Illumination of the plasmasphere by terrestrial very low frequency transmitters: Model validation

Illumination of the plasmasphere by terrestrial very low frequency

transmitters: Model validation

M. J. Starks,1,2 R. A. Quinn,3 G. P. Ginet,1 J. M. Albert,1 G. S. Sales,4 B. W. Reinisch,4

and P. Song4

Received 21 February 2008; revised 29 May 2008; accepted 2 July 2008; published 27 September 2008.

[1] A composite model of wave propagation from terrestrial very low frequency (VLF)transmitters has been constructed to estimate the wave normal angles and fields of whistlermode waves in the plasmasphere. The model combines a simulation of the fields in theEarth-ionosphere waveguide, ionospheric absorption estimates, and geomagnetic field andplasma density models with fully three-dimensional ray tracing that includes refraction,focusing, and resonant damping. The outputs of this model are consistent with those ofseveral previous, simpler simulations, some of which have underlying component modelsin common. A comparison of the model outputs to wavefield data from five satellitesshows that away from the magnetic equator, all of the models systematically overestimatethe median field strength in the plasmasphere owing to terrestrial VLF transmitters byabout 20 dB at night and at least 10 dB during the day. In addition, wavefield estimates atL < 1.5 in the equatorial region appear to be about 15 dB too low, although measuredfields there are extremely variable. Consideration of the models’ similarities anddifferences indicates that this discrepancy originates in or below the ionosphere, whereimportant physics (as yet not conclusively identified) is not being modeled. Adjustmentof the low-altitude field estimates downward by constant factors brings the model outputsinto closer agreement with satellite observations. It is concluded that past and future use ofthese widely employed trans-ionospheric VLF propagation models should be reevaluated.

Citation: Starks, M. J., R. A. Quinn, G. P. Ginet, J. M. Albert, G. S. Sales, B. W. Reinisch, and P. Song (2008), Illumination

of the plasmasphere by terrestrial very low frequency transmitters: Model validation, J. Geophys. Res., 113, A09320,

doi:10.1029/2008JA013112.

1. Introduction

[2] Large ground-based transmitters have operated in thevery low frequency (VLF) band below 30 kHz for decades,generally for maintaining communication with submarines.In addition to penetrating the Earth’s oceans, significantenergy from these transmitters also leaks through theionosphere, propagates in the whistler mode, and interactswith the population of stably trapped electrons in the Earth’sradiation belts [Vampola, 1977]. Inan et al. [1984] modeledthis anthropogenic process to compute regions of electronprecipitation as guidance for future ground-based experi-ments. To estimate its relative importance compared withnatural processes, Abel and Thorne [1998] developed asimple model of the combined contributions of all of the

major ground-based VLF transmitters to the decay of theradiation belts produced by the STARFISH high-altitudenuclear explosions in 1962. They concluded that terrestrialtransmitters significantly influence the energetic particledistribution at certain radiation belt L shells. This calcula-tion was later revisited for a space-borne VLF transmitter byInan et al. [2003].[3] As part of their model, Abel and Thorne used a

representation of the transmitter power distribution takenfrom Inan et al. [1984] and estimates of ionospheric VLFabsorption computed by Helliwell [1965]. These modelscontinue to find wide application; for example, they havealso been used to model the effects of lightning-producedVLF [e.g., Bortnik et al., 2003, 2006]. Together withvarious types of wave power propagators, these approxi-mations produce estimated values of transmitted VLFenergy in the plasmasphere. However, the results soobtained are far from definitive, lack systematic validation,and are inadequate for predicting quantitative effects ofspecific transmitters on specific particle populations whengood fidelity is required.[4] To address this need, and as part of a comprehensive

examination of ground-based VLF transmitter effects onradiation belt particles, we have taken the next step inestimating the strength of transmitter electric fields in the

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, A09320, doi:10.1029/2008JA013112, 2008

1Space Vehicles Directorate, Air Force Research Laboratory, HanscomAir Force Base, Massachusetts, USA.

2Now at Space Vehicles Directorate, Air Force Research Laboratory,Kirtland Air Force Base, New Mexico, USA.

3Atmospheric and Environmental Research, Inc., Lexington,Massachusetts, USA.

4Center for Atmospheric Research, University of Massachusetts,Lowell, Massachusetts, USA.

Copyright 2008 by the American Geophysical Union.0148-0227/08/2008JA013112

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plasmasphere. More physically realistic models of transmit-ter output and radio wave propagation, combined withestimates of ionospheric absorption, have been developedand are described in section 2, where they are contrastedwith some earlier models still widely used. In section 3,various combinations of the old and new models are used toproduce three-dimensional maps of VLF electric field dis-tributions within the plasmasphere, and the results com-pared to actual VLF measurements of terrestrial transmittersacquired by the Radio Plasma Imager (RPI) instrumentaboard the Imager for Magnetopause-to-Aurora GlobalExploration (IMAGE) satellite [Reinisch et al., 2000], theOGO 1 and OGO 2 spacecraft [Heyborne, 1966], DynamicsExplorer (DE) 1 (taken from Inan et al. [1984]), andDEMETER. The overall accuracy of the model outputs,possible sources of observed discrepancies and their impli-cations, and suggestions for further improvements to themodel are presented in section 4. We finish with a summaryin section 5.

2. Models

2.1. Transmitter Models

[5] Terrestrial VLF transmitter power in the ionospherehas typically been estimated by combining a model ofpower in the Earth-ionosphere waveguide with an estimateof ionospheric absorption. This approach is not strictlycorrect, as the coupling of waveguide modes below theionosphere into upwardly propagating power at higheraltitudes is a complex process requiring full-wave electro-magnetic solutions. Unfortunately, in addition to beingcomputationally intensive to produce, full-wave estimatesof transmitter power in the ionosphere are highly dependenton frequency, transmitter location, and details of the iono-spheric plasma, and no such globally applicable modelshave thus far emerged. We have therefore adopted the two-model approach for our effort.[6] A simple, commonly used waveguide power model is

the relation developed by Crary [1961] from explicitelectric field computations and adapted by Inan et al.[1984]. This model applies a straightforward attenuationwith distance from the transmitter, and produces power fluxestimates at 90 km altitude like those shown in Figure 1a forthe 21.4 kHz 423 kW Navy VLF transmitter NPM, locatedat Lualualei, Hawaii (20.4�N, 201.8�E). Figure 1 wasproduced for transmitter midnight. For this work, we usedthe more advanced LFCOM code (R. Rutherford and B.Gambill, LFCOM: A Fortran code for evaluation of spreaddebris effects on long wave propagation links, vol. 1: User’smanual, in preparation, 2005), maintained by the DefenseThreat Reduction Agency (DTRA), to calculate electricfields in the Earth-ionosphere waveguide over the entiresurface of the Earth and to validate the outputs of the Crarymodel. LFCOM is a mode-theory code that explicitlymodels most physical quantities that affect wave propaga-tion. The code provides a relatively detailed analysis of longwave propagation characteristics by using a high-accuracyEarth-ionosphere waveguide propagation model to producea realistic picture of electric field distributions over largeareas. These fields are then converted to equivalent powerflux below the ionosphere by assuming free space imped-ance. Figure 1b shows the LFCOM power flux distribution

at 90 km altitude from the NPM transmitter. The output ofthis model generally agrees in magnitude with the outputs ofthe similar LWPC code [Ferguson et al., 1989] and (in asmoothed form) with the Crary [1961] model, as shown bythe profile in Figure 1c, but naturally manifests fine detailsof the mode superposition caused by ionization gradientsand variations in magnetic declination.[7] To model ionospheric absorption of the upgoing VLF

transmissions, we apply the curves computed by Helliwell[1965, Figures 3–35], who used representative ionosphericdensity models and collision profiles and assumed verticallyincident waves. Technically of limited applicability, theseresults have long represented the state-of-the-art for VLFionospheric absorption estimates, but there is ongoing workto refine them using full-wave electromagnetic solutions[e.g., Hu and Cummer, 2006]. Helliwell generated curvesfor 2 kHz and 20 kHz for typical nighttime and daytimeconditions. In order to apply them on a global basis, they areinterpolated in frequency and extended to continuouslycover all local times. The latter is accomplished by applyinga sharp transition function between the day and night curvesas a function of the solar zenith angle. The transition isintended to mimic the rapid production and recombinationof plasma due to solar illumination of the D region, which isthe dominant source of VLF absorption. The resultingestimate of power transmitted through the ionosphere isshown in Figure 1d. When comparing model outputs tosatellite measurements in section 3, we always run themodels for the local times at which the measurements weremade.

2.2. Propagation Models

[8] The power flux values so obtained form the initialconditions for propagation codes that distribute the escapingVLF energy into the upper ionosphere and plasmasphere.Inan et al. [1984] introduces a ‘‘ducted’’ model of VLFpropagation, which is adopted by Abel and Thorne [1998].In this model, upgoing VLF is assumed to travel strictlyalong the Earth’s magnetic field, propagating with field-aligned wave normal vectors and diminishing in power asthe ratio of the local ambient magnetic flux to that at1000 km altitude. Inan et al. [1984] identify severaldeficiencies in this simple model, chief among which isthe complete lack of realistic information about the anglethat the VLF wave normals make to the backgroundmagnetic field, which is required information for computingwave-particle interactions. While VLF waves may propa-gate in field-aligned ducts, they more commonly propagatein a nonducted fashion in which their raypaths and wavenormal angles are determined by the slowly varying densityand magnetic field gradients [Smith and Angerami, 1968].For this reason, more recent work has adopted ray tracing asa more sophisticated method of wave propagation.[9] Two-dimensional ray tracing has been used for VLF

propagation modeling for some time [e.g., Inan and Bell,1977], although owing to its computational costs it is oftenavoided (as above) or applied only over a limited area. Two-dimensional tracing by necessity confines rays to themagnetic meridional plane, an approximation that is poorin the general case and difficult to validate in specific casesunless the initial wave normal angle of the incident wave isknown to lie within that plane. In addition, two-dimensional

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ray tracing cannot accurately model ray focusing or prop-agation through density irregularities that are not azimuth-ally symmetric. Fully three-dimensional ray tracing, such asthat used by Inan et al. [2003], is therefore preferred,despite the added computational burden.[10] To improve model fidelity, the work reported here

passes the power flux estimates described above to the AirForce Research Laboratory’s VLF Propagation Code (whichincorporates the Power Tracer of Starks [2002]) for propa-gation through the ionosphere and plasmasphere. The Pow-er Tracer combines a modular three-dimensional ray tracingprogram with algorithms that estimate power flux changesdue to divergence, focusing, and damping. Bundles of raysare traced from initial points spread over a 97,200-pointequal-area grid defined within the ionosphere and with

intensities given by the outputs of the transmitter andionospheric absorption models. As in the work of Starks[2002], no horizontal density gradients are postulated and itis assumed that owing to refraction the wave normals of theupgoing rays are initially aligned with the gradient of theionospheric density, i.e., in the radial direction. Rays arethen traced in the whistler mode into the plasmasphere untilthey reenter the ionosphere and are presumed lost. Althoughthe multispecies density (see below) and propagation mod-els support magnetospheric reflection [Kimura, 1966], itgenerally does not occur for whistler mode waves fromterrestrial transmitters of interest, which have relatively highfrequencies. The three-dimensional computation permitsraypaths to vary freely within and across magnetic meri-dians, subject only to the constraints imposed by the cold

Figure 1. The initial conditions models for the NPM transmitter at local midnight. (a) Output of theCrary relation used by Inan et al. [1984]. Mottling near the pole results from the equal-area grid.(b) Output of the LFCOM model showing mode structure. (c) Longitudinal section of Figures 1a and 1bthrough the transmitter latitude, showing agreement of the models. (d) LFCOM outputs at 150 kmaltitude, after applying ionospheric absorption curves.


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plasma dispersion relation. There are no field-aligned ductspresumed in this model.

2.3. Environment Models

[11] The accuracy of the Power Tracer depends heavilyon the two classes of environmental models used in thesimulation: ambient magnetic field and plasma density.Indeed, the effects of these models on the final powerdistribution are areas of active research [e.g., Quinn et al.,2006]. For the initial efforts at validating this propagationmodel, we have elected to use simple models that arecomputationally inexpensive. The quality of the modeloutputs, as established by the fiducial satellite measure-ments (see section 3), determines how much refinement isrequired to achieve sufficient accuracy (see section 4).[12] The Earth’s magnetic field is modeled using a tilted

offset dipole [Schmidt, 1934; Fraser-Smith, 1987], based onthe first eight Gauss coefficients of the International Geo-magnetic Reference Field (IGRF) [Peddie, 1985], epoch2000. The ambient magnetic field primarily affects thepropagation of whistler mode waves at higher altitudes,well above the strong density gradients of the ionosphere.As we shall see below, the overall envelope of the powerflux distribution is also controlled by the contour of thebackground magnetic field along which the electron cyclo-tron frequency equals the wave frequency. The tilted offsetdipole model is a good approximation to the actual geo-magnetic field at most of the latitudes of concern in thiswork. This was verified by performing a comparativetracing using the World Magnetic Model (WMM) [McLeanet al., 2004], another spherical harmonic model very similarto IGRF. Comparisons of power distributions for eachmodel (e.g., results similar to those illustrated in Figure 3discussed below) show that the differences introduced bythe simpler model are minor. The component of the geo-

magnetic field driven by magnetospheric components hasbeen ignored since it contributes less than 5% of theambient field at the highest altitudes and latitudes consid-ered in this study.[13] To model the ambient plasma environment, we

utilize a multispecies diffusive equilibrium density modelderived from a multifluid pressure balance equation, solvedusing the ‘‘temperature modified geopotential height’’approach of Angerami and Thomas [1964]. We haveneglected the centripetal force, but included the magneticforce along flux tubes [Chiu et al., 1979] and incorporated africtional ionosphere [Thomson, 1987]. The density distri-butions so derived are sensitive to the assumed temperaturegradients of the component species along the geomagneticfield lines, for which we use the simple form given byThomson [1987] (which yields an analytic solution). Thedensity is rolled off at a plasmapause location of L = 5.14, asgiven by Carpenter and Anderson [1992] for Kp = 1. Here,we model O+ and H+ as the ion species, where O+ dominatesin the Chapman-layer-like ionosphere [Chapman, 1931].Even in this ‘‘simple’’ form, this density model has six freeparameters. These parameters have been tuned so that thedensity falls off relatively quickly in the top-side and similarto the Carpenter and Anderson [1992] plasmasphere outsideL = 2. Some typical density profiles are shown in Figure 2.Through its input parameters, this model can be easily tunedto obtain different density distributions while remainingcomputationally efficient. In this study, we use two differentgeneral profile shapes labeled ‘‘dens-high’’ and ‘‘dens-low.’’Dens-low produces the Chapman layer profile with arelatively empty topside (�1000–6000 km) ionospheredescribed above; we use this as our standard model.Dens-high generates a very full topside ionosphere, similarto that used by Abel and Thorne [1998]; we use this toreveal any differences in VLF wavefield distributionsresulting from the density model.[14] The effects of resonant damping, which can signif-

icantly reduce whistler mode wave power at the frequenciesof interest [Thorne and Horne, 1994, 1996], have also beentaken into account. We follow the approach of Bortnik et al.[2003] and Bell et al. [2002], who postulate a continuouswarm electron population from 1 eV to 10 MeVon the basisof AE8 and Hydra data, then apply the method of Brinca[1972] to compute damping at every location within theplasmasphere. Like previous authors, we have found thatthe Landau and primary cyclotron modes are the onlyimportant contributors to damping of the waves of interest,although an arbitrary number of modes can be included inthe calculation.

2.4. Power Flux

[15] To compute the power flux at a given point in space,the magnetosphere has been partitioned into a set of volumeelements (voxels) one degree wide in latitude and longitudeand 120 km thick. In general, each voxel may containmultiple power flux values owing to multiple rays passingthrough it. Each ray may also have multiple data pointswithin the voxel, but the parameters associated with a givenray in a single voxel typically vary minimally and these maybe averaged. Since the power flux algorithm used gives anestimate of the power flux arriving in a voxel from aparticular initial location, the power flux from multiple rays

Figure 2. Equatorial profiles for the density models usedin this work, and the published models to which they havebeen fit.


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starting close to one another and arriving close togethermust be properly averaged since they represent the samewave packet. Conversely, the power flux from rayscorresponding to widely separated initial conditions repre-sent independent wave packets and should be summed,rather than averaged, to get the accurate total power fluxin the voxel. For the results presented in this paper we haveused the lower-bound-strongest (LBS) technique, wherebyonly the ray with the largest power flux is considered ineach voxel. This technique yields an approximate lowerbound on, and in most instances a good overall estimate to,the absolute wavefield in the voxel. The LBS estimate isquite good for terrestrial transmitters because rays that startfar from the LBS ray usually have wavefield strengths thatare comparatively smaller by orders of magnitude.[16] Typical output from the model is shown in Figure 3.

Both a meridional cross section (taken at the magneticlongitude of the transmitter, Figure 3a) and an equatorialcross section (Figure 3b) of the power envelope producedby the NPM transmitter are shown. Rays originating outsidethe plasmapause (at L � 5 here) have been suppressed.Several important features of this plot require explanation.First, propagating rays in the meridional plane are boundedby the Earth’s magnetic field and the whistler mode disper-sion relation, which restricts propagating waves to areaswhere the wave frequency is below the electron gyrofre-quency (enclosed by a dotted line in Figure 3). In practice,this boundary strongly refracts rays that approach it andproduces an exterior caustic that defines the outer extent ofthe power envelope. Note that as a result of this refraction,there are regions at high altitude (but within the cyclotronfrequency boundary) into which the NPM transmitter isunable to directly propagate any wave energy at all.

[17] The rays that encounter this caustic produce the mostremarkable feature of the power distribution, the shadowboundary indicated by the arrow in Figure 3a. Once abovethe ionosphere, rays from the northern hemisphere trans-mitter are constrained to propagate largely along the geo-magnetic field line upon which they originate, althoughcrossing to somewhat higher L shells. At higher latitudes,they propagate upward until they reach a location where theelectron gyrofrequency approaches the wave frequency. Asthey near this point, the rays refract sharply toward lowerL shells, cross the magnetic equator, and continue into theconjugate (southern) hemisphere along a downward, Lshell-crossing trajectory. This creates an abrupt shadowboundary in the conjugate hemisphere, beyond which themore powerful rays directly propagating from the trans-mitter do not reach. Beyond this boundary, wave energy inthe plasmasphere comes exclusively from comparativelyweaker rays propagating up through the conjugate iono-sphere. There is an analogous shadow boundary producedby upgoing rays from the southern hemisphere, but it isinvisible in Figure 3a owing to the relative weakness ofthose signals, which have traveled far from the transmitterin the Earth-ionosphere waveguide before penetrating intothe plasmasphere. It should be noted, however, that theboundary would be visible in satellite measurements thatare suitably resolved in wave vector.[18] The theory of these boundaries is rooted in catastro-

phe optics, and they cause significant problems for the raytracing technique because the geometric optics approxima-tion breaks down along the caustic, causing power fluxestimates to tend toward infinity. In reality, the wavefieldsproduce an Airy pattern approaching the caustic, andevanescent wave energy extends across and beyond the

Figure 3. Cross sections of the model 1 power flux outputs for the NPM transmitter (indicated by theorange triangle). (a) Meridional section, showing plasmapause, shadow boundary, and typical satellitetrajectories. The dotted line is the contour where electron cyclotron frequency equals the transmitterfrequency (b) equatorial section, manifesting local time dependence and the mapping of LFCOMstructure into space. Note the low-altitude region of weak power flux near the equator.


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caustic as an inhomogeneous wave [Budden, 1985]. In thismodel, we have taken steps to identify regions of unphysicalfocusing along the caustic and artificially limited the result-ing ray power flux. This involves watching for the devel-opment of an additional inflection point in the localrefractive index surface and preventing further wave focus-ing beyond that point along the raypath.[19] In section 3 we show that despite the Power Tracer’s

difficulties near the caustic, it is not merely a computationalartifact. Satellite VLF measurements demonstrate featuresconsistent with the shadow boundary, similar to thoseproduced by our model. The caustic and resulting shadowboundaries do not figure into the ‘‘ducted’’ propagationmodel described by Inan et al. [1984].[20] It is important to also note the region of weak

wavefields in Figure 3 at L < 1.5 near the magnetic equator,which result from the ionospheric absorption curves’ strongattenuation of upgoing VLF at those latitudes. This strongattenuation is not a factor at higher L shells, where the waveenergy originates at higher latitudes.[21] To summarize, the important components of this

modeling effort can be divided into five categories: initialconditions model (the transmitter fields within the Earth-ionosphere waveguide), ionospheric absorption (‘‘loss’’)

model, plasma density and geomagnetic field models, andwave propagator. Table 1 lists the different combinations ofmodels used to produce the results below. Model 1 is ournew Power Tracer-based code stack, using our best, mostrealistic models, and operating in a tilted offset dipolemagnetic field. It is later compared to model 7, which usesthe dens-high full-topside ionosphere model, and models8–9, which are based on the ducted propagator of Inan etal. [1984]. Models 2–6 operate in a centered dipole fieldand are used to connect our new work to other publishedresults. We will refer to Table 1 often as we describe ourvalidation efforts.

3. Validation Using Satellite Measurements

[22] The Power Tracer model stack has been evaluatedagainst 64 in situ sets of measurements of terrestrial VLFtransmitters obtained by five satellites during daytime andnighttime passes. Table 2 lists the parameters of the satellitepasses and the transmitters they observed. For each pass,predicted wavefield strengths have been generated usingvarious models from Table 1. The models selected shouldmake it possible to identify the cause of any observeddiscrepancies in their outputs.

Table 1. Models

Modela Propagatorb Initial Conditionsc Absorption Modeld Density Modele Field Model

1 Power Tracer LFCOM Helliwell dens-low tilted offset dipole2 ducted (Inan84) Crary approx-Helliwell dens-low � 2 centered dipole3 ducted (AFRL) Crary Helliwell dens-low � 2 centered dipole4 Power Tracer Crary Helliwell dens-low � 2 centered dipole5 ducted (AFRL) Crary Helliwell dens-low centered dipole6 Power Tracer Crary Helliwell dens-low centered dipole7 Power Tracer LFCOM Helliwell dens-high tilted offset dipole8 ducted (AFRL) Crary Helliwell dens-low tilted offset dipole9 ducted (AFRL) Crary Helliwell dens-high tilted offset dipoleaModel 1 is the newest, most physically realistic of the set and the subject of this article. Models 2–6 are used solely to compare against previous model

outputs given by Inan et al. [1984]. Models 7–9 are used to show the variability versus model 1 introduced by different propagators and density models.bPower Tracer, AFRL’s Power Tracer Code; ducted (Inan84), ducted model as described by Inan et al. [1984], with duct footprints at ground level;

ducted (AFRL), ducted model as described by Inan et al. [1984], with ducts at 1000 km.cLFCOM, Earth-ionosphere waveguide transmitter fields from the LFCOM simulator; Crary, Earth-ionosphere waveguide transmitter fields from fit to

Crary [1961] calculation.dHelliwell, VLF ionospheric absorption curves from Helliwell [1965, Figures 3–35]; approx-Helliwell, daytime VLF absorption curves using night

Helliwell values plus 26 dB.eDens-, modified Angerami and Thomas [1964] diffusive equilibrium ionosphere/plasmasphere model with either an ‘‘empty’’ Chapman layer topside

(dens-low) or a ‘‘full’’ Abel and Thorne [1998] topside (dens-high). Optionally divided by 2.

Table 2. Satellites, Pass Counts, VLF Transmitters, and Parameters

Satellite Altitude (km)Inclination

(deg) Transmitter LocationLat

(deg N)Lon

(deg E)Mag Lat(deg N)

Freq.(kHz)

Power(kW)

PassCount

Model-to-Data

Ratio [dB]

Day Night

DE-1 570 � 23300 90 OMDa LaMoure, ND 46.4 �98.3 56.3 13.1 10 1 7.2 NAIMAGE 45900 � 1000 40 NPM Lualualei, HI 20.4 �158.2 20.5 21.4 423 11 NA 22

NML LaMoure, ND 46.4 �98.3 56.3 25.2 233 16 NA 19NWC Exmouth, Australia �21.8 114.0 �32.8 19.8 1000 12 NA 22

OGO-I 280 � 149000 30 NAAb Cutler, ME 40.7 �67.3 53.0 17.8 885 2 NA 9NPGb Jim Creek, WA 48.2 �121.9 54.1 18.6 250 3 NA 17

OGO-II 415 � 1500 87 NAAb Cutler, ME 40.7 �67.3 53.0 17.8 885 3/2c 15 5NPGb Jim Creek, WA 48.2 �121.9 54.1 18.6 250 6/8c 29 15

DEMETER 700 � 684 98 NWC Exmouth, Australia �21.8 114.0 �32.8 19.8 1000 NA NA �20aTransmitter parameters as of the 1981 DE-1 flight. OMD is no longer active.bTransmitter parameters as of the 1966 OGO data set. NAA and NPG (now NLK) no longer operate on these frequencies.cValues are for day/night.


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[23] To quantify the comparison, we introduce the meanlog ratio of the model to satellite data values during pass j oftransmitter XMTR as

RXMTR jð Þ ¼ 1

Nj

XNj

i¼1

20 log10XMOD ið ÞXSAT ið Þ

� �ð1Þ

where X is the wavefield quantity of interest (electric ormagnetic) and the sum is over the Nj individual measure-ments i comprising the pass. A pass is defined as thesequence of measurements taken along a continuous satel-lite trajectory which does not visit any latitude more thanonce. The resulting ratios, expressed in dB, are listed inTable 2. We have assumed a lognormal distribution inselecting this metric, as examination of the distribution ofthe individual ratios suggests. Some constituent points ofcertain passes may be excluded from the average for variousreasons, as discussed in the text below.

3.1. Dynamics Explorer

[24] In order to provide a strong connection to previouswork and an initial validation of our code stack, we haveimplemented the ducted propagation model described inInan et al. [1984] and compared the outputs of both modelsto the Dynamics Explorer 1 (DE-1) measurements shown inthat paper [Inan et al., 1984, Figure 2]. Orbiting in a 570 �23,300 km orbit with 89.9� inclination and carrying a

magnetic loop antenna, DE-1 made a daytime pass overthe North Dakota Omega navigational transmitter (OMD)on 11 January 1982, and recorded VLF transmissionsbetween 10 and 16 kHz. The dots in Figure 4 are the13.1 kHz calibrated DE-1 data presented by Inan et al.[1984]. Note the sharp dropoff in the wave magnetic fluxoutside of L � 4, which may indicate the location of theplasmapause. The Inan84 line is a reproduction of theoriginal model output in that paper, taken directly fromthe published figure. To effect a meaningful comparison, wehave implemented the ducted propagation model describedin that paper, which consists of the Crary transmitter model,the Helliwell nighttime absorption curve adjusted by +26 dBfor the daytime pass, the ducted propagation model, acentered dipole geomagnetic field model and a specificdensity profile. The density profile best corresponds toour dens-low model, described in section 2, when dividingall densities by a factor of 2.[25] When running those models as described by Inan et

al. [1984], assuming field-aligned propagation starting atground level, we closely reproduce the published simulationoutputs as shown by the model 2 line in Figure 4. Havingreproduced the published result, we examined the effects ofusing more realistic assumptions in the ducted propagationmodel. The simplified daytime Helliwell curve was replacedby our time-resolved curves and radial propagation assumeduntil 1000 km altitude, after which field-aligned propaga-tion prevailed. A factor of

ffiffiffi2

p, obtained by properly time-

averaging the wavefields, was added to the computation inequation (5) of Inan et al. [1984]. Under these conditions,the composite model produces the model 3 line in Figure 4,which fits the DE-1 data more closely than the originalmodel for magnetic latitudes below 50 degrees. Above50 degrees, the satellite appears to have encountered theplasmapause: an effect not modeled in any of the ductedsimulations and occurring at a higher L shell in the PowerTracer models. The apparent latitude of the null over theOMD transmitter is shifted poleward as a result of presum-ing the rays to travel vertically to 1000 km altitude beforepropagating along the geomagnetic field. This results in thetransmissions following a higher magnetic L shell than thatat the ground.[26] To examine the effects of the chosen density and

propagation models, we have included results from threeadditional models in Figure 4. Model 4 is the same as theimproved ducted model 3, but substitutes the Power Tracerfor the propagator. This results in a better fit to the databelow 50 degrees. Note that the Power Tracer’s plasma-pause is fixed at L = 5.1. Finally, the lower-density profileused to match the Inan et al. [1984] profile was replacedwith our standard dens-low model (without division by 2)and the ducted and Power Tracer models used again toproduce the model 5 and model 6 curves, respectively.Notice that the higher densities lead to higher wave mag-netic flux through enhancement of the index of refraction.[27] Neglecting magnetic latitudes above 50 degrees

(where the plasmapause likely affects the comparison) andapplying (1), we obtain a model 4 output to observed dataratio of 7.2 dB for this single pass, as shown in Table 2. Onepass does not constitute validation, but Figure 4 doesdemonstrate that our results are consistent with previous

Figure 4. Comparison of DE-1 magnetic flux data to theoutputs of various models, listed in Table 1, plotted againstmagnetic latitude and L shell. The data were taken as thesatellite transited the Omega transmitter OMD in NorthDakota (shown at its dipole L shell). The data points arereproduced from Inan et al. [1984], as is the red modeloutput line (Inan84). Notice that the data drop off sharplyabove L � 4, which likely indicates the location of theplasmapause, and the shift in the null caused by differentpropagation assumptions. No model shows a clear advan-tage over the others.


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work. In the following sections we evaluate the models’performance using considerably more satellite data.

3.2. IMAGE

[28] The primary data source for this study was the radioplasma imager (RPI) instrument [Reinisch et al., 2000] onthe IMAGE satellite. IMAGE, launched in March 2000, wasin a polar orbit with a 1000 km perigee and an apogee of7.2 Earth radii. RPI consisted of three orthogonal pairs ofantennas and transmitted/received waves from 3 kHz to3 MHz. The RPI receivers were narrowband with a fixedbandwidth of 300 Hz. For the VLF ground transmittermonitoring study, the RPI operated in a passive mode overa small frequency range, 10–30 kHz, and fine frequencystepping, 300 Hz [Reinisch et al., 2006]. Observations weremade at a sampling rate of 3.2 ms and each measurementwas averaged over 8 samples, or 25.6 ms. Amplitudemeasurements at a particular frequency were repeated every3 to 4 min. The standard amplitude resolution was 0.125 dB,which is much smaller than signal fluctuations of naturalcauses.[29] The RPI system was designed to have a dynamic

range of the order of 90 to 100 dB. The absolute quietestobserved data, conventionally assumed to represent thepreamp/receiver noise level, is around 10 dB-nV/m. Anexamination of the dynamic spectrum data during theperiods of the VLF monitoring study shows amplitudesranging from a high of 100 dB-nV/m to a low of 40 dB-nV/m,substantially above the instrument noise floor. These meas-urements include both the signals from the VLF transmittersand the background plasma waves. To estimate the contri-bution of background plasma waves, measurements wereanalyzed from a band around 26.7 kHz during severaltransmitter passes. This frequency is sufficiently removedfrom the transmitter frequencies so that it provides areasonable measure of background activity, but closeenough so that the background amplitudes measured areapplicable to the transmitter bands. It was found that thebackground amplitude had an average less than 50 dB-nV/mbetween +/� 40 degrees latitude with occasional excursionsinto the range 55–60 dB-nV/m. This value of backgroundnoise is consistent with measurements made by the PlasmaWave Experiment aboard the CRRES satellite, whichobserved a background at 20 kHz of about 54 dB-nV/mat L = 2.55 inside the plasmapause [Meredith et al., 2004],and with background levels estimated from the OGO-1 andOGO-2 data inside the plasmasphere [Heyborne, 1966]. Athigher latitudes the background could sometimes extend to70–90 dB-nV/m but was always less than the amplitude inthe transmitter bands.[30] The absolute value of the wave electric field intensity

in the far-field was calculated as the measured voltagedifference between the two branches of a pair of theantennae divided by the effective length of the RPI dipoleantenna, taken to be L/2 where L is the tip-to-tip length[Balanis, 1997]. This is a valid estimate when the antennacurrent distribution is linear and when the antenna is shortrelative to the radio wavelength. In the whistler mode, theindex of refraction is generally about 6 and the wavelengthis about 2 km, i.e., much longer than the antennae. Duringthe IMAGE lifetime, the RPI antennas were damagedseveral times so that the physical lengths of the antennae

were known with an uncertainty of �20%, but the signalamplitude calculations take into account the changinglength of the RPI antenna. Combining the uncertainties inthe effective length and the voltage measurements, theestimated uncertainty in the absolute wave electric fieldamplitude is a factor of 0.5 to 2.0, or +/� 6 dB, which is inthe range of the uncertainties for most instruments of similartype.[31] The resulting wave electric field data points are

directly compared to the model 1 outputs. Figures 5a–5cshow the entire IMAGE data set as a function of magneticlatitude, plotted by transmitter. All of the IMAGE observa-tions for each transmitter have been overlaid on individualplots, as have the corresponding outputs from model 1. Tofacilitate comparison, a 50 dB-nV/m floor has been added tothe model wave electric field estimates. As this backgrounddoes not originate from the transmitters, it would nototherwise be modeled by the code. All of the satellite datawere obtained during nighttime passes over the transmitters,and the nature of the IMAGE orbit was such that all of theobservations occurred near periapsis at an altitude of about1500 km.[32] The plots clearly demonstrate that the model outputs

consistently overestimate the wavefields outside the equa-torial region by about 20 dB (a factor of 10). This is moreapparent in Figures 5d–5f where the statistics for theIMAGE electric field at each latitude have been plotted.Here, the dark lines represent the median measured wave-fields, while the shading indicates the first and thirdinterquartile region. The bounding black lines indicate themaximum and minimum measured wavefields. Only themedian model 1 outputs are shown in blue, as they varysignificantly less than the data. The curves for all trans-mitters are similar, and indicate that the model is consis-tently overestimating wavefield strengths at night in bothhemispheres by about 20 dB. The apparent underestimationin the low-altitude equatorial region is notable but of lessconsequence because the power there is typically small. Weaddress this issue in section 4.[33] A remarkable feature of all of these plots is the

extreme variability of the transmitter power observed nearthe equator (up to 60 dB), where the ionospheric absorptioncurves indicate that virtually no power should reach. Clearlya highly variable process exists that allows VLF trans-missions to propagate into this region under certain circum-stances. The varying prominence of the caustic in theobservations is also noteworthy.[34] Using the methodology of equation (1), the model to

data ratio for the NPM, NML, and NWC transmitters are22 dB, 19 dB, and 22 dB, respectively. Only locationswhere the model output is greater than 50 dB nV/m(the assumed background), and below 60� magnetic latitude(the plasmapause boundary at this altitude) are consideredin the ratio. This includes the regions typically receiving thebulk of the transmitted power.

3.3. OGO

[35] The Orbiting Geophysical Observatory (OGO) 1 and2 satellites flew in highly elliptical equatorial and nearlycircular polar orbits, respectively, in 1964–1965. They eachcarried 10-foot loop antennae and four VLF receivers, oneof which was used to acquire magnetic flux measurements


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of terrestrial Navy transmitters NPG (now NLK) in Wash-ington State and NAA in Maine over long trajectories,including during the daytime. The processed, scaled andplotted results were digitized from archival reports[Heyborne, 1966] and used as an additional data set tocomplement the IMAGE measurements in our validationeffort. Heyborne [1966] claims ±5 dB accuracy for theOGO observations.[36] Figures 6a and 6b present scatterplots of the OGO

1 data and models similar to those produced for the IMAGEdata, and Figures 6c and 6d show the analogous statistics.OGO 1 operated in a 280 � 149,000 km 30� inclinationorbit. The toroidal loop antenna was oriented such that itwould be sensitive to upgoing VLF in the transmitterhemisphere, where wave normal angles to the ambient

magnetic field are small. The altitude regime covered bythe OGO 1 observations is much higher than that of theother satellites in this study, making these measurementsespecially valuable. All of the data shown were taken atnight.[37] Figure 7 shows the OGO 2 data in a similar way, but

separated by day and night passes. OGO 2 flew in a 415 �1500 km 87� inclination orbit, and used a hexagonalantenna oriented somewhat more efficiently than that onOGO 1. For both satellites, the VLF wave magnetic fluxmagnitudes should be considered as lower bounds, essen-tially accurate in the transmitter hemisphere and potentiallyfar too low in the conjugate hemisphere equatorward of thecaustic, where the wave normal angles are generally verylarge.

Figure 5. A comparison of the IMAGE electric field data to outputs from model 1. Figures 5a–5coverplot all IMAGE passes for individual transmitters with the corresponding model outputs. Predictedshadow boundary locations are indicated. Figures 5d–5f show the derived IMAGE values for median(dark line), first and third interquartile region (shading), and minimum and maximum (bounding lines)versus the median model 1 output (blue line). Note the significant variability of the data, particularly inthe equatorial region, and the large differences between model and data.


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[38] Clearly the OGO passes are highly variable, but thestatistical plots again demonstrate that model 1 typicallyoverestimates the wavefields off the magnetic equator, andunderestimates them near the equator. Applying the formal-ism of (1) to these data and model outputs in a mannersimilar to that used for IMAGE yields a typical model-to-data ratio (away from the magnetic equator) of about 15 dB.The exact values are listed in Table 2, and vary considerablybetween day and night.

3.4. DEMETER

[39] The DEMETER satellite operates in a nearly circular700 km orbit at 98.3� inclination. The on-board ICE electricfield experiment [Berthelier et al., 2006] measures onecomponent of electric field over the 15 Hz–17.4 kHz band.The only large terrestrial VLF transmitter observable withICE is NWC, whose 19.8 kHz transmissions fall within theknown roll-off of the instrument’s band-select filter.[40] Although we have yet to perform detailed analysis of

the DEMETER satellite’s observations of NWC, we includeone data point in Table 2 to further bound the observations.DEMETER typically measures 100–120 dB-nV/m overNWC at night (C. Rodger and R. Gamble, private commu-nication, 2007). This is similar to, but somewhat higherthan, the magnitudes measured by the IMAGE spacecraft(Figure 5). However, IMAGE did not pass directly overNWC, thereby skirting the region of highest wavefieldintensity. When compared to the maximum wavefieldstrengths predicted by model 1 of about 140 dB-nV/m,the DEMETER observations are consistent with the 20 dBerror estimate computed in section 3.2. Like IMAGE,

DEMETER sees highly variable wavefield intensitiesaround the magnetic equator.

4. Discussion

[41] The data sets presented in section 3 indicate aconsistent bias in the model 1 wave electric field andmagnetic flux estimates when compared to observationsby the IMAGE and OGO spacecraft. Neglecting for themoment the highly variable equatorial region where, onaverage, the transmitter power is substantially less at lowaltitudes than that off the equator, we note that the satellitedata exhibit statistically between 10 and 30 dB smallermagnitude than the model outputs. Such a large biasstrongly suggests a fundamental physical issue with theunderlying models. We have shown (Figure 4) that thewavefield estimates from models using the Power Tracerwave propagator are similar to those of Inan et al. [1984]when using the same density and geomagnetic field modelsand the same initial conditions, despite the two models’completely dissimilar propagation methods. Both modelsseem to match the one DE-1 pass reasonably well, but thismay simply be fortuitous. A more detailed comparison of thetwo models over the larger data set is therefore warranted.[42] Figure 8 shows typical individual nighttime passes of

the IMAGE satellite over three Navy transmitters, overlaidwith the outputs of several models. We have used a numberof models from Table 1 for the comparison, including Craryand LFCOM waveguide field models and both the‘‘ducted’’ and Power Tracer propagation models. To visu-alize the effect of our density model, we have applied bothour standard ‘‘empty topside’’ model (dens-low) and the

Figure 6. As in Figure 5, but comparing OGO-1 magnetic flux data to outputs from model 1. Figures 6aand 6b overplot all OGO-1 passes for individual transmitters, with the corresponding model outputs.Figures 6c and 6d show the derived OGO statistics and the median model 1 output. OGO data from theconjugate hemispheres are considered substantially less reliable. Again note the substantial differencesbetween model and data.


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Abel and Thorne [1998] ‘‘full topside’’ model (dens-high).We have also run the Power Tracer with and without theLandau and cyclotron damping computations (not shown).[43] It is evident from Figure 8 that the use of the

‘‘ducted’’ propagation model (all other things being equal)does not significantly alter the predicted wave electric fieldsover any of the passes shown, except for its expectedinability to predict the location of the shadow boundary(visible in many of the IMAGE passes) in the conjugate

hemisphere. The variations due to density (shown) anddamping (not shown) models also appear to be minor.Notice the strong effect of the caustic in Figures 8a and 8bnear 30�S latitude, in both the observations and the powertracing models, and the significant variability observedthrough the equatorial region. Model to data ratios for eachpass are listed on the plots, and amount to about 20 dB.[44] For comparison, Figure 9 shows all of the model

predictions compared to two OGO passes. These also

Figure 7. As in Figure 6, but for OGO-2, separated by night and day.


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demonstrate the same �20 dB overestimation of theexpected wave magnetic flux. Note the almost completelack of observed signal fade in the equatorial regions of theplots, where the model outputs are typically 10–15 dB toosmall.[45] When plotted over the region covered by the satellite

measurements, the ratio of observed to model 1 predictedwavefields takes the form shown in Figure 10, whichconfirms that for all practical purposes, an essentiallyconstant +20 dB bias seems to exist in the model outputsoff the equator. Figure 10a shows the model to data ratio bymagnetic latitude and radius, while Figure 10b shows onlythe latitudinal dependence. Near the equator the wavefieldsare sometimes very small, so that the 50 dB-nV/m floormatches that observed in the data and the ratio is close to0 dB, and sometimes very large, so that the imposed floorsignificantly undershoots the data and the ratio can be aslow as �40 dB. At magnetic latitudes exceeding 60� at thelow altitudes, the model is operating outside of the plasma-

Figure 9. As in Figure 8, but for two OGO-2 passes.Notice the strong signals throughout the equatorial region.

Figure 8. Individual IMAGE passes for three VLF trans-mitters, overlaid with outputs from four models. The meanmodel-to-data ratios are listed for each pass and amount toabout 20 dB for all models. Notice the predicted and observedshadow boundaries observed conjugate to the transmitters.


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pause and yielding only the background value. Theselatitude regions have been shaded in Figure 10b. Noticethe increased variability at midlatitudes in the southernhemisphere, which is magnetically conjugate to all butone of the transmitters studied.[46] It is also interesting to note from Figure 10a that

(with the exception of the outlier points visible near 35�N inFigure 10b) the high-altitude OGO 1 passes demonstratethat the 20 dB model to data ratio maps along the geomag-netic field to high altitude as well, and that the ratio falls tolow values at the plasmapause, as expected. This indicatesthat the divergent behavior near the magnetic equator(underestimating wavefields rather than overestimating) isa low-altitude phenomenon related to the low incident wavepower in that region (see Figure 3), caused mostly byionospheric absorption.[47] Since the ‘‘ducted’’ and Power Tracer models differ

only in their propagators but produce outputs of the same

magnitude, it is reasonable to suspect that the problems arisefrom the initial conditions common to both. The Crarymodel is a simple relationship derived from a set of electricfield computations, while LFCOM is a first-principlesmode-theory simulation. Both compare favorably to oneanother, and to the LWPC code, and the mode theory codeshave received substantial validation efforts by the govern-ment agencies that maintain them. These facts warrantcloser examination of the ionospheric absorption curvesgiven by Helliwell [1965], and in the methodology bywhich they are combined with the waveguide field models.[48] The Helliwell absorption curves, although widely

used in calculations of VLF transmitter leakage into thenear-space environment, were originally calculated usingfairly restrictive assumptions. The wavefield is assumed tobe a plane wave with wave normal directed vertically,incident on a horizontally stratified ionosphere. The Dregion profile used in the calculation assumes a sharp lowerboundary, an ensemble-averaged density profile, and arepresentative collision frequency model. When using theresulting absorption estimates, an additional 3 dB polariza-tion loss must be imposed and losses due to reflection at thelower boundary of the ionosphere (estimated by Helliwell tobe 2 dB) are not included. Although the exercise producesplausible absorption curves (except at very low latitudesduring the day and latitudes below 45� magnetic during thenight, where the quasi-longitudinal approximation used inthe calculation breaks down), it certainly was neverintended for application to all possible times, longitudes,and distances from the transmitter. Nevertheless, the curvesshould be reasonably accurate directly over high-latitudetransmitters, where the assumptions involved are usuallyappropriate. The 20 dB discrepancy observed in our modelsover the transmitters therefore suggests that the absorptioncurves alone are not the source of the problem.[49] In fact, our study appears to suggest that it is the

methodology of combining a (well-validated) field modelfor the Earth-ionosphere waveguide with the (reasonablyaccurate) Helliwell absorption model which is invalid.Many of the potential problems inherent in this methodol-ogy are actually pointed out explicitly by Inan et al. [1984].To test this hypothesis, finite difference frequency domain(FDFD) [Hu and Cummer, 2006] and full-wave techniques[Lehtinen and Inan, 2008] have very recently been broughtto bear on this problem, generating three dimensional full-wave solutions over limited areas for the entire transmitter-ionosphere system. Although computationally expensive,these independent numerical models can directly computewave electric fields at an altitude of 150km from terrestrialtransmitters, avoiding the need for ionospheric absorptioncurves entirely. By passing some of these model outputs(S. A. Cummer, private communication, 2008; N. Lehtinen,private communication, 2008) directly into model 1, waveelectric field estimates are produced that match those of thelayered models reasonably well.[50] We are therefore left to conclude that none of the

transmitter models studied, layered or numerical, reflect theentire set of relevant physical processes. Given that themodels all agree at 150 km, and that the satellite data showssimilar error whether taken directly above the transmitter at600, 1500 or 7000 km, or conjugate to it at the end of a verylong interhemispheric propagation path, it is clear that the

Figure 10. Ratios of model 1 to the IMAGE and OGOsatellite data sets (a) by L shell and magnetic latitude and(b) bymagnetic latitude only. IMAGE data are in black; OGOdata are in blue. The transmitters are shown as triangles.Shaded areas denote regions outside the plasmapause orwhere the model predicts near-background noise levels. Notethe mapping of ratios along L shell in Figure 10a and thegreater overall variance visible in Figure 10b in thehemisphere conjugate to most of the transmitters.


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‘‘missing power’’ is lost somewhere in the ionosphere.Possible candidates for loss processes include enhancedD region reflectivity due to transmitter modification, scat-tering from transmitter-induced irregularities, and conver-sion to nonpropagating lower hybrid modes. Although weare able to simulate some of the latter waves, they would notbe detected efficiently by any of the satellite measurements,and are explicitly excluded from the comparison.[51] Taking these surprising findings into account, we

have implemented a simple constant correction factor,adjusting our initial conditions downward by 23 dB at nightand 10 dB during the day (with no changes to the addednoise floor). This produces the wavefield estimates shownin Figure 11, which mirror panels from Figures 4, 5, 8, and10. Figure 11a repeats the DE-1 daytime pass over OMDfrom Figure 4, showing both the ducted (models 2 and 5)

and the Power Tracer (model 6) outputs using the adjustedinitial conditions. Note that the ducted and raytracingmodels agree quite well, and that they reproduce the DEpass with good fidelity. Figure 11b repeats the nighttimeIMAGE NML statistics plot from Figure 5e, showing theeffects of reducing the model inputs by 23 dB. The medianmodel outputs now fit within the bounds of the observa-tions. Figure 11c replots the nighttime IMAGE NPM passof Figure 8a, and the revised models now reproduce thetransmitter and conjugate magnitudes quite well. Figure 11drevises the comprehensive model 1 to data ratio plot ofFigure 10b, demonstrating the transmitter and conjugatehemisphere ratios are now better approximated by a 0 dB fitline.[52] Figure 11 indicates that although the satellite data are

highly variable, the overall quality of agreement in regions

Figure 11. Model results compared to satellite data after adjusting by �10 dB for day and �23 dB fornight: (a) DE-1 daytime pass of OMD, (b) IMAGE nighttime NML observation statistics versus model 1output, (c) IMAGE nighttime NPM pass versus several models, and (d) model to IMAGE and OGO dataratios. Black is IMAGE; blue is OGO. The shaded regions are near the magnetic equator or outside theassumed plasmapause. The transmitters are indicated by triangles. This simple correction has greatlyimproved the overall fit.


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typically containing most of the power is significantlyimproved for all of the models when adjusting the initialconditions downward by constant factors for daytime andnighttime. A more sophisticated correction applied as afunction of magnetic latitude would improve the agreementeven more by adjusting the predicted wavefields upward byabout 15 dB in the equatorial region, filling in the low-power area near the magnetic equator in Figure 3. Our goalhere is not to propose an optimal set of correction factors,however, as additional focused research into the transiono-spheric propagation of whistler mode VLF radiation isclearly needed.

5. Conclusions

[53] Studies of the effects of terrestrial VLF transmitterson radiation belt particles like that of Inan et al. [1984] andAbel and Thorne [1998] require accurate models of VLFpropagation from the Earth-ionosphere waveguide and intothe near-Earth environment. By combining existing wave-guide field and ionospheric absorption computations with afully three-dimensional propagator, we have constructed apowerful simulation capable of producing wavefieldstrengths and wave normal angles everywhere in a smoothplasmasphere from an arbitrary source. We have evaluatedour wavefield estimates against the published model of Inanet al. [1984] and found them to be comparable.[54] To evaluate the model’s performance, we have com-

pared its output to published in situ observations of terres-trial VLF transmissions from the DE-1, OGO-1, and OGO-2satellites, as well as new measurements obtained by theIMAGE and DEMETER spacecraft. In the course of thisstudy, we have observed that all of the models overestimateelectric and magnetic wavefield strengths off the magneticequator by a factor of roughly 20 dB, and underestimate themedian fields near the equator by about 15 dB. By substi-tuting different models of transmitter output, propagation,damping, geomagnetic field, and plasma density, we havedetermined that the existing models of ionospheric penetra-tion by whistler mode VLF are inadequate for accuratelypredicting wavefields in the plasmasphere. It appears fromfull-wave electromagnetic simulations that unmodeled lossprocesses, such as mode conversion, scattering, or enhancedreflection, lie at the root of the discrepancy. Use of theselongstanding penetration models, then, should be undertak-en with appropriate caution, and past results so obtainedshould be evaluated carefully, as they likely overestimateterrestrial VLF transmitter wavefields in the plasmasphereby about 20 dB, and underestimate the magnitude of thosefields at low L shells near the equator. Additionally, workusing these field estimates to predict wave particle inter-actions would also tend to misjudge the role played by VLFtransmitters by the same amounts. It is worth noting alsothat the same methodology has been applied in the past toestimate the wavefields in the lower ionosphere due tolightning [Bortnik et al., 2003].[55] Despite the significant variability observed in the

natural environment, the effort described here has produceda good quantitative baseline model of VLF propagation.Using a modified estimate of transionospheric propagation,the model outputs are sufficiently accurate for use in a widerange of applications, including studying the effects of

ground-based transmitters, both existing and hypothetical,on radiation belt particles. With the wave normal informa-tion provided by the Power Tracer and the variabilityinformation from the satellite measurements, the model isespecially suited to performing this task in unprecedenteddetail. Forthcoming full-wave models of terrestrial trans-mitter fields in the plasmasphere and further research intothe penetration physics should further improve its useful-ness. Application of time-resolved models of trapped elec-tron flux responsible for resonant damping could alsoprovide insight into the observed amplitude variations.[56] It is exciting that VLF measurements from higher

altitudes within the plasmasphere and outer magnetosphereare expected to become available in the next decade with theflight of the Demonstration and Science Experiments mis-sion [Cohen et al., 2006]. These will provide further bench-marks on the shape and intensity distribution of the powerenvelope. As the number of fiducial observations increases,comparisons should be possible with more comprehensivedata sets like those of Green et al. [2005].

[57] Acknowledgments. Generous support for LFCOM was providedby Royden Rutherford of ITT Corporation, AES, and Mark Sward of theDefense Threat Reduction Agency. The authors wish to thank Tim Bell,Umran Inan, and Nikolai Lehtinen of Stanford University, Steven Cummerof Duke University, and Jacob Bortnik of UCLA for many helpfuldiscussions in the course of this effort. The assistance of Bright Smalland Matt Mattson of the U.S. Air Force and Dean Ascani of AER, Inc., incompleting this work is much appreciated. Essential supercomputer resour-ces were provided by the Department of Defense High PerformanceComputing Modernization Program.[58] Amitava Bhattacharjee thanks Richard Horne and another reviewer

for their assistance in evaluating this paper.

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Research Laboratory, 29 Randolph Road, Hanscom Air Force Base, MA01731, USA.R. A. Quinn, Atmospheric and Environmental Research, Inc., 131

Hartwell Avenue, Lexington, MA 02421, USA.B. W. Reinisch, G. S. Sales, and P. Song, Center for Atmospheric

Research, University of Massachusetts, 600 Suffolk Street, Lowell, MA01854, USA.M. J. Starks, Space Vehicles Directorate, Air Force Research Laboratory,

3550 Aberdeen Avenue SE, Building 464, Room 405, Kirtland Air ForceBase, NM 87117, USA. ([email protected])


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Illumination of the plasmasphere by terrestrial very low frequency transmitters: Model validation

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