Auroral Energy Flux Research Articles

Multiresolution Data Assimilation for Auroral Energy Flux and Mean Energy Using DMSP SSUSI, THEMIS ASI, and An Empirical Model

AbstractWe apply a multiresolution Gaussian process model (Lattice Kriging) to combine satellite observations, ground‐based observations, and an empirical auroral model, to produce the assimilation of auroral energy flux and mean energy over high‐latitude regions. Compared to a simple padding, the assimilation coherently combines various data inputs leading to continuous transitions between different datasets. The multiresolution modeling capability is achieved by allocating multiple layers of basis functions with different resolutions. Higher‐resolution fitting results capture more mesoscale (10–100 s km) structures such as auroral arcs, than the low‐resolution ones and the empirical model. To better reconcile different datasets, two preprocessing steps, temporal interpolation of satellite data and spatial down‐sampling of low‐fidelity data, are implemented. The inherent smoothing effect of the fitting, which causes an unrealistic spreading of the aurora, is mitigated by a post processing step: the K Nearest Neighbor (KNN) algorithm. KNN identifies the probability of a region with significant aurora and thereby eliminates those regions with low values. Thereby, this methodology can be used to maintain realistic and mesoscale auroral structures without boundary issues. We then run the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIEGCM) driven by the high‐ and low‐resolution auroral assimilations and compare total electron contents (TECs). TIEGCM driven by data assimilation produces enhanced TECs by a factor of ∼2 than the one driven by the empirical aurora, and high‐resolution results show mesoscale structures. Our study shows the value of incorporating realistic auroral inputs via assimilation to drive ionosphere‐thermosphere models for better understanding the consequences of mesoscale phenomena.

Global Driving of Auroral Precipitation: 1. Balance of Sources.

The accurate determination of auroral precipitation in global models has remained a daunting and rather inexplicable obstacle. Understanding the calculation and balance of multiple sources that constitute the aurora, and their eventual conversion into ionospheric electrical conductance, is critical for improved prediction of space weather events. In this study, we present a semi‐physical global modeling approach that characterizes contributions by four types of precipitation—monoenergetic, broadband, electron, and ion diffuse—to ionospheric electrodynamics. The model uses a combination of adiabatic kinetic theory and loss parameters derived from historical energy flux patterns to estimate auroral precipitation from magnetohydrodynamic (MHD) quantities. It then converts them into ionospheric conductance that is used to compute the ionospheric feedback to the magnetosphere. The model has been employed to simulate the 5–7 April 2010 Galaxy15 space weather event. Comparison of auroral fluxes show good agreement with observational data sets like NOAA‐DMSP and OVATION Prime. The study shows a dominant contribution by electron diffuse precipitation, accounting for ∼74% of the auroral energy flux. However, contributions by monoenergetic and broadband sources dominate during times of active upstream solar conditions, providing for up to 61% of the total hemispheric power. The study also finds a greater role played by broadband precipitation in ionospheric electrodynamics which accounts for ∼31% of the Pedersen conductance.

Assimilative Mapping of Auroral Electron Energy Flux Using SSUSI Lyman‐Birge‐Hopfield (LBH) Emissions

AbstractFar ultraviolet (FUV) imaging of the aurora from space provides great insight into the dynamic coupling of the atmosphere, ionosphere, and magnetosphere on global scales. To gain a quantitative understanding of these coupling processes, the global distribution of auroral energy flux is required, but the inversion of FUV emission to derive precipitating auroral particles' energy flux is not straightforward. Furthermore, the spatial coverage of FUV imaging from Low Earth Orbit (LEO) altitudes is often insufficient to achieve global mapping of this important parameter. This study seeks to fill these gaps left by the current geospace observing system using a combination of data assimilation and machine learning techniques. Specifically, this paper presents a new data‐driven modeling approach to create instantaneous, global assimilative mappings of auroral electron total energy flux from Lyman‐Birge‐Hopfield (LBH) emission data from the Defense Meteorological System Program (DMSP) Special Sensor Ultraviolet Spectrographic Imager (SSUSI). We take a two‐step approach; the creation of assimilative maps of LBH emission using optimal interpolation, followed by the conversion to energy flux using a neural network model trained with conjunction observations of in‐situ auroral particles and LBH emission from the DMSP Special Sensor J and SSUSI instruments. The paper demonstrates the feasibility of this approach with a model prototype built with DMSP data from 17 February 2014 to 23 February 2014. This study serves as a blueprint for a future comprehensive data‐driven model of auroral energy flux that is complementary to traditional inversion techniques to take advantage of FUV imaging from LEO platforms for global assimilative mapping of auroral energy flux.

Auroral Energy Flux and Joule Heating Derived From Global Maps of Field-Aligned Currents.

We calculate auroral energy flux and Joule heating in the high‐latitude ionosphere for 27 geomagnetically active days using two‐dimensional maps of field‐aligned currents determined by the Active Magnetosphere and Planetary Response Experiment. The energy input to the ionosphere due to Joule heating increases more rapidly with geomagnetic activity than that due to precipitating particles. The energy flux varies more smoothly with time than Joule heating, which is impulsive in nature on time scales from minutes to tens of minutes. These impulsive events correlate well with recoveries in the Sym‐H index, with the maximum correlation when compared to Sym‐H recoveries 70 min later. Because of prior studies that have associated transient recoveries of Sym‐H with substorm expansions, the delay found here suggests that dissipation of energy in the ionosphere occurs during the substorm growth phase prior to the release of magnetic energy caused by diversion of tail currents.

Hemispheric asymmetry of the dayside aurora due to imbalanced solar insolation

Unlike the nightside aurora, which is controlled mainly by magnetic field reconnection in the magnetotail, the dayside aurora is closely associated with magnetic field merging at the dayside magnetopause. About two decades ago, it was discovered that the aurora is also controlled by solar insolation. Because the finding was based on data acquired mainly in the Northern Hemisphere, an outstanding question is if the auroral solar insolation effect also exists in the Southern Hemisphere. The present study addresses this question by studying dayside auroras from both hemispheres. We analyze 6 years’ worth of Earth disk emissions at far ultraviolet wavelengths acquired by the Global UltraViolet Imager on-board the Thermosphere Ionosphere Mesosphere Energetics and Dynamics satellite from 2002 to 2007. It is found that the solar insolation effect also exists in the Southern Hemisphere. In essence, the energy flux deposited as electron precipitation, is larger when the polar hemisphere is sunlit and is smaller when the polar hemisphere is dark. Because auroras are produced mainly by electron precipitation and because electrons are the main current carrier, this north–south asymmetry is consistent with the previous finding that larger (smaller) field-aligned currents are flowing out of the sunlit (dark) hemisphere. This trend is independent of the solar wind driving, suggesting that it is an effect associated with solar insolation. A small north–south asymmetry in the dayside auroral energy flux was identified. We discuss the asymmetry in the context of magnetospheric current and voltage generators.

Hemispheric Asymmetry of the Premidnight Aurora Associated With the Dawn‐Dusk Component of the Interplanetary Magnetic Field

AbstractIt has been known for decades that the nightside aurora in the Northern Hemisphere (NH) tends to be brighter when the interplanetary magnetic field (IMF) measured at Earth has a dawnward (negative y) component compared to a duskward (positive y) component. This asymmetric response to the polarity of IMF By has been explained by an interhemispheric current flowing out of the NH due to a nonuniform “penetration” of IMF By onto the magnetotail. If such a hypothesis is correct, it should predict a brighter aurora in the nightside Southern Hemisphere (SH) for positive IMF By than negative IMF By. Here we investigate this hypothesis using Thermosphere, Ionosphere, Mesosphere, Energetics and Dynamics/Global Ultraviolet Imager data. The present study not only reproduces the result previously found in NH but also shows an opposite change to its Northern Hemispheric counterpart in SH in response to the different IMF By polarity. When comparing north to south, for negative IMF By, the premidnight auroral energy flux is greater in NH than that in SH. The result becomes opposite for positive IMF By. This result is consistent with the hypothesis of the existence of an interhemispheric field‐aligned current.

Auroral Energy Flux Distribution Over the Nightside Auroral Oval Observed by the DMSP F16/SSUSI: Seasonal, Geomagnetic, and Solar Activity Dependences

AbstractThe present work investigates variations in the relative strengths of average premidnight and postmidnight aurorae. The average auroral energy flux data for the southern hemisphere in 2004–2015 are taken from the Special Sensor Ultraviolet Spectrographic Imager onboard the Defense Meteorological Satellite Program F16 satellite. The main findings are as follows: (1) In local winter, the maximum auroral energy flux over the oval is located in the premidnight sector (18:00–00:00 magnetic local time) under geomagnetically quiet condition (Kp = 1) and moves toward the postmidnight sector (00:00–06:00 magnetic local time) as the Kp index increases. (2) In local summer, the maximum energy flux occurs in the postmidnight for higher solar activities (F10.7 > 100 sfu). (3) The premidnight bulge of the auroral energy flux is most prominent under winter, solar minimum and geomagnetically quiet (Kp = 1) conditions. (4) Relatively more auroral energy tends to be deposited in the postmidnight sector than in the premidnight sector as Kp increases. These results show that the auroral energy over the nightside oval is redistributed on average as the season, solar flux, and geomagnetic activity change. This would substantially affect the thermosphere and ionosphere at high latitudes.

Effects of High‐Latitude Forcing Uncertainty on the Low‐Latitude and Midlatitude Ionosphere

AbstractEnsemble simulations are performed using the Thermosphere‐Ionosphere‐Electrodynamics General Circulation Model (TIE‐GCM) in order to understand the role of high‐latitude forcing uncertainty on the low‐latitude and midlatitude ionosphere response to the April 2010 geomagnetic storm. The ensemble is generated by perturbing either the high‐latitude electric potential or auroral energy flux in the assimilative mapping for ionosphere electrodynamics (AMIE). Simulations with perturbed high‐latitude electric potential result in substantial intraensemble variability in the low‐latitude and midlatitude ionosphere response to the geomagnetic storm, and the ensemble standard deviation for the change in NmF2 reaches 50–100% of the mean change. Such large intraensemble variability is not seen when perturbing the auroral energy flux. In this case, the effects of the forcing uncertainty are primarily confined to high latitudes. We therefore conclude that the specification of high‐latitude electric fields is an important source of uncertainty when modeling the low‐latitude and midlatitude ionosphere response to a geomagnetic storm. A multiple linear regression analysis of the results indicates that uncertainty in the storm time changes in the equatorial electric fields, neutral winds, and neutral composition can all contribute to the uncertainty in the ionosphere electron density. The results of the present study provide insight into the possible uncertainty in simulations of the low‐latitude and midlatitude ionosphere response to geomagnetic storms due to imperfect knowledge of the high‐latitude forcing.

Solar activity dependence of nightside aurora in winter conditions

AbstractThe dependence of the nightside (21:00–03:00 MLT; magnetic local time) auroral energy flux on solar activity was quantitatively studied for winter/dark and geomagnetically quiet conditions. Using data combined from Thermosphere, Ionosphere, Mesosphere Energetics and Dynamics/Global Ultraviolet Imager and Defense Meteorological Satellite Program/Special Sensor Ultraviolet Spectrographic Imager observations, we separated the effects of geomagnetic activity from those of solar flux on the nightside auroral precipitation. The results showed that the nightside auroral power was reduced by ~42% in solar maximum (F10.7 = 200 sfu; solar flux unit 1 sfu = 10−22 W m−2 Hz−1) with respect to that under solar minimum (F10.7 = 70 sfu) for the Kp = 1 condition, and this change rate became less (~21%) for the Kp = 3 condition. In addition, the solar cycle dependence of nightside auroral power was similar with that from both the premidnight (21:00–23:00 MLT) and postmidnight (01:00–03:00 MLT) sectors. These results indicated that as the ionospheric ionization increases with the enhanced auroral and geomagnetic activities, the solar activity dependences of nightside auroral power become weaker, at least under geomagnetically quiet conditions.

Predominance of ECH wave contribution to diffuse aurora in Earth's outer magnetosphere

AbstractDue to its importance for global energy dissipation in the ionosphere, the diffuse aurora has been intensively studied in the past 40 years. Its origin (precipitation of 0.5–10 keV electrons from the plasma sheet without potential acceleration) has been generally attributed to whistler‐mode chorus wave scattering in the inner magnetosphere (R < ~8 RE), while the scattering mechanism beyond that distance remains unresolved. By modeling the quasi‐linear diffusion of electrons with realistic parameters for the magnetic field, loss cone size, and wave intensity (obtained from Time History of Events and Macroscale Interactions during Substorms (THEMIS) observations as a function of magnetospheric location), we estimate the loss cone filling ratio and electron cyclotron harmonic (ECH) wave‐induced electron precipitation systematically throughout the entire data set, from 6 RE out to 31 RE (the THEMIS apogee). By comparing the wave‐induced precipitation directly with the equatorially mapped energy flux distribution of the diffuse aurora from ionospheric observations (OVATION Prime model) at low altitudes, we quantify the contribution of auroral energy flux precipitated due to ECH wave scattering. Although the wave amplitudes decrease, as expected, with distance from the Earth, due to the smaller loss cone size and stretched magnetic field topology, ECH waves are still capable of causing sufficient scattering of plasma sheet electrons to account for the observed diffuse auroral dissipation. Our results demonstrate that ECH waves are the dominant driver of the diffuse aurora in the outer magnetosphere, beyond ~8 RE.

OVATION‐SM: A model of auroral precipitation based on SuperMAG generalized auroral electrojet and substorm onset times

OVATION‐SM, an empirical model for different types of auroral energy flux, has been developed. OVATION‐SM is a linear combination of the SME index (or square root of SME index for monoenergetic auroras), time since the last substorm onset, and time until the next substorm onset. Because OVATION‐SM is based on ground magnetometer data and products of that data, it is possible to calculate continuous auroral power at a 1 min cadence for 30+ years. OVATION‐SM captures the gross auroral morphology, including onsets and other brightening and dimming events. The detailed spatial auroral morphology is beyond the scope of the current version of OVATION‐SM. OVATION‐SM explains more than 70% of the variance in Polar UV Imager nightside auroral power, which makes it a better predictor of nightside auroral power than any other model currently available.

Poleward arcs of the auroral oval during substorms and the inner edge of the plasma sheet

An analytical model for the connection between the near‐Earth edge of the plasma sheet at substorm onset and the auroral arcs at the poleward edge of the auroral oval is presented. The connection is established through the existence of a Boström type I current system. Its generator is assumed to be constituted by a narrow high‐beta plasma layer located at the interface between the near‐Earth plasma sheet and the outer edge of the near‐dipolar field of the magnetosphere. The energy balance between the downward Poynting flux and the energy conversion in the auroral acceleration region and ionosphere provides a relation for the electric fields as a function of the upward field‐aligned current. Only the upward current region is being considered in this work. An interesting effect, incorporated in the energy balance, is the feedback of the auroral electrojet on the magnetospheric plasma by dragging the latter eastward from below under the action of a Hall generator. Thereby a relation arises between the westward electric field, tangential to the arc, and the equatorward polarization field. Quantitative solution of the energy equation is achieved by using the empirical relations between auroral energy flux and electron energy and the integrated Hall and Pedersen conductivities. Accommodation of the downward energy flux requires the existence of a minimum arc length. The resulting quantities are consistent with typical auroral data sets. Relating the downward energy flux to the parameters of the generator reveals a strong dependence of polarization electric field, overall energy dissipation, and total current strength on the plasma beta of the generator. The dumping of excess energy from the high‐beta plasma layer into the auroral arc(s) allows the stretched tail field lines to transform into dipolar field lines. It opens, so‐to‐speak, the gate into the outer magnetosphere.

Auroral arcs as current transformers

We treat the effects of an electric field tangential to an auroral arc on the basis of an analytical model according to which auroral arcs are energized by the release of magnetic shear stresses and associated internal energy (Haerendel, 2007). If the tangential field exceeds a certain (low) threshold, the ionosphere acts as a current generator, or better transformer, and the magnetosphere as the load. The reason is that energy supplied by a longitudinal Type I current system, as defined by Boström in 1964, is transformed into energy of the latitudinal Type II current system attached to the arc and is mostly consumed by the auroral acceleration process. Closure of the transformer current in the upper magnetosphere and energy deposition in form of internal energy and shear stresses, although small, are crucial for the operation of this process. It can be visualized as a dragging of magnetic field and plasma along the arc in the direction of higher magnetospheric pressure enforced by the electric polarization field. This energy deposition from below is superimposed on the release of free energy supplied by the magnetospheric generator. Formulation of this scenario leads to a set of algebraic equations, whose solution provides quantitative answers on the interdependence of current closure, energy deposition, and enhanced auroral energy flux in relation to the imposed tangential electric field. Contrary to earlier expectations, the polarization field appears not as a consequence of current blockage, but as manifestation of its continuation by field‐aligned currents and their closure in the magnetosphere. Another consequence of the energy deposition from below is a small modification of the arc's proper motion in the ambient plasma frame. A procedure for evaluating applicable measurements in terms of the underlying physics is given and a concrete example added.

Seasonal, Kp, solar wind, and solar flux variations in long‐term single‐pass satellite estimates of electron and ion auroral hemispheric power

Electron auroral energy flux is characterized by electron hemispheric power (Hpe) estimated since 1978 from National Oceanic and Atmospheric Administration (NOAA) and Defense Meteorological Satellite Program (DMSP) satellites after the estimates were corrected for instrumental problems and adjusted to a common baseline. Similarly, intersatellite adjusted ion hemispheric power (Hpi) estimates come from one MetOp and four NOAA satellites beginning in 1998. The hemispheric power (Hp) estimates are very crude, coming from single satellite passes referenced to 10 global activity levels, where the Hpi estimates are the difference between the total and the electron Hp (Hpi = Hpt‐Hpe). However, hourly averaged NOAA/DMSP Hpe and Hpi estimates correlate well with hourly Polar Ultraviolet Imager (UVI) Hpt and Imager for Magnetopause‐to‐Aurora Global Exploration (IMAGE) far ultraviolet (FUV) Hpe and Hpi estimates. Hpe winter values were larger than summer values ∼65% of the time (when geomagnetic activity was moderate or higher), and Hpe were larger in the summer ∼35% of the time (typically for low geomagnetic activity). Hpe was ∼40% larger at winter solstice than summer solstice for the largest Hp from mostly nightside increases, and Hpe was ∼35% larger in summer than winter for the smallest Hp owing to dayside auroral enhancements. Ion precipitation differed from electron precipitation because it was almost always larger in summer than winter. Hpe and Hpi increased with Kp, solar wind speed (Vsw), and negative Interplanetary Magnetic Field (IMF) Bz, similar to previous studies. Hpi also increased strongly with positive Bz. For quiet conditions, Hpe increased with increasing 10.7‐cm solar flux (Sa), while Hpi increased with Sa up to Sa ∼115 for all conditions.

Precipitation and total power consumption in the ionosphere: Global MHD simulation results compared with Polar and SNOE observations

Abstract. We compare the ionospheric electron precipitation morphology and power from a global MHD simulation (GUMICS-4) with direct measurements of auroral energy flux during a pair of substorms on 28-29 March 1998. The electron precipitation power is computed directly from global images of auroral light observed by the Polar satellite ultraviolet imager (UVI). Independent of the Polar UVI measurements, the electron precipitation energy is determined from SNOE satellite observations on the thermospheric nitric oxide (NO) density. We find that the GUMICS-4 simulation reproduces the spatial variation of the global aurora rather reliably in the sense that the onset of the substorm is shown in GUMICS-4 simulation as enhanced precipitation in the right location at the right time. The total integrated precipitation power in the GUMICS-4 simulation is in quantitative agreement with the observations during quiet times, i.e., before the two substorm intensifications. We find that during active times the GUMICS-4 integrated precipitation is a factor of 5 lower than the observations indicate. However, we also find factor of 2-3 differences in the precipitation power among the three different UVI processing methods tested here. The findings of this paper are used to complete an earlier objective, in which the total ionospheric power deposition in the simulation is forecasted from a mathematical expression, which is a function of solar wind density, velocity and magnetic field. We find that during this event, the correlation coefficient between the outcome of the forecasting expression and the simulation results is 0.83. During the event, the simulation result on the total ionospheric power deposition agrees with observations (correlation coefficient 0.8) and the AE index (0.85).

Effects of suprathermal tails on auroral electrodynamics

The auroral current density‐voltage and energy flux density‐voltage relationships are derived under the assumption that magnetospheric electrons above the auroral acceleration region are described by the κ distribution function. To illustrate the effects of this boundary condition on auroral precipitation, a two‐dimensional model of auroral electrodynamics similar to that of Lyons [1980] has been developed by imposing current continuity in a region of converging electric field in the auroral zone. The current carried by precipitating magnetospheric electrons inside auroral arcs connects to return current regions at the arc edges via ionospheric Pedersen currents. A key feature is the ability to parameterize the magnetospheric boundary electron population as either a κ or Maxwellian distribution. For equal density and temperature a κ = 5 boundary condition yields a parallel potential drop ∼ 5% larger and a precipitating energy flux structure ∼ 5% wider than those of its Maxwellian counterpart. More significant differences emerge between these two distributions when the density is held constant but the spectral shape of the distributions are allowed to differ. The κ distribution results predict up to double the peak auroral energy flux and as much as a 20–30% increase in the latitudinal width of the auroral energy flux as compared with the Maxwellian results. The width and intensity of the inverted V structures in the model results are found to be closely related to the level of thermal energy flux outside the inverted V.

Transport‐theoretic model for the electron‐proton‐hydrogen atom aurora: 1. Theory

The first self‐consistent transport‐theoretic model for the combined electron‐proton‐hydrogen atom aurora is presented. This is needed for accurate modeling of the diffuse aurora, particularly in the midnight sector, for which a statistical study (Hardy et al., 1989) indicates that the proton contribution to the total auroral energy flux is (on the average) about 20 to 25% of that of the electrons. As a result, the ionization yield as well as the yields of many emission features will be underestimated (on the average) by about the same percentage if the proton‐hydrogen atom contributions are neglected. The model presented here can also be used to study a pure electron aurora or a pure proton‐hydrogen atom aurora by choosing the appropriate boundary conditions, namely, by setting the incident flux of one or the other particle population equal to zero. In the latter case, the new feature of the present model is the rigorous transport‐theoretic treatment of the contributions to ionization rates and to emission rates and yields from the secondary electrons produced by protons and hydrogen atoms. A coupled set of three linear transport equations is presented. Protons and hydrogen atoms are coupled only to each other through charge‐changing (charge exchange and stripping) collisions, while the electrons are coupled to both protons and hydrogen atoms through the secondary electrons that they produce. Source functions for the secondary electrons produced by the three primary particle populations are compared and contrasted, and the numerical methods for solving the coupled transport equations are described. Finally, formulas for calculating pertinent aurora‐related quantities from the particle fluxes are given. In the companion paper (Strickland et al., this issue), the model results are presented.

Bremsstrahlung X rays from Jovian auroral electrons

The spectrum of X rays from the planet Jupiter is calculated according to an auroral electron beam model. The electrons are assumed to be accelerated by a field‐aligned potential drop and penetrate into the atmosphere as a Maxwellian beam of primaries which are scattered, degraded in energy, and merged with a population of ionization secondaries having a power law energy distribution. The soft X rays observed by the Einstein Observatory satellite are due to bremsstrahlung from the secondary electrons in the H2 atmosphere. A good match to the X ray data is obtained if the power law spectral index of the secondary electrons, γe, is ≃2, yielding a power law slope for the photon flux γX = γe + 1 ≃ 3. The X ray intensity is best reconciled with a beam of primaries having a characteristic energy 30–100 keV and penetrating the homopause with an auroral energy flux typically of 10–20 ergs cm−2 s−1 but no greater than 50 ergs cm−2 s−1.

Modeled F region response to auroral dynamics based upon Dynamics Explorer auroral observations

Auroral images from the Dynamics Explorer 1 (DE 1) scanning auroral imager have been combined with in situ auroral precipitation data from the DE 2 low altitude plasma instrument to form a time‐dependent global auroral energy flux model. This model has both good time (12 min) and spatial (100 km) resolution compared to that currently available for global scale ionospheric and thermospheric modeling. The development and comparison of this model with others are discussed. Data from an aurorally active period, November 25, 1981, are presented and used as a case study for this model. Using a global ionospheric model, the effect of the DE auroral model is contrasted with that of a conventional empirical auroral energy flux model. Major differences in the modeled F region ionosphere are predicted from this comparative study. Specifically, F region densities differ by factors of two to four, while density boundary locations differ by up to 5° in latitude. The results indicate that “pixel size” auroral fine‐structure must be included in the global ionosphere and thermosphere models when they are tested against specific ground‐based or satellite data sets if an unambiguous result is to be obtained. The longer time constants of the F region are not enough to smooth‐out the auroral (spatial and temporal) dynamics.

Statistical and functional representations of the pattern of auroral energy flux, number flux, and conductivity

The Hardy et al. (1985) global patterns of the integral energy flux and average energy of precipitating auroral electrons are used to determine the global pattern of the electron‐produced, height‐integrated Hall and Pedersen conductivities. The conductivities were determined in spatial bins in magnetic local time (MLT)‐corrected geomagnetic latitude (CGL) coordinates for all MLTs and for CGLs greater than 50° and for seven levels of activity as measured by Kp. The conductivities vary smoothly with latitude and MLT typically having a single peak in latitude within the auroral oval at any MLT. On the nightside the two conductivities increase with increasing Kp. The largest conductivities are found near midnight, where the peak value of the Pedersen (Hall) conductivity varies from 3.09 (4.05) mhos to 12.5 (25.9) mhos as Kp varies from 0 to ≥6−. The peak conductivity decreases with MLT away from midnight with the lowest peak values found postnoon. At noon and on much of the morning side of the oval the Pedersen and Hall conductivities increase for Kp up to 2 and then decrease for higher Kp. The highest ratios of the Hall to Pedersen conductivity are on the morning side of the oval and at noon. The peak conductivities on the dayside are significant compared to the conductivities produced by solar radiation at all seasons of the year. The global maps of the integral energy flux, integral number flux, and height‐integrated Hall and Pedersen conductivities at each level of Kp were fit using both spherical harmonic and Epstein functions. The Epstein functions were found to reproduce better the original maps. At Kp = 2 the distribution of differences between the Epstein function fit and the original data is roughly symmetric about zero with a full width at half maximum of 16 (20)% for the Pedersen (Hall) conductivity and 32 (40)% for the integral energy (number) flux. The distribution of differences broadens with increasing and decreasing activity.