Radio Science

Radiation impedance over a thunderstorm



[1] In the summer of 2002 the Altus Cumulus Electrification Study obtained radiated Poynting flux measurements in the near vicinity of lightning discharge events. These measurements not only allow a determination of radiated power but also allow a calculation of the radiation impedance above a thunderstorm when the thunderstorm was acting as an antenna. This impedance is significant since it defines the level of displacement currents propagating into the middle atmosphere and, as applications demonstrate, is a critical quantity in understanding the relationship between power and displacement current in the near vicinity of a thunderstorm. We find that the radiation impedance of the thunderstorm is surprisingly low in the VLF and varies inversely with frequency consistent with a capacitive-like coupling from the thunderstorm to middle atmosphere.

1. Introduction

[2] In the summer of 2002 an atmospheric electricity package was integrated into the ALTUS uninhabited aerial vehicle (UAV) for a series of flights over southern Florida thunderstorms. The name of this project was the Altus Cumulus Electrification Study, or ACES. There were three primary science objectives to ACES. (1) Examine the lightning-storm relationship from storm birth to death. (2) Determine the storm's electromagnetic budget including both DC and AC contributions to the global atmospheric electric circuit. (3) Further validate space-based lightning sensors such as TRMM/LIS. This work focuses on the second objective, specifically addressing the ability of AC currents to flow from the cloud top to the middle atmosphere (i.e., 20–70 km), and in particular quantifying the radiation impedance in thunderstorm near and intermediate fields.

[3] Thunderstorms possess two different natures, illustrated in Figure 1. First, during their charging phase, thunderstorms act as a quasi-DC voltage source (i.e., a battery), with storm dipole electrostatic fields driving current upward from the lower atmosphere to the ionosphere [Volland, 1982]. Such upward conduction currents were hypothesized by Wilson [1920] and subsequently observed numerous times [Gish and Wait, 1950; Stergis et al., 1957; Vonnegut et al., 1966; Blakeslee et al., 1989]. Second, during their impulsive discharge phase, a thunderstorm undergoes a quick change in its electric dipole moment, in essence behaving as an electric antenna trapped between the two conducting plates of the ionosphere and ground. Coupling of displacement currents from the lightning channel antenna to the Earth/ionosphere waveguide is frequency-dependent and rather complex in the ultralow-frequency (ULF) regime [Wait, 1960; Harth, 1982; Dejnakarintra and Park, 1974; Greifinger and Greifinger, 1976; Volland, 1984].

Figure 1.

Two-sided nature of a thunderstorm as a current source. (top) Volland's [1984] DC model indicates that the thunderstorm acts as an electrostatic current source with about 0.5 A flowing through atmospheric resistance RH into the ionosphere (Ri). (bottom) For short periods, the thunderstorm becomes an antenna, radiating power to the middle atmosphere where AC displacement currents propagate into the Earth/ionosphere waveguide.

[4] As described by Greifinger and Greifinger [1976], displacement currents are important since they will transform into conduction currents at heights where σ(z) = ɛoω and hence will act to move charge in the upper atmosphere. Specifically, as the thunderstorm-emitted electromagnetic waves propagate to higher altitudes, the medium becomes increasingly conductive (because of the exponentially increasing conductivity profile with height). At a given height, zo, where σ(zo) = ɛoω the conduction currents generated by the electric field (σ (zo) E) become comparable to the displacement currents (ɛoω E), and this electric field begins to induce charge movement in the lower boundary of the ionosphere. At heights greater than zo the electric field is considered to be electrostatic, with conduction currents dominating over displacement currents.

[5] In order to understand these very different natures and associated electrical energy coupling to the middle atmosphere, the ACES project flew a remotely piloted vehicle in the near vicinity of thunderstorms. An objective was to get above the storms and also in horizontal proximity to capture AC electric and magnetic wave fields directly from their source before they couple to the Earth-ionosphere waveguide. Previous ER-2 overflights of thunderstorms indicated that substantial and significant displacement currents flow upward from a storm into the middle atmosphere during and immediate following lightning discharges [Blakeslee et al., 1989]. However, corresponding magnetic field measurements were not available on these flight, and wave Poynting flux/power input into the middle atmosphere could not be quantified. Thus, even though displacement currents were found to be large, it is unclear that there is substantial power transfer from the lower atmosphere to middle atmosphere via electromagnetic coupling.

[6] Blakeslee et al. [1989] addressed electrical measurements above thunderstorms and we now extend that original work with added new power and impedance determinations, particularly emphasizing the AC portion of the energy. We focus on observations from a Poynting Vector System (PVS) designed to derive the Poynting flux over a thunderstorm during lightning discharges. We demonstrate via observation that the power and electric field are related via the radiation resistance near and above the thunderstorm. This resistance is not uniform but in fact dependant on both location relative to the storm and wave frequency. We compare the power carried in displacement currents to the electrostatic dissipated power to determine the significance of this second current source.

2. Platform, Instrument, and Flight Description

[7] General Atomics' Altus UAV is the commercial derivative of the more recognized Predator drone. With a ∼7.3 m length, ∼16.7 m wingspan, ∼136 kg science payload capacity, 8 hour endurance capability, and ∼16.7 km ceiling, it is an ideal platform for thunderstorm research. Specifically, to achieve the science objectives, the platform had to remain in the near vicinity of a potential storm cloud for long periods of time. Fast jet aircraft, like the ER-2, make repeated encounters from distant to near-vicinity regions. Their speed and large turn radius limits the time in close to the storm. In contrast, the ALTUS loiter speed of ∼30 m/s allows the platform to remain continually in the near vicinity for constant monitoring during storm maturation. On occasion during the ACES mission the platform passed to within a few hundred meters of the thundercloud tops.

[8] The Altus faring was modified to incorporate six DC field mills, optical pulse sensors, a slow antenna, a Gerdien conductivity probe, a DC magnetometer, and a Poynting vector system located on a forward mounted boom (Figure 2). A flight data system obtained and saved measurements from this sensor suite in both slow continuous mode and in fast “triggered” format. The fast-sampling trigger mode captured measurements in predefined 16 channels at 200 kS/s in a 1/3 s window, when activated by a specific sensor (signal above a predefined threshold). Lightning-generated optical and electrical pulses represented near-perfect trigger sources and over 4300 such fast-sampling snapshots were captured during the month-long mission.

Figure 2.

General Atomics' Altus uninhabited aerial vehicle during an Altus Cumulus Electrification Study (ACES) flight. The Poynting vector system is located in the bulb at the end of the nose-extending boom.

[9] The Poynting Vector System (PVS), the instrument of primary focus in this paper, consists of orthogonal E and B sensors sensitive between 10 Hz and 100 kHz. The electric field sensors are short monopoles with local preamps and the magnetic field sensors are search coils also with local preamps. In order to reduce noise (from both the forward payload bay and aft engine) the sets of sensors were placed on a 1 m boom extending from the ALTUS nose (see Figure 2). The Altus engine noise was substantial and continuously detected in the PVS system during flights. While a concern, we also understood that the lightning emission in proximity of the thunderstorm would be very intense, exceeding the engine noise levels. For example, during flights, the VLF E field noise level was near 100 mV/m, but lightning transient VLF emission levels could exceed tens of volts per meter, yielding >45 dB of noise-free dynamic range for thunderstorm emission detection. We note that we have flown the PVS on smaller UAV platforms, but the proximity of the sensor suite to the engine noise source on these platforms created an EMI environment that either saturated the sensor and/or did not allow easy detection of thunderstorm emissions. With the use of a larger platform like the ALTUS, we were able to locate the sensor suite as far as mechanically possible (i.e., nose-extended boom) from the rear-located engine, thereby reducing platform noise and increasing the dynamic range for thunderstorm emission detection.

[10] There were 18 ACES flights, including 7 test flights (4 of which occurred in the Mojave Desert) and 11 formal science flights on site from Key West. Of those 11 flights, 6 flights resulted in very direct and prolonged encounters with thunderstorms. The science analysis presented herein will highlight measurements from an active flight on 10 August 2002 (DOY 222).

[11] On 10 August, the Altus took off from Key West at 1542 UT and for nearly three hours was in reconnaissance over the South Florida coast, anticipating the encounter of a cumulus cloud in the process of maturization into a thunderstorm. While trailing a candidate cloud formation, a second cell just southward became electrically active (near 1820 UT). The Altus moved southward to intercept this storm and, once intercepted, proceeded to make a series of “figure eight” passes over the storm for the next 45 min. Figure 3 shows the peak VLF Ex magnitudes (from the lightning EMP signal in the triggered system between 7 and 14 kHz) in 5 min intervals throughout the flight. The peak in activity between 1830 and 1900 UT is associated with the repeated passes of the UAV over the storm. Clearly the storm was electrically active with lightning signals reaching nearly 20 V/m over the storm top. After 1900 UT, emissions from a second active cell approximately 30–40 km southeast were also detected, and activity from the nearby cell (being overflown) was gradually decreasing. Near 1915 UT the UAV left the disintegrating storm cell to return to Key West. Thunderstorms remained in the near vicinity during the return, accounting for the ∼2 V/m signal levels between 1930 and 2000 UT. Upon approach to Key West the AC electric fields again increased (after 2000 UT) to nearly 20 V/m, this associated with lightning from a mature storm cell located just to the northwest of the Key West Naval Air Station.

Figure 3.

(top) Peak VHF electric field in 5 min intervals along with the figure eight flight path of the Altus (blue) over (bottom left) a south Florida storm and (bottom right) the storm located northwest of Key West.

3. Radiation Impedance

[12] A primary objective of the ACES mission was to determine the upward energy contribution into the middle atmosphere. As a DC/electrostatic generator, the thunderstorm acts like a 50 MV battery that drives about 0.5 A of conduction current upward through the highly resistive (∼108 MΩ) upper atmosphere [Volland, 1984]. The equivalent circuit of the upper atmosphere DC currents over a thunderstorm is illustrated by Volland [1984, Figure 5.5]. In contrast, thunderstorms also generate impulsive radiation from lightning, and for these short periods, the thunderstorm can be considered a broadband antenna. Radiative/displacement currents can be comparable or exceed their conductive counterparts for these short periods [Blakeslee et al., 1989]. However, given the long wavelength emission and the close proximity to the storm, where E and B fields become very complex, it is unclear how these large displacement currents relate to actual upward power. The radiation impedance, Z, is a fundamental quantity that relates the radiated power flux, S, from a transmitting antenna to the associated electric field, E, and displacement current. Far from a radiation source, Z is its free space value of 377 ohms. As we discuss below, for the long wavelengths under consideration (160–3000 km), the UAV/source proximity of 10–40 km, and the source size of 2–10 km, intermediate and near fields dominate, and one should not expect a free space radiation impedance.

[13] Using the ACES PVS measurements, the radiation impedance can be determined by calculating the ratio of E2/S where E is the magnitude of the electric field and S is the magnitude of the Poynting flux. To directly calculate the impendence, ∣Z∣, both power flux and electric field are required. If just the electric field sensors were flown alone, the Poynting flux (S = E × Bo) could not be derived, making a unique determination of Z impossible. The added information provided by the search coil's B field allows a unique determination of power flux, and hence Z. During the 45 min overflights on DOY 222, lightning events were detected from two storms: the primary storm of the overflight and a second cell located about 40 km to the southeast. Lightning-generated emissions were examined to determine if they had enough intensity to give a substantial magnetic signal for a noise-free determination of the Poynting flux. Eight such events were detected between 1830 and 1915 UT.

[14] Waveform measurements from these eight events were used to derive the Poynting flux, and then the measurements were Fourier transformed into five frequency bands: 100–316 Hz (178 Hz band), 316–1000 Hz (562 Hz band), 1000–3160 Hz (1780 Hz band), 3160–10000 Hz (5620 Hz band), and 10–31.6 kHz (17.8 kHz band). Figure 4a shows the peak electric field ∣E∣, Figure 4b shows the peak Poynting flux ∣S∣, and Figure 4c shows the associated radiation impedance E2/S for these events as a function of frequency.

Figure 4.

Discharge-related (a) electric field, (b) Poynting flux, and (c) radiation impedance as a function of frequency, for lightning events in the vicinity of the Altus during 1830–1930 UT on 10 August 2002. The events identified with “n” originate from the storm nearby and were overflown by the Altus, and those labeled “se” originate from a storm located about 35 km to the southeast of the Altus. Note that the events become nicely ordered when considering radiation impedance.

[15] In Figure 4 we have indicated emissions from the nearby cell (being overflown by the UAV) as “n” and those from the cell 40 km to the SE as “se”. In Figure 4a it is clear that the events from the nearby cell tend to have the larger E fields at lower frequencies suggesting that the UAV is immersed in the slowly varying quasi-electrostatic fields from these nearby event. In Figure 4b, we find that the peak radiated power occurred at VLF frequencies, above 3 kHz, but considerable Poynting flux still exists at lower frequencies. In both Figures 4a and 4b there are fairly large variations on an event-by-event basis, with the most powerful radiation originating from an event located in the more distant southeast storm (see Figure 4b).

[16] While there are fairly extensive variations in emitted electric field and Poynting flux (Figures 4a and 4b, respectively), the events become highly organized when their impedance is calculated (Figure 4c). As suggested by Figure 4, there are three notable and distinct attributes of the measured impedance: First, the impedance shows a 1/f variation with frequency. Near 10 kHz the values range from 100 to 400 ohms but increase as frequency decreases to 1000–30,000 ohms at 178 Hz. Second, this 1/f effect is very pronounced at frequencies below 5000 Hz, but appears to flatten out at the highest frequencies, possibly suggesting a transition from near- to intermediate-field variations. This flattening (and in some cases the appearance of an f-like variation) is very pronounced in the high-frequency portion of the more distant southeast events. As suggested by Figure 4, frequency-independent free space radiation resistance values (377 ohms) are not the norm. Finally, while all the curves display a 1/f character below 5000 Hz, individual curves of Z(f) appear to vary on the basis of distance from the storm, with the southeast events having (mostly) consistently lower Z(f) curves as compared to the near events. Hence, when considering the radiation impedance, the events become organized on the basis of both wave frequency and distance from the source.

4. Analytical Expression for Near-Field Impedance

[17] Initially, the variation in radiation impedance was surprising, but it is actually understandable via modest calculations of the antenna near fields. In the near vicinity (r equation image λ, r ∼ a, a is the source size) the AC wave electric field in close proximity over top of a thunderstorm is describable using the static term of the electric dipole. In general, the electric field in the vicinity of a dipole is

equation image

[Reitz et al., 1979], where M is the thunderstorm electric dipole, r is the radial vector, and θ is the colatitude angle relative to the dipole direction. Considering locations over the dipole, the fields are aligned primarily along the vertical direction, with θ ∼ 0° and r ∼ z. Hence equation (1) can be reexpressed as

equation image

where r = (z2 + ρ2)equation image ∼ z (for top side applications). As derived by the induction equation, above the storm, the changing electric flux through a horizontal circular area (vertical normal) of radius ρ will induce a magnetic field,

equation image

with ϕ being the azimuth direction about the vertical. The Poynting flux, which is radiated primarily horizontally outward above the storm is

equation image

The radiation impedance then becomes

equation image

Equation (5) contains the variations observed in Figure 4c. The 1/f variation of the radiation impedance is explainable by considering the fields in the near region of a dipole; the inverse nature of the frequency variation is indicative of a capacitive-like coupling to the regions of space surrounding the antenna (consistent with the physical situation). The inverse variation with distance ρ indicates that Z will increase as the UAV gets closer to the stroke, a trend also observed in Figure 4c.

[18] The formalism equations (1)–(5) applies for observations made directly over the storm where Eρ is small. In regions above but with a horizontal displacement, the Poynting vector will develop a vertical component as well. However, the variation of impedance remains inverse with distance and frequency.

5. Application

[19] Blakeslee et al. [1989] reported large low-frequency displacement currents during and following lightning stokes, these comparable to the conduction currents flowing from the cloud tops to the ionosphere. However, do these large displacement currents translate to large power transfer? As an example, we can compare the conduction currents and electrostatic power dissipation to the displacement currents and radiated power for the lightning event occurring at 1837:13 UT. For the 1 min period immediately preceding this event, the DC E field as measured by the ACES field mills at ∼15 km altitude was small, but immediately after the discharge it jumped to ∼1 kV/m, remaining at this level for about 2 min (until the next discharge at 1839 UT). The upward conduction current density is ∼730 pA/m2 (using σ(z = 15 km)E, with σ(z) ∼ 6 × 10−14 exp (z/L) S/m with L = 6 km [Greifinger and Greifinger, 1976]). The upward electrostatic postdischarge current through a 10 km radius horizontal surface over the storm (A = 3 × 108 m2) is thus ∼0.2 A, consistent with the Volland [1984] model which indicates that, in general, each thunderstorm contributes about 0.5 A in upward currents to the global circuit. This conduction current is smaller than those generated from storms overflown by Blakeslee et al. [1989], suggesting that this storm in south Florida was comparably weak. The power dissipated through the atmosphere above the storm is I2R, R being the atmospheric resistance from the dipole top to the Altus location (R = A−1∫ σ(z)−1dz ∼ 108 ohms). The power dissipation during this postdischarge period is then estimated to be ∼4 MW.

[20] In contrast, the radiated power flux measurement by the PVS at low frequencies (100–316 Hz) is about 0.05 W/m2. The horizontally directed radiated power through a cylindrical surface of 10 km height and 10 km radius is ∼30 MW. Given an estimate for the radiation impedance (via equation (4) and PVS-derived value), we can estimate the displacement current as ID = (P/Z)1/2 ∼ 30 A. We conclude that even though the low-frequency displacement current is over 100 times larger than the conductive current, the powers differ only by a factor of 10. Thus a large displacement current does not automatically translate to an equally large and significant powers. This result is understandable since the power-to-square-current relationship varies with impedance, Z(f), which is a large resistive value at DC and more capacitive-like for AC, progressively decreasing with increasing frequency. The power-to-square-current ratio for conductive processes is ∼108 while for radiative processes (near 100 Hz) is ∼3 × 104.

[21] There is now enough information to consider the significance of the ULF displacement currents reported by Blakeslee et al. [1989]. Specifically, the conduction currents were reported to be about 3 A, and the atmospheric resistance from the cloud top to the ER-2 height (near the same altitude as the ALTUS) is ∼108 ohms, corresponding to a dissipated power of ∼109 W. The displacement currents reported by Blakeslee et al. [1989] were about 1 A (their conduction current subtracted from the Maxwell current). The radiation impedance at a point 10 km from the storm at ∼10 Hz is ∼3 × 105 ohms (via equation (5)). Hence the radiated power associated with these reported displacement currents is ∼4 MW. We thus conclude that while Blakeslee et al. [1989] reported displacement currents comparable to the conduction currents flowing into the middle atmosphere over a lightning storm, the power associated with these displacement currents is substantially smaller (by a factor of 1000) compared to the conductive current power dissipation. Again, we conclude the displacement currents, while large, are not as significant in the surrounding thunderstorm electrodynamics as compared to the electrostatic processes, because of the differing impedance values associated with the currents.

6. Single Station Source Localization Analysis

[22] One intrinsic value of the near-vicinity impedance is it allows a comparison of differing stoke emission characteristics from a specific source independent of the stoke amplitude. The discharge currents that form stokes can be as low as 1 kA (intracloud stokes) and as large as 300 kA (large plus CG strokes), corresponding to a dynamic range of 50 dB. Hence the same thunderstorm could emit widely differing emission amplitudes. However, Z in the near vicinity allows a determination of source range independent of this widely varying emission strength. As indicated in the derivation of equation (5), the dipole magnitude, M, is included in both E and B. A dipole of length L is related to the current in the discharge via M(ω) = I(ω)L/ω [Reitz et al., 1979], and thus M varies as extremely as I. However, Z is functionally related to E/B, and consequently M (and its dependence on current I) cancels from the expression for Z. The variation of Z with distance is then related only to the proximity of the observer to the dipole radiator (Z being intrinsically related to r/2hs, 2hs being the size of the dipole).

[23] As an example, consider the lightning stoke at 1837:13 UT. The NLDL location of this stroke placed it about 16.3 km away at a location due west of the UAV. The PVS can derive direction of arrival of the stroke in the frame of the aircraft. This direction of arrival is illustrated in Figure 5 which indicates a Poynting vector azimuth orientation ∼45° to the right of the nose. At the time, the plane was oriented almost northwest and the discharge's nearly due west location is consistent with this arrival angle.

Figure 5.

Elevation and azimuth of the lightning radiation between 7 and 14 kHz at 1837:13 UT in the Altus' frame of reference. The aircraft nose is pointed toward the origin (0, 0). Note that the emission originates from a source located ∼45° from the nose.

[24] Further, using ρ ∼ 2/ɛoωZ to obtain an approximate range, we obtain 〈z〉 ∼ 11 km with a spread of values ranging from 7 to 16 km. Thus, using a PVS in the near vicinity of a storm, one can derive an approximate lightning source location from a single station, with the Poynting vector defining the angle of arrival and radiation impedance, Z, yielding an approximate range estimate. This near-source direction of arrival system using Poynting flux and near-source radiation impedance is unique and has applications in areas beyond basic science, possibly as a hazard alert.

7. Conclusions

[25] Many previous lightning electric studies did not carry a triaxial magnetic field sensor. Hence the Poynting vector (radiated power flux) could not be uniquely derived. The ACES package carried a Poynting vector system consisting of a triaxial electric and magnetic wave sensor to characterize the radiated power flux from lightning between 10 and 100 kHz.

[26] The addition of the magnetic component cannot be understated: Given a wave's E and B, the Poynting vector can be determined, and this information, along with the E can be combined to derive a unique value for the radiation impedance, Z, in the vicinity of a thunderstorm. This fundamental quantity was found to be consistent with being in the near field of a dipole radiator, with Z varying inversely with both frequency and distance from the dipole. The value of Z is critical for translating observed displacement currents into power estimates.

[27] Atmospheric electricity modelers create equivalent circuits of thunderstorm DC and AC activity [Volland, 1984], with the DC/electrostatic activity fully modeled with currents and resistances which allow a determination of dissipated power. Blakeslee et al.'s [1989] observation of conduction currents also included complementary in situ atmospheric conductivity measurements which combined yields a determination of dissipation power. However, their displacement current observations did not include a complementary impedance determination (which requires B), which we now provide here in a general way. Hence with observed displacement currents and Z we add information of the fundamental AC parameters in the model electric circuit in the near vicinity of a thunderstorm.

[28] The ACES mission demonstrated the utility of a UAV to perform near-continuous electrostatic and electromagnetic monitoring of a thunderstorm. New results highlighted here include (1) the determination of radiated Poynting flux over lightning discharge, (2) a new calculation of the thunderstorm radiation impedance in the complicated near-field region, and (3) a comparison of the electrostatic and electromagnetic current and power output to the middle atmosphere. Our objective was to determine the significance of large displacement currents over thunderstorms as reported previously by Blakeslee et al. [1989]. We find displacement currents can be comparable to or exceed DC conduction currents. However, the corresponding radiative power is not as significant as conduction dissipation power, because the associated AC impedance is substantially less than the DC resistance. Thus in the near vicinity of thunderstorms the observation of large displacement currents does not automatically translate to large power fluxes because of the lower 1/f-varying impedance. While the determination of radiation impedance is derived via lightning EMP measurements, the results can be applied in a general way to understand ULF and ELF radiative coupling to the middle atmosphere from power lines, VLF transmitters, and other long wavelength emitters.