On determining the noon polar cap boundary from SuperDARN HF radar backscatter characteristics

Previous work has shown that ionospheric HF radar backscatter in the noon sector can be used to locate the footprint of the magnetospheric cusp particle precipitation. This has enabled the radar data to be used as a proxy for the location of the polar cap boundary, and hence measure the flow of plasma across it to derive the reconnection electric field in the ionosphere. This work used only single radar data sets with a field of view limited to 2 h of local time. In this case study using four of the SuperDARN radars, we examine the boundary determined over 6 h of magnetic local time around the noon sector and its relationship to the convection pattern. The variation with longitude of the latitude of the radar scatter with cusp characteristics shows a bay-like feature. It is shown that this feature is shaped by the variation with longitude of the poleward flow component of the ionospheric plasma and may be understood in terms of cusp ion time-of-flight effects. Using this interpretation, we derive the time-of-flight of the cusp ions and find that it is consistent with approximately 1 keV ions injected from a subsolar reconnection site. A method for deriving a more accurate estimate of the location of the open-closed field line boundary from HF radar data is described.     

A numerical method to compute Euler potentials for non dipolar magnetic fields

The magnetospheric magnetic field may be conveniently described by two scalar functions (α, β), known as the Euler potentials. They are not uniquely defined, and they may be difficult to derive for configuration more complex than a simple dipole. We propose here a simple numerical method to compute one possible pair (α, β). In magnetospheric regions of closed field lines, α can be chosen as a function of the tube volume of unit magnetic flux. The method can be applied to a wide class of magnetic fields which describe the magnetospheric domain of closed field lines and the conjugated ionosphere. Here, it is used with the T87 Tsyganenko model. The results coincide with the dipolar potentials at close distances from the Earth. At larger distances, they display an increasing distortion with the radial distance (or the invariant latitude in the ionosphere) and the magnetic activity. In the magnetosphere, the contours of α and β are stretched towards the nightside. In the ionosphere, they also extend towards the nightside and present major distortions in a narrow ring at the polar cap boundary, which mapsdistant boundary layers in the magnetosphere.     

Comparison of the measured and modelled electron densities and temperatures in the ionosphere and plasmasphere during 20/30 January, 1993

We present a comparison of the electron density and temperature behaviour in the ionosphere and plasmasphere measured by the Millstone Hill incoherent-scatter radar and the instruments on board of the EXOS-D satellite with numerical model calculations from a time-dependent mathematical model of the Earths ionosphere and plasmasphere during the geomagnetically quiet and storm period on 20/30 January, 1993. We have evaluated the value of the additional heating rate that should be added to the normal photoelectron heating in the electron energy equation in the daytime plasmasphere region above 5000 km along the magnetic field line to explain the high electron temperature measured by the instruments on board of the EXOS-D satellite within the Millstone Hill magnetic field flux tube in the Northern Hemisphere. The additional heating brings the measured and modelled electron temperatures into agreement in the plasmasphere and into very large disagreement in the ionosphere if the classical electron heat flux along magnetic field line is used in the model. A new approach, based on a new effective electron thermal conductivity coefficient along the magnetic field line, is presented to model the electron temperature in the ionosphere and plasmasphere. This new approach leads to a heat flux which is less than that given by the classical Spitzer-Harm theory. The evaluated additional heating of electrons in the plasmasphere and the decrease of the thermal conductivity in the topside ionosphere and the greater part of the plasmasphere found for the first time here allow the model to accurately reproduce the electron temperatures observed by the instruments on board the EXOS-D satellite in the plasmasphere and the Millstone Hill incoherent-scatter radar in the ionosphere. The effects of the daytime additional plasmaspheric heating of electrons on the electron temperature and density are small at the F-region altitudes if the modified electron heat flux is used. The deviations from the Boltzmann distribution for the first five vibrational levels of N₂(v) and O₂(v) were calculated. The present study suggests that these deviations are not significant at the first vibrational levels of N₂ and O₂ and the second level of O₂, and the calculated distributions of N₂(v) and O₂(v) are highly non-Boltzmann at vibrational levels v > 2. The resulting effect of N₂(v > 0) and O₂(v > 0) on NmF2 is the decrease of the calculated daytime NmF2 up to a factor of 1.5. The modelled electron temperature is very sensitive to the electron density, and this decrease in electron density results in the increase of the calculated daytime electron temperature up to about 580 K at the F2 peak altitude giving closer agreement between the measured and modelled electron temperatures. Both the daytime and night-time densities are not reproduced by the model without N₂(v > 0) and O₂(v > 0), and inclusion of vibrationally excited N₂ and O₂ brings the model and data into better agreement.     

CUTLASS observations of a high-m ULF wave and its consequences for the DOPE HF Doppler sounder

The CUTLASS (Co-operative UK Twin Located Auroral Sounding System) Finland HF radar, whilst operating in a high spatial and temporal resolution mode, has measured the ionospheric signature of a naturally occurring ULF wave in scatter artificially generated by the Tromsø Heater. The wave had a period of 100 s and exhibited curved phase fronts across the heated volume (about 180 km along a single radar beam). Spatial information provided by CUTLASS has enabled an m-number for the wave of about 38 to be determined. This high-m wave was not detected by the IMAGE (International Monitor for Auroral Geomagnetic Effects) network of ground magnetometers, as expected for a wave of a small spatial scale size. These observations offer the first independent confirmation of the existence of the ground uncorrelated ULF wave signatures previously reported in measurements recorded from an HF Doppler sounder located in the vicinity of Tromsø. These results both demonstrate a new capability for geophysical exploration from the combined CUTLASS-EISCAT ionospheric Heater experiment, and provide a verification of the HF Doppler technique for the investigation of small scale ULF waves.     

On the current-voltage relationship in fluid theory

The kinetic theory of precipitating electrons with Maxwellian source plasma yields the well-known current-voltage relationship (CV-relationship; Knight formula), which can in most cases be accurately approximated by a reduced linear formula. Our question is whether it is possible to obtain this CV-relationship from fluid theory, and if so, to what extent it is physically equivalent with the more accurate kinetic counterpart. An answer to this question is necessary before trying to understand how one could combine time-dependent and transient phenomena such as Alfvnic waves with a slowly evolving background described by the CV-relationship. We first compute the fluid quantity profiles (density, pressure etc.) along a flux tube based on kinetic theory solution. A parallel potential drop accumulates plasma (and pressure) below it, which explains why the current is linearly proportional to the potential drop in the kinetic theory even though the velocity of the accelerated particles is only proportional to the square root of the accelerating voltage. Electron fluid theory reveals that the kinetic theory results can be reproduced, except for different numerical constants, if and only if the polytropic index γ is equal to three, corresponding to one-dimensional motion. The convective derivative term v∇v provides the equivalent of the “mirror force” and is therefore important to include in a fluid theory trying to describe a CV-relationship. In one-fluid equations the parallel electric field, at least in its functional form, emerges self-consistently. We find that the electron density enhancement below the potential drop disappears because the magnetospheric ions would be unable to neutralize it, and a square root CV-relationship results, in disagreement with kinetic theory and observations. Also, the potential drop concentrates just above the ionosphere, which is at odds with observations as well. To resolve this puzzle, we show that considering outflowing ionospheric ions restores the possibility of having the acceleration region well above the ionosphere, and thus the electron kinetic (and fluid, if γ=3) theory results are reproduced in a self-consistent manner. Thus the inclusion of ionospheric ions is crucial for a feasible CV-relationship in fluid theory. Constructing a quantitative fluid model (possibly one-fluid) which reproduces this property would be an interesting task for a future study.     

Mid-latitude ionospheric perturbation associated with the Spacelab-2 plasma depletion experiment at Millstone Hill

Elevation scans across geomagnetic mid latitudes by the incoherent scatter radar at Millstone Hill captured the ionospheric response to the firing of the Space Shuttle Challenger OMS thrusters near the peak of the F layer on July 30, 1985. Details of the excitation of airglow and the formation of an ionospheric hole during this event have been reported in an earlier paper by Mendillo et al.. The depletion (factor 2) near the 320 km Shuttle orbital altitude persisted for 35 min and then recovered to near normal levels, while at 265 km the density was reduced by a factor of 6; this significant reduction in the bottomside F-region density persisted for more than 3 hours. Total electron content in the vicinity of the hole was reduced by more than a factor of 2, and an oscillation of the F-region densities with 40-min period ensued and persisted for several hours. Plasma vertical Doppler velocity varied quasi-periodically with a 80-min period, while magnetic field variations observed on the field line through the Shuttle-burn position exhibited a similar 80-min periodicity. An interval of magnetic field variations at hydromagnetic frequencies (95 s period) accompanied the ionospheric perturbations on this field line. Radar observations revealed a downward phase progression of the 40-min period density enhancements of -1.12° km–1, corresponding to a 320-km vertical wavelength. An auroral-latitude geomagnetic disturbance began near the time of the Spacelab-2 experiment and was associated with the imposition of a strong southward IMF Bz across the magnetosphere. This created an additional complication in the interpretation of the active ionospheric experiment. It cannot be determined uniquely whether the ionospheric oscillations, which followed the Spacelab-2 experiment, were related to the active experiment or were the result of a propagating ionospheric disturbance (TID) launched by the enhanced auroral activity. The most reasonable conclusion is that the ionospheric oscillations were a result of the coincident geomagnetic disturbance. The pronounced depletion of the bottomside ionosphere, however, accentuated the oscillatory behavior during the interval following the Shuttle OMS burn.     

The role of vibrationally excited nitrogen and oxygen in the ionosphere over Millstone Hill during 16-23 March, 1990

We present a comparison of the observed behavior of the F region ionosphere over Millstone Hill during the geomagnetically quiet and storm period on 16/23 March, 1990, with numerical model calculations from the time-dependent mathematical model of the Earths ionosphere and plasmasphere. The effects of vibrationally excited N₂(v) and O₂(v) on the electron density and temperature are studied using the N₂(v) and O₂(v) Boltzmann and non-Boltzmann distribution assumptions. The deviations from the Boltzmann distribution for the first five vibrational levels of N₂(v) and O₂(v) were calculated. The present study suggests that these deviations are not significant at vibrational levels v = 1 and 2, and the calculated distributions of N₂(v) and O₂(v) are highly non-Boltzmann at vibrational levels v > 2. The N₂(v) and O₂(v) non-Boltzmann distribution assumption leads to the decrease of the calculated daytime NmF2 up to a factor of 1.44 (maximum value) in comparison with the N₂(v) and O₂(v) Boltzmann distribution assumption. The resulting effects of N₂(v > 0) and O₂(v) > 0) on the NmF2 is the decrease of the calculated daytime NmF2 up to a factor of 2.8 (maximum value) for Boltzmann populations of N₂(v) and O₂(v) and up to a factor of 3.5 (maximum value) for non-Boltzmann populations of N₂(v) and O₂(v). This decrease in electron density results in the increase of the calculated daytime electron temperature up to about 1040/1410 K (maximum value) at the F2 peak altitude giving closer agreement between the measured and modeled electron temperatures. Both the daytime and nighttime densities are not reproduced by the model without N₂(v > 0) and O₂(v > 0), and inclusion of vibrationally excited N2 and O2 brings the model and data into better agreement. The effects of vibrationally excited O2 and N2 on the electron density and temperature are most pronounced during daytime.     

Correlations between SAR arc intensity and solar and geomagnetic activity

We present a study of statistical relationships between SAR arc intensities acquired by the Pacific Northwest Laboratory Photometer Network during 1978–1988 and solar and geomagnetic activity indices Dst, F10.7, and Kp by use of the method of multiple regression analysis. We found significant correlations between intensity and all of the indices involved. In the present work we show for the first time that the partial correlation coefficients depend on the time offset, t, between the time of SAR arc intensity observations and the onset of the geomagnetic storm recovery phase, with the largest correlations being observed when 8 d t d 16 h. It is also shown that there are significant differences between partial correlation coefficients calculated for SAR arcs associated with strong (Dst_min > −100 nT) and weak (Dst_min > −100 nT) geomagnetic storms. We observe also that the multiple correlation coefficients for strong storms are much larger than for weak ones. We found that the variations in the electron temperature, T_e, in the SAR arc region are not mainly produced by variations in the electron density of the ionosphere but are strongly driven by the additional heating of the electron gas due to an interaction of the ring current ions and the plasmaspheric electrons. As a result, variations of T_e in the SAR arc region with characteristic time scales from several minutes to several hours are stipulated by time variations of ring current parameters.     

Simultaneous optical and radar signatures of poleward-moving auroral forms

Dayside poleward moving auroral forms (PMAFs) were detected between 06:30 and 07:00 UT on December 16, 1998, by the meridian scanning photometer and the all-sky camera at Ny Ålesund, Svalbard. Simultaneous SuperDARN HF radar measurements permitted the study of the associated ionospheric velocity pattern. A good general agreement is observed between the location and movement of velocity enhancements (flow channels) and the PMAFs. Clear signatures of equatorward flow were detected in the vicinity of PMAFs. This flow is believed to be the signature of a return flow outside the reconnected flux tube, as predicted by the Southwood model. The simulated signatures of this model reproduce globally the measured signatures, and differences with the experimental data can be explained by the simplifications of the model. Proposed schemes of the flow modification due to the presence of several flow channels and the modification of cusp and region 1 field-aligned currents at the time of sporadic reconnection events are shown to fit well with the observations.     

Dayside ionospheric response to changes in IMF polarity: optical and plasma-flow observations

The response of the dayside ionosphere to changes in polarity of the interplanetary magnetic field was observed by two independent techniques. The signatures were seen in the 630.0 nm red-line emission, measured by a meridian scanning photometer at Ny-Ålesund on Svalbard, and also in the line-of-sight plasma velocities monitored by the Finland CUTLASS SuperDARN radar. A time difference of some 6 to 8 min occurred between the responses of the two techniques, with the flows being first to respond. In the present case study, the longer delay in the optics suggests that ion precipitation controls the auroral emission.     

A flux transfer event observed at the magnetopause by the Equator-S spacecraft and in the ionosphere by the CUTLASS HF radar

Observations of a flux transfer event (FTE) have been made simultaneously by the Equator-S spacecraft near the dayside magnetopause whilst corresponding transient plasma flows were seen in the near-conjugate polar ionosphere by the CUTLASS Finland HF radar. Prior to the occurrence of the FTE, the magnetometer on the WIND spacecraft ≈226 R_E upstream of the Earth in the solar wind detected a southward turning of the interplanetary magnetic field (IMF) which is estimated to have reached the subsolar magnetopause ≈77 min later. Shortly afterwards the Equator-S magnetometer observed a typical bipolar FTE signature in the magnetic field component normal to the magnetopause, just inside the magnetosphere. Almost simultaneously the CUTLASS Finland radar observed a strong transient flow in the F region plasma between 78° and 83° magnetic latitude, near the ionospheric region predicted to map along geomagnetic field lines to the spacecraft. The flow signature (and the data set as a whole) is found to be fully consistent with the view that the FTE was formed by a burst of magnetopause reconnection.     

Characteristics of a stable are based on FAST and MIRACLE observations

A stable evening sector are is studied using observations from the FAST satellite at 1250 km altitude and the MIRACLE ground-based network, which contains all-sky cameras, coherent radars (STARE), and magnetometers. Both FAST and STARE observe a northward electric field region of about 200 km width and a field magnitude of about 50 mV/m southward of the arc, which is a typical signature for an evening-sector arc. The field-aligned current determined from FAST electron and magnetometer data are in rather good agreement within the arcs. Outside the arcs, the electron data misses the current carriers of the downward FAC probably because it is mainly carried by electrons of smaller energy than the instrument threshold. Studying the westward propagation speed of small undulations associated with the arc using the all-sky cameras gives a velocity of about 2 km//s. This speed is higher than the background ionospheric plasma speed (about 1 km//s), but it agrees rather well with the idea originally proposed by Davis that the undulations reflect an E × B motion in the acceleration region. The ground magnetograms indicate that the main current flows slightly south of the arc. Computing the ionospheric conductivity from FAST electron data and using the ground magnetograms to estimate the current yields an ionospheric electric field pattern, in rather good agreement with FAST results.     

High-latitude HF Doppler observations of ULF waves: 2. Waves with small spatial scale sizes

The DOPE (Doppler Pulsation Experiment) HF Doppler sounder located near Tromsø, Norway (geographic: 69.6°N 19.2°E; L = 6.3) is deployed to observe signatures, in the high-latitude ionosphere, of magnetospheric ULF waves. A type of wave has been identified which exhibits no simultaneous ground magnetic signature. They can be subdivided into two classes which occur in the dawn and dusk local time sectors respectively. They generally have frequencies greater than the resonance fundamentals of local field lines. It is suggested that these may be the signatures of high-m ULF waves where the ground magnetic signature has been strongly attenuated as a result of the scale size of the waves. The dawn population demonstrate similarities to a type of magnetospheric wave known as giant (Pg) pulsations which tend to be resonant at higher harmonics on magnetic field lines. In contrast, the waves occurring in the dusk sector are believed to be related to the storm-time Pc5s previously reported in VHF radar data. Dst measurements support these observations by indicating that the dawn and dusk classes of waves occur respectively during geomagnetically quiet and more active intervals.     

The ionospheric footprint of antiparallel merging regions on the dayside magnetopause

The antiparallel merging hypothesis states that reconnection takes place on the dayside magnetopause where the solar and geomagnetic fields are oppositely directed. With this criterion, we have mapped the predicted merging regions to the ionosphere using the Tsyganenko 96 magnetic field model, distinguishing between regions of sub-Alfvénic and super-Alfvénic magnetosheath flow, and identifying the day-night terminator. We present the resulting shape, width and latitude of the ionospheric dayside merging regions in both hemispheres, showing their dependence on the Earths dipole tilt. The resulting seasonal variation of the longitudinal width is consistent with the conjugate electric fields in the northern and southern cusps, as measured by the SuperDARN HF radars, for example. We also find a seasonal shift in latitude similar to that observed in satellite cusp data.     

Multi-instrument study of footprints of magnetopause reconnection in the summer ionosphere

Results are presented from a multi-instrument investigation of the signatures of equatorial reconnection in the summer, sunlit ionosphere. Well-established ion dispersion signatures measured during three DMSP satellite passes were used to identify footprints in ionospheric observations made by radio tomography, and both the EISCAT ESR and mainland radars. Under the prevalent conditions of southward IMF with the B_z component increasing in magnitude, the reconnection footprint was seen to move equatorward through the ESR field-of-view. The most striking signature was in the electron temperatures of the F2 region measured by the EISCAT mainland radar that revealed significantly enhanced temperatures with a steep equatorward edge, in general agreement with the leading edge of the ion dispersion. It is suggested that this sharp transition in the electron temperature may be an indicator of the boundary, mapping from the reconnection site, between closed geomagnetic field lines and those opened along which magnetosheath ions precipitate.     

Localized structure in the cusp and high-latitude ionosphere: a modelling study

The ionospheric signature of a flux transfer event (FTE) seen in EISCAT radar data has been used as the basis for a modelling study using a new numerical model of the high-latitude ionosphere developed at the University of Sheffield, UK. The evolution of structure in the high-latitude ionosphere is investigated and examined with respect to the current views of polar patch formation and development. A localized velocity enhancement, of the type associated with FTEs, is added to the plasma as it passes through the cusp. This is found to produce a region of greatly enhanced ion temperature. The new model can provide greater detail during this event as it includes anisotropic temperature calculations for the O⁺ ions. This illustrates the uneven partitioning of the energy during an event of this type. O⁺ ion temperatures are found to become increasingly anisotropic, with the perpendicular temperature being substantially larger than the parallel component during the velocity enhancement. The enhanced temperatures lead to an increase in the recombination rate, which results in an alteration of the ion concentrations. A region of decreased O⁺ and increased molecular ion concentration develops in the cusp. The electron temperature is less enhanced than the ions. As the new model has an upper boundary of 10 000 km the topside can also be studied in great detail. Large upward fluxes are seen to transport plasma to higher altitudes, contributing to the alteration of the ion densities. Plasma is stored in the topside ionosphere and released several hours after the FTE has finished as the flux tube convects across the polar cap. This mechanism illustrates how concentration patches can be created on the dayside and be maintained into the nightside polar cap.     

A case study of electron precipitation in the late substorm growth phase on and nearby a preonset arc

We follow the electron precipitation characteristics on and nearby a preonset arc using the high resolution Freja TESP instrument. Our data coverage extends from about 10 min before onset up to 1 min before onset. The arc is the most equatorward one (around MLAT 62°) of a system of growth phase arcs, and it was close to the radiation belt precipitation. Within the preonset arc, inverted-V type precipitation dominates. Poleward of the arc we also find some precipitation regions, and here there is systematically a cold electron population superposed with a warm population. Using single and double Maxwellian fits to the measured electron spectra we find the ionosphere-magnetosphere coupling parameters (field-aligned conductance K and the parallel potential drop V) as well as the effective source plasma properties (density and temperature) during the event. Compared to typical expansion phase features, the preonset parallel potential drop is smaller by a factor of ten, the electron temperature is smaller by a factor of at least five, and the field-aligned conductance is about the same or larger. The fact that there are two isotropic superposed electron populations on the poleward side of the preonset arc suggests that the distance between warm trapped electrons on dipolar field lines and colder electrons on open field lines has become so small near the onset that mixing e.g. due to finite electron Larmor radius effects can take place.     

The influence of the interplanetary medium on SuperDARN radar scattering occurrence

The effects of the characteristics of the interplanetary medium on the radar scattering occurrence, related to the whole array of SuperDARN radars installed in the Northern Hemisphere, have been studied over a two-year period. Statistically significant correlations of the variation of the scattering occurrence are found with the merging electric field and with the negative B_z component of the interplanetary magnetic field, independent of the seasonal period considered. This result demonstrates that the merging rate (and in particular the reconnection process) between the interplanetary magnetic field and the magnetosphere is a relevant factor affecting the occurrence of scattering. For comparison, we note that no statistically significant correlations are obtained when the interplanetary ion density or the solar wind speed are considered, although also these variables affect to a small degree the scattering occurrence variation. The study of the latitudinal and magnetic local time dependence of the observations shows an association between the considered correlation and the location of the auroral oval and the cusp/cleft region.     

Possible role of magnetosphere-ionosphere coupling in auroral arc generation

Three models for the magnetosphere-ionosphere coupling feedback instability are considered. The first model is based on demagnetization of hot ions in the plasma sheet. The instability takes place in the global magnetosphere-ionosphere system when magnetospheric electrons drift through a spatial gradient of hot magnetospheric ion population. Such a situation exists on the inner and outer edges of the plasma sheet where relatively cold magnetospheric electrons move earthward through a radial gradient of hot ions. This leads to the formation of field-aligned currents. The effect of upward field-aligned current on particle precipitation and the magnitude of ionospheric conductivity leads to the instability of this earthward convection and to its division into convection streams oriented at some angle with respect to the initial convection direction. The growth rate of the instability is maximum for structures with sizes less than the ion Larmor radius in the equatorial plane. This may lead to formation of auroral arcs with widths about 10 km. This instability explains many features of such arcs, including their conjugacy in opposite hemispheres. However, it cannot explain the very high growth rates of some auroral arcs and very narrow arcs. For such arcs another type of instability must be considered. In the other two models the instability arises because of the generation of Alfven waves from growing arc-like structures in the ionospheric conductivity. One model is based on the modulation of precipitating electrons by field-aligned currents of the upward moving Alfven wave. The other model takes into consideration the reflection of Alfven waves from a maximum in the Alfven velocity at an altitude of about 3000 km. The growth of structures in both models takes place when the ionization function associated with upward field-aligned current is shifted from the edges of enhanced conductivity structures toward their centers. Such a shift arises because the structures move at a velocity different from the E × B drift. Although both models may work, the growth rate for the model, based on the modulation of the precipitating accelerated electrons, is significantly larger than that of the model based on the Alfven wave reflection. This mechanism is suitable for generation of auroral arcs with widths of about 1 km and less. The growth rate of the instability can be as large as 1 s^-1, and this mechanism enables us to justify the development of auroral arcs only in one ionosphere. It is hardly suitable for excitation of wide and conjugate auroral arcs, but it may be responsible for the formation of small-scale structures inside a wide arc.Polar Geophysical Institute, Apatity, Russia     

Combined ESR and EISCAT observations of the dayside polar cap and auroral oval during the May 15, 1997 storm

The high-latitude ionospheric response to a major magnetic storm on May 15, 1997 is studied and different responses in the polar cap and the auroral oval are highlighted. Depletion of the F₂ region electron density occurred in both the polar cap and the auroral zone, but due to different physical processes. The increased recombination rate of O⁺ ions caused by a strong electric field played a crucial role in the auroral zone. The transport effect, however, especially the strong upward ion flow was also of great importance in the dayside polar cap. During the main phase and the beginning of the recovery phase soft particle precipitation in the polar cap showed a clear relation to the dynamic pressure of the solar wind, with a maximum cross-correlation coefficient of 0.63 at a time lag of 5 min.