Estimated energy balance in the jovian upper atmosphere during an auroral heating event

We present an analysis of a series of observations of the auroral/polar regions of Jupiter, carried out between September 8 and 11, 1998, making use of the high-resolution spectrometer, CSHELL, on the NASA InfraRed Telescope Facility (IRTF), Mauna Kea, Hawaii; these observations spanned an “auroral heating event.” This analysis combines the measured line intensities and ion velocities with a one-dimensional model vertical profile of the jovian thermosphere/ionosphere. We compute the model line intensities both assuming local thermodynamic equilibrium (LTE) and, relaxing this condition (non-LTE), through detailed balance calculations, in order to compare with the observations. Taking the model parameters derived, we calculate the changes in heating rate required to account for the modelled temperature profiles that are consistent with the measured line intensities. We compute the electron precipitation rates required to give the modelled ion densities that are consistent with the measured line intensities, and derive the corresponding Pedersen conductivities. We compute the changes in heating due to Joule heating and ion drag derived from the measured ion velocities, and modelled conductivities, making use of ion-neutral coupling coefficients derived from a 3-D global circulation model. Finally, we compute the cooling due to the downward conduction of heat and the radiation-to-space from the molecular ion and hydrocarbons. Comparison of the various heating and cooling terms enables us to investigate the balance of energy inputs into the auroral/polar atmosphere. Increases in Joule heating and ion drag are sufficient to explain the observed heating of the atmosphere; increased particle precipitation makes only a minor heating contribution. But local cooling effects—predominantly radiation-to-space—are shown to be too inefficient to allow the atmosphere to relax back to pre-event thermal conditions. Thus we conclude that this event provides observational, i.e. empirical, evidence that heat must be transported away from the auroral/polar regions by thermally or mechanically driven winds.     

The high latitude circulation and temperature structure of the thermosphere near solstice

The neutral gas temperature and circulation of the thermosphere are calculated for December solstice conditions near solar cycle maximum using NCAR's thermospheric general circulation model (TGCM). High-latitude heat and momentum sources significantly alter the basic solar-driven circulation during solstice. At F-region heights, the increased ion density in the summer hemisphere results in a larger ion drag momentum source for the neutral gas than in the winter hemisphere. As a result there are larger wind velocities and a greater tendency for the neutral gas to follow the magnetospheric convection pattern in the summer hemisphere than in the winter hemisphere. There is about three times more Joule heating in the summer than the winter hemisphere for moderate levels of geomagnetic activity due to the greater electrical conductivity in the summer E-region ionosphere.

The results of several TGCM runs are used to show that at F-region heights it is possible to linearly combine the solar-driven and high-latitude driven solutions to obtain the total temperature structure and circulation to within 10–20%. In the lower thermosphere, however, non-linear terms cause significant departures and a linear superposition of fields is not valid.

The F-region winds at high latitudes calculated by the TGCM are also compared to the meridional wind derived from measurements by the Fabry-Perot Interferometer (FPI) and the zonal wind derived from measurements by the Wind and Temperature Spectrometer (WATS) instruments onboard the Dynamics Explorer (DE−2) satellite for a summer and a winter day. For both examples, the observed and modeled wind patterns are in qualitative agreement, indicating a dominant control of high latitude winds by ion drag. The magnitude of the calculated winds (400–500 m s⁻¹) for the assumed 60 kV cross-tail potential, however, is smaller than that of the measured winds (500–800 m s⁻¹). This suggests the need for an increased ion drag momentum source in the model calculations due to enhanced electron densities, higher ion drift velocities, or some combination that needs to be further denned from the DE−2 satellite measurements.     

The generation of vertical thermospheric winds and gravity waves at auroral latitudes—I. Observations of vertical winds

Observations of vertical and horizontal thermospheric winds, using the OI (3P-1D) 630 nm emission line, by ground-based Fabry-Perot interferometers in Northern Scandinavia and in Svalbard (Spitzbergen) have identified sources of strong vertical winds in the high latitude thermosphere. Observations from Svalbard (78.2N 15.6E) indicate a systematic diurnal pattern of strong downward winds in the period 06.00 U.T. to about 18.00 U.T., with strong upward winds between 20.00 U.T. and 05.00 U.T. Typical velocities of 30 m s^?1 downward and 50 m s^?1 upward occur, and there is day to day variability in the magnitude (30–80 m s^?1) and phase (+/- 3 h) in the basically diurnal variation. Strong and persistent downward winds may also occur for periods of several hours in the afternoon and evening parts of the auroral oval, associated with the eastward auroral electrojet (northward electric fields and westward ion drifts and winds), during periods of strong geomagnetic disturbances. Average downward values of 30–50 m s^?1 have been observed for periods of 4–6 h at times of large and long-lasting positive bay disturbances in this region. It would appear that the strong vertical winds of the polar cap and disturbed dusk auroral oval are not in the main associated with propagating wave-like features of the wind field. A further identified source is strongly time-dependent and generates very rapid upward vertical motions for periods of 15–30 min as a result of intense local heating in the magnetic midnight region of the auroral oval during the expansion phase of geomagnetic disturbances, and accompanying intense magnetic and auroral disturbances. In the last events, the height-integrated vertical wind (associated with a mean altitude of about 240 km) may exceed 100–150 m s^?1. These disturbances also invariably cause major time-dependent changes of the horizontal wind field with, for example, horizontal wind changes exceeding 500 m s^?1 within 30 min. The changes of vertical winds and the horizontal wind field are highly correlated, and respond directly to the local geomagnetic energy input. In contrast to the behaviour observed in the polar cap or in the disturbed afternoon auroral oval, the ‘expansion phase’ source, which corresponds to the classical ‘auroral substorm’, generates strong time-dependent wind features which may propagate globally. This source thus directly generates one class of thermospheric gravity waves. In this first paper we will consider the experimental evidence for vertical winds. In a second paper we will use a three-dimensional time-dependent model to identify the respective roles of geomagnetic energy and momentum in the creation of both classes of vertical wind sources, and consider their propagation and effects on global thermospheric dynamics.     

The calculated and observed diurnal variation of the ionosphere over Millstone Hill on 23–24 March 1970

A numerical model of current F-region theory is use to calculate the diurnal variation of the mid-latitude ionospheric F-region over Millstone Hill on 23–24 March 1970, during quiet geomagnetic conditions. From the solar EUV flux, the model calculates at each altitude and time step primary photoelectron spectra and ionization rates of various ion species. The photoelectron transport equation is solved for the secondary ionization rates, photoelectron spectra, and various airglow excitation rates. Five ion continuity equations that include the effects of transport by diffusion, magnetospheric-ionospheric plasma transport, electric fields, and neutral winds are solved for the ion composition and electron density. The electron and ion temperatures are also calculated using the heating rates determined from chemical reactions, photoelectron collisions, and magnetospheric-ionospheric energy transport. The calculations are performed for a diurnal cycle considering a stationary field tube co-rotating with the Earth; only the vertical plasma drift caused by electric fields perpendicular to the geomagnetic field line is allowed but not the horizontal drift. The boundary conditions used in the model are determined from the incoherent scatter radar measurements of T_e, T_i and O⁺ flux at 800km over Millstone Hill (Evans, 1971a). The component of the neutral thermospheric winds along the geomagnetic field has an important influence on the overall ionospheric structure. It is determined from a separate dynamic model of the neutral thermosphere, using incoherent scatter radar measurements.The calculated diurnal variation of the ionospheric structure agrees well with the values measured by the incoherent scatter radar when certain restrictions are placed on the solar EUV flux and model neutral atmospheric compositions. Namely, the solar EUV fluxes of Hinteregger (1970) are doubled and an atomic oxygen concentration of at least $\text{10}{}^{11}\text{cm}{}^3$ at 120 km is required for the neutral model atmosphere. Calculations also show that the topside thermal structure of the ionosphere is primarily maintained by a flow of heat from the magnetosphere and the night-time F2-region is maintained in part by neutral winds, diffusion, electric fields, and plasma flow from the magnetosphere. The problem of maintaining the calculated night-time ionosphere at the observed values is also discussed.     

A theoretical and empirical study of the response of the high latitude thermosphere to the sense of the “Y” component of the interplanetary magnetic field

The strength and direction of the Interplanetary Magnetic Field (IMF) controls the transfer of solar wind momentum and energy to the high latitude thermosphere in a direct fashion. The sense of “ Y” component of the IMF (BY) creates a significant asymmetry of the magnetospheric convection pattern as mapped onto the high latitude thermosphere and ionosphere. The resulting response of the polar thermospheric winds during periods when BY is either positive or negative is quite distinct, with pronounced changes in the relative strength of thermospheric winds in the dusk-dawn parts of the polar cap and in the dawn part of the auroral oval. In a study of four periods when there was a clear signature of BY, observed by the ISEE-3 satellite, with observations of polar winds and electric fields from the Dynamics Explorer-2 satellite and with wind observations by a ground-based Fabry-Perot interferometer located in Kiruna, Northern Sweden, it is possible to explain features of the high latitude thermospheric circulation using three dimensional global models including BY dependent, asymmetric, polar convection fields. Ground-based Fabry-Perot interferometers often observe anomalously low zonal wind velocities in the (Northern) dawn auroral oval during periods of extremely high geomagnetic activity when BY is positive. Conversely, for BY negative, there is an early transition from westward to southward and eastward winds in the evening auroral oval (excluding the effects of auroral substorms), and extremely large eastward (sunward) winds may be driven in the auroral oval after magnetic midnight. These observations are matched by the observation of strong anti-sunward polar-cap wind jets from the DE-2 satellite, on the dusk side with BY negative, and on the dawn side with BY positive.     

Time-dependent behaviour of a stable auroral red arc excited by an electric field

We examine the electric field hypothesis as a possible explanation of a stable auroral red arc. An electric field perpendicular to the geomagnetic field in the ionosphere heats the ambient F-region electrons and ions. Given large enough electric fields, the electrons can be heated sufficiently to excite the OI (¹D) term of atomic oxygen by electron impact, giving rise to the λ6300 emission characteristic of the red arc. The electron and ion heating rates are determined by the relative drift between the plasma and neutral gas.     

The consequences of high latitude particle precipitation on global thermospheric dynamics

A previous comparison of experimental measurements of thermospheric winds with simulations using a global self-consistent three-dimensional time-dependent model confirmed a necessity for a high latitude source of energy and momentum acting in addition to solar u.v. and e.u.v. heating. During quiet geomagnetic conditions, the convective electric field over the polar cap and auroral oval seemed able to provide adequate momentum input to explain the thermospheric wind distribution observed in these locations. However, it seems unable to provide adequate heating, by the Joule mechanism, to complete the energy budget of the thermosphere and, more importantly, unable to provide the high latitude input required to explain mean meridional winds at mid-latitudes. In this paper we examine the effects of low energy particle precipitation on thermospheric dynamics and energy budget. Modest fluxes over the polar cap and auroral oval, of the order of 0.4 erg cm ⁻²/s, are consistent with satellite observations of the particles themselves and with photometer observations of the OI and OII airglow emissions. Such particle fluxes, originating in the dayside magnetosheath cusp region and in the nightside central plasma sheet, heat the thermosphere and modify mean meridional winds at mid-latitudes without enhancing the OI 557.7 line, or the ionization of the lower thermosphere (and thus enhancing the auroral electrojets), neither of which would be consistent with observations during quiet geomagnetic conditions.     

Effects of interplanetary magnetic field and magnetospheric substorm variations on the dayside aurora

Photometric observations of dayside auroras are compared with simultaneous measurements of geomagnetic disturbances from meridian chains of stations on the dayside and on the nightside to document the dynamics of dayside auroras in relation to local and global disturbances. These observations are related to measurements of the interplanetary magnetic field (IMF) from the satellites ISEE-1 and 3. It is shown that the dayside auroral zone shifts equatorward and poleward with the growth and decay of the circum-oval/polar cap geomagnetic disturbance and with negative and positive changes in the north-south component of the interplanetary magnetic field (B_z). The geomagnetic disturbance associated with the auroral shift is identified as the DP2 mode. In the post-noon sector the horizontal disturbance vector of the geomagnetic field changes from southward to northward with decreasing latitude, thereby changing sign near the center of the oval precipitation region. Discrete auroral forms are observed close to or equatorward of the ΔH = 0 line which separates positive and negative H-component deflections. This reversal moves in latitude with the aurora and it probably reflects a transition of the electric field direction at the polar cap boundary. Thus, the discrete auroral forms observed on the dayside are in the region of sunward-convecting field lines. A model is proposed to explain the equatorward and poleward movement of the dayside oval in terms of a dayside current system which is intensified by a southward movement of the IMF vector. According to this model, the Pedersen component of the ionospheric current is connected with the magnetopause boundary layer via field-aligned current (FAC) sheets. Enhanced current intensity, corresponding to southward auroral shift, is consistent with increased energy extraction from the solar wind. In this way the observed association of DP2 current system variations and auroral oval expansion/contraction is explained as an effect of a global, ‘direct’ response of the electromagnetic state of the magnetosphere due to the influence of the solar wind magnetic field. Estimates of electric field, current, and the rate of Joule heat dissipation in the polar cap ionosphere are obtained from the model.     

On the dynamics of the jovian ionosphere and thermosphere.: IV. Ion-neutral coupling

We use the fully coupled, three-dimensional, global circulation Jovian Ionospheric Model (JIM) to calculate the coupling between ions in the jovian auroral ovals and the co-existing neutral atmosphere. The model shows that ions subject to drift motion around the auroral oval, as a result of the E×B coupling between a meridional, equatorward electric field and the jovian magnetic field, generate neutral winds in the planetary frame of reference. Unconstrained by the magnetic field, these neutral winds have a greater latitudinal extent than the corresponding ion drifts. Values of the coupling coefficient, k(h), are presented as a function of altitude and cross-auroral electric field strength, for different incoming electron fluxes and energies. The results show that, with ion velocities of several hundred metres per second to over 1 km s⁻¹, k(h) can attain values greater than 0.5 at the ion production peak. This parameter is key to calculating the effective conductivities required to model magnetosphere-ionosphere coupling correctly. The extent to which angular momentum (and therefore energy) is transported vertically in JIM is much more limited than earlier, one-dimensional, studies have predicted.     

The influence of neutral winds on He+ distributions in the equatorial ionosphere

The effects of F-region neutral winds on the distribution of He⁺ in the equatorial ionosphere have been examined using a theoretical model and an observational data set. It is shown by the model that components of neutral wind in the magnetic meridian up to only 50 m s^? can produce He⁺ gradients in the northern and southern sectors of a flux tube that differ by more than 80%. This is associated with interhemisphere transport velocities of He⁺ as large as 15 m s^?1 at 800 km. A substantial latitude gradient in the He⁺ distribution across the dip equator also results from the redistribution of He⁺ The changes in the He⁺ concentration at the dip equator and the latitude distribution of He⁺ in response to different neutral wind components is determined from the model and used to construct longitude distributions of He⁺ to compare with observations made at equinox. Good agreement between the calculations and observations is obtained both at the geographic and geomagnetic equators using the relationship between neutral winds, interhemispheric transport velocity and He⁺ concentration derived from the model. If these relationships can be extrapolated to accommodate the different conditions expected during solstice, we can also discuss the He⁺ distributions expected during this season.     

Auroral heating and the composition of the neutral atmosphere

Heating of the neutral atmosphere by auroral particle fluxes and by orthogonal electric fields is responsible for large changes in the thermospheric composition that have been observed by satellite mass spectrometers. Vertical winds of a few meters per second are produced in the region subject to auroral heating; this vertical upwelling drives circulation cells that extend the effects of heating in the auroral region on a global scale. Our analysis focuses on the initial phase of a magnetic storm within the auroral region.     

Measurements of high latitude thermospheric winds by rocket and ground-based techniques and their interpretation using a three-dimensional,time-dependent dynamical model

A three-dimensional, time-dependent model of thermospheric dynamics has been used to interpret recent experimental measurements of high altitude winds by rocket-borne and ground-based techniques. The model is global and includes a self-consistent treatment of the non-linear, Coriolis and viscosity terms. The solar u.v. and e.u.v. energy input provides the major energy source for the thermosphere. Solar u.v. and e.u.v. heating appear to be inadequate to explain observed thermospheric temperatures if e.u.v. heating efficiency (ε) lies in the range 0.3 < ε < 0.35. If the recent solar e.u.v. data are correct, then a value of ε between 0.4 and 0.45 would bring fluxes and observed temperatures into agreement. The Heppner (1977) and Volland (1978) models of high-latitude electric field are used to provide sources of both momentum (via ion drag) and energy (via Joule heating). We find that the Heppner Model CO (equivalent to Volland Model 1) is most appropriate for very quiet geomagnetic conditions (K_p ? 2) while Model A (equivalent to Volland Model 2) provides the necessary enhancement at high latitudes for conditions of moderate activity (K_p ～ 4). Even with the addition of a polar electric field, there still appears to be a shortage of high-latitude energy input in that model winds tend to be 10 m s^?1 poleward of observed winds under quiet or average geomagnetic conditions. This extra energy cannot be provided by enhancing the polar electric fields since the extra momentum would cause disagreement with the observed high latitude winds. High latitude particulate sources of relatively low energies, ~100 eV, seem the most likely candidates depositing their energy above about 200km. Relatively modest amounts of energy are then required, < 10¹⁰W global, to bring the model into agreement with both high- and mid-latitude neutral wind results.     

The composition,structure, temperature and dynamics of the upper thermosphere in the polar regions during October to December 1981

During the period October to December 1981, the Dynamics Explorer-2 (DE-2) spacecraft successively observed the South polar and the North polar regions, and recorded the temperature, composition and dynamical structure of the upper thermosphere. In October 1981, perigee was about 310 km altitude, in the vicinity of the South Pole, with the satellite orbit in the 09.00–21.00 L.T. plane. During late November and December, the perigee had precessed to the region of the North Pole, with the spacecraft sampling the upper thermosphere in the 06.00 18.00 L.T. plane. DE-2 observed the meridional wind with a Fabry-Perot interferometer (FPI), the zonal wind with the wind and temperature spectrometer (WATS), the neutral temperature with the FPI, and the neutral atmosphere composition and density with the neutral atmosphere composition spectrometer (NACS). A comparison between the South (summer) Pole and the North (winter) Pole data shows considerable seasonal differences in all neutral atmosphere parameters. The region of the summer pole, under similar geomagnetic and solar activity conditions, and at a level of about 300 km, is about 300 K warmer than that of the winter pole, and the density of atomic oxygen is strongly depleted (and nitrogen enhanced) around the summer pole (compared with the winter pole). Only part of the differences in temperature and composition structure can be related to the seasonal variation of solar insolation, however, and both polar regions display structural variations (with latitude and Universal Time) which are unmistakeable characteristics of strong magnetospheric forcing. The magnitude of the neutral atmosphere perturbations in winds, temperature, density and composition within both summer and winter polar regions all increase with increasing levels of geomagnetic activity.The UCL 3-dimensional time dependent global model has been used to simulate the diurnal, seasonal and geomagnetic response of the neutral thermosphere, attempting to follow the major features of the solar and geomagnetic inputs to the thermosphere which were present during the late 1981 period.In the UCL model, geomagnetic forcing is characterized by semi-empirical models of the polar electric field which show a dependence on the Y component of the Interplanetary Magnetic Field, due to Heppner and Maynard (1983), It is possible to obtain an overall agreement, in both summer and winter hemispheres, with the thermospheric wind structure at high latitudes, and to explain the geomagnetic control of the combined thermal and compositional structure both qualitatively and quantitatively. To obtain such agreement, however, it is essential to enhance the polar ionosphere as a consequence of magnetospheric particle precipitation, reflecting both widespread auroral (kilovolt) electrons, and “soft” cusp and polar cap sources. Geomagnetic forcing of the high latitude thermosphere cannot be explained purely by a polar convective electric field, and the thermal as well as ionising properties of these polar and auroral electron sources are crucial components of the total geomagnetic input.     

Ionospheric warming by neutral winds

The effect of frictional heating by means of neutral winds on the ion and electron temperature in the undisturbed ionosphere is studied theoretically by solving a system of basic ionospheric and atmospheric equations. The study shows that both the electron and ion temperatures are increased in the night-time ionosphere through friction. In the region between 150 and 200 km T_i may exceed T₆ by as much as 130°. The increase of T_i due to friction amounts to about 100–200°, depending on the atmospheric model employed in calculating the neutral wind velocity. It is illustrated that frictional heating may be very important for the determination of the neutral temperature from measured ion temperature values.     

Atmospheric scattering effects on ground-based measurements of thermospheric winds

Inherent in observations of thermospheric winds from the ground with the Fabry-Perot interferometer is the assumption that the measured Doppler shift is a property of the source medium viewed by the instrumental line of sight. However, ground based airglow observations in regions of weak airglow emission near large intensity gradients may be contaminated by scattered light. Light from areas where the emission is strong can be scattered by the lower atmosphere into the field of view of the observations. Thermospheric winds deduced from the observed Doppler shifts will then show apparent convergence or divergence with respect to the site of observation. Examples of this effect are found in observations by the Michigan Airglow Observatory station located near the auroral zone at Calgary, Alberta. Simulation calculations based upon an experimental model for a significant scattering atmosphere also showed results with either convergence or divergence in the apparent neutral wind field observed by the station.     

The westward thermospheric jet-stream of the evening auroral oval

One of the most consistent and often dramatic interactions between the high latitude ionosphere and the thermosphere occurs in the vicinity of the auroral oval in the afternoon and evening period. Ionospheric ions, convected sunward by the influence of the magnetospheric electric field, create a sunward jet-stream in the thermosphere, where wind speeds of up to 1 km s^?1 can occur. This jet-stream is nearly always present in the middle and upper thermosphere (above 200 km altitude), even during periods of very low geomagnetic activity. However, the magnitude of the winds in the jet-stream, as well as its location and range in latitude, each depend on geomagnetic activity. On two occasions, jet-streams of extreme magnitude have been studied using simultaneous ground-based and satellite observations, probing both the latitudinal structure and the local time dependence. The observations have then been evaluated with the aid of simulations using a global, three-dimensional, time-dependent model of thermospheric dynamics including the effects of magnetospheric convection and particle precipitation. The extreme events, where sunward winds of above 800 ms^?1 are generated at relatively low geomagnetic latitudes (60–70°) require a greatly expanded auroral oval and large cross-polar cap electric field ( ~ 150 kV). These in turn are generated by a persistent strong Interplanetary Magnetic Field, with a large southward component. Global indices such as K_p are a relatively poor indicator of the magnitude and extent of the jet-stream winds.     

Atmospheric expansion through Joule heating by horizontal electric fields

Incoherent scatter measurements made along a magnetic field line into aurora during a period of high electric field in the recovery phase of a substorm show (1) considerably increased electron densities well above the normal F-region maximum, and (2) field-aligned plasma drifts that increase with altitude. A model invoking atmospheric expansion through Joule heating by the horizontal electric field driving the auroral electrojet is used to explain the observations. From this study it is concluded that during magnetically disturbed periods (1) Joule heating by the auroral electrojet raises the neutral temperature and density in the auroral zone ionosphere at F-region heights, (2) ionization formed by the aurora is transported upward by the expanding atmosphere, at times producing an appreciable increase in lower exospheric plasma densities on the field lines containing the aurora, and (3) combined satellite, radar, and optical observations during periods of aurora and high electric field could provide measured F-region collision frequencies.     

An analysis of the upper atmospheric wind observed by LOGACS

Wind velocities at 140–200 km altitude were observed by a Low-G Accelerometer Calibration System (LOGACS) flown on an Agena satellite during a geomagnetic storm. An interesting wind reversal observed by the satellite at auroral latitudes is satisfactorily explained by the neutral air motion caused by the $\text{E × B}$ drift deduced from the ground-based geomagnetic data recorded at stations near the meridian of the satellite orbit.     

Ionospheric conductivities, electric fields and currents associated with auroral substorms measured by the EISCAT radar

E-region electron density profiles with high resolution in time and altitude (5 s and 2 km, respectively) measured by the EISCAT incoherent scatter radar are used to examine the conductivity changes during substorm growth, onset and expansion phases for seven substorms occurring in the local evening sector. The measurements are related to electric fields and neutral winds measured by the radar, to ground magnetometer and riometer records, and to optical features, including the westward-travelling surge and auroral bulge. Auroral features are identified using all-sky camera photographs and images from the Viking satellite. Conductances and electric fields in the zone of diffuse aurora corresponding to the westward substorm electrojet are found to be consistent with existing models. Conductances in the discrete auroral arcs marking the expanding edge of the substorm are found to be much higher, and electric fields rather lower, than previously assumed. The magnetic signatures of the discrete arcs are found to be best explained by Hall and Pedersen currents driven by a southward neutral wind, as is observed by the radar. The highest conductances observed, with Hall and Pedersen conductances reaching 120 and 48 S, respectively, are found to be associated with arcs appearing at the southern edge of activity in the vicinity of a westward-travelling surge.