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

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113,, doi: /2008ja013112, 2008 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. Song 4 Received 21 February 2008; revised 29 May 2008; accepted 2 July 2008; published 27 September [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 whistler mode waves in the plasmasphere. The model combines a simulation of the fields in the Earth-ionosphere waveguide, ionospheric absorption estimates, and geomagnetic field and plasma density models with fully three-dimensional ray tracing that includes refraction, focusing, and resonant damping. The outputs of this model are consistent with those of several previous, simpler simulations, some of which have underlying component models in common. A comparison of the model outputs to wavefield data from five satellites shows that away from the magnetic equator, all of the models systematically overestimate the median field strength in the plasmasphere owing to terrestrial VLF transmitters by about 20 db at night and at least 10 db during the day. In addition, wavefield estimates at L < 1.5 in the equatorial region appear to be about 15 db too low, although measured fields there are extremely variable. Consideration of the models similarities and differences indicates that this discrepancy originates in or below the ionosphere, where important physics (as yet not conclusively identified) is not being modeled. Adjustment of the low-altitude field estimates downward by constant factors brings the model outputs into closer agreement with satellite observations. It is concluded that past and future use of these 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,, doi: /2008ja Introduction [2] Large ground-based transmitters have operated in the very low frequency (VLF) band below 30 khz for decades, generally for maintaining communication with submarines. In addition to penetrating the Earth s oceans, significant energy from these transmitters also leaks through the ionosphere, propagates in the whistler mode, and interacts with the population of stably trapped electrons in the Earth s radiation belts [Vampola, 1977]. Inan et al. [1984] modeled this anthropogenic process to compute regions of electron precipitation as guidance for future ground-based experiments. To estimate its relative importance compared with natural processes, Abel and Thorne [1998] developed a simple model of the combined contributions of all of the 1 Space Vehicles Directorate, Air Force Research Laboratory, Hanscom Air Force Base, Massachusetts, USA. 2 Now at Space Vehicles Directorate, Air Force Research Laboratory, Kirtland Air Force Base, New Mexico, USA. 3 Atmospheric and Environmental Research, Inc., Lexington, Massachusetts, USA. 4 Center for Atmospheric Research, University of Massachusetts, Lowell, Massachusetts, USA. Copyright 2008 by the American Geophysical Union /08/2008JA major ground-based VLF transmitters to the decay of the radiation belts produced by the STARFISH high-altitude nuclear explosions in They concluded that terrestrial transmitters significantly influence the energetic particle distribution at certain radiation belt L shells. This calculation was later revisited for a space-borne VLF transmitter by Inan et al. [2003]. [3] As part of their model, Abel and Thorne used a representation of the transmitter power distribution taken from Inan et al. [1984] and estimates of ionospheric VLF absorption computed by Helliwell [1965]. These models continue to find wide application; for example, they have also been used to model the effects of lightning-produced VLF [e.g., Bortnik et al., 2003, 2006]. Together with various types of wave power propagators, these approximations produce estimated values of transmitted VLF energy in the plasmasphere. However, the results so obtained are far from definitive, lack systematic validation, and are inadequate for predicting quantitative effects of specific transmitters on specific particle populations when good fidelity is required. [4] To address this need, and as part of a comprehensive examination of ground-based VLF transmitter effects on radiation belt particles, we have taken the next step in estimating the strength of transmitter electric fields in the 1of16

2 plasmasphere. More physically realistic models of transmitter output and radio wave propagation, combined with estimates of ionospheric absorption, have been developed and are described in section 2, where they are contrasted with some earlier models still widely used. In section 3, various combinations of the old and new models are used to produce three-dimensional maps of VLF electric field distributions within the plasmasphere, and the results compared to actual VLF measurements of terrestrial transmitters acquired by the Radio Plasma Imager (RPI) instrument aboard the Imager for Magnetopause-to-Aurora Global Exploration (IMAGE) satellite [Reinisch et al., 2000], the OGO 1 and OGO 2 spacecraft [Heyborne, 1966], Dynamics Explorer (DE) 1 (taken from Inan et al. [1984]), and DEMETER. The overall accuracy of the model outputs, possible sources of observed discrepancies and their implications, and suggestions for further improvements to the model are presented in section 4. We finish with a summary in section Models 2.1. Transmitter Models [5] Terrestrial VLF transmitter power in the ionosphere has typically been estimated by combining a model of power in the Earth-ionosphere waveguide with an estimate of ionospheric absorption. This approach is not strictly correct, as the coupling of waveguide modes below the ionosphere into upwardly propagating power at higher altitudes is a complex process requiring full-wave electromagnetic solutions. Unfortunately, in addition to being computationally intensive to produce, full-wave estimates of transmitter power in the ionosphere are highly dependent on frequency, transmitter location, and details of the ionospheric plasma, and no such globally applicable models have thus far emerged. We have therefore adopted the twomodel approach for our effort. [6] A simple, commonly used waveguide power model is the relation developed by Crary [1961] from explicit electric field computations and adapted by Inan et al. [1984]. This model applies a straightforward attenuation with distance from the transmitter, and produces power flux estimates at 90 km altitude like those shown in Figure 1a for the 21.4 khz 423 kw Navy VLF transmitter NPM, located at Lualualei, Hawaii (20.4 N, E). Figure 1 was produced for transmitter midnight. For this work, we used the more advanced LFCOM code (R. Rutherford and B. Gambill, LFCOM: A Fortran code for evaluation of spread debris effects on long wave propagation links, vol. 1: User s manual, in preparation, 2005), maintained by the Defense Threat Reduction Agency (DTRA), to calculate electric fields in the Earth-ionosphere waveguide over the entire surface of the Earth and to validate the outputs of the Crary model. LFCOM is a mode-theory code that explicitly models most physical quantities that affect wave propagation. The code provides a relatively detailed analysis of long wave propagation characteristics by using a high-accuracy Earth-ionosphere waveguide propagation model to produce a realistic picture of electric field distributions over large areas. These fields are then converted to equivalent power flux below the ionosphere by assuming free space impedance. Figure 1b shows the LFCOM power flux distribution at 90 km altitude from the NPM transmitter. The output of this model generally agrees in magnitude with the outputs of the similar LWPC code [Ferguson et al., 1989] and (in a smoothed form) with the Crary [1961] model, as shown by the profile in Figure 1c, but naturally manifests fine details of the mode superposition caused by ionization gradients and 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 ionospheric density models and collision profiles and assumed vertically incident waves. Technically of limited applicability, these results have long represented the state-of-the-art for VLF ionospheric absorption estimates, but there is ongoing work to refine them using full-wave electromagnetic solutions [e.g., Hu and Cummer, 2006]. Helliwell generated curves for 2 khz and 20 khz for typical nighttime and daytime conditions. In order to apply them on a global basis, they are interpolated in frequency and extended to continuously cover all local times. The latter is accomplished by applying a sharp transition function between the day and night curves as a function of the solar zenith angle. The transition is intended to mimic the rapid production and recombination of plasma due to solar illumination of the D region, which is the dominant source of VLF absorption. The resulting estimate of power transmitted through the ionosphere is shown in Figure 1d. When comparing model outputs to satellite measurements in section 3, we always run the models for the local times at which the measurements were made Propagation Models [8] The power flux values so obtained form the initial conditions for propagation codes that distribute the escaping VLF energy into the upper ionosphere and plasmasphere. Inan et al. [1984] introduces a ducted model of VLF propagation, which is adopted by Abel and Thorne [1998]. In this model, upgoing VLF is assumed to travel strictly along the Earth s magnetic field, propagating with fieldaligned wave normal vectors and diminishing in power as the ratio of the local ambient magnetic flux to that at 1000 km altitude. Inan et al. [1984] identify several deficiencies in this simple model, chief among which is the complete lack of realistic information about the angle that the VLF wave normals make to the background magnetic field, which is required information for computing wave-particle interactions. While VLF waves may propagate in field-aligned ducts, they more commonly propagate in a nonducted fashion in which their raypaths and wave normal angles are determined by the slowly varying density and magnetic field gradients [Smith and Angerami, 1968]. For this reason, more recent work has adopted ray tracing as a 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 often avoided (as above) or applied only over a limited area. Twodimensional tracing by necessity confines rays to the magnetic meridional plane, an approximation that is poor in the general case and difficult to validate in specific cases unless the initial wave normal angle of the incident wave is known to lie within that plane. In addition, two-dimensional 2of16

3 Figure 1. The initial conditions models for the NPM transmitter at local midnight. (a) Output of the Crary 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 1b through the transmitter latitude, showing agreement of the models. (d) LFCOM outputs at 150 km altitude, after applying ionospheric absorption curves. ray tracing cannot accurately model ray focusing or propagation through density irregularities that are not azimuthally symmetric. Fully three-dimensional ray tracing, such as that 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 Air Force Research Laboratory s VLF Propagation Code (which incorporates the Power Tracer of Starks [2002]) for propagation through the ionosphere and plasmasphere. The Power Tracer combines a modular three-dimensional ray tracing program with algorithms that estimate power flux changes due to divergence, focusing, and damping. Bundles of rays are traced from initial points spread over a 97,200-point equal-area grid defined within the ionosphere and with intensities given by the outputs of the transmitter and ionospheric absorption models. As in the work of Starks [2002], no horizontal density gradients are postulated and it is assumed that owing to refraction the wave normals of the upgoing rays are initially aligned with the gradient of the ionospheric density, i.e., in the radial direction. Rays are then traced in the whistler mode into the plasmasphere until they reenter the ionosphere and are presumed lost. Although the multispecies density (see below) and propagation models support magnetospheric reflection [Kimura, 1966], it generally does not occur for whistler mode waves from terrestrial transmitters of interest, which have relatively high frequencies. The three-dimensional computation permits raypaths to vary freely within and across magnetic meridians, subject only to the constraints imposed by the cold 3of16

4 Figure 2. Equatorial profiles for the density models used in this work, and the published models to which they have been fit. plasma dispersion relation. There are no field-aligned ducts presumed in this model Environment Models [11] The accuracy of the Power Tracer depends heavily on the two classes of environmental models used in the simulation: ambient magnetic field and plasma density. Indeed, the effects of these models on the final power distribution are areas of active research [e.g., Quinn et al., 2006]. For the initial efforts at validating this propagation model, we have elected to use simple models that are computationally inexpensive. The quality of the model outputs, as established by the fiducial satellite measurements (see section 3), determines how much refinement is required 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 on the first eight Gauss coefficients of the International Geomagnetic Reference Field (IGRF) [Peddie, 1985], epoch The ambient magnetic field primarily affects the propagation 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 power flux distribution is also controlled by the contour of the background magnetic field along which the electron cyclotron frequency equals the wave frequency. The tilted offset dipole model is a good approximation to the actual geomagnetic field at most of the latitudes of concern in this work. This was verified by performing a comparative tracing using the World Magnetic Model (WMM) [McLean et al., 2004], another spherical harmonic model very similar to IGRF. Comparisons of power distributions for each model (e.g., results similar to those illustrated in Figure 3 discussed below) show that the differences introduced by the simpler model are minor. The component of the geomagnetic field driven by magnetospheric components has been ignored since it contributes less than 5% of the ambient field at the highest altitudes and latitudes considered in this study. [13] To model the ambient plasma environment, we utilize a multispecies diffusive equilibrium density model derived from a multifluid pressure balance equation, solved using the temperature modified geopotential height approach of Angerami and Thomas [1964]. We have neglected the centripetal force, but included the magnetic force along flux tubes [Chiu et al., 1979] and incorporated a frictional ionosphere [Thomson, 1987]. The density distributions so derived are sensitive to the assumed temperature gradients of the component species along the geomagnetic field lines, for which we use the simple form given by Thomson [1987] (which yields an analytic solution). The density is rolled off at a plasmapause location of L = 5.14, as given by Carpenter and Anderson [1992] for Kp = 1. Here, we model O + and H + as the ion species, where O + dominates in the Chapman-layer-like ionosphere [Chapman, 1931]. Even in this simple form, this density model has six free parameters. These parameters have been tuned so that the density falls off relatively quickly in the top-side and similar to the Carpenter and Anderson [1992] plasmasphere outside L = 2. Some typical density profiles are shown in Figure 2. Through its input parameters, this model can be easily tuned to obtain different density distributions while remaining computationally efficient. In this study, we use two different general profile shapes labeled dens-high and dens-low. Dens-low produces the Chapman layer profile with a relatively empty topside ( km) ionosphere described above; we use this as our standard model. Dens-high generates a very full topside ionosphere, similar to that used by Abel and Thorne [1998]; we use this to reveal any differences in VLF wavefield distributions resulting from the density model. [14] The effects of resonant damping, which can significantly reduce whistler mode wave power at the frequencies of interest [Thorne and Horne, 1994, 1996], have also been taken into account. We follow the approach of Bortnik et al. [2003] and Bell et al. [2002], who postulate a continuous warm electron population from 1 ev to 10 MeV on the basis of AE8 and Hydra data, then apply the method of Brinca [1972] to compute damping at every location within the plasmasphere. Like previous authors, we have found that the Landau and primary cyclotron modes are the only important contributors to damping of the waves of interest, although an arbitrary number of modes can be included in the calculation Power Flux [15] To compute the power flux at a given point in space, the magnetosphere has been partitioned into a set of volume elements (voxels) one degree wide in latitude and longitude and 120 km thick. In general, each voxel may contain multiple power flux values owing to multiple rays passing through it. Each ray may also have multiple data points within the voxel, but the parameters associated with a given ray in a single voxel typically vary minimally and these may be averaged. Since the power flux algorithm used gives an estimate of the power flux arriving in a voxel from a particular initial location, the power flux from multiple rays 4of16

5 Figure 3. Cross sections of the model 1 power flux outputs for the NPM transmitter (indicated by the orange triangle). (a) Meridional section, showing plasmapause, shadow boundary, and typical satellite trajectories. The dotted line is the contour where electron cyclotron frequency equals the transmitter frequency (b) equatorial section, manifesting local time dependence and the mapping of LFCOM structure into space. Note the low-altitude region of weak power flux near the equator. starting close to one another and arriving close together must be properly averaged since they represent the same wave packet. Conversely, the power flux from rays corresponding to widely separated initial conditions represent independent wave packets and should be summed, rather than averaged, to get the accurate total power flux in the voxel. For the results presented in this paper we have used the lower-bound-strongest (LBS) technique, whereby only the ray with the largest power flux is considered in each voxel. This technique yields an approximate lower bound on, and in most instances a good overall estimate to, the absolute wavefield in the voxel. The LBS estimate is quite good for terrestrial transmitters because rays that start far from the LBS ray usually have wavefield strengths that are 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 magnetic longitude of the transmitter, Figure 3a) and an equatorial cross section (Figure 3b) of the power envelope produced by the NPM transmitter are shown. Rays originating outside the plasmapause (at L 5 here) have been suppressed. Several important features of this plot require explanation. First, propagating rays in the meridional plane are bounded by the Earth s magnetic field and the whistler mode dispersion relation, which restricts propagating waves to areas where the wave frequency is below the electron gyrofrequency (enclosed by a dotted line in Figure 3). In practice, this boundary strongly refracts rays that approach it and produces an exterior caustic that defines the outer extent of the power envelope. Note that as a result of this refraction, there are regions at high altitude (but within the cyclotron frequency boundary) into which the NPM transmitter is unable to directly propagate any wave energy at all. [17] The rays that encounter this caustic produce the most remarkable feature of the power distribution, the shadow boundary indicated by the arrow in Figure 3a. Once above the ionosphere, rays from the northern hemisphere transmitter are constrained to propagate largely along the geomagnetic field line upon which they originate, although crossing to somewhat higher L shells. At higher latitudes, they propagate upward until they reach a location where the electron gyrofrequency approaches the wave frequency. As they near this point, the rays refract sharply toward lower L shells, cross the magnetic equator, and continue into the conjugate (southern) hemisphere along a downward, L shell-crossing trajectory. This creates an abrupt shadow boundary in the conjugate hemisphere, beyond which the more powerful rays directly propagating from the transmitter do not reach. Beyond this boundary, wave energy in the plasmasphere comes exclusively from comparatively weaker rays propagating up through the conjugate ionosphere. There is an analogous shadow boundary produced by upgoing rays from the southern hemisphere, but it is invisible in Figure 3a owing to the relative weakness of those signals, which have traveled far from the transmitter in the Earth-ionosphere waveguide before penetrating into the plasmasphere. It should be noted, however, that the boundary would be visible in satellite measurements that are suitably resolved in wave vector. [18] The theory of these boundaries is rooted in catastrophe optics, and they cause significant problems for the ray tracing technique because the geometric optics approximation breaks down along the caustic, causing power flux estimates to tend toward infinity. In reality, the wavefields produce an Airy pattern approaching the caustic, and evanescent wave energy extends across and beyond the 5of16

6 Table 1. Models Model a Propagator b Initial Conditions c Absorption Model d Density Model e Field Model 1 Power Tracer LFCOM Helliwell dens-low tilted offset dipole 2 ducted (Inan84) Crary approx-helliwell dens-low 2 centered dipole 3 ducted (AFRL) Crary Helliwell dens-low 2 centered dipole 4 Power Tracer Crary Helliwell dens-low 2 centered dipole 5 ducted (AFRL) Crary Helliwell dens-low centered dipole 6 Power Tracer Crary Helliwell dens-low centered dipole 7 Power Tracer LFCOM Helliwell dens-high tilted offset dipole 8 ducted (AFRL) Crary Helliwell dens-low tilted offset dipole 9 ducted (AFRL) Crary Helliwell dens-high tilted offset dipole a Model 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. b Power 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. c LFCOM, Earth-ionosphere waveguide transmitter fields from the LFCOM simulator; Crary, Earth-ionosphere waveguide transmitter fields from fit to Crary [1961] calculation. d Helliwell, VLF ionospheric absorption curves from Helliwell [1965, Figures 3 35]; approx-helliwell, daytime VLF absorption curves using night Helliwell values plus 26 db. e Dens-, 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. caustic as an inhomogeneous wave [Budden, 1985]. In this model, we have taken steps to identify regions of unphysical focusing along the caustic and artificially limited the resulting ray power flux. This involves watching for the development of an additional inflection point in the local refractive index surface and preventing further wave focusing 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 computational artifact. Satellite VLF measurements demonstrate features consistent with the shadow boundary, similar to those produced by our model. The caustic and resulting shadow boundaries do not figure into the ducted propagation model 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 strong attenuation of upgoing VLF at those latitudes. This strong attenuation is not a factor at higher L shells, where the wave energy originates at higher latitudes. [21] To summarize, the important components of this modeling effort can be divided into five categories: initial conditions model (the transmitter fields within the Earthionosphere waveguide), ionospheric absorption ( loss ) model, plasma density and geomagnetic field models, and wave propagator. Table 1 lists the different combinations of models used to produce the results below. Model 1 is our new Power Tracer-based code stack, using our best, most realistic models, and operating in a tilted offset dipole magnetic field. It is later compared to model 7, which uses the dens-high full-topside ionosphere model, and models 8 9, which are based on the ducted propagator of Inan et al. [1984]. Models 2 6 operate in a centered dipole field and are used to connect our new work to other published results. We will refer to Table 1 often as we describe our validation efforts. 3. Validation Using Satellite Measurements [22] The Power Tracer model stack has been evaluated against 64 in situ sets of measurements of terrestrial VLF transmitters obtained by five satellites during daytime and nighttime passes. Table 2 lists the parameters of the satellite passes and the transmitters they observed. For each pass, predicted wavefield strengths have been generated using various models from Table 1. The models selected should make it possible to identify the cause of any observed discrepancies in their outputs. Table 2. Satellites, Pass Counts, VLF Transmitters, and Parameters Satellite Altitude (km) Inclination (deg) Transmitter Location Lat (deg N) Lon (deg E) Mag Lat (deg N) Freq. (khz) Power (kw) Pass Count Model-to- Data Ratio [db] Day Night DE OMD a LaMoure, ND NA IMAGE NPM Lualualei, HI NA 22 NML LaMoure, ND NA 19 NWC Exmouth, Australia NA 22 OGO-I NAA b Cutler, ME NA 9 NPG b Jim Creek, WA NA 17 OGO-II NAA b Cutler, ME /2 c 15 5 NPG b Jim Creek, WA /8 c DEMETER NWC Exmouth, Australia NA NA 20 a Transmitter parameters as of the 1981 DE-1 flight. OMD is no longer active. b Transmitter parameters as of the 1966 OGO data set. NAA and NPG (now NLK) no longer operate on these frequencies. c Values are for day/night. 6of16

7 Figure 4. Comparison of DE-1 magnetic flux data to the outputs of various models, listed in Table 1, plotted against magnetic latitude and L shell. The data were taken as the satellite transited the Omega transmitter OMD in North Dakota (shown at its dipole L shell). The data points are reproduced from Inan et al. [1984], as is the red model output line (Inan84). Notice that the data drop off sharply above L 4, which likely indicates the location of the plasmapause, and the shift in the null caused by different propagation assumptions. No model shows a clear advantage over the others. [23] To quantify the comparison, we introduce the mean log ratio of the model to satellite data values during pass j of transmitter XMTR as R XMTR ðþ¼ j 1 X Nj X MOD ðþ i 20 log N 10 j X SAT ðþ i i¼1 where X is the wavefield quantity of interest (electric or magnetic) and the sum is over the N j individual measurements i comprising the pass. A pass is defined as the sequence of measurements taken along a continuous satellite trajectory which does not visit any latitude more than once. The resulting ratios, expressed in db, are listed in Table 2. We have assumed a lognormal distribution in selecting this metric, as examination of the distribution of the individual ratios suggests. Some constituent points of certain passes may be excluded from the average for various reasons, as discussed in the text below Dynamics Explorer [24] In order to provide a strong connection to previous work and an initial validation of our code stack, we have implemented the ducted propagation model described in Inan et al. [1984] and compared the outputs of both models to the Dynamics Explorer 1 (DE-1) measurements shown in that paper [Inan et al., 1984, Figure 2]. Orbiting in a ,300 km orbit with 89.9 inclination and carrying a ð1þ magnetic loop antenna, DE-1 made a daytime pass over the North Dakota Omega navigational transmitter (OMD) on 11 January 1982, and recorded VLF transmissions between 10 and 16 khz. The dots in Figure 4 are the 13.1 khz calibrated DE-1 data presented by Inan et al. [1984]. Note the sharp dropoff in the wave magnetic flux outside of L 4, which may indicate the location of the plasmapause. The Inan84 line is a reproduction of the original model output in that paper, taken directly from the published figure. To effect a meaningful comparison, we have implemented the ducted propagation model described in that paper, which consists of the Crary transmitter model, the Helliwell nighttime absorption curve adjusted by +26 db for the daytime pass, the ducted propagation model, a centered dipole geomagnetic field model and a specific density profile. The density profile best corresponds to our dens-low model, described in section 2, when dividing all densities by a factor of 2. [25] When running those models as described by Inan et al. [1984], assuming field-aligned propagation starting at ground level, we closely reproduce the published simulation outputs as shown by the model 2 line in Figure 4. Having reproduced the published result, we examined the effects of using more realistic assumptions in the ducted propagation model. The simplified daytime Helliwell curve was replaced by our time-resolved curves and radial propagation assumed until 1000 km altitude, after p ffiffiffi which field-aligned propagation prevailed. A factor of 2, obtained by properly timeaveraging the wavefields, was added to the computation in equation (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 original model for magnetic latitudes below 50 degrees. Above 50 degrees, the satellite appears to have encountered the plasmapause: an effect not modeled in any of the ducted simulations and occurring at a higher L shell in the Power Tracer models. The apparent latitude of the null over the OMD transmitter is shifted poleward as a result of presuming the rays to travel vertically to 1000 km altitude before propagating along the geomagnetic field. This results in the transmissions following a higher magnetic L shell than that at the ground. [26] To examine the effects of the chosen density and propagation models, we have included results from three additional models in Figure 4. Model 4 is the same as the improved ducted model 3, but substitutes the Power Tracer for the propagator. This results in a better fit to the data below 50 degrees. Note that the Power Tracer s plasmapause is fixed at L = 5.1. Finally, the lower-density profile used to match the Inan et al. [1984] profile was replaced with our standard dens-low model (without division by 2) and the ducted and Power Tracer models used again to produce the model 5 and model 6 curves, respectively. Notice that the higher densities lead to higher wave magnetic flux through enhancement of the index of refraction. [27] Neglecting magnetic latitudes above 50 degrees (where the plasmapause likely affects the comparison) and applying (1), we obtain a model 4 output to observed data ratio of 7.2 db for this single pass, as shown in Table 2. One pass does not constitute validation, but Figure 4 does demonstrate that our results are consistent with previous 7of16

8 work. In the following sections we evaluate the models performance using considerably more satellite data IMAGE [28] The primary data source for this study was the radio plasma imager (RPI) instrument [Reinisch et al., 2000] on the IMAGE satellite. IMAGE, launched in March 2000, was in a polar orbit with a 1000 km perigee and an apogee of 7.2 Earth radii. RPI consisted of three orthogonal pairs of antennas and transmitted/received waves from 3 khz to 3 MHz. The RPI receivers were narrowband with a fixed bandwidth of 300 Hz. For the VLF ground transmitter monitoring study, the RPI operated in a passive mode over a small frequency range, khz, and fine frequency stepping, 300 Hz [Reinisch et al., 2006]. Observations were made at a sampling rate of 3.2 ms and each measurement was averaged over 8 samples, or 25.6 ms. Amplitude measurements at a particular frequency were repeated every 3 to 4 min. The standard amplitude resolution was db, which is much smaller than signal fluctuations of natural causes. [29] The RPI system was designed to have a dynamic range of the order of 90 to 100 db. The absolute quietest observed data, conventionally assumed to represent the preamp/receiver noise level, is around 10 db-nv/m. An examination of the dynamic spectrum data during the periods of the VLF monitoring study shows amplitudes ranging from a high of 100 db-nv/m to a low of 40 db-nv/m, substantially above the instrument noise floor. These measurements include both the signals from the VLF transmitters and the background plasma waves. To estimate the contribution of background plasma waves, measurements were analyzed from a band around 26.7 khz during several transmitter passes. This frequency is sufficiently removed from the transmitter frequencies so that it provides a reasonable measure of background activity, but close enough so that the background amplitudes measured are applicable to the transmitter bands. It was found that the background amplitude had an average less than 50 db-nv/m between +/ 40 degrees latitude with occasional excursions into the range db-nv/m. This value of background noise is consistent with measurements made by the Plasma Wave Experiment aboard the CRRES satellite, which observed a background at 20 khz of about 54 db-nv/m at L = 2.55 inside the plasmapause [Meredith et al., 2004], and with background levels estimated from the OGO-1 and OGO-2 data inside the plasmasphere [Heyborne, 1966]. At higher latitudes the background could sometimes extend to db-nv/m but was always less than the amplitude in the transmitter bands. [30] The absolute value of the wave electric field intensity in the far-field was calculated as the measured voltage difference between the two branches of a pair of the antennae divided by the effective length of the RPI dipole antenna, taken to be L/2 where L is the tip-to-tip length [Balanis, 1997]. This is a valid estimate when the antenna current distribution is linear and when the antenna is short relative to the radio wavelength. In the whistler mode, the index of refraction is generally about 6 and the wavelength is about 2 km, i.e., much longer than the antennae. During the IMAGE lifetime, the RPI antennas were damaged several times so that the physical lengths of the antennae were known with an uncertainty of 20%, but the signal amplitude calculations take into account the changing length of the RPI antenna. Combining the uncertainties in the effective length and the voltage measurements, the estimated uncertainty in the absolute wave electric field amplitude is a factor of 0.5 to 2.0, or +/ 6 db, which is in the range of the uncertainties for most instruments of similar type. [31] The resulting wave electric field data points are directly compared to the model 1 outputs. Figures 5a 5c show the entire IMAGE data set as a function of magnetic latitude, plotted by transmitter. All of the IMAGE observations for each transmitter have been overlaid on individual plots, as have the corresponding outputs from model 1. To facilitate comparison, a 50 db-nv/m floor has been added to the model wave electric field estimates. As this background does not originate from the transmitters, it would not otherwise be modeled by the code. All of the satellite data were obtained during nighttime passes over the transmitters, and the nature of the IMAGE orbit was such that all of the observations occurred near periapsis at an altitude of about 1500 km. [32] The plots clearly demonstrate that the model outputs consistently overestimate the wavefields outside the equatorial region by about 20 db (a factor of 10). This is more apparent in Figures 5d 5f where the statistics for the IMAGE electric field at each latitude have been plotted. Here, the dark lines represent the median measured wavefields, while the shading indicates the first and third interquartile region. The bounding black lines indicate the maximum and minimum measured wavefields. Only the median model 1 outputs are shown in blue, as they vary significantly less than the data. The curves for all transmitters are similar, and indicate that the model is consistently overestimating wavefield strengths at night in both hemispheres by about 20 db. The apparent underestimation in the low-altitude equatorial region is notable but of less consequence because the power there is typically small. We address this issue in section 4. [33] A remarkable feature of all of these plots is the extreme variability of the transmitter power observed near the equator (up to 60 db), where the ionospheric absorption curves indicate that virtually no power should reach. Clearly a highly variable process exists that allows VLF transmissions to propagate into this region under certain circumstances. The varying prominence of the caustic in the observations is also noteworthy. [34] Using the methodology of equation (1), the model to data ratio for the NPM, NML, and NWC transmitters are 22 db, 19 db, and 22 db, respectively. Only locations where 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 considered in the ratio. This includes the regions typically receiving the bulk of the transmitted power OGO [35] The Orbiting Geophysical Observatory (OGO) 1 and 2 satellites flew in highly elliptical equatorial and nearly circular polar orbits, respectively, in They each carried 10-foot loop antennae and four VLF receivers, one of which was used to acquire magnetic flux measurements 8of16

9 Figure 5. A comparison of the IMAGE electric field data to outputs from model 1. Figures 5a 5c overplot all IMAGE passes for individual transmitters with the corresponding model outputs. Predicted shadow 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 in the equatorial region, and the large differences between model and data. of terrestrial Navy transmitters NPG (now NLK) in Washington State and NAA in Maine over long trajectories, including during the daytime. The processed, scaled and plotted results were digitized from archival reports [Heyborne, 1966] and used as an additional data set to complement the IMAGE measurements in our validation effort. Heyborne [1966] claims ±5 db accuracy for the OGO observations. [36] Figures 6a and 6b present scatterplots of the OGO 1 data and models similar to those produced for the IMAGE data, and Figures 6c and 6d show the analogous statistics. OGO 1 operated in a ,000 km 30 inclination orbit. The toroidal loop antenna was oriented such that it would be sensitive to upgoing VLF in the transmitter hemisphere, where wave normal angles to the ambient magnetic field are small. The altitude regime covered by the OGO 1 observations is much higher than that of the other satellites in this study, making these measurements especially valuable. All of the data shown were taken at night. [37] Figure 7 shows the OGO 2 data in a similar way, but separated by day and night passes. OGO 2 flew in a km 87 inclination orbit, and used a hexagonal antenna oriented somewhat more efficiently than that on OGO 1. For both satellites, the VLF wave magnetic flux magnitudes should be considered as lower bounds, essentially accurate in the transmitter hemisphere and potentially far too low in the conjugate hemisphere equatorward of the caustic, where the wave normal angles are generally very large. 9of16

10 Figure 6. As in Figure 5, but comparing OGO-1 magnetic flux data to outputs from model 1. Figures 6a and 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 the conjugate hemispheres are considered substantially less reliable. Again note the substantial differences between model and data. [38] Clearly the OGO passes are highly variable, but the statistical plots again demonstrate that model 1 typically overestimates the wavefields off the magnetic equator, and underestimates them near the equator. Applying the formalism of (1) to these data and model outputs in a manner similar to that used for IMAGE yields a typical model-todata ratio (away from the magnetic equator) of about 15 db. The exact values are listed in Table 2, and vary considerably between day and night DEMETER [39] The DEMETER satellite operates in a nearly circular 700 km orbit at 98.3 inclination. The on-board ICE electric field experiment [Berthelier et al., 2006] measures one component of electric field over the 15 Hz 17.4 khz band. The only large terrestrial VLF transmitter observable with ICE is NWC, whose 19.8 khz transmissions fall within the known 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 include one data point in Table 2 to further bound the observations. DEMETER typically measures db-nv/m over NWC at night (C. Rodger and R. Gamble, private communication, 2007). This is similar to, but somewhat higher than, the magnitudes measured by the IMAGE spacecraft (Figure 5). However, IMAGE did not pass directly over NWC, thereby skirting the region of highest wavefield intensity. When compared to the maximum wavefield strengths predicted by model 1 of about 140 db-nv/m, the DEMETER observations are consistent with the 20 db error estimate computed in section 3.2. Like IMAGE, DEMETER sees highly variable wavefield intensities around the magnetic equator. 4. Discussion [41] The data sets presented in section 3 indicate a consistent bias in the model 1 wave electric field and magnetic flux estimates when compared to observations by the IMAGE and OGO spacecraft. Neglecting for the moment the highly variable equatorial region where, on average, the transmitter power is substantially less at low altitudes than that off the equator, we note that the satellite data exhibit statistically between 10 and 30 db smaller magnitude than the model outputs. Such a large bias strongly suggests a fundamental physical issue with the underlying models. We have shown (Figure 4) that the wavefield estimates from models using the Power Tracer wave propagator are similar to those of Inan et al. [1984] when using the same density and geomagnetic field models and the same initial conditions, despite the two models completely dissimilar propagation methods. Both models seem to match the one DE-1 pass reasonably well, but this may simply be fortuitous. A more detailed comparison of the two 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, overlaid with the outputs of several models. We have used a number of models from Table 1 for the comparison, including Crary and LFCOM waveguide field models and both the ducted and Power Tracer propagation models. To visualize the effect of our density model, we have applied both our standard empty topside model (dens-low) and the 10 of 16

11 Figure 7. As in Figure 6, but for OGO-2, separated by night and day. Abel and Thorne [1998] full topside model (dens-high). We have also run the Power Tracer with and without the Landau 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 fields over any of the passes shown, except for its expected inability 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) and damping (not shown) models also appear to be minor. Notice the strong effect of the caustic in Figures 8a and 8b near 30 S latitude, in both the observations and the power tracing models, and the significant variability observed through the equatorial region. Model to data ratios for each pass 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 11 of 16

12 demonstrate the same 20 db overestimation of the expected wave magnetic flux. Note the almost complete lack of observed signal fade in the equatorial regions of the plots, where the model outputs are typically db too small. [45] When plotted over the region covered by the satellite measurements, the ratio of observed to model 1 predicted wavefields takes the form shown in Figure 10, which confirms that for all practical purposes, an essentially constant +20 db bias seems to exist in the model outputs off the equator. Figure 10a shows the model to data ratio by magnetic latitude and radius, while Figure 10b shows only the latitudinal dependence. Near the equator the wavefields are sometimes very small, so that the 50 db-nv/m floor matches that observed in the data and the ratio is close to 0 db, and sometimes very large, so that the imposed floor significantly undershoots the data and the ratio can be as low as 40 db. At magnetic latitudes exceeding 60 at the low altitudes, the model is operating outside of the plasma- Figure 8. Individual IMAGE passes for three VLF transmitters, overlaid with outputs from four models. The mean model-to-data ratios are listed for each pass and amount to about 20 db for all models. Notice the predicted and observed shadow boundaries observed conjugate to the transmitters. Figure 9. As in Figure 8, but for two OGO-2 passes. Notice the strong signals throughout the equatorial region. 12 of 16

13 Figure 10. Ratios of model 1 to the IMAGE and OGO satellite data sets (a) by L shell and magnetic latitude and (b) by magnetic latitude only. IMAGE data are in black; OGO data are in blue. The transmitters are shown as triangles. Shaded areas denote regions outside the plasmapause or where the model predicts near-background noise levels. Note the mapping of ratios along L shell in Figure 10a and the greater overall variance visible in Figure 10b in the hemisphere conjugate to most of the transmitters. pause and yielding only the background value. These latitude regions have been shaded in Figure 10b. Notice the increased variability at midlatitudes in the southern hemisphere, which is magnetically conjugate to all but one 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 in Figure 10b) the high-altitude OGO 1 passes demonstrate that the 20 db model to data ratio maps along the geomagnetic field to high altitude as well, and that the ratio falls to low values at the plasmapause, as expected. This indicates that the divergent behavior near the magnetic equator (underestimating wavefields rather than overestimating) is a low-altitude phenomenon related to the low incident wave power in that region (see Figure 3), caused mostly by ionospheric 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 arise from the initial conditions common to both. The Crary model is a simple relationship derived from a set of electric field computations, while LFCOM is a first-principles mode-theory simulation. Both compare favorably to one another, and to the LWPC code, and the mode theory codes have received substantial validation efforts by the government agencies that maintain them. These facts warrant closer examination of the ionospheric absorption curves given by Helliwell [1965], and in the methodology by which they are combined with the waveguide field models. [48] The Helliwell absorption curves, although widely used in calculations of VLF transmitter leakage into the near-space environment, were originally calculated using fairly restrictive assumptions. The wavefield is assumed to be a plane wave with wave normal directed vertically, incident on a horizontally stratified ionosphere. The D region profile used in the calculation assumes a sharp lower boundary, an ensemble-averaged density profile, and a representative collision frequency model. When using the resulting absorption estimates, an additional 3 db polarization loss must be imposed and losses due to reflection at the lower boundary of the ionosphere (estimated by Helliwell to be 2 db) are not included. Although the exercise produces plausible absorption curves (except at very low latitudes during the day and latitudes below 45 magnetic during the night, where the quasi-longitudinal approximation used in the calculation breaks down), it certainly was never intended for application to all possible times, longitudes, and distances from the transmitter. Nevertheless, the curves should be reasonably accurate directly over high-latitude transmitters, where the assumptions involved are usually appropriate. The 20 db discrepancy observed in our models over the transmitters therefore suggests that the absorption curves 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 model for the Earth-ionosphere waveguide with the (reasonably accurate) Helliwell absorption model which is invalid. Many of the potential problems inherent in this methodology 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 brought to bear on this problem, generating three dimensional fullwave solutions over limited areas for the entire transmitterionosphere system. Although computationally expensive, these independent numerical models can directly compute wave electric fields at an altitude of 150km from terrestrial transmitters, avoiding the need for ionospheric absorption curves entirely. By passing some of these model outputs (S. A. Cummer, private communication, 2008; N. Lehtinen, private communication, 2008) directly into model 1, wave electric field estimates are produced that match those of the layered models reasonably well. [50] We are therefore left to conclude that none of the transmitter models studied, layered or numerical, reflect the entire set of relevant physical processes. Given that the models all agree at 150 km, and that the satellite data shows similar error whether taken directly above the transmitter at 600, 1500 or 7000 km, or conjugate to it at the end of a very long interhemispheric propagation path, it is clear that the 13 of 16