This study draws together the available observations in the Schumann resonance frequency range to examine the general issue of sensitivity of ionospheric height variations to changes in ionizing radiation from the Sun on different timescales. Ionospheric height can be formally defined, and two characteristic heights are recognized in the Schumann resonance frequency range. In general, order of magnitude changes in radiation are needed to cause relative changes in ionospheric height as large as 10%, as is the case on both the diurnal and 11-year timescales. Changes in EUV radiation are probably insufficiently strong to account for either the 27-day or the 11-year variation in ionospheric height. More ionization-effective X radiation is needed, but much smaller height changes are expected on the solar rotation timescale because the variations in X radiation on this timescale are only tens of percent and not orders of magnitude. The annual variation in radiation from the Sun is only 7%, with an expected height variation less than 100 m, and this remains to be verified by observations. The general insensitivity of the Schumann resonance cavity to changes in ionizing radiation lends stability to the medium that is valuable toward quantifying absolute changes in the global lightning activity on various timescales within the cavity.
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 The thin layer of air between the conductive Earth and the conductive ionosphere provides the medium for both the global electrical circuit and the electromagnetic waveguide for the Earth's Schumann resonances. The ionosphere forms the variable outer wall of the waveguide. The recognition that the Schumann cavity forms a natural framework for global monitoring has also intensified interest in the stability of its outer wall (the lower ionosphere) to changes in ionizing radiation from the Sun and outer space [Sentman and Fraser, 1991; Schlegel and Füllekrug, 1999; Sátori et al., 2000, 2005; Nickolaenko and Hayakawa, 2002; Kulak et al., 2003; Roldugin et al., 2004]. The usual steadiness of galactic cosmic radiation and ultraviolet radiation from the Sun lend considerable stability to this medium, but improvements in observational methods at ELF and VLF [Schlegel and Füllekrug, 1999; Füllekrug et al., 2002] have identified small but distinctive variations in ionospheric height caused by changes in ionizing radiation.
 This study is concerned with an integration of the various observations and mechanisms for modifying the height of the Schumann resonance waveguide by solar radiation and as a consequence, the intensity of the electromagnetic field within it. Theoretical analyses of the electromagnetic field within a uniform spherical waveguide have shown that the wave amplitude is inversely proportional to the height of the waveguide [Wait, 1972]. That is to say that a halving of waveguide height would double the amplitude, with no change in the lightning source. In observational studies of waveguide height, variations have been noted on the diurnal timescale, the solar X-ray burst timescale ranging from minutes to hours, the timescale of solar proton events (hours to days), the 27-day solar cycle, and the 11-year solar cycle. The possible detection of changes in characteristic height on the annual timescale is also considered. The results are interpreted on the basis of current understanding for two characteristic heights in the ionosphere in the Schumann resonance region [Madden and Thompson, 1965; Greifinger and Greifinger, 1978; P. Greifinger et al., On modeling the lower characteristic ELF altitude from aeronomical data, submitted to Radio Science, 2006, hereinafter referred to as Greifinger et al., submitted manuscript, 2006].
2. Diurnal Timescale
 Large changes in ionizing radiation impinging on the ionosphere from the Sun occur between daytime and nighttime. Lyman α (121.6 nm) in the EUV is the main ionizing component in the solar spectrum [Thomas, 1974; Laštovička and Boška, 1982], at least at solar minimum when solar X rays are substantially less prevalent [Sátori et al., 2005]. On the nightside of the Earth, one might expect the ionosphere to be nonexistent, and hence the day/night contrast in ionization to be essentially infinite. The presence of a nightside upper D region (the upper “wall” for the Earth-ionosphere waveguide) is however well established. The leading explanation for its maintenance is low-level Lyman α radiation from the exosphere, also called “nightglow” [Kupperian et al., 1958; Donahue and Fastie, 1963; Donahue, 1964; Ogawa and Tohmatsu, 1966]. This source of ionization dominates over the galactic cosmic radiation as a source of ionization at the altitude of the lower characteristic layer [Tohmatsu, 1990], and this layer is the one most strongly impacted on the diurnal timescale. The day-to-night ratio in this ionizing radiation has been measured in conjunction with solar eclipses, with estimates varying from 100 to 700 [Dickinson, 1972; Smith, 1972; Thomas, 1974]. Several studies of the D region height variations associated with these large changes in ionization on the diurnal timescale have been undertaken. Sentman and Fraser  assumed a simple sinusoidal diurnal variation of height at each of two measurement stations, and determined the amplitude and phase of the sinusoid that maximized the agreement in observed magnetic intensity between the two stations. The absolute height was not addressed or studied in this analysis, but physically speaking, we expect the lower characteristic height (Greifinger et al., submitted manuscript, 2006) to be the important reflector here. Their results showed 50% increases in height from daytime to nighttime, which given the heights of the lower characteristic layers of Greifinger et al. (submitted manuscript, 2006) would translate to an actual height change of 30 km (50% of 60 km).
Williams and Sátori  later made corrections to remove Schumann resonance (SR) amplitude variations due to the day-night asymmetry of the ionospheric height and to consider the SR amplitude/intensity changes attributable to the different source-observer geometry when comparing the African and South American lightning activity.
Heckman  and Greifinger et al.  monitored the electric and magnetic intensities at a Schumann resonance station operated by the Massachusetts Institute of Technology in West Greenwich, Rhode Island, through the dawn and dusk terminators and noted pronounced changes over short periods (<1 hour) near the terminator. Greifinger et al.  applied a theoretical analysis of the lower characteristic altitude of the ionosphere to these observations and inferred a nighttime-to-daytime height ratio varying from 1.20 to 1.23. Sátori et al.  have more recently documented SR amplitude variations with clocklike accuracy (timescale of a few minutes) at ionospheric sunrise and sunset, at ionospheric height.
3. Solar X-Ray Burst Timescale
 Large-scale perturbation of the ionospheric D region can be produced by changes in solar X radiation on the different timescales of solar activity. The shortest variations are the solar X-ray bursts with durations from minutes to hours. Changes of X-ray flux amounting to three orders of magnitudes can occur on this short timescale. Increases of Schumann resonance frequencies of some tenths of Hertz were observed simultaneously in the different SR modes of the vertical electric and horizontal magnetic field component in distant stations [Roldugin et al., 2004; Sátori et al., 2005]. As a consequence, similar ionospheric height variation can be expected on the timescale of X-ray bursts as during the 11-year solar cycle described by Sátori et al. .
4. Solar Proton Events
Schlegel and Füllekrug  pioneered the use of simple theoretical models of the D region [Greifinger and Greifinger, 1978; Sentman, 1990] to understand high-energy particle precipitation events from the Sun, lasting days to weeks. Changes in Schumann resonance frequencies were used to diagnose the height changes on the basis of a globally representative model. The nine strongest solar proton events in Solar Cycle 22 were examined. A global height change of 2.5 km was inferred for the strongest event, but with expected local (polar cap) height changes up to 12 km. Roldugin et al.  analyzed the solar proton event on 14 July 2000 by examining Schumann resonance frequency variations. Unfortunately, these authors do not extend their interpretation to the height variation of the ionosphere.
5. Solar Rotation (27-Day) Timescale
Füllekrug et al.  have studied systematic changes in Schumann resonance electromagnetic frequencies (8–45 Hz) on the nominal 27-day timescale of the solar rotation period. Both characteristic heights were considered. These frequency variations are interpreted in the context of a theoretical model for the ionosphere in which the observed variations translate to mean variations in ionospheric height on the order of 100 m. The height variations were attributed to variations in solar extreme ultraviolet (EUV) radiation from the Sun [Heroux and Hinteregger, 1985; Donnelly et al., 1986; Lean et al., 1995, 2003; Woods et al., 2005]. The EUV range is generally considered to include the important Lyman alpha radiation crucial for the ionospheric D region below 90 km, and to extend down to 10–30 nm at the short-wavelength end [Donnelly et al., 1986; Lean et al., 2003]. All these observations are consistent in showing variations in EUV irradiance of the order of a few tens of percent. More energetic X radiation from the Sun is also prevalent on the 27-day timescale. In contrast with EUV, virtually all of the X-ray energy is available for ionization and conductivity enhancement. Bailey et al.  record simultaneous irradiances from the Sun in soft X rays (2–10 nm) and in hard X rays (0.1– 0.8 nm) on the 27-day timescale. Though the largest relative variations are noted in the hard X rays (factors of 2–3 or more), the mean irradiance level (ergs/cm2/s) is an order of magnitude smaller than that of the soft X rays The variation of the soft X rays on the 27-day timescale is several tens of percent, and is capable of producing maximal ionization in the upper D region (between 85–100 km), as shown by profiles of Hargreaves . In contrast, the maximal ionizing effect of the EUV radiation occurs at higher altitude, extending into the E region (near 110 km) of the ionosphere. For all of these reasons, the mean height variations documented by Füllekrug et al.  are more likely attributable to X radiation than to EUV. It is important to note that the documented height variations on the solar rotation timescale are based on composite analysis of several individual events [Füllekrug et al., 2002], a distinction with all other height determinations in this study. Woods et al.  document changes in EUV ionizing radiation on the 13.5 day timescale which is about half that of the 27 day timescale. The variation of soft X rays on this timescale was not examined in that study. Zieger and Sátori  documented more pronounced 13.5 day periodicity than at 27 days both in SR amplitudes and frequencies. Note that the half solar rotational period is sometimes stronger than the fundamental 27-day periodicity [Mursula and Zieger, 1996]. As far as we are aware, no ionospheric height variations have been documented on the 13.5-day timescale.
6. Annual Variation
 The solar radiation incident on the ionosphere varies systematically on the annual time scale, not because of an intrinsic variation of the Sun, but because the Sun-Earth distance varies because of the slightly elliptical orbit of the Earth. This orbit of the Earth about the Sun minimizes the separation in January and maximizes it in July. The peak-to-trough variation in solar radiation (at all wavelengths, including the ionizing components) is about 7% of the mean [List, 1951; Woods et al., 2005]. Though substantial variations in the intensity of the Earth's Schumann resonances have been well documented on the annual timescale [Sátori and Zieger, 1996; Nickolaenko et al., 1998; Sátori et al., 1999], no evidence for variations in ionospheric height has yet appeared in the literature. It may be at the limits of detection with Schumann resonance methods.
 Following simple physical considerations by Greifinger and Greifinger  and Greifinger et al. , two characteristic ionospheric heights emerge in the ELF frequency range where dissipation of energy is concentrated. Both heights are controlled by the vertical profile of electrical conductivity. Here we assume changes in ionizing radiation that preserve the scale heights (primarily controlled by profiles of air density but also affected by the nature of the ionizing radiation) in the vicinity of the respective characteristic heights, and thereby assume simple shifts in the local conductivity profile [Schlegel and Füllekrug, 1999]. That is to say, if the initial vertical profile is
and the adjusted (final) profile in response to increased ionizing radiation is
Then it is easily shown that the decrease in characteristic height (either upper or lower) is given by
where fC is the fractional increase in reference conductivity, given by
The expected height changes are conveniently measured in conductivity scale heights (2–10 km), which are well recognized to be small in comparison to ionospheric heights (60–100 km). More importantly, the height changes are logarithmically dependent on the conductivity ratio, so that large changes in conductivity are needed for appreciable changes in ionospheric height.
 The atmosphere's response to ionizing radiation is complicated and nonlinear. Detailed models involve a host of chemical species and processes [e.g., Cole and Pierce, 1965; Reid, 1986; Liu and Pasko, 2004]. Few analyses of conductivity profiles treat the details of the ionizing radiation because it is often not well known quantitatively. Indeed, the measurements of ionizing radiation outside the atmosphere (i.e., by satellites) are generally carried out completely independently of any documentation of the atmospheric conductivity or ionization. Here we make additional simplifying assumptions to assess analytically the response of ionospheric height to ionizing radiation. First let us assume that the local conductivity is proportional to the radiation intensity. (Such a solution appears in the complicated electron-ion balance equations when electrons completely dominate the charge carrier population, and the creation of new electrons by ionization is balanced by simple electron attachment [e.g., Mechtly et al., 1972].) Under this assumption, it follows that
where fR is the fractional increase in local ionizing radiation (fR = fC), namely,
Second, let us assume that local conductivity is proportional to the square root of radiation intensity, consistent with the exact steady state solution when ions dominate the electrical conductivity [e.g., Shreve, 1970]. Then we have a slightly modified prediction for height change:
These two predictions for height decreases in response to fractional increases in radiation intensity are shown in Figure 1. The measured changes in ionospheric height together with estimates for scale-height-normalized changes in ionizing radiation intensity from Table 1 are also plotted in Figure 1. (The nondimensional quantity is used in Table 1 because HS is dependent on both air density and the nature of the ionizing radiation.) In general, the scale heights are taken from the modeling attempts of the various radiation scenarios, when available.
 It is important to note in Figure 1 that height changes are measured relative to the conductivity scale height HS, of order 5 km. The same height changes relative to the characteristic heights of the Schumann resonance waveguide (of order 100 km) are substantially smaller. The height changes relative to the waveguide height are more relevant to changes in the amplitude/intensity of the Schumann resonances.
 Previous theoretical work on this problem has demonstrated that the behavior of the characteristic heights of the ionosphere is closely linked with the atmospheric profile of electrical conductivity [Madden and Thompson, 1965; Greifinger and Greifinger, 1978; Greifinger et al., submitted manuscript, 2006]. The timescale in this study for which the most information is available on conductivity profiles is the diurnal. Unfortunately, however, the details on the ionizing Lyman alpha radiation at nighttime remain scant and so the estimates in Table 1 over the diurnal cycle are only approximate ones. Observations [Hale, 1984] and modeling studies [Reid, 1986] show day/night contrasts in electrical conductivity varying from one to three decades within the two characteristic ELF layers. These changes are bounded by the simplifying assumptions relating conductivity and ionizing radiation used here. The scale heights are variable in both the observations and the models, but the selection of matched scale heights between day and night does not seem grossly at odds with the available experimental profiles. This choice is also is consistent with recent selections for profiles in analytical models (Greifinger et al., submitted manuscript, 2006).
 The two estimates for height variations on the diurnal timescale are reasonably consistent with the approximate (analytic) treatment, as shown in Figure 1. (It is important to emphasize that none of these three estimates on the diurnal timescale is based on measured ELF frequency variations.) The largest estimate by far is found in the work of Sentman and Fraser , and this point lies above both theoretical curves. This point is the most notable “outlier” in Figure 1. (We have assumed here a scale height of 2 km on the basis of work by Greifinger et al.  because the Sentman and Fraser  study gave no consideration to vertical conductivity profiles. Because of the way this height change was obtained by Sentman and Fraser (by measuring diurnal intensity variations), it is likely that some of the contribution to height change is inadvertently associated with (lightning) source variations, both spatial (geographical) and temporal [Melnikov et al., 2004; Sátori et al., 2007; O. Pechony et al., Relative importance of the day-night asymmetry in Schumann resonance amplitude records, submitted to Radio Science, 2006]. This suggestion is supported by the finding of Sentman and Fraser  that the minimum ionospheric height was offset from local noon, when the Lyman α radiation is known to be maximum. Their methodology did not attempt to distinguish the contributions from the source-proximity effect and the day-night asymmetry of the ionosphere. Some difference in height is noted between the ELF estimates of Sentman and Fraser  and Greifinger et al. . This is to be expected theoretically, as the characteristic heights are frequency-dependent [Greifinger and Greifinger, 1978]. For example, the lower the frequency, the greater is the sensitivity to lower altitudes and weaker conductivity in the lower characteristic height.
 It is useful to discuss the 27-day and the 11-year solar cycle variations together, for reasons that will soon be clear. Füllekrug et al.  and Sátori et al. [2000, 2005], using different models for the ionosphere, have both inferred height changes in the upper characteristic layer of 6 km over the 11-year solar cycle. Füllekrug et al.  studied height changes on both the 11-year timescale and the 27-day timescale and inferred that both variations were caused by solar EUV radiation. The variation of EUV on the 27 day timescale is only some tens of percent, consistent with the small change in height z in Figure 1. However, not all of the EUV radiation is available for ionization, and furthermore the EUV is not as effective an ionizing source in the height range observed by Füllekrug et al.  (85–100 km). The variation of soft X radiation is at least as large as the EUV on the 27-day timescale [Bailey et al., 1999], and for all of these reasons, variations in X radiation are the more likely cause of the height changes documented by Füllekrug et al.  on this timescale.
Sátori et al. [2000, 2005] showed the need for solar X-ray variations on the 11-year timescale to explain the observed frequency variations, a result that also cast doubt about the efficacy of EUV radiation which varies by only a factor of 2–3 (in contrast to more than two decades for the X rays). The height diminishments associated with solar X-ray bursts [Roldugin et al., 2004; Sátori et al., 2005], for which X-ray changes predominate as ionizing agents, are similar to those dominated on the 11-year timescale, thereby substantiating the primary role for X rays.
 No attempts are known to determine Schumann resonance frequency variations or height variations on the annual timescale. The results shown in Figure 1 (and in particular the adjacent point for the solar rotation period) suggest that it may be marginally detectable, with a change in the lower characteristic height of less than 3% of the corresponding scale height, but one must consider carefully the noise floor for picking changes in frequency. On the basis of our analyses of SR frequency variations [Sátori et al., 2005] this noise floor is 0.02–0.04 Hz, depending on the recording system, the local noisiness of the site, and the spectral method applied.
 The preferred data points for solar X-ray bursts, solar proton events, the 27-day solar rotation period, and the 11-year solar cycle all lie appreciably below the rough theoretical predictions in Figure 1. The assumptions made in deriving the two theoretical curves in Figure 1 are highly simplified. It is important to note that in none of these solar radiation scenarios is the Earth irradiated uniformly from all directions, as we are implicitly assuming in the approximate theoretical model. It is possible that we are underestimating the full height variations for these timescales because, in certain Schumann resonance measurements (i.e., frequency), we are necessarily averaging over both irradiated and unirradiated hemispheres, a procedure that will naturally dilute the height effect on the more strongly irradiated hemisphere. We are obviously taking this hemispherical asymmetry into account more effectively in treating the diurnal timescale.
 The reasons for the differences between theory and observation in Figure 1 are difficult to assess. The theory is highly simplified, and cannot be relied upon for great accuracy. However, a highly accurate model is probably not needed to establish the difficulty in making appreciable changes in the height of the ionosphere by extratropospheric radiation, since both approximations show small relative changes in the ionospheric heights.
 As far as interest in the use of the Schumann cavity as a natural framework for monitoring global change is concerned, the great insensitivity of cavity geometry to changes in ionizing radiation (embodied in the logarithmic dependence in equations (3) and (5)) is welcome news. Rather large changes in ionizing radiation are needed to have appreciable impacts on the measured field intensity within the waveguide, a quantity traditionally used as a measure of globally integrated electrified convection [Clayton and Polk, 1977; Sentman and Fraser, 1991; Heckman et al., 1998; Sátori et al., 1999]. Note again in Table 1 that appreciable changes in ionospheric height require large order of magnitude changes in ionizing radiation. The great insensitivity is also likely responsible for the negative results in searches for Schumann resonances effects due to extraterrestrial ionization sources [Sentman et al., 1996; Price and Mushtak, 2001].
 The main conclusions drawn from this study are as follows.
 X radiation, rather than EUV radiation, is needed to account for the observed Schumann resonance frequency changes and associated changes in ionospheric height on both the 27-day solar rotation timescale, and on the 11-year timescale of the solar cycle.
 Order of magnitude changes in ionizing radiation are required for changes in the characteristic height of the ionosphere on the order of the scale height for conductivity (several km). Such variations do occur and have been documented on the diurnal, the X-ray burst and the 11-year solar cycle. The impact of such variations on the amplitudes of the Schumann resonances, inversely proportional to ionospheric height, is modest compared to the variations caused by natural changes in lightning activity. The largest height changes occur on the diurnal timescale, for which the impact on intensity is still only of order ten percent.
 The logarithmic dependences in equations (5) and (7) lend considerable stability to the medium of the Schumann cavity, a favorable circumstance from the standpoint of monitoring changes in global lightning activity within the cavity.
 Discussions with T. M. Donahue, M. Füllekrug, L. Hale, J. Lean, K. Schlegel, and V. Mushtak are greatly appreciated. The first author's studies of Schumann resonances are supported by the U.S. National Science Foundation, grant ATM-0337298. The second author's work was supported by grant NI 61013 from the Hungarian Science Foundation.