effects of high-latitude ionospheric electric field variability on

reported, based on NCAR/TIEGCM simulations of 20–30 January 1993, that the model neutral temperatures wereless than those observed by Millstone Hill incoherent scatterradar at 300 km by about 100K. For these simulations high-latitude forcing was specified with/without AMIE but with noadjustment to the Joule heating term. Fesen et al. [1997]suggested that an underestimate of high-latitude heating maybe the cause of the discrepancy and that an increase in theheating would also improve the agreement with electrondensity observations at Millstone Hill. Codrescu et al. (M. V.Codrescu et al., Validation of the coupled thermosphereionosphere plasmasphere electrodynamics model: CTIPE -MSIS temperature comparison, submitted to Space Weather,2007) (hereinfater referred to as Codrescu et al., submittedmanuscript, 2007) conducted a comprehensive comparisonof the global mean neutral temperature at 300 km betweenthe Mass Spectrometer Incoherent Scatter Radar (MSIS)�86 model [Hedin, 1987] and the Coupled ThermosphereIonosphere Plasmasphere Electrodynamics (CTIPe) model[Millward et al., 2001], and showed that the model temper-atures are always lower than the MSIS temperature when theempirical model of ionospheric convection of Weimer[1995] alone is used.[4] Challenges associated with specification of magneto-

spheric inputs remain obstinate in spite of recent improve-ments of monitoring and modeling of high-latitude globalconvection patterns, for example, by the Super Dual AuroralRadar Network (SuperDARN) HF radar [Greenwald, 1995],empirical models derived from in situ plasma drift measure-ments [e.g., Weimer, 2001; Foster et al., 1986; Heelis et al.,1982], and data assimilation techniques such as AMIE.Some of the difficulty originates from lack of comprehen-sive monitoring of upstream solar wind conditions and frominsufficient understanding of magnetospheric processes ofhighly dynamic and transient nature. Moreover, directobservations of ionospheric electrodynamic quantities aretoo spatially or temporally limited to adequately specifythese quantities globally.[5] The connection between the electric field variability

and the insufficient high-latitude energy input to the polarupper atmosphere in GCMs has drawn increasing attentionsince its quadratic effect on the Joule heating was pointedout by Codrescu et al. [1995]. They noted that the electricfield variability may not be adequately described by clima-tological empirical electric potential models [e.g., Weimer,2001; Foster et al., 1986], which are often used to drive thehigh-latitude ion drifts and to determine Joule heating ratein TIGCMs.[6] Their study has inspired a number of subsequent

studies to characterize the electric field variability fromground and space-based observations of the plasma driftvelocity. Codrescu et al. [2000] and Matsuo et al. [2003]have characterized the variability in terms of the samplestandard deviation from the mean determined by climato-logical empirical electric potential models, using plasmadrift measurements from the Millstone Hill incoherentscatter (IS) radar and the Dynamics Explorer-2 (DE-2)satellite, respectively. These studies have shown that theelectric field variability characterized as the standard devi-ation is of significant magnitude, often as large as the meanitself. Cosgrove and Thayer [2006] have shown the magni-tude of the variability, measured in terms of the standard

deviation estimated from the Sondrestrom incoherent scatterradar plasma drift measurements, scales linearly with the Kpindex. Regarding the temporal variation of the electric field,Crowley and Hackert [2001] conducted a spectrum analysisof AMIE convection patterns and concluded that a majorityof the variability arises from variations with periods lessthan 1 hour. Using the SuperDARN HF radar data Shepherdet al. [2003] have shown how the region of high temporalelectric field variability is associated with convection fea-tures such as the cusp, convection throat, and convection-reversal boundaries. On the other hand, based on theanalysis of DE-2 across-track plasma drift measurementsJohnson and Heelis [2005] reported that spatially structured(<128 km) plasma drift velocities were more likely to befound in areas of strong gradients in the bulk drift velocity.Regarding the high-latitude ionospheric electric field var-iability as turbulence or self-similar spatial structures,Golovchanskaya et al. [2006] have demonstrated therelationship of turbulent structures in the electric field tothe Field Aligned Current (FAC) using the DE-2 electric andmagnetic field measurements.[7] The electromagnetic energy transfer process between

the magnetosphere and ionosphere can be expressed accord-ing to Poynting’s theorem:

@w

@tþr � E� B

m0

� �þ J � E ¼ 0 ; ð1Þ

where w is the electromagnetic energy density, m0 refers tothe magnetic permeability of free space, E is the electricfield in the Earth frame of reference, B is the magnetic field,and J is the ionospheric current density [e.g., Thayer andVickrey, 1992]. Under steady state conditions, the conver-gence or divergence of the Poynting flux r � (E � B/m0)that refers to the electromagnetic energy flux flowing into/out of the ionosphere from/to the magnetosphere balanceswith the energy dissipated (J � E > 0) or generated (J � E <0) within the ionosphere. In this case the divergence ofPoynting flux E � B/m0 equals the divergence of theperturbation Poynting flux E � dB/m0, where dB = B � B0,B0 is the geomagnetic main field derived from a magneticpotential, and E is electrostatic and therefore also expressedas the negative gradient of a potential. E � dB/m0 isusually downward above the ionosphere and small belowthe ionosphere, and therefore usually converges within theionosphere. Most of the energy is deposited where thePedersen conductivity is large, around 110–160 km altitudeunder sunlit or auroral conditions. The electromagneticenergy transfer rate J � E can be divided into two terms as

J � E ¼ J � Eþ U� Bð Þ þ U � J� Bð Þ ; ð2Þ

where U is the wind velocity. The first and second termson the right respectively denote the total Joule heating rateand the mechanical energy transfer rate due to the workdone to the neutral atmosphere by the Lorenz force or ion-drag force J � B. Whether electromagnetic energy isconverted to the mechanical energy of the neutral gas (sink)or is generated by the neutral wind dynamo (source) ismanifested as a positive/negative sign of U� (J � B).

A07309 MATSUO AND RICHMOND: EFFECTS OF ELECTRIC FIELD VARIABILITY

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Because of the large inertia of the neutral gas compared tothe ions, the response of neutral winds to changes in ion-drag force is not immediate.[8] The goal of this study is to investigate effects of high-

latitude ionospheric electric field variability on both globalJoule heating rate

RJ�(E + U � B) dV and mechanical

energy transfer rateRU�(J � B) dV by incorporating

realistic spatial and temporal characteristics of electric fieldvariability into the forcing of a thermosphere ionosphereelectrodynamic general circulation model. Spatial and tem-poral coherence of the electric field variability is expected toinfluence neutral wind feedback effects on the electromag-netic energy transfer processes which were previouslyexamined numerically by Thayer et al. [1995] and Lu etal. [1995] without consideration of the electric field vari-ability. In general circulation modeling studies by Codrescuet al. [2000] and Codrescu et al. (submitted manuscript,2007) the effects of the electric field variability was exam-ined without accounting for the spatial and temporal coher-ence of the variability.[9] In a stochastic modeling approach presented in this

study, the electric field forcing is given by the sum of theclimatological mean determined by Weimer [2001], thevariability on scales above the resolution of general circu-lation model (resolved-scale), and the subgrid-scale vari-ability. While the subgrid-scale electric field variability isconsidered to be uncorrelated in space and time, weprescribe spatial and temporal correlation of the resolved-scale electric field variability by using a covariance modelobtained from statistical analyses of the comprehensive dataset of DE-2 along-track and cross-track plasma drift meas-urements. In order to adaptively estimate parameters of thecovariance model for a particular event of 10 January 1997,observations of electromagnetic variables taken during thisperiod are also used. In the numerical experiments con-ducted in this study with the NCAR/TIEGCM no arbitraryfactor is used to alter the global Joule heating rate tocompensate for the insufficient magnetospheric energyinput represented by the climatological model alone.

2. DE-2 Electric Field Observations

[10] The DE-2 spacecraft was launched into a 90� inclina-tion low-altitude orbit (perigee: 309 km, apogee: 1012 km,and period: 98 minutes) in August 1981, and the missionlasted until February 1983. The DE-2 data set used in thisstudy includes the 1.5 years (from day 249 in 1981 to day47 in 1983) of the complete bulk ion drift velocity V, whichwas obtained by combining the along-track velocity fromthe Retarding Potential Analyzer (RPA) [Hanson et al.,1981] with the cross-track velocity from the Ion Drift Meter(IDM) [Heelis et al., 1981] with the resolution of 3.8 km(0.5 s). E is then computed from the plasma velocity V andthe International Geomagnetic Reference Field (IGRF)model magnetic field B0 according to E = � V � B0.(See Matsuo et al. [2003] for more information on process-ing of the DE-2 data.)

2.1. Residual Field

[11] In this study we first characterize the residual field,which is left after subtracting the smooth mean electric fieldpredicted by the climatological model of ionospheric con-

vection [Weimer, 2001] from the DE-2 electric field. Byexamining the residual field, we intend to elucidate theinadequacy of commonly used empirical electric potentialmodels [e.g., Weimer, 2001; Foster et al., 1986; Heelis etal., 1982] to describe the degree of observed electric fieldvariability. The residual field is given as

E0 r; tð Þ ¼ E r; tð Þ � E r; tð Þ ; ð3Þ

where E (r, t) denotes the mean field, r refers to the locationon the polar plane. For the sake of analysis, it is presumedthat the electric field variation observed during a givensatellite traverse over the polar region (20 minutes)represents purely spatial variations, and that t is the centraltime of the traverse. The hourly IMF and solar wind data(composed of both Interplanetary Monitoring Platform 8and International Sun-Earth Explorer 3 satellite measure-ments) are employed to invoke the electric potential modelof Weimer [2001] for a given DE-2 orbital path. Figure 1ashows the along-track field E for a given DE-2 satellitetraverse and the predicted mean electric field by Weimer[2001]. The residual electric field E0 for the same path isshown in Figure 1b. Note that the residual electric field(especially on resolved-scales defined below) depends on agiven choice of the empirical electric potential model.Additionally, the resolution and accuracy of solar windobservations that are used to evoke the model of Weimer[2001] will also influence the result shown in this study.

2.2. Resolved and Subgrid Scales

[12] To facilitate statistical modeling of the spatial andtemporal coherence of residual electric field variability, theresidual field is further decomposed into resolved- andsubgrid-scales as follows. (Remember that we can onlyprescribe the space-time structures of the variability onscale sizes above the general circulation model resolution.)

E0 r; tð Þ ¼ E0r r; tð Þ þ E0

s r; tð Þ ; ð4Þ

and E0s (r, t) and E0

r (r, t) are defined as

E0s r; tð Þ ¼

Z 1

kc

E0 k; tð Þeikrdk ; ð5Þ

E0r r; tð Þ ¼

Z kc

0

E0 k; tð Þeikrdk ; ð6Þ

where E0s and E0

r denote subgrid-scale and resolved-scaleelectric fields for a given pass at t,k is wave number and kcis the cutoff wave number that corresponds to double theTIEGCM grid size (5�), and spectral elements E0(k,t) arecalculated from a windowed Fourier transform applied tothe residual electric field on a pass-by-pass basis. All theDE-2 data except for the passes with sample length shorterthan 400 km are included in the analysis. Note that thecutoff wave number used in this study is purely dictated bythe grid size of general circulation model of our choice.Even though the spectral analysis reveals that the powerfalls off quickly with decreasing scale size, mostlyaccording to a power law, as shown in the middle panels


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of Golovchanskaya et al. [2006, Figure 1] no particularspectral signature at this cutoff wave number is detected. InFigures 1c and 1d, the subgrid-scale residual electric fieldE0

s(r,t) (i.e., high-pass filtered data) and the resolved-scaleresidual electric field E0

r(r,t) are shown for the same path asfor Figures 1a and 1b.

2.3. Subgrid Scale Electric Fields: Seasonal andIMF Clock Angle Dependence

[13] Filtered data are binned according to their magneticlocal time (MLT) and magnetic latitude (mlat) location, withthe bin size 5� in mlat and 1 hour in MLT at the lowestlatitude, in the same manner as by Matsuo et al. [2003].

Figure 1. Example of spectral analysis of the DE-2 electric field observation: (a) the along-trackcomponent of electric field observed every 0.5 s along the DE-2 satellite orbital path (black) and theprediction of the Weimer [2001] model (gray), at UT 1030–1055 on Day 269 in 1981 (under southwardIMF conditions). (b) The residual electric field: the along-track component of electric field observedevery 0.5 s along the DE-2 satellite orbital path, minus the prediction of theWeimer [2001] model. (c) Thesubgrid-scale residual electric field: the high-pass filtered residual electric field with the cutoff wavenumber corresponding to 10�. (d) The resolved-scale residual electric field: the residual electric fieldminus the high-pass filtered residual electric field with the cutoff wave number corresponding to 10�.


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Furthermore, the data are sorted for four interplanetarymagnetic field (IMF) clock angles, where the clock angleis given by the phase angle of Bz + iBy (i =

ffiffiffiffiffiffiffi�1

p), By and

Bz being Geocentric Solar-Magnetospheric (GSM) IMFcomponents, and are also sorted for winter, equinox, andsummer conditions, which are defined in terms of the dipoletilt angle toward the Sun in the GSM X-Z plane (>12.35�for summer conditions and <�12.35� for winter condi-tions). Hourly IMF data are used for sorting.[14] Figures 2, 3, and 4 display the root-mean squared

(RMS) subgrid-scale electric field E0s(r,t) estimated for each

of the mlat-MLT bins. In general the subgrid scale electricfield is largest in winter and smallest in summer. Underwinter conditions its magnitude is the most pronounced inthe prenoon sector when the IMF orients northward. Thisis consistent with the finding reported by Golovchanskayaet al. [2006] for the DE-2 all-season Vector Electric FieldInstrument (VEFI) along-track electric field for the scale of3.8 km. (In our study the subgrid-scale electric field isintegrated over scales between 3 km and 500 km.)Golovchanskaya et al. [2006] show that this prenoonsector of strong turbulence collocates with the center of the

upward northward Bz (NBZ) current. Morphologicallyspeaking, it appears that the subgrid-scale electric field isalso prevalent in the vicinity of the region 1 (FAC) based onthe similarity of the RMS shown in Figures 2–4 to Figure 2 ofGolovchanskaya et al. [2006]. We find that E0

s on the dawnside, where the region 1 is downward, is slightly larger thanon the dusk side.[15] Figures 5a–5c respectively show the RMS values of

the residual electric field E0(r,t), the resolved-scale electricfield E0

r(r,t), the subgrid-scale electric field E0s(r,t), esti-

mated for the entire high-latitude region above 60�, as afunction of four IMF clock angles for winter and summerconditions. (Note that the polar average of the residualelectric field E0

r(r,t) is estimated higher than that by Matsuoet al. [2003], because some of the samples were excludedfrom the total DE-2 electric field data set for the sake ofspectral analysis described above.) The magnitude of thesubgrid-scale electric field is greater when the polar regionis in darkness, whereas the resolved-scale electric fieldexhibits small seasonal variation. The contribution of thesubgrid-scale electric field to the mean squared residualelectric field is the largest under winter northward IMF

Figure 2. Root mean squared subgrid-scale electric field estimated at each of mlat-MLT bins for fourIMF clock angles during winter conditions: IMF Bz positive, IMF By positive, IMF Bz negative, IMF Bynegative in clockwise from the top.


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conditions (about 50%) and is smallest under summer south-ward IMF conditions (about 20%). On the other hand, theelectric field on scales larger than 500 km is less dependenton the background ionospheric electric conductance.

3. Electric Field Driver

3.1. Multivariate Normal Model of ResidualElectric Field

[16] In this study we use a multivariate normal model tocharacterize the variability of the residual field, which ispresumed to be composed of the subgrid-scale field E0

s thatis treated as being uncorrelated in space and time and theresolved-scale field E0

r with space-time coherence. Here, E0s

and E0r are assumed to be independent of each other and of

E. The electric field driver for TIEGCM simulations pre-sented later is then given as

E r; tð Þ ¼ E r; tð Þ þ E0 mð Þr r; tð Þ þ E0 mð Þ

s r; tð Þ ð7Þ

where E is the mean electric field specified by aclimatological electric potential of Weimer [2001], andE0r(m) and E0

s(m) respectively refer to the mth realizations of

random normal (Gaussian) fields, sampled from thefollowing multivariate normal distributions:

E0 mð Þr r; tð Þ N 0;FT

nr~Anttn tð ÞFnr

� �; ð8Þ

E0 mð Þs r; tð Þ N 0;s2 r; tð Þ

� �; ð9Þ

where N (0, X) signifies a random sample out of the normalprobability distribution with zero mean and covariance X,Fnr

T Anttn(t)Fnr is the time-dependent space-time nonsta-tionary covariance, Fnr denotes a set of n empiricalorthogonal functions (EOFs) evaluated at location r,Anttn(t) refers to the 4th-order covariance tensor, which issimplified as the time-dependent covariance matrix for timefor each order of the EOFs in this study (i.e., if an elementof Anttn(t) is given by Anititjnj

(t) where ti and tj refer to ith andjth discrete time element and ni and nj refer to ith and jthorder of EOFs, Anititjnj

(t) is simplified as Atitj(t,n) where ni = nj

given below), and s denotes the standard deviation atlocation r and time t. The orthogonal functions F are givenby the EOFs of Matsuo et al. [2002]. For this study the EOFanalysis is repeated using the residual field E0(r,t) where themean is determined by the climatological model of Weimer

Figure 3. Same as Figure 2 but during equinox conditions.


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[2001] instead of the sample mean as by Matsuo et al.[2002]. s(r,t) is specified using the RMS values of E0

s

estimated from the DE-2 observations, as shown for fourIMF clock angles and three seasons in Figures 2–4 butweighted according to the magnitude of IMF

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiBy2 þ Bz2

pas well.

3.2. Covariance Model

[17] While the spatial coherence of the residual electricfield is characterized by EOFs, its temporal coherence isrepresented by an e-folding factor specific to each EOF. Weuse a power law model to describe the variance of the EOFcoefficients and a double exponential function to specify the

Figure 4. Same as Figure 2 but during summer conditions.

Figure 5. (a) Polar average of the root mean squared residual electric fields, which is estimated at eachmlat-MLT bin, for four different IMF clock angle criteria is displayed for winter and summer conditionsby solid and dashed lines, respectively. (b) Polar average of the root mean squared resolved-scale electricfields. (c) Polar average of the root mean squared subgrid-scale electric fields.


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temporal coherence of each of the EOFs. For a given EOForder n and at time t the nonstationary temporal covarianceis

Atitj t; nð Þ ¼ q1 tð Þn�q2 tð Þexp �jti � tjj=q3 nð Þ� �

ð10Þ

where n is the order of EOFs, q1 and q2 are time-dependentparameters of the power law model, and q3(n) is thetimescale for each of the EOFs. In equation (10) thecorrelation of nth EOF coefficient specified by exp(�jti �tjj/q3(n)) is stationary in time (i.e., it only depends on the lagtime distance jti � tjj), but nonstationarity is introducedthrough the time-dependent variance q1(t) n

�q2(t).[18] The power law model for the variance of EOF

coefficients is based on the analysis of EOF coefficientsobtained from the DE-2 data by Matsuo et al. [2002]. Onthe other hand, in order to make the covariance parametersq1(t) and q2(t) adaptive to the geophysical conditions on 10January 1997, these parameters are estimated by the max-imum-likelihood method from electromagnetic observationsduring this period (see in section 4), as has been describedby Matsuo et al. [2005]. It should be pointed out that in thisstudy we took 1-hour running mean of maximum-likelihoodestimates of q1 and q2 obtained at each 5-minute time stepby Matsuo et al. [2005]. The e-folding timescale for eachEOF, q3(n), is then computed from the auto-correlationanalysis of the EOF coefficients obtained by Matsuo et al.[2005].

4. 10 January 1997

[19] TIEGCM experiments presented in this study areconducted under the geophysical conditions of the magneticcloud event that occurred on 10 January 1997. In responseto the interplanetary magnetic cloud that hit the Earth in theearly hours of 10 January a geomagnetic storm (a minimumDst of about �85 nT) developed and persisted for the rest ofthe day. During this geomagnetic storm there was substan-tial substorm activity (a maximum AE of about 2000 nT).The polar ionospheric response to this magnetic cloud eventhas been investigated by Lu et al. [1998] using the AMIEprocedure, and the response of the thermosphere andionosphere has been previously simulated using theTIEGCM by Lu et al. [2001]. Our intention here is to focuson the difference in the thermospheric response due to theeffects of residual electric field variability, rather thanreproducing the event study of Lu et al. [2001]. Theobservations available during the period of 9–11 January1997, are used to estimate the covariance parameters (q1 andq2), or in other words, spatial and temporal characteristics ofthe residual electric field, but not to estimate the mean stateitself.[20] In order to incorporate realistic temporal and spatial

coherence of the residual electric field into the TIEGCMsimulations, the covariance parameters q1 and q2 are adap-tively estimated by the maximum likelihood method usingthe observations of various high-latitude electrodynamicvariables available during the period of 9–11 January1997 [Matsuo et al., 2005]. The data set includes thecross-track plasma drift measurements taken by the IDMon board the DMSP F12 and F13 satellites and averaged to20-s resolution, the plasma drift measurements from six

SuperDARN high frequency (HF) radars located in thenorthern hemisphere at about 2-minute resolution as wellas from Sondrestrom incoherent scatter (IS) radar at about5-min resolution, and the 5-minute averaged magneticperturbations observed at 119 ground magnetometer sta-tions. (See Lu et al. [1998] for details.)

5. TIEGCM Simulations

[21] Effects of high-latitude ionospheric convection onboth resolved and subgrid scales (defined above) on theestimation of mechanical energy transfer rate and Jouleheating rate are investigated. We incorporate the character-istics of residual electric fields derived from observationsinto the forcing of the TIEGCM. As described in section 3.1the variability of the residual electric field is characterizedas multivariate normal random fields, and their statisticalcharacteristics are derived from the combination of the DE-2 electric field data and several types of measurements ofionospheric electrodynamic quantities available during 10January 1997.[22] The TIEGCM solves the neutral and plasma dynam-

ics by including the dynamo effects of thermospheric windson electric fields and currents in a self-consistent manner. Itis developed by Richmond et al. [1992] as an extension ofthe thermosphere-ionosphere general circulation model(TIGCM) of Roble et al. [1988], and uses a realistic geo-magnetic field geometry (i.e., magnetic Apex coordinates[Richmond, 1995]). The model calculates global distributionsof neutral gas temperature, winds, mass mixing ratios of themajor constituents O2, N2, and O, and of the minor constit-uents N(2D), N(4S), NO, He, and Ar. The Eulerian model ofthe ionosphere solves for global distributions of electron andion temperatures and number densities of O+, O2

+, NO+, N2+,

N+ in mutual coupling with the thermosphere at every timestep and at each point of geographic grid. The TIEGCM has a5� latitude by 5� longitude grid with 25 constant pressuresurfaces between approximately 95 km and 500 km altitude,with a vertical resolution of 2 grid points per scale height.The model requires the specification of the following externalforcings: the solar EUV and UV spectral irradiance, auroralparticle precipitation, the convection electric field at high-latitudes, and upward propagating tides and other disturban-ces from the middle atmosphere. The auroral particle precip-itation is prescribed in terms of a Maxwellian energydistribution characterized by its mean energy and total energyflux [Roble and Ridley, 1987], and the effects of auroralionization (height-resolved auroral conductivities) are incor-porated in the TIEGCM. The location, diameter, and width ofthe auroral oval is specified in a similar manner as explainedby Roble and Ridley [1987]. The tidal forcing from the loweratmosphere is set by the Global Scale Wave Model clima-tology [Hagan and Forbes, 2002]. The solar radiation flux isparametrized in terms of the F10.7 index. On 10 January1997, which is during a minimum of the sunspot cycle, theF10.7 index is recorded as 72.9 � 10�22W/m2/Hz. Inthe current study the time step of the TIEGCM is set to1 minute.[23] Note that the models of auroral precipitation and of

electric field variability are specified independently, basedon separate statistical information about each. In this studythe manner in which the auroral precipitation is specified


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does not explicitly take into account any spatial correlationsthat may exist between the precipitation and the electricfield variability, since such correlations have not yet beenadequately determined over the entire high-latitude regionfor the variety of geophysical conditions simulated. Itremains to be determined whether or not spatial correlationsbetween the precipitation and electric field variability mayhave a significant effect on the energy input and thermo-spheric response.

5.1. Mechanical Energy Transfer Rate

[24] While the ions respond to changes of electric fieldforcing instantaneously, the neutral species have consider-able inertia at thermospheric heights. For example, it takesthem on the order of 2–3 hours to fully respond to the ion-drag force about 150 km in the sunlit or auroral ionosphere.Therefore the momentum transfer from the ion-drag forcingto the neutral species becomes more effective when the ion-drag force has some persistence in time, making theirresponse sensitive especially to temporal scales of electricfield forcing.[25] To highlight the effect of space-time coherence or

incoherence of the electric field forcing on the mechanicalenergy transfer rate, the first set of TIEGCM experiments isconducted with two sets of resolved scale electric fieldrandom fields: one given by equation (8) and the other onewith the same variance but without space-time correlation.Figure 6 displays the hemispherically integrated mechanicalenergy transfer rate from the control simulation with themean electric field in black and from the two simulationswith uncorrelated/correlated electric field plus the mean inred/blue. With consideration of the space-time structure, the

residual electric fields become more effective in influencingthe neutral winds and therefore affecting the estimate of themechanical energy transfer rate. On the other hand, theuncorrelated electric fields modulate the mechanical energytransfer rate about its control level by a small amount.[26] The second set of experiments is designed to exam-

ine how the effect of the correlated electric field forcing onthe mechanical energy transfer rate manifests differently inwinter (northern hemisphere) and summer (southern hemi-sphere). As suggested from Figure 5, the resolved-scaleelectric fields exhibit small summer-to-winter variation, andhence the same resolved scale electric field random field isapplied to both hemispheres. 20 realizations of multivariatenormal random fields (i.e., E0

r(m) where m = 1–20) is

sampled from the multivariate normal distribution (8). InFigures 7a–7b the hemispherically integrated mechanicalenergy transfer rate is shown for the winter and summerhemispheres, respectively. The mechanical energy transferrate from the control simulation is shown in black, and theone from simulations with 20 realizations of the resolved-scale random electric fields plus the mean are shown in bluewith their ensemble mean in red. The ion-drag forcing thatvaries in a spatially temporally organized manner has anopposite impact between two hemispheres. It is more likelyto act to decrease the mechanical energy transfer rate fromthe control level in the winter, but on the other hand in thesummer it tends to increase it. Because the ion-drag coef-ficient is higher in summer due to the higher backgroundelectron density at the altitudes below 200 km where mostof the energy transfer occurs, the momentum transfer fromthe ions to the neutrals is more effective in summer.Ponthieu et al. [1988] has shown from the analysis of

Figure 6. Mechanical energy transfer rate computed in TIEGCM simulations during 10 January 1997.The result from the control simulation only with the mean electric field forcing is shown in black. Thealtered estimation of mechanical energy transfer rate due to an additional forcing of temporally andspatially correlated/uncorrelated random residual electric field on resolved scales is shown in blue/magenta.


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DE-2 and AE-C plasma and neutral density observationsthat the timescale for the neutrals to respond to the ion-dragforcing is significantly shorter in summer (on the order of100 minutes) than in winter hemisphere (on the order of1000 minutes) during solar minimum. It therefore acceler-ates stronger winds but also makes the neutrals more likelyto follow the variable ion-drag forcing. Remember that themechanical energy transfer rate is given as a dot-product ofthe neutral wind U and the Lorenz force J � B and that theion-drag acceleration is given as J � B/r, where r is the gasdensity. In the winter the neutral winds are less likely tofollow the variable ion-drag forcing due to the lower ion-drag coefficient. Why the addition of forcing associatedwith E0

r results in a net decrease rather than increase of totalmechanical energy transfer rate in the winter hemisphere isunclear. We suspect it is related to the fact that ion-drag-driven winds in the polar regions do not respond linearly tothe forcing, owing to the nonlinear influence of momentumadvection [e.g., Fuller-Rowell and Rees, 1984; Gundlach etal., 1988; Walterscheid and Brinkman, 2003; Kwak andRichmond, 2007].[27] In the last set of TIEGCM experiments, the effect of

both resolved and subgrid-scale residual electric fields on themechanical energy transfer rate is examined. Figure 8 dis-plays in blue the ensemble mean of mechanical energytransfer rate computed from 20 simulations forced respec-tively by the sum of a sample of uncorrelated subgrid-scalerandom electric fields (9), a sample of correlated resolved-scale random electric fields (8), and the mean. As reference,the ensemble mean (red line) shown in Figure 7 is plotted inred in Figure 8 as well. It is clear that the subgrid-scaleelectric field, modeled here as space-time incoherent Gauss-

ian random fields, has little impact on the mechanical energytransfer rate.

5.2. Joule Heating Rate

[28] From the last set of TIEGCM experiments, the Jouleheating increase due to the residual electric field is inves-tigated for both resolved and subgrid scales. The uncorre-lated subgrid-scale electric field has little impact on themechanical energy transfer rate but acts as a significantextra heat source for the neutral atmosphere. The subgrid-scale random electric field has a different magnitude betweenwinter and summer hemispheres, reflecting the respectivesample standard deviation shown in Figures 2–4. On theother hand, the same resolved-scale electric field is applied tothe winter and summer hemispheres. Figures 9a–9b show thehemispherically integrated Joule heating rate estimated for10 January 1997 in northern (winter) and southern (summer)hemispheres. Again, the result is presented in terms of theensemble mean of the 20 simulations: the control simulationresult shown in black, the ensemble mean of the simulationswith resolved-scale residual electric fields plus the meanshown in red, the ensemble mean of the simulations withboth resolved-scale and subgrid-scale residual electric fieldsplus the mean shown in blue.[29] The additional Joule heating due to the subgrid-scale

electric field becomes relatively more important duringgeomagnetically quiet periods, whereas during geomagnet-ically active periods the spatially temporally structuredelectric field on resolved scales plays a dominant role ingenerating additional Joule heating. Because of the highersolar EUV-induced electric conductance in the summer, theJoule heating from the control simulation is estimated to behigher in the summer hemisphere. In contrast, the Joule

Figure 7. Mechanical energy transfer rate computed in TIEGCM simulations during 10 January 1997.The result from the control simulation only with the mean electric field forcing is shown in black. Themechanical energy transfer rate obtained from simulations with an additional forcing of correlatedrandom residual electric field on resolved scales is shown in blue. Here, the TIEGCM simulation isrepeated with 20 independent draws of the multivariate normal distribution for the resolved-scale residualfield. The ensemble mean of 20 simulation results is shown in red.


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heating due to the residual electric field is larger, on theaverage, in the winter hemisphere, mainly because thesubgrid-scale electric field magnitude is larger in the winter.Our result needs to be interpreted with caution, as we are

not taking account of effects of correlation between theconductance and the electric field. Nonetheless, it is inter-esting to note that with inclusion of the residual electricfield into the TIEGCM electric field forcing, the global

Figure 9. Joule heating rate computed in TIEGCM simulations during 10 January 1997. The blue line isthe ensemble mean computed from 20 simulations forced respectively by the sum of a sample ofuncorrelated subgrid-scale random electric fields given by equation (9), a sample of correlated resolved-scale random electric fields given by equation (8), and the mean. The Joule heating rate due to anadditional forcing of correlated random residual electric field on resolved scales and of uncorrelatedrandom residual electric field on subgrid scales is shown in blue in terms of the ensemble mean of 20simulations. The red line is the ensemble mean computed from 20 simulations forced withoutuncorrelated subgrid-scale random electric fields (i.e., the sum of a sample of correlated resolved-scalerandom electric fields given by equation (8) and the mean).

Figure 8. Mechanical energy transfer rate computed in TIEGCM simulations during 10 January 1997.The same as in Figure 7 except that the ensemble mean of 20 simulation results with an additional forcingof both correlated random residual electric field on resolved scales and uncorrelated random residualelectric field on subgrid scales is now shown in blue.


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Joule heating rate is estimated to have similar magnitudes inthe winter and summer hemispheres.[30] Although not shown, the electromagnetic energy

transfer rate is the sum of Joule heating rate and themechanical energy transfer rate (equation (2)), and it is verysimilar to the Joule heating rate shown in Figure 9. Note thatthe mechanical energy transfer rate is smaller by an order ofmagnitude than the Joule heating rate.

6. Discussion

[31] The subgrid-scale electric field, integrated overscales from 3.8 km to 500km in this study, shows a strongpreference toward the darker hemisphere. This behavior isgenerally consistent with the reported scale-dependent roleof the magnetospheric generator. According to the analysisof magnetic and electric field measurements on spatialscales between 80 km and 3 km from the HILAT satellitepresented by Vickrey et al. [1986], the magnetosphere tendsto act as a current generator imposing constant current onthe ionosphere, and therefore the electric fields on thesescales are likely to be anticorrelated with the magnitude ofthe solar-induced electric conductance. On the other hand,the global-scale current system is more likely to be imposedby the magnetosphere behaving as a voltage generator [e.g.,Fujii et al., 1981] so that the electric fields on large scalesare rather independent of the background ionospheric elec-tric conductance.[32] Furthermore, within discrete aurora arcs the electric

conductance has been reported to be anticorrelated with theelectric fields [de la Beaujardiere and Vondrak, 1982;Marklund, 1984; Mallinckrodt and Carlson, 1985]. TheJoule heating estimation from the simultaneous observa-tions of the electric field and conductance from Super-DARN and the GUVI UVI have also suggested the effectof anticorrelating electric field and conductance [Baker etal., 2004]. On the other hand, the Joule heating estimatedfrom simultaneous observations of the Low Altitude PlasmaInstrument electron flux and the IDM/RPA plasma driftswas affected very little by the positive/negative correlationof the electric field and conductance on average (Barbara A.Emery private communication, 2007). Even though theeffect of electric field variability on the Joule heating isquadratic and is considered to be of primary importance, thefact that the correlation between the electric conductanceand field is not taken into consideration in the current studypases a limitation on the quantitative interpretation of ourresults.[33] The seasonal variation of the residual electric field

reported by Codrescu et al. [2000], in which the magnitudewas found to be large during geomagnetically moderatelydisturbed conditions in winter and during severely disturbedconditions in spring, is consistent with the behavior of theRMS subgrid scale fields found in this study with respect tothe IMF clock angles under winter and equinox conditions.On the other hand, the RMS of the residual electric field onresolved scales (>500 km) shows small seasonal variation,but varies with respect to IMF clock angles and is thestrongest when the IMF is in the southward direction. Thissuggests its relationship to the geomagnetic activity level,and might be related to the strong dependence of theresidual electric field variability on the Kp index reported

in Cosgrove and Thayer [2006] might be more influencedby the variation of electric field on scales larger than500 km.[34] The current study is also limited in terms of the

spatial resolution of GCMs, which dictates our choice ofcut-off wavelength as 5�. Future studies with GCMs such asa thermosphere-ionosphere nested grid model developed byWang [1998] and a Global Ionosphere-Thermosphere Model(GITM) with an adaptive grid capability developed byRidley et al. [2006] can bring out further understandingon this topic. Using the GTIM Deng and Ridley [2007] hasshown that the increased model resolution (from 5� to1.25�) alone, without consideration of the residual electricfields, results in an increase in the neutral gas heating rate at200 km altitude by 20%.[35] Future modeling of the residual electric field E0

might benefit significantly by parametrizing its stochasticcharacteristics as a function of the bulk quantities such asFACs and the ionospheric convection and its gradient, andby adopting a nonnormal probability distribution model.Sporadic occurrence of strong heating, which would arisefrom a probability distribution with heavier tails, might havea substantial impact on the thermospheric mixing and windacceleration processes. In fact, Golovchanskaya et al.[2006] has reported a self-similar turbulent structure ofelectric field and its non-Gaussian signature from analysisof the power spectrum density and probability distributionfunction for DE-2 VEFI observations. This property canalso be taken into account in stochastic parametrization ofthe residual electric field in the future.

7. Conclusion

[36] The previous study by Matsuo et al. [2003] hasshown that the climatological electric potential model[e.g., Weimer, 2001] considerably underestimates the elec-tric field inferred from in situ plasma drift measurementsalong the DE-2 satellite trajectory, leaving residual fields aslarge as the mean climatological electric fields itself. Thismotivated us to further examine the spatial and temporalproperties of the residual fields, and their impact on theglobal thermospheric Joule heating.[37] A spectral analysis of DE-2 plasma drift measure-

ments has revealed that the subgrid-scale electric fieldcontributes to the residual fields to a significant extentespecially in the winter, and behaves in a manner distinctfrom that of the resolved-scale residual electric field withrespect to seasons and IMF-variation. The subgrid-scaleelectric field exhibits a strong seasonal variation, whereasthe resolved-scale electric field exhibits little. The relativecontribution of subgrid-scale electric fields is largest underwinter northward IMF conditions and is smallest undersummer southward IMF conditions.[38] The effects of the spatial and temporal coherence of

the residual electric field variability on the mechanicalenergy transfer rate as well as the Joule heating rate areexamined. Space-time correlated random fields are sampledfrom a multivariate normal distribution with the covariancemodeled based on the DE-2 observations as well as obser-vations during the storm period of 10 January 1997. Withconsideration of the space-time structure, the residual elec-tric fields become more effective in influencing the neutral


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winds and therefore affecting the mechanical energy transferrate. On the other hand, the uncorrelated electric fieldsmodulate the mechanical energy transfer rate about controllevel, but there is essentially no net neutral wind feedback tothe integrated mechanical energy transfer estimation (seeFigure 6).[39] The higher ion-drag in the summer due to higher

electron density at altitudes where most of the energytransfer occurs makes the momentum transfer in the summerhemisphere more efficient, and therefore the neutral windsare more likely to follow the varying ion-drag forcing. Inthe winter the neutral winds are less likely to follow thevariable ion-drag forcing due to lower ion-drag. Eventhough the size of the resolved scale electric fields iscomparable between winter and summer hemispheres, itsimpact on the mechanical energy transfer rate is hemispheri-cally asymmetric.[40] The Joule heating increase due to the residual electric

field is larger in the winter hemisphere mainly because thesubgrid-scale electric field magnitude is larger in winter.The Joule heating due to the subgrid scale electric fieldbecomes relatively more important during geomagneticallyquiet periods, whereas during geomagnetically active peri-ods the structured electric field on resolved scales plays adominant role in generating additional Joule heating.

[41] Acknowledgments. We thank Yue Deng for her helpful com-ments. This study was supported by NASA LWS grant NNH05AB54I.NCAR is sponsored by the National Science Foundation. The DE-2 datawere acquired from the NASA Data Archive and Distribution Service(NDADS) mass storage system at the National Space Science Data Center(NSSDC) using the SPyCAT Web interface. The IMF and solar wind datawere obtained from the NSSDC OMNIWeb.[42] Wolfgang Baumjohann thanks I. Golovchanskaya and Mihail

Codrescu for their assistance in evaluating this paper.

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��T. Matsuo, Cooperative Institute for Research in Environmental Sciences,

University of Colorado, Space Weather Prediction Center, 325 Broadway(W/N P9), Boulder, CO 80305, USA. ([email protected])A. D. Richmond, National Center for Atmospheric Research, P.O. Box

3000, Boulder, CO 80307, USA.


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effects of high-latitude ionospheric electric field variability on

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