

and D. N. BAKER?

*Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024-l 567, U.S.A. ; t Laboratory for Extraterrestrial Physics, Goddard Space Flight Center, NASA, Greenbelt, MD 20771, U.S.A. (Received injinalform

24 June 1992 ; accepted 30 July 1992)

Abstract-A magnetospheric substorm is the sequence of processes which occur throughout the magnetosphere following a southward turning of the interplanetary magnetic field and the onset of dayside reconnection. An isolated substorm consists of three phases, growth, expansion and recovery. Two primary processes make up a substorm. The directly driven component visible in the global, two cell current system is powered by the direct projection of the solar wind electric field onto the conducting ionosphere. The unloading component seen as the one cell intensification of the westward electrojet near midnight is powered by processes internal to the plasma sheet. The intensity of substorms can be measured by a variety of activity indices, the most common of which are magnetic indices. The solar wind controls the intensity of substorms through the process of magnetic reconnection. Time series analysis has established that 40 min after a southward turning of the interplanetary magnetic field the strength of the electrojets is correlated with solar wind parameters through a nonlinear coupling function similar to V*B Sin4(0/2) (where B = IMF clock angle about Sun vector). Linear filter analysis of the magnetospheric system response shows that the average impulse response for the AL index is a Rayleigh function peaking at a lag time of 60 min and diminishing to zero after 3 h. The average response function for a sequence of moderate substorms is bimodal with peaks at 25 and 70 min, while more intense activity is uni-modal with only the 25 min peak. Response functions for individual substorms have peak amplitudes and delays that can be substantially different from the average. The linear analysis predicts less than half the variance in the AL index when high resolution indices are used. These results imply that reconnection on the day and night side are delayed relative to the solar wind by differing amounts which vary with conditions in the solar wind, magnetosphere, and ionosphere. Currents are driven through the ionosphere that are proportional to the reconnection rates which are in turn proportional to the solar wind electric field, but their strength depends on ionospheric conductivity. Conductivity depends on season, prior activity, and the way in which a particular substorm develops. Computer simulation of substorms with a simple ‘leaky tap’ model suggests that one reason for lack of short term predictabilty is likely to be that the magnetosphere is nonlinear with behavior depending both on previous conditions and the strength and wave form of the solar wind input. New techniques of analysis of magnetic indices support this conjecture. As with the Earth’s surface weather, accurate space weather predictions will probably require extensive real-time observatory networks both in the solar wind and magnetosphere.

I.INTRODUCTION What is a substorm?

To determine what factors control the intensity of a magnetospheric substorm we must first decide what a substorm is. The term substorm was first used by AKAWFU and CHAPMAN (1961) to describe the rapid, repeatable magnetic variations that occur in polar regions during the development of a magnetic storm. The intimate association of these variations with the main phase of the storm suggested that they were a discrete phenomenon, and that several in a sequence create the storm time ring current. As an integral component of magnetic storms they were therefore called polar magnetic substorms. The name was clearly influenced by the early work of Birkeland who used the term ‘elementary polar magnetic storms’ to

describe the same phenomena (BIRKELAND,1913). A few years after introducing the concept of a magnetic substorm AKA.WFU (1964) used the term aurora1 substorm to describe the ordered collection of features observed in all sky photographs of the aurora. Because it was evident that distinct features in the aurora and magnetic disturbance were always correlated, they must be manifestations of some more general phenomenon. JELLEY and BRICE (1967) developed this idea in a paper that noted that with a short delay dayside electron precipitation always follows an aurora1 substorm on the night side. In recognition of Birkeland’s work they suggested that the underlying phenomenon be called an ‘elementary magnetospheric storm.’ MCF'HERRON et al. (1967) and CORONITI et al. (1968) reported similar observations, but suggested instead that the phenomenon be called

1091

! 097

I< 1. M(~Pt-Il.KKoN

hnal intcrlal during which the indlcch return to thclr haselincs. The expansion phase ofsubstorms has fine structure be a component of storm disturbance. AKAS~EU (1968) used this term in the title of his book which called intensifications (BONN~N:R cr trl., I970 ; KISAdescribed all of the phcnomcna known to occur during HETH and ROSTOKER,197 I : CLACIEKand MCPHLRRON. 1974 : WEINS and ROSTOKKR.1975). Latitude chains substorms. Today the term is universally used to refer ,I ‘magnetospheric substorm’ in recognition of’ Aka~ofu’s work, and because the events really appear to

to the collection of processes that occur throughout the magnetosphere in conjunction with an aurora1 disturbance. Several attempts have been made to provide a precisc definition of a substorm (AKASOFU, 1979; ROSYOKW ef uf.,1980, 1987; BAKER rr rrl., 1984). Fundamental to all of these is the recognition that a substorm must include at least one aurora1 breakup followed by a poleward expansion. However, most substorm expansions consist of a sequence of quasiperiodic intensifications of the aurora and electrojet. If one of these is of short duration (- 5 min) and is not followed by a poleward expansion it is referred to as a pseudo-breakup. The first in a sequence of intensifications producing a poleward expansion is referred to as the expansion phase onset. Subsequent activations in the sequence are called intensifications (ROSTOKERet al.. 1987). Phases

ofa substorm

An isolated magnetospheric substorm is produced by a short interval of southward interplanetary magnetic field (- 3060 min). Such substorms provide the best example of the sequence of events which make up a substorm. Isolated substorms have three distinct phases : growth (MCPHERRON,1970,1972) ; expansion and recovery (AKASOFU,1968). Expansion and recovery phases were part of the original model of the aurora1 substorm (AKASOKI, 1964) but the growth phase was not. Its introduction caused substantial controversy for many years (AKASOFUand SNYDER, I972 ; DESSLER,1973 ; SISCOE,1980 ; COWLEY,1982a, b), but it is now generally accepted as part of an isolated substonn. Figure 1 provides an example of the AU and AL indices during a fairly typical isolated substorm which has been extensively studied in the CDAW-6 workshop (MCPHERRONand MANKA, 1985 and accompanying papers). The growth phase is the initial interval of slow development of the AUand AL indices caused by gradual increases in the strength of the eastward and westward electrojets. The expansion phase is the second interval of an isolated substorm during which the AL index rapidly falls to a minimum. It is caused by a sudden enhancement of the westward electrojet in the premidnight sector. The onset of the expansion phase can frequently be identified by a sudden change in slope of AL. The recovery phase is the

have shown that this structure is produced by a sequence of filamentary electrojets. which tend to form progressively northward of the preceding one. Each terminates at its western end in an aurora1 surge (OPGEhNRTH et d.. 1983). The recovery phase may also have fine structure. HONES (1985) describes a phenomenon called the poleward leap of amoral and magnetic activity which occurs at the beginning of the recovery phase. MISHIN (1991) refers to this same phenomenon as the second active phase of the expansion phase. When the IMF remains southward for long intervals the response of the magnetosphere becomes more complex than during isolated substorms. In some circumstances the AL index exhibits a sequence of expansion and recovery phases without clear growth phases. In others the indices become relatively steady without identifiable signatures of any of the substorm phases. Such intervals have been referred to as convection bays (PYTTE?f 01.. 1978). Substorw~sas the superposition of’two types ofprocesses

In his original description of aurora1 substorms AKASOFU(1964) characterized the expansion phase as an expiosiue phenomenon intrinsic to the magnetosphere. However, more than a decade later he reversed his position describing the magnetosphere as being primarily driven by the solar wind dynamo (PERREAULT and AKASOFU,1978 ; AKASOFU,1979). In his later view the expansion phase is simply a nonlinear effect of increasing current along field lines connccting the ionosphere to the solar wind (AKASOFU, 1981, 1982). The existence of a growth phase. however, led MCPHERRON(1970) to conclude that the energy released in the explosive expansion phase was stored earlier. AKASOFU (1979) characterized the difference between these two views by the terms driven process and unloading process. Figure 2 illustrates this distinction using the waveforms of a solar wind energy input parameter and a magnetospheric energy dissipation parameter. A driven process is one for which the waveforms of the input and output arc virtually identical with perhaps at most a small time delay as shown in panel (a). In contrast, an unloading process is one in which the input wave form is integrated (stored) without a corresponding output, until after a long time delay the energy is unloaded

lo!?3

Intensity of magnetospheric substorms PHASES OF A MAGNETOSPHERIC SUBSTORM

600

-600 1 -800 t RECOVERY I

1434 11

I1124 11.5

12

12.5

UniversalTime

/1300 13 13.5 m22 has 13-&c-91 igpplucla

Fig. I. The aurora1 ekctrojet indices for the CDAW-6 substorm at 1054 UT, 22 March 1979 (MCPHERRON and MANKA,198.5).Variations in the AL (aurora1 lower) index can be divided into three phases : growth,

expansion and recovery. These phases are defined by the features of s&storm called start substorm, expansion onset, hesin recovery, and end substorm. Pseudo-breakups (not shown) and intensifications of the expansion phase complicate the simple picture.

(released) as shown in panel (b). As envisioned by Akasofu, unloading is internal to the magnetosphere and hence its wave form bears little resemblance to the wave form of the input. AKAXNU (1979) noted the possibility that the magnetosphere actually responds as a su~~sition of both types of processes as illustrated in panel (c). However, in numerous reports he argued that the magnetosphere is primarily driven (e.g. AKASOFU,1979, 1981a). The question, ‘Is magnetic activity caused by a driven or unloading process? is closely related to a long standing arg~ent conning the geometry of the ionospheric current system responsible for polar magnetic substorms. In studies of the disturbance variation during magnetic storms CHAPMANand BARTELS (1962) concluded that the source of disturbance was a two-celled ionospheric current system symmetric about the noon-midnight meridian (SD (cf. fig. 22 on p. 302). This current was sheet-like across the polar cap, but was concentrated in two electrojets as it returned along the dawn and dusk segments of the aurora1 oval. However, AKAMRJ et al. (1965) in their study of polar magnetic substorms, suggested

instead that the main current was a westward eiectrojet across midnight with one weak return cell in the polar cap and another stronger cell concentrated in the dusk oval as the eastward electrojet. In contrast to this idea, BIRKELAND (1913) had much earlier sug gested that the westward current across midnight was part of a three-dimensional current system now known as the substorm current wedge (MCPHERRON et al., 1973). A partial answer to questions about the nature of the current system responsible for substorms was provided by FUKUS~~ (1969). He showed that in a uniformly conducting ionosphere a vertical incident current produces ground perturbations that exactly cancel the effects of its radial spreading in the ionosphere. When this is taken into account the residual westward closure of the Birkeland system produces exactly the same effect as the ionospheric current suggested by Akasofu. However, this did not explain why statistical studies of polar disturbances such as those described by CHAPMANand BUTEU (1962) produced a current pattern rotated 90” with respect to that found in individual substorms. The explanation as

(a)

DRIVEN PROCESS

(cl

e j-(6D)dt D

INTERMEOIPTE

PROCESS

Fig. 2. Definition of driven and unloading processes within a magnetospheric substorm. A driven process shown in panel (a) has input and output waveforms that differ by a time delay. An unloading process shown in panel (b) has an output waveform unrelated to input except the areas under the input and output waveforms must be proportional. Panel (c) suggests that substorms might consist of a superposition of both types of processes (AKASOJW, 1979).

below is that a typical isolated substorm is by superposition of the two current patterns

current system (COWLEY,1982a, b). The current exists because drifting ions collide more frequently with (ROSTOKER,1968; BAUMJOHANN,1983). The Chapatmospheric neutrals than do drifting electrons thus man pattern is characteristic of the substorm growth moving slower and creating a current in a direction phase and extended intervals of activity (NISHIDA, opposite to the drift. &WOE and HUANG (1984) have 1978), while the Birkeland pattern is associated with developed a model showing how this current system the expansion phase (IIJIMA and NAGATA, 1972; can be produced if only magnetic reconnection on the KOKUBUN, 1972 ; ROSTOKERand HUGHES, 1979). day side drives the convection. In essence closed field Because the latter is present only a fraction of the lines are drawn sunward along the ovals from the time, and because it is highly variable in its location nightside plasma sheet to become newly opened field it tends to disappear in the statistical averages. Thus lines in an expanding polar cap. This current is responstatistical patterns are dominated by the DP-2 type of sible for the magnetic disturbances of the substorm current system. growth phase. M~~FZS et al. (1989) extrznded the SISCOEand HUANG DP-2 and DP- 1 current systems (1984) model of convection by considering the possiThe ionospheric current system identified by Chapbility that reconnection occurs only on the night side, man is now known as the DP-2 current system (NISH- or both on the day and night side simultaneously. IDA, 1978). It is a Hall current produced by solar wind Because of the simplifying assumptions in their model, coupling to the ionosphere. According to either the nightside reconnection is the inverse of dayside reconviscous coupiing model (AXFORDand HINES, 1961), nection. Open field lines frsm the tail lobes are reconor the reconnection coupting model (DUWGEY,1961), nected at an x-line and driven sunward along the ovals the ionospheric intersection of convecting field lines to replace closed field lines previously lost from the traces out a pattern which is the reverse of the SD day side. In the process the polar cap shrinks as open discussed produced

Intensity of magnetospheric substorms

1095

field lines are closed. The result, however, is a twoappears to be rotated 90” relative to that produced by celled system that is the inverse of that produced by day side reconnection. There are some observable effects close to midnight day side reconnection. According to this model, the Chapman S,, current pattern is produced either by from the Hall current system driven by nightside time averaging the effects of day side reconnection reconnection. The most evident are at the western end of the substorm current wedge. Here the outward followed by night side r~onnection, or by balanced field-aligned current is highly localized and the ionoreconnection occurring simultaneously at both locations. spheric Hall current circulates counter clockwise (viewed from above) about the outward field-aligned In the real magnetosphere the dayside ionosphere is generally created by photoionization while on the current. This current produces the positive D-spikes night side it is created by particle precipitation from that are characteristic of the aurora1 surge that forms where the current leaves the ionosphere. Inward fieldthe plasma sheet. On the day side the field lines aligned currents at the eastern end of the Cowling involved in reconnection map to the exterior of the magnetosphere while on the night side they map to channel are observed to be extended in the east-west the interior of the plasma sheet. The consequence of direction. Circulation of the Hall current about this these differences is that the electric field produced by inward current produces positive H perturbations in the polar cap (eastward Hall current), and negative day side reconnection is projected onto the entire perturbations to the south, thus apparentfy extending polar cap which is large and has a relatively uniform the region of negative bay signatures into the morning conductivity. Then by Fukushima’s arguments the sector. Some of the current also closes across the polar effects of the Region 1 field-aligned current system flowing into the ionosphere on the dawn side and out cap in the manner described by the MOSESet al. (1989) model. This portion of the system contributes to the on the dusk side are canceled by the effects of their DP-2 system in the polar cap maintaining it even after ionospheric Pedersen closure across the polar cap. Thus on the ground the primary effects of day side day side reconnection has ceased and currents driven by it are dying away. reconnection are those associated with the ionospheric The difference between the DP-2 and DP-I equiHall current as described above. These effects produce the two-celled DP-2 current system described by valent current systems is well illustrated by Fig. 3 taken from the KAMIDE and BAUMJOHANN(1985) Chapman. study of the CDAW-6 substorm mentioned earlier On the night side the westward electric field of the with reference to Fig. 1. DP-2 alone is shown in the plasma sheet, presumably produced by nightside left panel at 1040 UT, and predominantly DP-1 is reconnection, is projected into a narrow east-west shown in the right panel at 1140 UT. As discussed by band across midnight. Because this band is also a zone (1985), BAKERet al. (1984) of high conductivity the Pedersen current driven by KAMIDEand BAUMIOHANN this field cannot spread out and cancel the effects and CLAUERand KAMIDE(1985) the DP-2 system is present during the substonn growth phase, but both of the field-aligned portion of the three-dimensional DP-1 and DP-2 can usually be identified in the expansystem. A Hall current is also driven by the westward sion and recovery phases. field and Bows poleward across the band as it does According to the foregoing description, the DP-2 for the day side. However, the high Hall conductivity contrast at the edges of the band cause the band to current is primarily created by day side reconnection polarize (CORONITIand KENNEL,1972 ; BAUMJOWANN, while the DP-1 current is created by night side reconnection Because the day side x-line is in intimate 1983). A southward polarization electric field develops contact with the solar wind it seems likely that reconreducing the net poleward Hall current. The polarnection at this location is directly controlled by the ization field drives a secondary Hall current westsolar wind. Thus we conclude that the DP-2 current ward, parallel to the channeled Pedersen current. system (growth phase) is directly driven by the solar Ground magnetic effects are thus produced by the wind with only a short delay as envisioned by superposition of fields from these two westward ionospheric currents, and from the field-aligned closure of AKASOFU(198 1b). However, nightside reconnection begins at the center of the plasma sheet (in the nearthe Pedersen current at the ends of the channel. The Earth neutral line model) and is thus less directly net ionospheric current in the channel is referred to as connected to the solar wind. We therefore expect its a Cowling current. The equivatent ionospheric current beginning to have dynamics of its own that are only pattern produced by these currents is the one indirectly, and perhaps, nonlinearly related to the described by Akasofu and is referred to as the DP-1 current system. Because the ground magnetic effects solar wind. Thus, in general, we expect the beginning of the DP-1 current system (onset of expansion phase) are dominated by the net westward current the system

Fig. 3. A comparison of ionospheric and field-aligned substorm of 1054 UT, 1-2 March 1979 ~C‘I.~ITK and

currents K4Mlrw.

m

I__

__

substorm growth (top). and during substorm expansion (bottom). during the CDAW-6 1985). Growth phase current system consists of two cells \bhilr the expansion phase system is predominantly one cell.

during

m

FIELD-ALIGNED CURRENT I7

IONOSPHERIC CURRENT

EQUIVALENT CURRENT I,

m

m

CURRENT

_m

-FIELD-ALIGNED 13

m

EQUIVALENT CURRENT

Intensity of magnetospheric substorms

to be determined by internal magnetospheric parameters. Once reconnection progresses to the last closed field lines bounding the plasma sheet, open field lines of the lobe begin to reconnect. If the IMF (interplanetary magnetic field) has turned northward by the time this happens as is usually the case for isolated substorms, then the energy stored in the tail lobes is unloaded, and through the process of magnetic reconnection converted to thermal and kinetic energy of earthward flow in the plasma sheet. The electric field in this flow is applied to the night side ionosphere as described above and drives the DP- 1 current system as well as maintaining the DP-2 system at a lower level than in the growth phase. At this point the field lines reconnecting at the nightside x-line are directly connected to the solar wind. It is possible that once this occurs the solar wind controls the rate of reconnection. Then, indirectly, the solar wind also drives the DP-1 current system by controlling the rate of night side reconnection. However, because this process begins after a long and variable delay (-2G 120 min) dissipation in the ionosphere appears to be uncorrelated with the solar wind input. A remarkable example which seems to support the foregoing model was studied in the CDAW-6 workshop [McPIIERRoN and MANKA (1985)]. Figure 4 taken from BAKER et al. (1985) displays waveforms of the rectified solar wind electric field and ionospheric Joule heating during this substorm. It is apparent that weak heating began shortly after the IMF turned SUBSTORY EXPANSION

ONSET

STORAGE d I

I

I

22

MARCH

I

1979

Fig. 4. A comparison of the solar wind electric field with the total ionosnheric Joule heating rate during the CDAW-6 substorm (BAKER et al., 1985). Moderate heating rates occurred during the growth phase, but intense heating occurred only after the IMF turned northward and the expansion phase was well under way.

1097

southward upstream of the bow shock. It increased slowly throughout the growth phase, and the initial stage of the expansion phase (begimming at 1054 UT). However, the most significant heating occurred after the second and third intensifications of the expansion phase (1104 and 1124 UT). We emphasize that the rapid increase in heating was correlated with a northward turning of the IMF, and that most of the heat deposited in the ionosphere was while the IMF was northward. According to the driven model, dissipation should decrease shortly after the IMF turns northward, counter to these observations. In contrast, the unloading model which includes growth phase effects predicts that some dissipation is directly driven and will be evident in the growth phase, and some is related only to unloading of stored energy in the expansion phase.. Apparently, at least in this substorm, ionospheric heating was primarily due to unloading.

2. MEASURES OF SUBSTORM INTENSITY How is substorm intenstiy measured?

In the preceding section we defined a substorm, but were ambiguous concerning what is meant by substorm intensity. According to our definition a substorm is a time ordered collection of two classes of processes, driven and unloading. There are, however, many specific processes of each class. Each unique physical process must have associated with it a time history of energy dissipation during a substorm. If such histories could be measured then they could be used to address the question of what factors control them. An aggregate measure such as the total rate of energy dissipation during a substorm seems less useful, since in the end, virtually every solar wind and magnetospheric parameter must contribute to this. Unfortunately, many processes are not sufficiently understood, or accessible to observation, that their power dissipation rates can be measured. In this case we are forced to use proxy measures. In some cases it might be possible to carry out the calculation, but the cost would be prohibitive. For all of these reasons activity indices, particularly magnetic indices, are the most common measures of substorm intensity. This fact was implicit in our definition of substorms in terms of the DP-2 and DP-1 current systems. There is no guarantee that an activity index will be related in a direct way to energy dissipation in a particular process. Thus, there is no reason to expect that the parameters which control its intensity time history will have units of energy. This is not an insurmountable obstacle as it is still possible to determine what factors affect the index, and thereby come to a

qualitative understanding of the physical processes involved. None the less. it makes it difficult to assess the relative importance of competing processes of energy dissipation in substorms.

Magnetic indices arc the most common measures of intensity used in substorm studies. These indices can be divided into three types; character indices, range indices, and electrical current indices (LINCOLN. 1967 ; ROSTOKEK, 1972 ; MAYAUD. 1980; BAUMJotiAK’N. 1986; MENVIELI.E and BEKTHELIER, 1991). Character indices (e.g. C,) are seldom used as they are simply a world-wide average of subjective classifications of daily observatory records into one of three classes: quiet. moderate. disturbed. Range indices (K,,. A,,, arr, and cmz) represent attempts to obtain a measure of the peak-to-peak amplitude of the disturbance present in a fixed interval of time (normally 3 h) at a ‘standard’ station. However, there is no attempt made to isolate the physical cause of the disturbance. The electrical current indices, P,, AU. AL, D,,, and A.s~nz. on the other hand, try to isolate a specific physical process important in the magnetosphere, and to do so at very high time resolution (up to 1 min). The aurora1 electrojet indices (AU, AL and AE) were originally defined by DAVIS and SUGIURA (1966) to quantify the strength of the eastward electrojet (AU), the strength of the westward electrojet (AL), and their total (AE = AU-AL). If the electrojets were infinite sheet currents in the ionosphere, and the network of stations defining them were infinitely dense, then the AU and AL indices would be proportional to the maximum ionospheric sheet current densities present anywhere in the corresponding electrojets. The ring current indices I),, and Asym measure the strength of the symmetric and asymmetric ring currents, respectively (CHAPMAN and BARTELS, 1962). It has been shown that in a purely symmetric ring current II),, is proportional to the total energy of the drifting particles creating the current (DESSLERand PARKER, 1959). The enhancement of the ring current on the dusk side indexed by Asym is produced by a three-dimensional current system draining the electrojets near midnight and feeding them near noon (HUGHES and ROSTOKER, 1977). The polar cap index PC is a measure of the current density flowing from midnight to noon across the polar cap (TROSHICHEVrt ul., 1988). Like the AE indices it is a measure of the overhead current density.

Electric indices would be of great importance in substorm studies if they were easy to obtain. After all,

it is the ionospheric electric field that drives current through the ionosphere producing the magnetic disturbances characterized by the magnetic indices. Thus far the only index obtainable on a routine basis is the Integrated dawn to dusk electric tield measured by polar orbiting spacecraft. This quantity is called the polar cap potential. Unfortunately, this is not an instantaneous measure, since it represents an average over the situation that existed for the 20 min in takes a spacecraft lo cross a pole. In a few limited cases such as the CDAW-6 study a high resolution time history of polar cap potential has been obtained by inverse modeling techniques (KAMIDE cz d., 1981). Jonospheric radars can measure the spatial distribution of electric fields over limited spatial regions, but thus far. there arc too few of these to determine the instantaneous distribution over the entire polar cap and no indices analogous to those obtained with magnetometers have been defined. Prirtick~ indice.r A substantial amount of energy is deposited in the atmosphere during substorms by particle precipitation. This energy is the primary cause of ionization on the night side producing the electrical conductivity that controls the intensity of substorm associated currents. The spatial and temporal development of this quantity is the third unknown in the equations that relate electric field through conductivity to current and magnetic perturbations. Some attempts have been made to determine the statistical pattern of particle precipitation during substorms (HARDY et al.. 1987), and these have been used to calculate model conductivity distributions (SPIRO, 1982). FOSTER rt al. (1986) have used successive passes of a polar orbiting spacecraft to estimate a hemispherical particle precipitation index. Because of the limited data from which they are derived this index is very crude and probably of little use in detailed studies of substorms. Aurorul luminosity indices Potentially the most useful particle indices would be those derived from continuous images of the auroral oval by a spacecraft above the pole. If obtained in several wavelengths, at one minute time resolution and about 50 km spatial resolution, such images could be used to derive a number of important parameters. These include: location of the center of the aurora1 oval, size of the polar cap, width of the oval, location of polar cusp, integrated aurora1 luminosity, location of intense precipitation, distribution of precipitating particle energy, estimates of ionospheric conductivity. By combination with existing global magnetic

Intensity of magnetospheric substorms

measurements the polar cap electric field distribution could be inferred, and then field-aligned currents and JouIe heating could be estimated. It would seem that this approach has such potential that it would be the number one priority for future missions designed to study substorms. Unfortunately, to date the existing aurora1 images have only occasionally been used to calculate some of these quantities (FRANK and CRAVEN, 1988). Magnetospheric stress or strain indices

The interaction of the solar wind with the magnetosphere transfers energy across the magnetopause and produces global convection in the magnetosphere. Because this convection system rarely reaches a steady state there are continual changes in the configuration of the magnetosphere as magnetic flux is transported from one region to another. These changes are apparent in a variety of physical parameters which are systematically associated with substorms and can be used to measure the intensity of substorms. Such measures include the magnitude of the tail lobe magnetic field, the inclination of the synchronous magnetic field, particle anisotropy at synchronous orbit, and the strength of the Region 1 and Region 2 field-aligned currents systems. When available the magnitude of the tail lobe field is the best and most direct of these measures of stress and strain (CAAN et al., 1975). Because the total pressure (magnetic plus plasma) is constant everywhere in a given cross-section of the tail, and there is negligible plasma in the lobes, the field magnitude must be the same everywhere in the cross-section. Thus, the field intensity should not depend on where the field is measured within a given cross-section of the lobe. If both plasma and field data are available then the total pressure can be used to infer the lobe field even when a spacecraft is inside the plasma sheet. Furthermore, a recent study suggests that during substorms the cross-section of the magnetosphere decreases on the sunward side of X(GSM) = -3R, while it increases tailward of this distance (SIBECKet al., 1991). Thus close to the Earth, the time history of total magnetic flux in the tail lobes may be approximated from the field ma~itude observed at a fixed radial distance. In the reconnection model of substorms it is this reservoir of flux that supplies the energy released in the unloading processes of the expansion and recovery phases. Once reconnection begins there is an induced electric field in the magnetotail proportional to the time rate of change of lobe flux. This field adds to the electrostatic field of the solar wind and their sum drives current through the ionosphere during the expansion

1099

phase. Thus we expect measures of these currents such as the AL index to be proportional to changes in lobe fhlx. Another parameter closely related to the lobe magnetic field is the inclination of the field at synchronous orbit (KOKUBUNand MCPHERRON,1981; BAKERand MCPHERRON,1990). For the flux in the lobe to increase the cross tail current must grow as well. This change causes the field at synchronous orbit to become increasingly tail-like as the growth phase develops. During the expansion phase this current is diverted along field lines as the substorm current wedge. Within the angular sector of the wedge the effect of the current is to increase the vertical magnetic field, returning the net field to a more dipoIar configuration. Thus the inclination of the synchronous field interior to the wedge measures the change in tail lobe field strength, and can be used as another measure of substorm intensity. A parameter closely related to synchronous field inclination is the pitch angle dist~bution of electrons at synchronous orbit (BAKER et al., 1978). The reduction of total field which occurs at the synchronous magnetic equator causes particles of 90” pitch angle to drift on shells closer to the Earth than they do in more quiet conditions. This allows particles of low pitch angle to dominate the dist~bution. A parameter that characterizes this distribution is ‘C2’. C2 increases as the particles become field-aligned during substorm growth phase and decreases as they return to normal distributions during substorm expansion. Thus the parameter mimics the tail field, and the inclination of the synchronous field. However, because electrons drift rapidly across the night side it is a more global measure of night side field inclination, and can provide information in regions outside the substorm current wedge as well as within the wedge region. Wme indices

Indices of wave power can also be used as measures of substorm activity. The most familiar of these is the Pi 2 index (BAUMJOHANN,1986). These ULF waves have periods of about 60 s. They typically accompany any onset or intensification of a substorm expansion, and are therefore very useful in establishing the phases of a substorm. Unfortunately, their amplitude does not seem to be directly related to the strength of the substorm with which they are associated (KUWASHIMA,1978). At much higher frequencies aurora1 kilometric radiation is also a useful indicator of changes in substorm phase and crudely of its intensity (?%o~s et al., 1977). AKR is thought to be generated by

instabilities in the field-aligned current systems associated with arcs on the polcward edge of the aurora1 bulge. Pi c is another typo of ULF wave with a period of about IO--SO s (HE.~c‘o~x, 1967). These waves are

produced in the morning sector of the westward eiectrojet by unknowtl ionosplleric processes. Althotlgh these and other types of waves are good indicators of substorm phases their correlation with more common measures ofsubstorm intensity is sufficiently poor that they are not normally used for quantifying substorm intensity.

3. SOLARWINDCORRELATIONSWITH MAGNETIC INDICES Very soon after the discovery of the solar wind most researchers postulated that it was responsible for geomagnetic activity and associated phenomena. Two theories were propounded : viscous interaction (AXFORDand HINES,1961) and magnetic reconnection (DUNGEY, 1961). Kn the viscous interaction model solar wind momentum is transferred into two boundary layers lying in the ma~etos~heric equatorial plane on the flanks of the magnetosphere. Closed field lines inside the magnetopause are set in motion and circulate in two cells centered on the dawn and dusk terminators. In magnetic reconnection. southward pointing field lines of the solar wind are pressed against the day side magnetic field merging with it. The newly opened field lines are carried by the solar wind over the polar caps and added to the tail lobes. Eventually they reconnect in the night side plasma sheet returning as closed field lines to the day side as in the viscous interaction. In either case one expects that geomagnetic activity should be correlated with the speed of the solar wind. For magnetic reconnection the important quantity is the rate at which magnetic flux (VII,) reaches the subsolar magnetopause. However, HOLZER and SLAVIN (1978) have speculated that dayside reconnection ef-liciency might increase with solar wind velocity. MAEZAWA and M~AYAMA (f986) have suggested that particle precipitation on the night side is controlled by the solar wind velocity, enhancing reconnection-driven ionospheric currents for a given rate of dayside reconnection. They also suggest that viscous interaction may contribute co-operatively to solar wind coupling by increasing the etliciency of the reconnection process. It was demonstrated early in the spacecraft era that on a short term, substorms and storms only occur when the interplanetary magnetic field (IMF) is south-

ward (FAIRFIELUand CAHILL, 1Y65). Figure 5 illus. trams this point very clearly. The top two panels show the magnitude and southward component of the IMF, while the bottom two panels display data from which the .4E:and /1,,-.dsyn1 indices arc derived. An isolated sL~bsto~ occurred near 12 UT on 13 January 1967. and then prolonged, overlapping substorms and a magnetic storm began late in the day. It can be seen that these occurred only while lMF-B, was negative. Shortly after the IMF turned northward aurora1 zone magnetic activity vanished while at lower latitudes the effects of the storm-time ring current slowly disappcarcd , In more recent studies it has been found that the product VR, in the two hours preceding a substorm was better correlated with AE than all other quantities tested {ARNOLUY,1971). HIRSHRERC; and C~LERUKN (t969j demonstrated that the highest correlation between 8, and magnetic activity measured by k; is obtained in the GSM coordinate system. CROOKERet al. (1977) demonstrated that yearly averages of Ap were linearly related to the square of the solar wind velocity. FRRREAULT and AKASOFU(1978) in the belief that weak magnetic activity occurs during northward IMFt suggested that activity is proportional to sin’ (#/2) where Bis the dock angle of the IMF around the Earth-Sun line measured from the plane of the Earth’s dipole. Other, more complex angular dependencies were suggested by a variety of theoretical considerations. GARRETT (1974) showed a significant dependence of activity on hourly variance in solar wind parameters, as well as on the averages themselves. However, RUSSELL( 1974) argued that this was an artifact of using hourly averages which hide short intervals of southward 8,. MURAYAMAet d (1980) made use of this concept to correct hourly averages of IMF-B, by its hourly variance. Studies such as those mentioned above have established that magnetic activity indices are related to complex functions of several solar wind parameters (BAKERef al., 198 1, 1983). Because these ‘coupling functions’ are nonlinear it is difficult to establish the proper form of the coupling function with finear regression techniques. None the less, empirical studies (e.g. MURAYANIA, 1986) have determined, for example, that AL data are well organized by a function of the form k*(fI,+0.5)VZ. Figure 6 illustrates this point, but also demonstrates that the dependence of AI, on this function is nonlinear. Other indices are best organized by slightly different coupling functions (MURAYAMA,1982). More detailed studies indicate that some indices exhibit a significant dependence on IMF-R,, and the tilt of the dipole as well (HAKAMADA et Cl/.. 1980).

1101

#J ixp33 Bz

08

18 12 13Jan I967

24

06

12 18 14 Jan I967 UT

24

Fig. 5. Relation of IMF-B, to magnetic activity indices during a moderate magnetic storm in January 1967 (WOLFet al., 1986). Top two panels display field magnitude and southward component of the IMF. Bottom two panels show traces of the H component along chains of amoral zone and midlatitude magnetometers. Intervals of activity occur only during southward IMF.

4. WHAT IS THJ3 BEST COUPLING FUNCTION?

Studies like those described in the preceding section raise the question of how one defines the ‘best’ solar

wind-magnetosphere coupling function. The answer clearly depends on what measure of substorm intensity one uses. AgAxxu (1981a) suggested that the interesting quantity is the rate at which energy is extracted

uhcrc I,, is the radius of the eyui\alcnt aperture on the dayside magnetopause through which solar wind

cncrgy enters, and I,‘, Rand 0 arc the usual solar wind quantities correlated with gcomagnctic activil). The functional dependence of epsilon on sol;tr wind vclocit! and magnetic from quantities shown

field strength is so cliffercnt to bc best related to the i31,

index that we must ask whcher it is thecorrect measure of energy input to the magnctospherc. VASYLIWAS cf d. ( 1982) have considered this question using the principle of dimensional analysis. Basically this principlc requires that when an energy ~~irarnet~r is used to measure the output of a system, then the inpur parameter should have the same physical units. However, this can be accomplished by multiplying an energy parameter like the Hux of kinetic energy in the solar wind by an arbitrary function of the dimensionless variables important in the process of solar

-400

wind coupling. For magnetic reconnection these arc the solar wind Mach number and the IMF clock angle.

-200

0

-600

-400 EZIC V9600

u

-200

nr il./*

*rh*rr

0

-I

0

500

1000

1500

2000

Fig. 6. Dependenceof the AL index on various combinations of solar wind parameters. Four panels show the increasingly better organization of the AL index for extreme values of B and V obtained by using various coupling functions (MAEZAWAand MIJRAYAMA, 1986).

from the solar wind and therefore advocated the total ma~~tospheric energy dissipation function lJ,. As originally defined by PERREAU~Tand AKASOFU(1978), U, is the sum of the ring current dissipation rate, the Joule heating rate and the particle precipitation rate. Since measurements of the last two quantities are rarely available, the authors used correlations with magnetic activity indices (AE) to estimate them. In principle, such a function should include every form of magnetospheric energy dissipation including energy returned to the solar wind, wave energy, etc. Propefiy defined, and correctly measured such a function should on the average be equal to the energy input to the ma~etosphere by the solar wind. For the latter quantity PERREAULTand AICASOFU(1978) ~n~~u~ed the epsilon parameter de@d as a fraction of the instantaneous interplanetary Poynting vector, or epsilon = 16VB2 sin4 (O/2)

They suggest the simplest such function is a product of the kinetic energy flux, the Mach number to a power (M, ‘>1,and a nonlinear gating function such as used in epsilon. Empirical studies can then detcrmine the ‘best’ exponent for this simple coupling function. KAN and AKASOFU(1982) applied these ideas to the U, parameter and concluded that epsilon was the best coupling function. However, BAKC;A.~ZEet ~1. (1984) used essentially the same data and concluded virtually the opposite, that a parameter close to the solar wind electric field, namely p “‘VB, (whet-c p is solar wind dynamic pressure) was best. A close study of these two works reveals that KAN and AKASOFU( 1982) did not allow the diameter of the magnetosphere to change with dynamic pressure as it should according to the principles of dimensional analysis. l-lowcver, we note that BARGAZE cl al. (1984) also examined the form of the gating function and concluded that sin’(Oi2) was a better gating function than the pure half wave rectifier normally used in many correlation studies. As we noted in the introduction any parameter measuring the total energy dissipation in the magnetosphere depends on virtually all parameters in the solar wind and many within the magnetosphere. Thus there is little hope that a total dissipation parameter can be used to study the factors that control a specific process important in dissipation such as Joule heating. Furthermore parameters such as the AL index which are closely related to some specific process are not necessarily proportional to energy dissipation. Thus, there is no reason to expect that they will satisfy the principle of dimensional analysis. Clearly this is the

Intensity of magnetospheric substorms

1103

intensifications are evident in the aurora1 oval as new filaments of westward electrojets and multiple westward traveling surges (KISAB~ and RCEXOKER, 197 1, 1973). At midlatitudes they appear as positive bay onsets (CLAUERand MCF’HEXRON,1974; WEINS and ROSTOKER,1975). At synchronous orbit they are seen as expansions of the substorm current wedge. 5. TIME SCALES ASSOCIATED WITH SUBSTORM Occasionally they can be discerned in the tail lobe as ACTIVITY changes in the rate of decrease of the tail flux. The As discussed earlier, the duration of a typical isotypical range of delays between these intensifications lated substorm of moderate intensity is about 3 h. Its is IO-30 min. Most of these intensifications are associgrowth phase is typically 1 h, its expansion phase 30ated with the expansion phase. However, some occur 60 min and its recovery phase 90 min. FOSTER et al. during the growth phase and are called pseudo-break(1971) showed that on the average such substorms are ups. Others occur in the recovery phase and are evicreated by an interval of southward IMF cordent as intensifications of aurora on the poieward responding to the growth phase, or about _ 1 h. When edge of the aurora1 bulge (HONE.Set al., 1990). the IMF remains continuously southward for times There are no known periodicities in the occurrence longer than this, activity becomes very complex with of substorms. Since their typical duration is 3 h, the the various phases of a substorm overlapping. most that could be distinguished as separate entities Occasionally, a near steady-state will develop and is about eight per day. Since they usually have more none of the phases are recognizable (PYTTE et al., than one onset or intensification per substorm the 1978). However, every change in the solar wind should number of these could be considerably larger, perhaps cause a change in the level of magnetic activity. These 20 or more. When activity becomes continuous it is changes are not instantaneous and delays must be no longer clear whether distinct intensifications are taken into account when correlating solar wind coupoccurring. At these times the AE indices fluctuate ling functions with measures of substorm intensity. strongly about some constant value, but this appears The typical delay between a change just upstream of to be a result of omega bands in the morning sector the bow shock and the first detectable effect in the modulating the DP-2 current system (KAWASAKIand ionosphere is about 8 min (FRIIS-CHRISTENSEN et al., ROSTOKER,1979). Spectra of long intervals of the AE 1985), however, the overall, average time scale for index do not normally show any major spectral peaks these changes to be manifested is 20 min (BURCH, (TSURUTANIet al., 1990), although ROBERTSet al. 1974; MENC and TSURWTANI,1973 ; BARGATZEet al., (1991) have identified a peak at 15 min which may be 1985). significant. One of the first attempts to determine the characteristic time scale of substorms was carried out by ROSTOKERet al. (1972). They found that the cross6. HOW PREDICI’ABLE ARE INTENSITY MEASURES? correlation between the dawn-dusk component of the solar wind electric field and the AE index was 40 Linear prediction filtering We showed in an earlier section that regression min. This delay is comparable to the duration of the and correlation analysis demonstrates that substorm substorm growth phase and MC~~ON (1972) interindices are controlled by the solar wind. However, preted it as evidence for energy storage in the magtime delays between the solar wind input and the netotail. MENG and TSURUTANI(1973) obtained the same result, but interpreted it as an artifact related to magnetospheric output are a source of difficulty in establishing this relationship. Much of the work on differences in the waveforms of the two signals used solar wind coupling has effectively ignored this by in the correlation analysis. More recent demonstrations of this characteristic delay are those of using averages or integral measures. For example, MURAYAPAA et al. (1980) used 3-h averages. In contrast B~~~~etaL(1981, 1983)andT~~~~~~~1etai.(l985) HOLZERand SLAVIN(1982) used time integrals over the latter of whom studied the CDAW-6 substorms complete disturbed periods of the rectified solar wind used in preceding illustrations. electric field and the AL index. Others like CROOKER Another characteristic time related to substorms et al. (1977) have even used yearly averages. The is the repetition rate of intensifications during the correlation coefficients obtained in such studies can substorm expansion phase. In a typical isolated subbe very high (0.97) (HOLZER and SLAYIN, 1982). In storm there may be several of these, but some subcontrast to these studies which average out the time storms may have as many as five or more. These

case, because the AL index is best related to a function which does not satisfy this principle. We thus conclude that the factors which control a given process must be determined empirically rather than by this principle.

dependence. cross-correlations as a llrnction of lag using high resolution data rarely give correlation coefkients that exceed 0.7 -0.8 (f%~likx et d., l%il, lY83). Neither the technique of linear regression with long term averages. nor cross-correlations as a function o! lag are completely suited to the problem of predicting measures of substorm intensity. In the former method details of the time development arc ignored. In the latter method there is no reason to expect that the wave form of the output will be identical to that of the input. Most physical systems attenuate and delay different frequency components of the input by different amounts. When these arc combined in the output a different wave form results and therefore cannot correlate perfectly with the input. One way to study such systems is to use the technique of linear prediction filtering (CLAUEK, 19%). A linear prediction fitter is the most general possible linear relationship between a system’s input and output. Let us suppose that we are able to stimulate a system by a single pulse of unit amplitude, and then measure its output. This impulse response is the system’s prediction filter. This can be understood by visualizing a typical digitized input to the system as a train of impulses of different amplitudes. If the system is time invariant and linear then its output will consist of the supposition of the scaled response to each pulse in the input. Thus the output at any particular time must depend on the input at all times within at least one impulse response interval before this time. The technique of linear prediction filtering is based on Fourier transform theory as summarized in Fig. 7. The impulse response of a linear system is defined as the Fourier transform of the system’s transfer function which itself is defined as the ratio of the Fourier transform of the output to the input. The inverse transform of this relation is called the convolution integral. This integral states that the convolution of the impulse response of the system with some specified input predicts the output. All information about the characteristics of the system are contained within the impulse response. This response function can be obtained empirically from the past history of input and output to the system (WEINER.1942). In practice the impulse response or prediction filter is obtained in a somewhat different manner as discussed in detail by CLAUER(1986). The output of a system is expressed as a summation over preceding times of the discrete inputs multiplied by weight factors. One then uses the technique of least squares to find the weights that minimize the power in the residual between the predicted output and the observed outpul. This leads to a matrix equation of

LINEAR SYSTEM

ANALYSIS

LINEAR SYSTEM r(t)

--0(t)

TRANSFER FUNCTION O(u) = G(w). I(w) IMPULSE RESPONSE FT

gW--+Gkd

B(w)

= z[w)

CONVOLUTION THEOREM O(t) = J&l

I (i-r)

dr

Fig. 7. Definition of a linear prediction filter using theory of Fourier transforms. The predictor for a liriear, t~~jnvariant system is the impulse response obtained by inverse transforming the ratio of the output to input Fourier transforms.

the form (&a = e, where a is a cofumn vector of unknown weights, c is a column vector containing the cross-covariance between input and output, and (R) is a matrix with rows containing the auto-correlation function of the input shifted by one more Iag in each successive row. The quality of the prediction is normally expressed by the prediction etIiciency defined as (I - VA R(resid)/I/AR(orig)). The correlation coefficient between the observed output and the predicted output is the square root of the prediction efficiency and is always larger than efficiency since efficiency is less than one. Predjct~on~lter~ forthe AL index An illustration of the quality of typical predictions of the AL index is presented in Fig. 8. For this analysis (MCPHERRONet al., 1988) an interval of 54 days was used, and V& measured 40-60 RO upstream of the Earth was taken as the input. The e&iency with which the filter predicted the data used to define it was about 45%. The thin lines in the Figure are the observed index values while the more slowly varying solid line is the prediction. It is immediately apparent

Intensity of ma~etosphe~~ C;OMPARISON

substorms

1105

OF PREDICTED WITH OBSERVED

AL INDEX 2

T

-300

5

-500

-700

00

10

ke

06

Arbitrary

24

(hours)

Fig. 8. Comparison of predicted and observed AL index for periods of moderate (top) and strong (bottom) activity. Ekh frame shows a plot of the solar wind input function VB, at the top with the predicted (solid line) and observed (thin iine) AL index underneath.

that the filter fails to predict the sudden changes in AL we normally associate with the substorm expansion phase or the DP- I current system. It seems to do much better in predicting the background variations in the current or DP-2. Two different levels of activity are shown in the top and bottom panels of Fig. 8. CLAUERet al. (1981) showed that filters for moderate and strong activity intervals are not the same. The active filter seems to peak at shorter delay and have a stronger peak than the moderate filter. BARGATZEet al. (1985) further studied this activity dependence obtaining the results summarized in Pig. 9. Their results suggest that the AL response function is bi-modal at moderate levels of activity and uni-modal at high levels. Both response functions have a peak at 30 min, but the amplitude of this peak depends on activity. Both also appear to have a peak at 70 min, but in the strong activity case

FILTER FILTER

0.02

_I -1

4 0

TIME

810 ~ 027..------..

, 2

I

LAG

I 3

(hours)

Fig. 9. The impulse response relating the rectified solar wind electric field VBs to the AL index for two different levels of geomagnetic activity. The response at short delay is considerably enhanced during disturbed intervals.

it is swampcct

by lhe larger response at shorter lag. Behavior such as this is not characteristic of linear, lime-invari~~nt systems as wc assumed in the analysis. and it is iinp~~rtallt to consider the ill~plica~i~)nsofthis. A prediction ctlicicncq of 45% impiics that 55”1i,of the variance in the AL index is not systematically correlated with the assumed input i’N,. There arc a variety ofpossible explanations. ARASOFU c’t~1.(1983)

COMPARiSON OF SOLAR WIND INPUT WITH AURORAL ZONE MAGNETIC OUTPUT 17:OO UT April 4, 1978

has suggested that the ,-iE index is not good enough f’or use in such analysis, that it is biased by both random and systematic w-ors. If this were the only

explanation 55% of the variance in ,4L would bc noise, but the non-random occurrence of the largest residuals during substorm expansions is not consistent with this explanation. Another possibility is that the wrong coupling function was chosen for the input, and the system does not linearly transform solar wind electric field into the AL index. CI.AUPR et 01. (1981) considered this possibility and discovered that the least square technique optimizes the prediction filter for whatever combination of input and output are used, and the overall prediction efficiencies arc not much different, although VB, gave better predictions than epsilon most of the time. One likely cause of low prediction efficiency is that some of the processes which contribute to the index arc not directly controlled by the solar wind. This would be the case, for example, if the unloading processes are controlled by internal magnetospheric parameters. This seems quite likely. According to the near-Earth neutral line model unloading occurs as the consequence of an x-lint in the near-Earth plasma sheet. Its creation depends on, among other things, the thickness of the plasma sheet and the curvature of field lines which pass through it. These depend on previous substorm activity, ionospheric conductivity, as well as the rate of dayside reconnection. Other models I;or unloading such as current sheet disruption (Lur t’t al.. 1990) would lead to similar results since they also depend on internal parameters. An alternative explaIlation could be that the onset of the substorm expansion depends on some parameter in the solar wind other than the variation of its electric field. Caa~ t’t al. (I 977) showed that one such parameter is a sudden northward fluctuation of the IMF-R, component. Figure IO tskcn from the work of MCPHERRONef al. (I 986) shows a relatively unambiguousexample. About 50% of all isolated substorms having sharp onsets can be associated with a B= fluctuation of some sort (MCPHERRONet cd., 1986). The superposed epoch results of FOSTERet al. (197 I) showing that isolated substorms have expansion onsets about the time of the northward turning supports this eolltention. Sudden dynamic pressure pulses

2 -400 ;i -600 -aoo_,

ALIndex

’

-2

(

tG:,vr

&.

(H&s)

2

3

Fig. 10. An example of a substorm expansion that appears to have been triggered by a northward turning of the IMF during an interval of relatively stable dynamic pressure (MCPHERKON c/al.,1988). Vertical line denotes the time of a sharp onset in the .4L index. are also known to trigger expansion onset (BURCH, l972), but with less frequency than do northward turnings. We emphasize, however, that exampfes of expansion onset during perfectly stable solar wind and IMF are frequently found proving that unloading must be an internal magnetospheric process. The hi-modul magnetosphere

The bi-modal response function obtained by BARet cd. (1985) seems to contradict the idea that the substorm expansion is an internal process. According to these authors the first peak at 20 min accounts for the development of the driven current system (DP-2), and the second at 60 min for the unloading system (DP-I). We can idealize the response function obtained by BARGATZEet ui. (1985) by two delta functions centered on each peak, each multiplied by constants proportional to the area under the peaks. Then the convolution integral is easily interpreted. The AL index is directly proportional to the solar wind electric field, but as a sum constructed from a signal twice delayed and twice scaled, rather than only once as originally envisioned by AKA~~FU (1979). This would be an entirely driven system if it predicted all of the AL variance. ~~~~E~~O~ et al. (1988) have used this idealized model to study the two isotated CDAW-6 s~b~to~s. They found that 80-90% of the AL variance was GATZE

Intensity of magnetospheric substonns predictable. However, the time delays and scale factors are different for the two substorms. BLANCHARD et al. (199 1) have reported an extension of this analysis. Using a slightly improved model they find that on the average, 85% of the AL variance is predictable for a set of ten isolated substorms provided the time delays and scale factors are adjusted for each substorm. These results support the idea that ionospheric currents are driven by the solar wind electric field, but not through a single current system, and not with fixed time delays and scale factors. If it is possible to find what factors control the time delays and scale factors in this simple model a remarkable fraction of the AL variance could be predicted provided the control factors are routinely measurable and not the result of stochastic processes. A physical model for the bi-modal AL response What is the physical significance of the success of the simple, four-parameter model of the bi-modal response function? Our interpretation is the following. When a southward interplanetary magnetic field is pressed against the subsolar magnetopause it begins to merge along an x-line oriented parallel to the magnetopause current. Reconnection then occurs at a rate that allows a fixed fraction of the magnetic flux transported by the solar wind to merge with the Earth’s field. Newly opened field lines are carried over the polar caps and accumulated in the tail lobes. The onset of reconnection induces a return flow of closed field lines within the magnetosphere. This onset propagates around the Earth and into the plasma sheet as a rarefaction wave which thins the plasma sheet. These magnetospheric flows drive the twocelled DP-2 Hall current system within the ionosphere. The polar cap PC index is a measure of the rate at which the feet of open field lines are flowing antisunward over the polar cap. The AU index is a measure of the rate at which they are returning sunward along the oval on the dusk side, and AL is a measure of their return rate on the dawn side. In addition, the tail lobe field strength measures the magnetic flux accumulated in the tail, while the synchronous field inclination measures a combination of the increase in cross-tail current and changes in the plasma sheet. Together these processes produce the growth phase of the substorm. There are significant time delays in establishing the growth phase current system. These include solar wind propagation from an upstream monitor to the dayside magnetopause, Alfven transients between the merging region and the polar cusp ionosphere, solar wind propagation along the tail magnetopause,

1107

propagation of the rarefaction wave into the plasma sheet, and the creation of the Region l-Region 2 field-aligned current system. This last is probably the predominant factor. The L/R time constant associated with the establishment of this system is estimated to be 10-20 min (WEIMER,1992), and this is close to the time of the first peak in the AL response function. In summary, the electric field of the solar wind is imposed oti the ionosphere through newly opened magnetic field lines. Current flows along these field lines, but is limited by the inductive effects of the growing magnetic perturbations around these currents. Closure of these currents through the ionosphere dissipates energy in the form of Joule heating. The Hall current system and the PC, AU, and AL indices which respond to different parts of this current are a secondary effect of the entire process. The sunward flow induced by dayside reconnection, and the magnetic flux added to the lobe eventually cause the expansion onset. The sunward flow transports closed field lines from the night side to the day side allowing the plasma sheet to thin. Increased magnetic pressure in the tail lobe squeezes the plasma sheet contributing further to thinning. Eventually, the scale of the tail current sheet becomes comparable to an ion gyro radius and magnetic reconnection begins near the center of the plasma sheet. In the near-Earth neutral line model reconnection begins at the center of the plasma sheet near the end of the growth phase. Within a few minutes the last closed field lines bounding the plasma sheet are severed and magnetic flux in the tail lobes begins to reconnect. From the results of the bi-modal model the time for severance is typically 60 min (expansion phase delay). Tail current is diverted along field lines and flows westward through the midnight ionosphere as a filamentary westward electrojet. Magnetic effects of this DP-1 current system are added to those of the pre-existing DP-2 system and are measured by the AL index. Also, effects of the current diversion are seen at synchronous orbit as dipolarization of the field, and in the lobes as reduction in lobe field strength. To explain the results of the bi-modal impulse analysis we must assume that the ionospheric current that flows in the expansion phase is again proportional to the solar wind electric field, but with a longer delay and different scale factor than the growth phase current. Since the tail lobe field is decreasing as these expansion phase effects occur, we presume this means that the DP-1 current, and some of the DP-2 current is driven by reconnection at the near-Earth x-line. To be consistent with the prediction filtering results the reconnection rate must somehow be controlled by the solar wind. We suppose this happens because the solar

wind electric field across the open field lines somehow determines the drift speed of open flux across the tail lobes. We point out that this model does not correspond to the usual unloading model. In the usual model the rate of reconnection is controlled by intcrnal magi~etospheric processes hence the name unloading process. Our filtering results imply that the nightside reconnection rate changes in time proportional to the pattern of electric field imbedded in the solar wind. The substorm current wedge and the DP-I current system of the expansion phase have a signi~cantiy different geometry than that of the growth phase currents. Furthermore, the conductivity of the ionosphere through which it closes differs from that in the growth phase as a result ofparticle precipitation. Both factors lead to differences in the time delays and hence the precise shape of the second peak of the response function. In the MCP~KRRONrt d. (1988) bi-modal model there are four significant parameters required to predict the AL index for individual substorms. These are the inductive time constant of the Region I-Region 2 current system, the scale factor relating growth phase .4L. to the solar wind electric field, the time delay to the start of the expansion phase current system, and the scale factor for this current. What factors control these four parameters, and hence the intensity of a substorm as indexed by AL‘? They must include the geometry of the Region I---Region 2 currents, the initial conductivity of the ionosphere, the geometry of the substorm current wedge. and how particle precipitation alters conductivity. However, each of these must depend in some way on the previous history of substorm activity. Is there already excess flux in the lobe? Is the plasma sheet unusually thick, or hot, or dense? Are there particles in the radiation beIt available for precipitation? These also depend on the solar wind. Is the magnetosphere of unusual size because of dynamic pressure? Is the electric field unusually large, or steady, or fluctuating‘? Arc there trigger pulses in the solar wind that will destabilize nightside reconn~tion sooner than expected? Empirical studies may eventually determine the eft‘ect of each of these and provide a means for advance prediction of the four model parameters, and hence provide a means for predicting substorm development. 7. ARE SUBSTORMSMANIFESTATIONS OF NONLINEARPROCESSF,S Deterministic chaos

In the preceding section we showed that a linear, time-invariant model cannot predict more than about

45% oi’thc vartancc of the relation hctwccn high time resolution measures oi’thc solar wind electric tieid and thu .,lL index. Furthcrmoro, much of the unprcdictable residuals seem to be systematic rather than random suggesting that the main problem is the model not the data. However. WCalso showed that a slmplc, four-porametcr, time-varying version of the same model can account for an avcragc of 85% of the variance. provided the parameters are changed from substorm to substorm. Presently the factors which influence these parameters are not known, but it seems likely that they include soiar wind_ ~lagnet~~spheric and ionospheric variables. A possible explanation for the need to change the model parameters from event to cvcnt is that the equations that govern the relation between the solar wind input and magnetospheric output are intrinsically nonlinear. It is weii known that even simple nonlinear systems like the forced, damped, pendulum can exhibit unpredictable behavior (BAKERand GOLLUB, 1990). Although this system is completely deterministic, its behavior at future times is especially sensitive to initial conditions. Because of this, miniscule errors in the determination of initial conditions, or minor ~rturbations in the variables due to other processes, can cause a rapid deviation between the actual and predicted solution (GLEICK, 1988). One of the characteristics of such systems is that the response is a function of the level of input. In particular. it has been shown that as the level of input changes, the number of pe~odicities evident in the output wiil double, then double again. At very high levels of input so many periodicities are possible, and transitions between them so frequent that the output appears to be random. However, because the governing equations arc deterministic this state of the system is called chaotic rather than stochastic. AsH~)uR-AB~A~LAand BAKER(199I ) have recently edited a discussion of the applicability of these concepts to the Earth’s magnetosphere.

A demoustrat~on that the magnetosphere might exhibit deterministic chaos has been carried out by BAKERet al. (1990). Stimulated by a suggestion of HONES (1979) that a substorm was like a ‘drippy tap’, BAKERef al. (1990) constructed the mechanical analog illustrated in Fig. il. In this model the behavior of magnetic Aux in &he tail is simulated by a variable mass on the end of a spring. Initially the mass is stationary with the downward force of gravity balanced by the upward force of the spring. The spring is then loaded further by adding mass at a constant

Intensity of magnetospheric substorms

Fig. 11. A mechanical analog of loading and unloading of the tail lobes during substorms. A variable mass is attached to a spring and dashpot. Mass is added at a constant rate until a critical extension is exceeded, whereafter mass is unloaded at a constant rate.

rate. The spring begins to extend trying to reach a new equilibrium. The motion of the mass is retarded by a damping device which produces a retarding force proportional to velocity. Mass continues to be added until the extension exceeds some critical distance. At this distance mass begins to be unload4 at a constant rate. Unloading continues until the extension is less than the critical distance at which point loading begins again. This system can be described by a 3-component state vector y = [d, u, m], where d is the extension of the spring, u the velocity of the mass, and m is the total mass. Three first-order differential equations describe the time rate of change of these three variables. There are also three parameters that characterize the system p = [k, a, dm/dt], where k is the spring constant, u the damping rate, and dm/dt the rate at which mass is loaded or unloaded. The parameters k and a are constant, but dmldt varies with extension, and possibly with time as well. The equations that describe this system are nonlinear because the resonant frequency sqrt(k/m) varies with mass, because products of state variables appear in the equations, and because the loading rate depends on extension. Also the rate of unloading is set proportional to the velocity of the system when it reaches critical extension. As a result of the nonlinearity, the solutions to this equation are very sensitive to both initial conditions, and the loading rate. Numerical solutions display

1109

periodicities that depend on the loading rate. A typical solution for a moderate loading rate is displayed in Fig. 12. The top panel shows that the mass is fluctuating with at least two rather well defined periods. The bottom panel shows a projection of the state vector in the d-v plane. The motion is roughly repetitive with the two main trajectories corresponding to the two periods present in the mass vs time series. Shorter cycles than these are also evident at times. At lower levels of input the system displays a single periodicity. At very high levels so many periods are present that the system is completely chaotic and unpredictable. The drippy tap model is too simple to do more than demonstrate that a basic loading-unloading model can display chaotic and unpredictable behavior. A somewhat more realistic simulation of the tail flux called the Faraday loop model has been developed by KLIMAS et al. (1991). In this model flux is added to the tail at a rate proportional to the solar wind electric field, causing the area of the lobe and the magnetopause flaring angle to grow proportionally. Flux continues to accumulate up to a fixed threshold where unloading begins. Thereafter flux is decreased by an unspecified mechanism at a rate proportional to the rate at which flux had been accumulating at the time it passed the threshold.

8. DOESCHAOS

PLAY A ROLE IN SURSTORMS?

Embedding analysis applied to magnetic indices

A dynamical system is described by the time histories of each of the independent variables needed to characterize the system. These variables form the components of the system state vector space. The behavior of the system is then described by a set of first order equations which prescribe how each component of the state vector changes with time. The dimension N of the system is the number of variables and hence the number of first-order equations needed to describe the system. A mathematical space with m orthogonal coordinates corresponding to each variable is the phase space for the system. For a given set of initial conditions the equations may be integrated to obtain the time history of the state vector which can be represented as a trajectory through phase space. For deterministic systems there is a unique trajectory corresponding to each set of initial conditions. These trajectories can never cross, otherwise the system would not be deterministic. When the dynamical system is driven by some explicit function of time it is convenient to introduce an additional independent variable and dimension related to the

I

.qs i

.a

.75

.? L 1l0E

450

500

600

550

650

700

750

800

TIME .2

PROP'V TRNH GEAR 0 = .962 v = -.02a2 MASS = .9296 OMEGR LORD = .01 OUMP = 10. COW

FRICT

=

= 1.~57

.3

.05 :: I+ f=j 0. i: >

-.05

t

.7

.75

.8

.85

.9

.95

I.

! .a

DISPLACEMENT

Fig. 12. The response of the mechanical magnetosphere to moderate mass loading. Top panel shows the time history of total mass. The bottom panel displays a phase portrait of the conjugate coordinates position and velocity. Two dominant periods are present in the system response.

to eliminate this dependence producing an autonomous set of equations. An unforced dissipative system will eventually decay to an equilibrium state~described by a line in phase space. If the phase space is projected into a hypersurface perpendicular to the time variable (the phase of the driving function

Poincare section), the line collapses- to a point which has a dimension of zero. Ifthe system displays periodic motion in only one variable xe t&en a projection into the eon&rte plane, x and dx/dt, will exhibit a closed path which has dimension one. This concept ofdimension can be extended to the N-dimensional space of

Intensity of magnetospheric substorms all variables where it is clear that the dimension of the trajectory cannot exceed the dimension of the phase within which it is embedded. For nonlinear systems there are many regimes of the parameters controlling the system behavior where the trajectory will wander throughout some subspace of the system phase space. When these trajectories are projected into a Poincare section they form fractal curves which are often localized or ‘attracted’ to certain regions within the section. The dimension of these curves provides a lower limit for the number of variables and hence the number of differential equations that describe the system. If this dimension is low it should in principle be possible to describe the system rather simply. A special issue of Geophysical Research Letters (ASHOUR-ABDALLA and BAKER, 1991 and following papers) is devoted to an attempt to determine this number for magnetic activity indices. Fortunately, it has recently been proven that it is not necessary to have a complete Poincare section to determine the dimensionality of a dynamic system. Instead it can be determined from a single variable (TAKENS, 1981). This is done by constructing a pseudo-phase space of dimension m from samples of the measured variable. The instantaneous system state vector in this phase space at one time is obtained by taking the value of the variable at time tk, V(t,J, and its values at (m- 1) subsequent time delays AT later as the components of an m-dimensional state vector. The subsequent pseudo-state vector is obtained by advancing tk by one sample interval 6t. The attractor for the trajectory of this pseudo-state vector has many of the same properties as the one constructed from the Poincare section of all system variables. To determine the dimension of the original system one successively determines the dimension of the attractor in pseudo-spaces of dimension m = 2, 3,. . J. When the dimensionality of the phase portrait ceases to increase with m then it is assumed this value of m is close to the number of equations needed to describe the system. The dimension of the attractor depends on how completely the fractal hypersurface fills the phase space. The correlation dimension d (GRASSBERGER and PROCACCIA,1983) is obtained from the behavior of the correlation function C(R) defined as C(R) = (jil where xi and the Heaviside vectors in the simply counts

$

I

2 H(R-Ix,-xjl) I,,=

xj are points on the attractor, function, and N is the number pseudo-space. The Heaviside the number of points within

1 H(v) is of state function a sphere

1111

of radius R centered on the point xi, and C(R) gives the average fraction of points within R. It can be shown that as R approaches zero, C(R) N R”. Thus the dimension is found from the slope of a graph of log C(r) vs log R. ROBERTSet al. (1991) has reviewed and extended attempts to measure the dimension of the magnetospheric system as characterized by the AE and AL indices. Figure 13 taken from his work shows in the top panel a graph of log C(R) vs log R for different values of m = 2,4. .16 plotted from top to bottom. The slopes of these curves as a function of log R are plotted in the bottom panel. For a limited range of log R, the slopes converge to a value of d = 4 for curves corresponding to m = 4 and greater. Thus it appears that a set of only four differential equations is needed to describe the generation of AL. Lumped circuit models of the substorm AE indices Results of the sort presented in the preceding section encouraged GOERTZet al. (1993) to construct a simple model of solar wind coupling. Their model assumes that the eastward electrojet and hence the AU index is directly driven by a fraction of the solar wind electric field applied to the ionosphere by dayside reconnection. Assuming an inductive coupling and a constant ionospheric conductivity produced by solar illumination they obtain the relatively simple equation dAL r,,,‘” + AL, = A,E& For the AL index they assume the westward electrojet is driven by an electric field in the nightside plasma sheet inductively coupled to the ionosphere by an equation of the same form as for AU. Then a series of considerations which include pressure balance in the GSM x and z directions, Faraday’s law in the lobe and plasma sheet, and the relation of the plasma sheet density to pressure and specific entropy leads to a set of two more first-order differential equations that couple the development of the plasma sheet electric field and lobe magnetic field. The model is completed by assuming that the Pedersen conductivity of the nightside ionosphere is a function of the flux of plasma sheet particles in the loss cone which is estimated from the development of the lobe field. There are thus three equations for the AL index and one equation for AU. These four equations have six parameters which in turn depend on the inductive time constants, initial Pedersen conductivities, and the ratios of Hall and Pedersen conductivities on the day and night side, as well as the solar wind merging efficiency, mapping

I I I-’

1

2

1.5

(a)

log(r)

iJ _.

_,...._ .:

.:

2.5

:-.

(

,. _:

t

;,+...~.......................... ............................

f

0

0.5

I

1.5

.

1

i ........ . .... ......il,.,....,,..I,,.

2

2.5

3

Fig. 13. Determination of the correlation dimension of the chaotic attractor produced by the end point of a pseudo-state vector derived from the AL index (ROBEKTS. 1991). Top panel shows plots of the correlation integral vs radius of a hypersphere in an m-dimensional phase space. Bottom panel shows the slope of the correlation integral as a function of radius. Different curves show results for phase spaces of dimension 216 by 2’s.

Intensity of magnetospheric substorms Moy 18-19,

I

*

1 *

-

L

‘.

1113

1979

’

1

I

‘.

‘,

g.

*

’

(af

UT (hr)

3o

Solar wind trowel time

AL vs. A$

1I

40

I

0

20 UT (min)

40

0

0

10

20

UT (hr)

30

49

Fig. 14. A prediction of the AL index during a 48-h interval using the equations of Gcm~z et al_ (1993). Top panel is the predicted AL. Bottom panel compares the predictian with observations. The left middle panel is the correlation between observed and predicted AL as a function of lag. The right middle panel shows the average travel time from ISEE- to the Earth as a function of UT in h.

factors for the day and nightside ma~etic field, and finally two arbitrary time delays corresponding to the time to propagate measured upstream electric fields to the dayside and nightside magnetopau~. Figure 14 summarizes the S.nal results obtained for a 48 h interval of AL. The middle left panel indicates that the correlation coefficient between observations and predictions was about 0.8. However, the authors note that the correlation coe&ient for AE was 0.92, which when squared equals a prediction efficiency of 0.85. This is a very high prediction efficiency ifit could be obtained for other intervals without changing the parameters in the equations. However, in a pres-

entation at the IUGG in Vienna the authors reported that the prediction efficiency for other intervals was considerably smaller. We point out that the residuals between predicted and observed AL index are very similar to those obtained by linear prediction filtering as discussed with reference to Fig. 8. In part&far sudden changes during the expansion phase are not well predicted. 9. CONCLUSONS

In this paper we have attempted to answer the question ‘what controts the intensity of a substomy To

tlo this we tirst defined a subbtorm as an interval of time during which the IMF is southward and there is at least one intensification and polcward expansion of the aurora and westward electrojct. The typical isolated substorm is produced by the superposition of effects of two kinds of processes, those directly driven by the solar wind through dayside reconnection and those driven by unloading through nightside reconnection. These two types of processes are evident in various ionospheric phenomena. but most clearly in the aurora1 electrojet indices AL’ and AL. The time variation of the AL index during a typical substorm is divided into three phases. growth, expansion and recovery. Growth and recovery phases are dominated by a two cell ionospheric current system called DP-2. This current is present in the expansion phase but is usually overpowered by the DP-I current system. Most studies of the cause of substorms have utilized the aurora1 clectrojet indices. These have unambiguously demonstrated that it is the interaction of the solar wind with the Earth’s magnetic field that produces substorms. The single factor that determines whether a substorm will occur or not is the clock angle of the interplanetary magnetic field (IMF) around the Earth-Sun line. Only when this field points south of the GSM equatorial plane do the AE indices depart from their quiet values. For a given clock angle the level ofactivity increases with increasing IMF strength and with increasing solar wind velocity. These results have been interpreted as evidence that magnetic reconnection is the physical process responsible for substorms. Numerous regression studies have been carried out to determine the form of the coupling function which produces the highest correlation between the solar wind and magnetic indices. These studies typically utilize averages over entire substorms. For the AL index the optimum coupling function has been found to have the form AL = k V2B Sin’(U/2)F(x,

B,)

where x is the tilt of the dipole and B,. is the GSM y component of the IMF. This is a highly nonlinear combination of the various solar wind parameters which affect magnetic activity. Attempts have been made to define ‘energy coupling’ functions. If it is assumed that the AL index is a measure of energy dissipation then the optimum function turns out to be proportional to p “6 VB, where p is dynamic pressure. and B, is the southward component of the IMF. However, this assumption is unlikely to be true and the optimum empirical function mentioned above is probably a better predictor.

The regression studies do not take into account the time delays inherent in the magnctospheric system and hence cannot predict the output while it is changing. The tcchniquc of linear prediction filtermg does this bt determining empirically &he most general linear. tints-invariant filter that transforms an arhi.trary input coupling function into a given output index. For the AL index it is Ibund on the average that the magnetosphere acts like a low pass filter attenuating all freyuencics in the input above IO ’ Hertz and time shifting them by a constant 20 min. However, it is found that these filters are ruther poor predictors a~coLinting for less than half the AL variance. The prediction residuals are nonrandom and seem to be ;I consequence of not predicting the precise dcvclopment of the substorm expansion phase. This may be interpreted in several ways as either stochastic processes such as triggering by changes in solar wind or ~ilagnetospheri~ parameters. or as nonstationary behavior caused by changes in the system transfer function with time, or finally as evidence that the magnetosphere performs a nonlinear transformation of the coupling function. The idea that the magnetosphere behaves in a nonlinear manner seems to be supported by the observation that the prediction filter for moderate activity is bi-modal while for high activity it tends towards uni-modal. This observation has stimulated various researchers to examine the properties of the AL index as if it were one of the dynamic variables produced by a nonli~lear set of di~erentia1 equations. These studies conclude that the magnetosphere may be characterized by a strange attractor with dimension of order 4 or less. Thus it should bc possible to model the interaction by a set of four or five first-order differential equations. Several attempts have been made to construct a low-dimensional physical model for the magnetosphere. One of these claims a prcdiction efficiency for the AL index ofabout 0.64. However, the parameters in the model are highly dependent on conditions in the solar wind, magnetosphere and ionosphere in ways not specified by the model so it seems unlikely that the model can account for long runs of the indices any better than does the emFiricall~ derived prediction filter for AL. The alternative possibility that the magnetosphere behaves in a linear manner, but with time varying parameters has also been examined using the linear prediction technique. We found that a simpie, five parameter model allows one to model individual substorms with an average efficiency of 84%. This model is very similar to the physical model mentioned above. In the empirical mode1 it is assumed that the AL index is produced by the superposition of two currents, DP-

Intensity of magnetospheric substorms

2 and DP-I, each proportional to the rectified solar wind electric field at some earlier time. Four of the parameters are the time delays and scale factors that relate these currents to the solar wind, and the fifth is an average inductive time constant that filters the delayed solar wind electric field as it is projected onto the ionosphere by inductive field line currents. Extensions of this work should reveal whether the time delays and scale factors are well ordered by factors such as solar wind dynamic pressure (size of system), prior activity and season (ionospheric conductivity), IMF-BY (location of dominant currents in polar cap), and other factors. In summary the answer to the question posed is the following. The solar wind controls the intensity of substorms through the process of magnetic reconnection. However, reconnection on the day and night side are delayed relative to the solar wind by differing amounts that vary with the conditions in the solar wind, magnetosphere and ionosphere. Currents are driven through the ionosphere by electric fields proportional to the reconnection rates which are in turn controlled by the solar wind electric field, but the current strengths depend on ionospheric conductivity. Conductivity depends on season, prior activity and the way in which a particular substorm develops. Long-term averages of global activity indices are highly predictable, but as the time and space resolution are increased they become less so.

10. DISCUSSION In the preceding presentation we emphasized recent studies which have considered the magnetosphere as a nonlinear system described by at most a few nonlinear equations. We recognize, however, this is quite a simplification. In our opinion there are probably at least four different modes of behavior. The first is for northward IMF. Many studies indicate that during these conditions reconnection switches from the subsolar point to points poleward of the polar cusps. Strong currents flow in the polar cap, but they are invisible to the stations monitoring the electrojet indices. The second mode is the one described above which applies to isolated substorms. The third may be relevant to pseudo-breakups, and the fourth to convection bays. We ask here what these events might be from the viewpoint of the near-Earth neutral line model (MCFHERRON,1991). An essential feature of the near-Earth neutral line model is that Iobe field lines are always open and therefore there is an x-line in the distant tail. The model postulates that it is not this x-line which returns

1115

flux to the dayside, but rather a second x-line that forms close to the Earth. This x-line must initially form at the center of the plasma sheet and if it is ~muthally localized, must be connected at its ends to a corresponding o-line. Reconnection at first involves only closed field lines within the plasma sheet (BAKER and MCPHERRON,1990). Cutting these lines produces a bubble of plasma within the plasma sheet threaded by circular field lines. We suggest that a pseudobreakup is the ionospheric manifestation of this phenomenon when reconnection does not succeed in cutting the last closed field lines connected to the distant x-line at the boundary of the plasma sheet. Then the open field lines of the lobe do not become involved and virtually none of the energy stored there is released. These events cannot be directly driven by the solar wind since they are not directly connected to it. If reconnection at the near-Earth x-line reaches the boundary of the plasma sheet then the x-line becomes topologically connected to the distant x-line. The oline attaches to the disconnected segment of the distant x-line and the plasmoid is ejected from the tail leaving a nearly empty channel down its center. Reconnection then continues along the near-Earth portion of x-line. Open field lines of the lobe are converted to closed field lines and the projection of the separatrix onto the ionosphere expands poleward at the top of the aurora1 bulge. Isolated substorms are created by an IMF that turns northward after a brief interval. We propose that the cessation of dayside reconnection stops the earthward flow from this xline and forces the near-Earth x-line to move tailward. As it does, newly reconnected field lines are accreted to the region earthward of its position thus continuing the unloading of lobe magnetic energy even as recovery phase begins. Eventually the x-line retreats to its distant location and reconnection must cease or the open lobes would be destroyed. For a sequence of typical substorms to occur the near-Earth x-line must retreat far enough between substorms so that a new x-line can form inside the expanded plasma sheet. This suggests that pulses of southward IMF further apart than the typical 2-3 h duration of the magnetospheric impulse response will produce a sequence of well defined substorms. These are the typical substorms that occur during moderate activity and produce bi-modal impulse response functions. What happens if the IMF remains continuously southward? This is the situation during stronger activity. We suggest it is not necessary for the nearEarth x-line to retreat to great distances after the first expansion phase and plasmoid release. If it remains

! I Ih

K. L.. M~PHEKK~Nand I). N. BAK~:K

close to the Earth and the rate of nightside reconncction matches that on the day side with little delay then quasi-equilibrium can be established. Under these conditions there would he no dramatic changes in the overall configuration of the magnetosphere due to unbalanced flux transfer, and no obvious need to form additional near-Earth x-lines and plasmoids. In this case the magnetosphere would appear to he entirely driven by the solar wind. Some variations should be expected as the x-line probably moves radially in response to changing conditions. or the thin current sheet tailward of the x-line tears and segments are lost downstream. These circumstances are very much like that which occur during convection bays. It is also these circumstances which produce the unimodal response function in the prediction fifter analysis. The foregoing remarks suggest that the change in behavior found in the transition from bi-modal to uni-modal response may not be that characteristic of bifurcation of solutions for sets of nonlinear differentiaf equations when a control parameter is continuousty increased, but a change in the physical model describing the system. Thus it is the wave form of the input signal that determines how the system responds more than the strength of the input. When the IMF is northward, reconnectj~~n occurs only at two lines poleward of the polar cusps. When the IMF is sporadically southward the system produces multiple near-Earth x-lines and plasmoids. When the system is continuously southward it switches yet again to a balanced pair of day and nightside x-lines. Given the highly variable nature of the solar wind it is probably very rare that the magnetosphere ever reaches equilibrium in response to a constant input. Thus it seems likely that the observed variations in various indices are always the transient response of one of the various models to new solar wind conditions. In this case we are uncertain whether analyses of magnetic indices based on the theory of nonlinear dynamic systems is entirely appropriate. In general the chaotic attractor for which the embedding analysis determines the dimension is the asymptotic state of a fixed model driven by a steady input once the initial transients have died away. If it is not appropriate then what is the meaning of the consistently

low dimension obtained in these studies? Thts IS the subject ofactive investigations by groups at Goddard. fairyland and Iowa [Sharma. Prim. Commun.]. The physical arguments used in the model by GO~:Kr%PI ul. (1993) suggest to us that the dimension of the system should bc higher than three or four cvcn though the authors reduced the problem to three equations. Their equations have six control paramctcrs and two arbitrary time delays. These parameters arc never fixed from substorm to substorm, nor constant through a substorm since they depend on such things as dipole tilt, merging efficiency. IMFB,.. residual Aux in the lobes. precipitation of previously injected particles, the size of the magnetosphere, etc. It would seem that ~ldd~tion~llequations are needed to prescribe the time development of these quantities as well. The fact that the GQEKTL rt trl. (1993) equations did not fit other active intervals as well as the one used in their tirst study supports this contention, The preliminary results of BLANCIIARD et crl. (1991) that each isolated substorm requires five tailored parameters supports this view as well. The possibility that the magnetosphere is described by a low-dimensional set of nonlinear differential equations has stimuiated considerable interest in the possibiiity of representing it by lumped circuit models. Careful studies of high quality magnetic indices shouid reveal the form of these equations and determint how the control parameters change with solar wind conditions. Success in this endeavor would provide the benefits of predicting space weather from monitors upstream of the Earth. Such predictions arc of considerable value to both military and commercial systems that must operate in the magnetospheric environment. Acknobt’t~ng~~~t~ntsPrimary support for the preparation of this paperwas provided by the National Academy of Sciences through a Senior Research Associateship tu R.L.M. Additional support was provided by the Laboratory for ~xtrat~~~strial Physics at Goddard Space Flight Center where R.L.M. spent a portion of his sabbatical leave. The manuscript was completed at UCLA with support from the National Aeronautics and Space Administration NAGW2054. Support for portions of the work reviewed herein was provided by the National. Science Foundation Grant ATM87-21904. Additional support at GSFC was provided by NASA.

REFERENCFS

A~~sori~ S.-I.

1964

AKAX~FUS-1.

1958

The development of the amoral substorm. P&~aner. Space S+. 12,273-282. R&r ati ~~~eto~p~~rjc S~b.~torrns. D. Reidei. Dnr-

AKASOF~S.--I.

t979

What is a mag~e~sphe~c

drecht. snbsto~? tn ~~~rni~s oj Mcrgnetasphere, S.-I. AKASOFU(cd.), pp. 447,460. D. Reidel, Dordrecht.

Intensity of magnetospheric substorms

1117

AKAXXTJS.-I.

1981a

AKAXXU S.-I.

1981b

AKAS~FVS.-I.

1982

Hall curre&t as a sour& of the cross-tail current interruption, the asymmetric main phase field and the poleward expanding aurora1 bulge. Planet. Space Sci.

AKA~~FCJ S.-I., AHN B.-H., KAMIDEY. and ALLEN

1983

A note on the accuracy of the aurora1 electrojet indices.

J. H. AKASOFUS. I. and CHAPMANS.

1961

AKA~OFUS.-I., CHAPMANS. and MEG C. I.

1965

AKASOFUS.-I. and SNYDERA. L.

1972

ARNOLD~R. L.

1971

ASHOUR-ABDALLA M. and BAKERD. N.

1991

AXFOKDW. I. and HONEY G. 0.

1961

The ring current, geomagnetic disturbance, and the Van Allen radiation belts. J. geophys. Res. 66,1321-1350. The polar electrojet. J. atmos. terr. Phys. 27, 12751305. Comments on the growth phase ofma~etospheric substorms. J. geophys. Res. ?7,6275-6277. Signature in the interplanetary medium for substorms. J. geophys. Res. 76,s 189-5201. Chaos and stochasticity in space plasmas. Geophys. Res. I/l. 18, 1573-1574. A unifying theory of high-latitude geophysical phenomena and geomagnetic storms. Can. J. Phys. 39,1433-

BAG D. N., AKASOFUS.-I., BAUXJOHANN W.. BIEBERJ. W., FAIRFIELDD. H., HONESE. W. JR, MAUK B., MC-RON R. L. and MOORET. E. BAKERD. N., FRITZT. A., MCPHUIRONR. L., FAIRFIELD D. H., KAMIDE Y. and BAUMJOHANN W.

1984

Energy coupling between the solar wind and the magnetosphere. Space Sci. Rev. 2& 121-190. Magnetosphe~c substorms : a newly emerging model. Planet. Strace Sci. 29. 1069-1078.

30,389-393. J. geophys. Res. 88,5769-5772.

1985

BAKERG. L. and GOLLUBJ. P.

1990

BAKERD. N., Hrosra P. R., HONESE. W. and BELIAN R. D.

1978

BAKERD. N., Ho-

1981

E. W. JR, PAYNEJ. B. and

FELDMANW. C. BAKERD. N., KLIMASA. J., MCPHERRONR. L. and BUCHENRJ.

1990

BAKERD. N. and MCPHERRONR. L.

1990

BAKERD. N., ZWICKLR. I)., BAMES. J., HONFSE. W. JR, TSURUTANI B. T., S~~ITHE. J. and AKASOFUS.-I. BARGATZE L. F., BAKERD. N., MCPHERRONR. L.

1983

and HONIJS E. W. BARGATZEL. F., MCPHERRON R. L., BAKERD. N.

1464. Substorms in the magnetosphere,

Chapter 8, NASA Scientific and Technical Information branch, NASA Reference Publ. 1120. Magnetotail energy storage and release during the CDAW-6 substorm analysis intervals. J. geophys. Res. 90, 1202-1216. Chaotic D,vnamics : an Infroduction. Cambridge University Press, Cambridge. High-resolution energetic particle measu~ments at 6.6 Re. 3. Low-energy electron anisotropies and shortterm substorm predictions. .I. geophys. Res. 83,48634868. A high time resolution study of interplanetary parameter correlations with AE. Geophys. Res. Left. 8, 179-182. The evolution from weak to strong geomagnetic activity : an interpretation in terms of deterministic chaos. Geophys. Res. L&t. 17,414. Extreme energetic particle decreases near geostationary orbit : a manifestation ofcurrent diversion within the inner plasma sheet. J. geophys. Rex 95,6591-6599. An ISEE 3 high time resolution study of inte~lanetary parameter correlations with magnetospheric activity. J. geophys. Res. 88,6230-6242.

1985 1984

and HONESE. W. JR

Magnetospheric impulse response for many levels of geomagnetic activity. J. geophys. Res. 90,6387-6394. The application of dimensional analysis to solar windmagnetosphere energy coupling. Proceedings of COB.ference on Aehi~ements of the MS. 26-28 Jane 1984, Gruz. Austria. ESA SP-217, pp. 157-160.

BAUMJO~N~ W.

1983

Ionospheric and field-aligned current systems in the aurora1 zone : a concise review. Adcl. Space Res. 2( lo),

BAIJMJOHANN W.

1986

BAU~OHANNW. and GLASMEIER K.-H.

1986

Merits and limitations of the use of geomagnetic indices in solar wind--magnetosphere coupling studies. In Solar Wind Magnerosphere Coupling, Y. QMIDS and J. SLAVIN&is), pp. 3-15. Terra Scientific, Tokyo and D. Reidel, Dordrecht. The transient response m~hanism and Pi 2 pulsations at substorm onset-review and outlook. Pianer. Space Sci. 32(1 I), 1361-1370.

BIRKELAND K.

1913

52-62.

The ~orwegi~

Aurora Polaris Expedition 1902-1903,

Vol. I, 2nd section. Aschhoug, Christiania.

1970 1973

1973

1974

BURCHJ. L.

M. N.. MCPHERRON R. L. and RUSSELLC. T.

197s

CAA~:M. N., M~~RRON R. L. and RUSELL C. T.

1977

CHAPMANS. and BARTELS J.

t962

CLAUERC. R.

1986

CLAUERC. R. and KAMIUEY.

1985

CLAUERC. R. and MCPHERRONR. L.

1974

CLAUERC. R., MC~ERRON R. L.. SEARLSC. and hTLSON M. G. CORONIT~ F. V. and KENNELC. F.

1981

CAAN

Rate of erosion of dayside magnetic flux based on a quantitative study of the dependence of polar cusp latitude on the interplanetary magnetic field. Radio ,Sci. 8, 955. 961. Observations of interactions between interplanetary and geomagnetic fields. &c Gwphy,~. Spcm~ Phy.s. 12,363 37x. Substorm and interplanetary magnetrc field et?&% on the geomagnetic tail lobes. .I. ~&qx. Res. 80, 191 194. Characteristics of the association between the interplanetary magnetic field and substorms. J. ,~~~J~~~.s. I%. 82,4837 4842.

DAVIST. N. and SUGILJRA M.

I966

&ZSSLER A.J.

1973

The technique of linear prediction filters applied to studies of solar wind-magnetosphere coupling. In S&r Wind Magnetosphere Couptiny, Y. KAMIDEand J. SLAVIN (eds), pp. 39.-57. Terra Scientific, Tokyo and D. Reidel, Dordrecht. DPI and DP2 current systems for the March 22, 1979 rubstorms. J. qeophy. Res. 90, I343 1354. Mapping the local time universal time development of magnctospheric substorms using mid-latitude magnetic observations. J. geophys. Re.r. 79, 281 1 2820. Solar wind controi of aurora1 tone ge~lnagnclic activity. Geoph.v.s. Rm. Lett. 8, 915 918. Polarization of the aurora1 electrojet. J. ,qet@x Res. 77,2835-~2850. Studies of the magnetospheric substorm: 3. Concept of the magnetospheric substorm and its relation to electron precipitation and micropulsations. 1. yr@~~‘.c.Rcs. 73, 171S- 1722. The causes of convection in the earth’s magnetosphere : a review of developments during the IMS. Rev. tiwph,v.s. Spaw Phys. 24 53 I 565. Substorms and the growth phase problem. Nafure 295, 365 -366. On the high correlation between long-term averages of solar wind speed and geomagnetic activity. ,7 yrop&.s. Res. 82, 193% 1937. Aurora1 electrojet activity index AE and its universal lime variations. J. geqreophys.Res. 71,785-801. Soi;lrtcrrestriai physics. E@S Tmm. AGU 54, 925 _

DESSLEK A. J. and PARKERE. N.

1959

Hydrornagnetic

1972

CORONZTI

1968

COWL.EY S. W. H.

1982a

COWLEY

1982b

F. V., MCPHERROKR. L. and PARKSG. K.

s.\lir. w.

<‘KCGKER N.

U., FEYNMAN 1. and GOSLINGJ. T.

1977

927. theory of

magnetic storms. J. .#@[email protected].

Rex. 64,2239-2259. DUNGEY

J. W.

1961

Interplanetary

magnetic field and the aurora1 zones.

Phys. Res. Lett. 6, 47-48.

FAIRFIELD D. H. and CAHILLL. J. JR

1966

FOSTERJ. C., FAIRFIELDD. H., OGILVIEK. W. and ROSENBERG T. J.

197I

FOSTERJ. C., HOLTJ. M., MUSG~VE R. G. and EVANSD. S.

1986

FRANKL. A. and

1988

CRAVEN

J. D.

Transition region magnetic field and polar magnetic disturbances. J. geophy. Res. 71, 155. 169. Relationship of interplanetary parameters and OCCUFrmcc? of magnetospheric substorms. J. geophys. Rex 76.6971-6975. Ionospheric convention associated with discreti levels of particle precipitation. Geuph~s. Rm. Left. t&656hS9. tmagmg results from dynamics expiorer 1. Rcr. i&wphw. 26, 249. 283

Intensity of magnetospheric substorms FRIIS-CHRISTENSEN E., KAMIDEY., RICHMONDA. and MATSUSHITAS.

D.

1985

FUKUSHIMAN.

1969

GARRETTH. B.

1974

GLEICKJ.

1988

GOERTZC. K., SHAN L. H. and SMITHR. A.

1993

GRA~~BERGER P. and PROCACCIAI.

1983

HAKAMADAK., AOKI T. and MURAYAMA T.

1980

HARDY D. A., GU~SENHOVEN M. S. and RAISTRICKR.

1987

HEACOCKR. R.

1967

HIRSHBERG J. and COLBURND. S.

1969

HOLZER R. E. and SLAVINJ. A.

1978

HOLZER R. E. and SLAVINJ. A.

1982

HONEYE. W. JR

1979

HONESE. W. JR

1985

HONEYE. W. JR, ANGERC. D., BIRNJ., MURPHREEJ. S. and C~CGERL. L.

1987

HUGHEST. J. and ROST~KERG.

1977

IUIMAT. and NAGATAT.

1972

JELLEYD. and BRICEN.

1967

KAMIDEY. and BAUMJOHANN W.

1985

KAMIDEY., RICHMOND A. D. and MATXJSHITA S.

1981

KAN J. R. and AKASOFUS.-I.

1982

KAWASAKIK. and ROSTOKER G.

1979

KISABETH J. L. and ROSTOKER G.

1971

KISABETH J. L. and ROSTOKER G.

1973

1119

Interplanetary magnetic field control of high-latitude electric fields and currents determined from greenland magnetometer data. J. geophys. Rex 90, 13251338. Equivalence in ground geomagnetic effect of Chapman-Vestine’s and Birkeland-Alfven’s electric current system for polar magnetic substorms. Rept Ionos. Space Res. Japan 23,21%227.

The role of fluctuations in the interplanetary magnetic field in determining the magnitude of substorm activity. Planet. Space Sci. 22, 11l-l 19. Chaos, Making a New Science, 352 pp. Penguin Books, New York. Prediction of geomagnetic activity. J. geophys. Res. 98 (in press). Estimation of the Kolmogorov entropy from a chaotic signal. Phys. Rev. A 28,259l. Influence of the east-west component of the interplanetary magnetic field on the intensity of the auroral electrojet. Planet. Space Sci. 28,29-39. Statistical and functional representations of the pattern of aurora1 energy flux, number flux, and conductivity. J. geophys. Res. 92, 12,275-12,294. Two types of Pi micropulsations. J. geophys. Res. 72, 3905-3917. Interplanetary field and geomagnetic variations-a unified view. Planet. Space Sci. 17, 1183-1206. Magnetic flux transfer associated with expansions and contractions of the dayside magnetosphere. J. geophys. Res. 83,3831-3839.

An evaluation of three predictors of geomagnetic activity. J. geophys. Res. 87,2558-2562. Transient phenomena in the magnetotail and their relation to substorms. Space Sci. Rev. 23,393. The poleward leap of the aurora1 electrojet as seen in aurora1 images. J. geophys. Res. 90,5333-5337. A study of a magnetospheric substorm recorded by the Viking aurora1 imager. Geoph.ys. Res. Left. 14,41 l414. Current flow in the magnetosphere and ionosphere during periods of moderate activity. J. geophys. Res. 82, 2271-2282. Signatures for substorm development of the growth phase and expansion area. Planet. Space Sci. 20, 1095-l 112.

Association between increased radiation in the outer belt and polar aurora1 substorms (abstract). Trans. Am. Geophys. Union 48, 180. Estimation of electric fields and currents from International Magnetospheric Study magnetometer data for the CDAW-6 intervals: implications for substorm dynamics. J. geophys. Rex 90, 1305-1317. Estimation of ionospheric electric fields, ionospheric currents, and field-aligned currents from ground magnetic records. J. geophys. Res. 86,801-813. Dynamo process governing solar wind-magnetosphere energy coupling. Planet. Space Sci. 30,367-370. Perturbation magnetic fields and current systems associated with eastward drifing aurora1 structures. J. geophvs. Res. 84, 1464-1480. Development of the polar electrojet during polar magnetic substorms. J. geophys. Rex 76, 68156828.

Current flow in aurora1 loops and surges inferred from ground-based magnetic observations. J. geophys. Res. 78,5573-5584.

Kl..IMASA. I. BAIC~RI). N. and RI)HI:K.L.S D A.

1991

I971

K~K~~uN S. and MCPHERRON R. L.

19x1

KIJWASHIMAM.

1978

LINCOLN J. V.

1967

Lur A. T. Y., MALONEY PAPAVO~OLOUS K. and

A., CWANC C.-L., WV C. S.

MAEZAWA K. and MURAYAMA T.

1990

1986

I inear prediction filters for linear and nonhnc,r! modeled geomagnetic activity. Gwphys. Res. L,eil IX, 1573 1574. Relationship of interplanctar> mapnctic field structure with development 01’ substomm and storm main phase. Pll/?-X,l..s@J0~.sci. 20, 1033 1049. Suhstorm signatures at synchronous altitude. ./. ~~C~O/‘/7~S. Rcs. 86, I I.265 I 1,177. Wn\;e characteristics of magnetic PI 2 pulsations in the aurora1 region spectral and polarization studies. .blcnr. h’uln. li,sr. P&r Res. A/15), 1 79. Geomagnetic indices. In Pi7.rsrc.* of’ ~~~~)~zu~~~~j~ ~~7~~~~~~?~,~~/. Vol. i, S. MA~SIXHITA and W. Ii. C,\MPRIXI.(eds). pp. 67 100. Academic Press, New Yllrk. A current disruption mechanism in the neutral sheet : a possible trigger for substorm expansions. Gmphvs. R
In Solar Wind Maynetosphrre C’orqdin,q,Y. KAMIUE and J. SLAVIN (eds), pp. 59- 83.

MAYAUD P. N

1980

MCPHEKKON R. L.

1970

MCPHERRON R. L.

1972

M(~P~RRoN

1991

R. L.

MCPHERRON R. L., BAKER D. N., BARGATZE L. F., CLAUER C. R. and HOLZER R. E. MCPHERRONR. L. and MANKA R. H.

1988

MCPHERHON R. L., PARKS G. K. CORONITI F. V.

1967

and

1985

MCPHEHRON R. L., Ru~~ELI~C. T. and AUBRY M.

1973

M~~RR(~N

1986

R. L., TERASAWA T. and NISHIDA A.

MENC;C.-I. and TSURUTANIB.

1973

MENVIELLEM. and BERTHELIERA.

1991

MISHINV. M.

1991

SI~COEG. L., HEELISR. A. WINNINGHAM J. D. MURAvAMA T.

Moses J. J.,

and

1989 1982

Terra Scientific, Tokyo and D. Reidel, Dordrecht. Derivation. Meaning and Use of Geomagnetic Indices, 154pp.. Geophysical Monograph 22. American Geophysical Union, Washington. D.C. Growth phase of magnetospheric substorms. J. ~<‘opl~t~Res. 75, 5592-5599. Substorm related changes in the geomagnetic tail: the growth phase. ~~~~~~,i. .$ar;r~ St?. M, 1521 I539. Physical processes producing nlagnetospheri~ substorms and magnetic storms. ~e#~g~ez~~, Vol. 4, .l. JA~OHS (ed.). pp. 593 739. Academic Press, London. IMF control of geomagnetic activity. A&. Space Rr~.s. 8(9 IO), 71 86. Dynamics of the 1054 UT, March 22, 1979 substorm event : CDAW-6 J. geophys. Res. 90, Ill5 1190. Relation of correlated magnetic micropulsations and electron precipitation to the aurora1 substorm. ESSA Tech. Mem. IERTM-ITSA, 72, pp. in III-4.14-l 5 pp. Satellite studies of magnetospheric substorms on August I&1978.9. Phenomenologi~l model for substorms. J. grophys. Res. 78, 3131-3149. Solar wind triggering of substorm expansion onset. f. ~/~~J~~~~.Groelerl. 38, I Of% I 108. Cross-correlation analysis of the AE index and the interplanetary magnetic field B: component. .I. ~/zc~$ls. Res. 78, 6 IT--629. The K-derived planetary indices : description and availability. Rec. Geophys. 29, 415-432. The magnetogram inversion technique : applications to the problem ofrnagnetospheric substorms. .Space Sci. Rev. 57, 237 337. Polar cap deflation during magnetospheric substorms. J. ,~~oph,~~.Res. 94, 3785-3789. Coupling function between solar wind parameters and geomagnetic indices. Rez). Genphys Space Phy%s.20, 623 629.

MI~UAYAMAT

1986

Coupling function between the solar wind and the CIsr in&& In Sofar Wind ~~~ef~.~p~efg Coupling, Y. KAMIUE and J. SLAVINfeds), pp. Il9--126. Terra

MURAYAMA T., AOKI T.. NAICAIH. and HAKAMADA N

1980

Scientific, Tokyo and D. l&del,‘i‘)ordrecht. Empirical formula to relate the aurora1 electrojet intensity with interplanetary parameters. Plun~f. @a(,~ .Qi. 28. x03 8 13.

Intensity of magnetospheric substorms

1121

NISHIDA A.

1978

Geomagnetic Diagnosis of the Magnetosphere, 256 pp.

OPGENOORTH H. J., OK~MANJ., KAILA K. U., NIELSEN E. and BAUMJOHANN W.

1983

Springer, New York. Characteristics of eastward drifting omega bands in the morning sector of the aurora1 oval. J. geophys. Res.

PERREAULT P. and AKA~~EUS.-I.

1978

A study of geomagnetic storms. Geophys. JI R. astr.

Pvrr~ T., MCFQERRON WENTH. I. JR

1978

Multiple-satellite studies of magnetospheric substorms. III. Distinction between polar substorms and convection-driven negative bays. J. geophys. Res. 83, 663679. Indicators of low-dimensionality in magnetospheric dynamics. Geophys. Res. Lett. 18, 151-154. Macrostructure of geomagnetic bays. J. geophys. Res. 73,42174229. Geomagnetic indices. Rev. Geophys. Space Phys. 10, 9355950. The roles of direct input of energy from the solar wind and unloading of stored magnetotail energy in driving magnetospheric substorms. Space Sci. Rev. 46, 93-111. Magnetospheric substormsdefinition and signatures. J. geophys. Res. 85, 1663-1668.

B&9171-9185. sot. 54,547-573.

R. L., HONEYE. W. JR and

ROBERTS D. A., BAKERD. N. and KLIMASA.

1991

ROSTOKER G.

1968

ROSTOKER G.

1972

R~~TOKERG., AKA~~FUS.-I., BAUMJOHANN W., KAMIDEY. and MCPHERRONR. L.

1987

ROSTOKER G., AKA~~FUS.-I., FOSTERJ., GREENWALD R. A., KAMIDEY., KAWASAKIK., LUI A. T. Y., MCPHERRONR. L. and RUSSELLC. T. RCJ~T~KER G., HING-LANLAMand HUMEW. D.

1980

1972

ROSTOKER G. and HUGHEST. J.

1979

RUSSELLC. T.

1974

SIBECKD. G., LOPEZR. E. and ROELOFE. C.

1991

SISCOEG.

1980

SISCOEG. L. and HUANGT. S.

1984

SPIROR. W., REIFFP. H. and MAHERL. J. JR

1982

TAKENSF.

1981

TROSHICHEV 0. A., ANDREZEN V. G., VENNERSTROM S. and FRISS-CHRISTENSEN E.

1988

TSURUTANI B. T., SLAVINJ. A., KAMIDEY., ZWICKLR. D., KING J. H. and RUSSELLC. T. TSURUTANI B. T., SUGIURAM., IYEMORI T., GOLDSTEIN B. E., GONZALEZW. D., AKA~C~FU S.-I. and SMITHE. J. VASYLIUNA~ V. M., KAN J. R., SI~COEG. L. and AKA~OFLI S.-I. VASYLIUNA~ V. M. and WOLFR. A.

1985

Response time of the magnetosphere to the interplanetary electric field. Can. J. Geophys. SO, 544547. A comprehensive model current system for high-latitude magnetic activity-II. The substorm component. Geophys. JI R. astr. Sot. 58,571-581. The solar wind and magnetospheric dynamics. In The Magnetospheres of the Earth and Jupiter, V. FORMINSANO (ed.), pp. 347. D. Reidel, Dordrecht. Solar wind control of the magnetopause shape, location and motion. J. geophys. Res. 96,548s5495. What’s in the name ‘Magnetospheric Substorm’? J. geophys. Res. 85, 1643. Polar cap inflation and deflation. J. geophys. Res. 90, 543-547. Precipitating electron energy flux and aurora1 zone conductances-an empirical model. J. geophys. Res. 87, 8215-8227. Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence, Warwick 1980, A. DOLD and B. ECKMANN (eds), pp. 366-38 1. Springer, Berlin. Relationship between the polar cap activity index PC and the aurora1 zone indices AU, AL, AE. Planet Space Sci. 36, 1095.

1990

Coupling between the solar wind and the magnetosphere : CDAW-6. J. geophys. Res. (submitted). The nonlinear response of AE to the IMF Bs driver : a spectral break at 5 hours. Geophys. Res. Left. 17, 279-282.

1982 1973

VOOTSG. R., GURNETTD. A. and AKASOFUS.-I.

1977

WEIMERD. R.

1992

WEINERN.

1942

Scaling relations governing magnetospheric energy transfer. Planet. Space Sci. 30,359365. Magnetospheric substorms : some problems and controversies. Rev. Geophys. Space Phys. 11,181-189. Aurora1 kilometric radiation as an indicator of aurora1 magnetic disturbances. J. geophys. Res. 82, 22599 2266. Characteristic time scale of substorm expansion and recovery, Proceedings of the International Conference on Substorms (KS-I), pp. 581-586, ESA SP-335, Paris. CEDEX 15, France. Extrapolation, Interpolation, and Smoothing of Stationary Time Series with Engineering Applicaiions. MIT.

Press, Cambridge, Massachussetts.

I I??

lz, I..

M(.PtII.iwoN ;lnd 1) N. thK1.K