Spectral analysis of surface atmospheric electricity data at daily resolution is used to investigate heliospheric and cosmic ray effects on the global circuit. Using 42 years of Potential Gradient (PG) data (1963–2004) from Nagycenk Observatory, Hungary (47° 38′N, 16° 43′E), periodicities are found at annual, semi-annual and 1.7 year timescales. A quasi-periodicity centred on 1.68 years in surface neutron monitor data has previously been identified as of heliospheric origin; a similar signal was apparent in Voyager spacecraft cosmic ray measurements. The heliospheric signal is strongest during the 1980s and early 1990s, but absent before 1975. The 1.7 year periodicity in the Nagycenk PG data is present 1978–1990, but absent 1963–1977, and is clearest during fair weather when the global circuit and columnar air conductivities most readily contribute to the surface PG. When poor local weather influences the PG, the 1.7 year periodicity is reduced or absent.
 Cosmic rays generate molecular cluster ions in the lower atmosphere [Harrison and Carslaw, 2003], contributing to the small electrical conductivity of air. This permits a vertical current flow between the charged regions of the ionosphere and the surface, within the global atmospheric electrical circuit. The resulting vertical potential gradient (PG) can be measured near the surface. In fair weather, the PG is positive, and, in air of low aerosol content, is ∼50 to 150 Vm−1. Aerosol variations and weather changes modify the PG. In disturbed weather, the PG increases in magnitude and becomes variable, and is often negative during rainfall. Interpretation of surface PG measurements can consequently be complex: in fair weather conditions, the PG may be representative of the global circuit, but in disturbed weather conditions, the PG is dominated by the effects of local charged clouds and precipitation. During precipitation the PG generally becomes negative [Chalmers, 1967].
 Thunderstorms and disturbed weather are generally considered the principal sources of currents flowing in the global circuit, but interactions between the solar wind and the Earth's magnetic field generate additional currents at high latitudes [Rycroft et al., 2000]. As cosmogenic cluster ions contribute substantially to the troposphere's conductivity, cosmic ray changes can modulate the global circuit, influencing the fair weather atmospheric electric fields across the planet. Evidence for such an effect was provided by the positive correlation observed between ionospheric potential – a global circuit parameter preferred over surface PG measurements because of its low sensitivity to boundary layer aerosol changes [Märcz and Harrison, 2005] - and neutron monitor measurements of galactic cosmic rays [Markson, 1981]. Unfortunately the ionospheric potential has only been sparsely sampled temporally, in contrast with the PG for which high temporal resolution data exist at many sites globally. The surface PG may be modified through cosmic ray induced conductivity changes, if other strong local modulating effects are absent. Cosmic ray effects on the PG may be small, however, and are not readily detectable in recent data [Harrison, 2006]. A further PG modulation may arise from coupling of geomagnetically-induced changes in the magnetospheric dynamo through the global circuit. At high latitudes, such magnetospheric dynamo perturbations generate polar cap potential differences, which can cause surface PG variations of ±20% [Roble and Tzur, 1986].
 One approach to studying cosmic ray effects on the global circuit is through spectral analysis of surface atmospheric electricity data, as, away from the strong annual and semi-annual components, periodicities exist which are known to be associated with solar effects on cosmic rays. For example, a quasi-periodic oscillation centred on 1.68 years (614 days) associated with coronal hole fluctuations has been reported in surface neutron monitor data [Valdés-Galicia et al., 1996], as well as in the open solar flux from the radial interplanetary magnetic field and the aa-index [Rouillard and Lockwood, 2004] and in cosmic ray intensity measurements made in the outer heliosphere by the Voyager spacecraft [Kato et al., 2003]. This 1.68 year quasi-periodicity begins around 1975 in neutron data, and provides a possible hallmark of cosmic rays in other measurements. The presence of a similar timescale periodicity in the long series of surface PG data made at Nagycenk Observatory, Hungary is considered further here. Earlier analyses based on Nagycenk PG data covering about three decades have detected responses in surface PG to Forbush decreases, i.e. to significant changes in galactic cosmic rays on short timescales [Märcz, 1997].
 PG measurements have been made at Nagycenk Observatory since late 1962, using a radioactive probe sensor connected to a high impedance voltage amplifier. The measured probe voltages are recorded on paper tape, and the hourly values transcribed manually. The derived PG values are tabulated at 10 Vm−1 resolution in the Observatory yearbooks, including a remark if the instrument is in positive or negative saturation (>±300 Vm−1). The practice at Nagycenk has been to regard positive PG values up to 120 Vm−1 as characteristic of “fair weather” values, although the meteorological conditions are not independently recorded. (Values outside this range are therefore effectively those associated with “disturbed weather.”) Further, values recorded between 01 and 04 UT (the “dawn” hours) are known to show low variability, and have provided data for other studies.
 The Nagycenk PG series shows a decreasing long-term trend, mainly due to a gradual increase in the local electrostatic shielding by trees [Märcz and Harrison, 2003]. It has not been possible, however, to entirely reconcile the measured trend with calculated and modelled tree shielding. This may indicate that factors beyond the tree effect have contributed to the long-term change [Märcz and Harrison, 2006].
3. Data Analysis
 Hourly PG data between the beginning of 1963 and the end of 2004 have been used to produce a 42 year time series of daily average PG values for spectral analysis, computed using different criteria. Of the 15341 daily average values possible, there are 14847 (96.8%) daily averages available, if all hourly values are considered. Figure 1a shows daily averages calculated using all available values, i.e. when the measuring equipment was functional and ∣PG∣ ≤ 300 Vm−1. Figure 1b shows the associated histogram; it is clear that the daily PG values are mostly positive and days with negative values, associated with continuous precipitation, are rare. Three further data series were constructed, for fair and disturbed weather situations. For one fair weather series, daily averages were determined when there were 12hours or more “fair weather” values (defined as 0 ≤ PG ≤ 120 Vm−1), yielding 12458 days; in the other, the daily averages were further restricted to measurements from just the “dawn” hours (01 to 04 UT), for 3 or more fair weather hourly values, yielding 11896 days. In the final series, only hours having weather sufficiently disturbed to reverse the electric field were used (PG < 0 Vm−1), which yielded 5223 daily averages.
3.1. Spectral Analysis
 Before computing power spectra, the long-term trend in each data set of daily values was removed using linear regression. It was also necessary to consider missing values in the data, the abundance of which differs for the different daily averages considered. Missing data points were substituted with values selected randomly within the same data set. The spectral effect of this bootstrapping approach is to add white noise to the data, but it should not introduce any further periodicities. The choice of random values was repeated many times and the resulting spectra averaged to ensure that the features obtained were insensitive to the replacement values chosen.
Figure 2 shows power spectra obtained from the four daily time series produced: all values, fair weather values, dawn fair weather values and disturbed weather values. Confidence levels have also been added, against a white noise spectrum (using multiple randomised data from the same time series to calculate the spectral spread) and a red noise spectrum (using the spread of spectra generated from multiple realisations of noise having the same autocorrelation at a lag of 1 day as the time series considered). Figure 2a is the power spectrum for daily averages from all values, in which strong annual and semi-annual periodicities, as seen in Figure 1a, are identified, together with a small peak at 1.7 years. Figures 2b and 2c show similar analyses, but using fair weather and dawn fair weather daily averages respectively. In both fair weather spectra, annual and semi-annual periodicities are more distinct than in Figure 2a, and a 1.7 year periodicity is also present. (The fair weather data, Figure 2b, also shows a peak at the 27 day solar rotation timescale.) Figure 2d shows the spectrum derived from the disturbed weather daily averages. There are fewer available data values for computing Figure 2d than for Figures 2b, 2c, and 2d, and consequently the spectral power is weaker compared with the white noise level. The annual and semi-annual peaks remain above the confidence threshold, but no 1.7 year periodicity is present.
3.2. Temporal Variation in 1.7 Year Periodicity
 The 1.7 year PG periodicity apparent in fair weather is suggestive of the heliospheric signal, but it could have been generated by another process with coincidentally the same periodicity. The variation of the PG periodicity with time is therefore an important characteristic aspect to explore. Rouillard and Lockwood  showed that the 1.68 year periodicity was particularly strong between 1978 and 1990, but weak before 1978 and absent in neutron data before 1975.
 To investigate temporal variations in the 1.7 year PG periodicity, the fair weather PG data (used for Figure 2b) were divided into “earlier” (1963–1977), and “later” (1978–1990) periods. These correspond to periods when the heliospheric periodicity was weaker and stronger respectively, as observed in space and on earth. The shorter periods of data resulting cause difficulty for spectral analysis, as only a few cycles of periodicity can occur in each case. The Maximum Entropy Method (MEM) is well-suited for calculation of spectral features in short data series, and provides good spectral resolution at the expense of the amplitude information [Press et al., 1989]. Figure 3 shows MEM spectra calculated from the Climax neutron data and the Nagycenk PG data, for the same earlier and later periods. The earlier period (1963–1977) shows little 1.7 year periodicity in the Climax neutron data (Figure 3a) and no 1.7 year periodicity evident in the Nagycenk PG data (Figure 3b). During the later period (1978–1990), the Climax neutron data shows a stronger 1.7 year periodicity (Figure 3c), and a peak with similar periodicity occurs in the Nagycenk PG data (Figure 3d).
 A different approach to studying long term changes in the 1.7 year PG periodicity is to use a band-pass filter to extract the amplitude variations. Because of the quasi-periodic nature of the signal, Rouillard and Lockwood  used a filter with a broad pass band of 1.55 to 1.81 years. The same filter pass band has consequently been used here, with a Lanczos filter of length 8years constructed for daily data. Figure 4 shows the effect of the filter on the daily Climax neutron data (Figure 4a) and the daily Nagycenk fair weather PG data (Figure 4b). In both Figures 4a and 4b, it is apparent that the strongest amplitude response is in the early 1980s. There is, however, no phase coherence, and the amplitude response of the PG does not follow that of the neutron data after 1990. This suggests that other contributions beyond cosmic rays generate PG variations in the range of frequencies considered. For example, a more complicated phase response could arise from geomagnetic coupling of solar wind and interplanetary magnetic field changes into the atmospheric electrical system. Usoskin et al.  showed that cosmic ray changes were delayed from heliospheric changes by a variable phase difference of 0 to 20 months.
 To consider a geomagnetic link further, a measure of geomagnetic activity, the Kp index, was analysed using the same band-pass filter. The Kp index shows a 1.5 to 1.7 year periodicity during odd solar cycles [Mursula and Zieger, 2000]. Band-pass filtered Kp data (Figure 4c) show improved phase coherency with the filtered PG data (especially between 1980 and 1988 during solar cycle 21), supporting a geomagnetic contribution to the atmospheric electricity variability.
 Spectral analysis of long atmospheric electricity data series at high resolution provides a new basis to identify heliospheric or cosmic ray effects in atmospheric electricity. The 1.68 year heliospheric quasi-periodicity is a particularly appealing timescale, as several measurement cycles are potentially available in relatively short data series of duration 10 to 20 years. Using the 42 years of PG data from Nagycenk, a 1.7 year periodicity is apparent in fair weather conditions. This periodicity is less distinct if non-fair weather PG values are included, and absent if only negative PG values are used, which occur in locally disturbed weather. For the fair weather data, the periodicity is present during 1978–1990, and is weak or non-existent during 1963–1977, similar to the response in the Climax neutron monitor data. Band-pass filtering the Climax neutron monitor and Nagycenk fair weather PG data within 1.55 to 1.81 year periodicities illustrates that the largest amplitude response in the PG data occurs at similar times (early 1980s) to that in the neutron data.
 Another comparable timescale periodicity which can occur in atmospheric data is that of the quasi-biennial oscillation (QBO) in stratospheric winds. This oscillation varies in duration from one cycle to the next, but it has a mean period of 28 months [Baldwin et al., 2001]. During 1980–1985, the westerly phases of the QBO lasted less than 18months [Hamilton, 2002]. These timescales (<1.5 years) fall outside the band-pass filter applied to the PG data and are not apparent in Figure 3d, so they cannot straightforwardly provide an explanation for the amplitude response observed at 1.7 years.
 In conclusion, a spectral feature having the same (1.7 year) timescale as the known heliospheric signal in cosmic rays is present in surface PG data during the period 1978 to 1990. The strongest amplitude 1.7 year signal occurs in the early 1980s, at the same time as the heliospheric signal in surface neutron monitor data. The 1.7 year periodicity appears more distinct during fair weather conditions, and is reduced or absent during disturbed weather. Detection of the periodicity during fair weather, when modulation in the global circuit is most likely to be observed, suggests cosmic ray and/or geomagnetic modulation through air conductivity or more complex geophysical mechanisms. Spectral analysis alone cannot rigorously discriminate between a cosmic ray air conductivity mechanism and a heliosphere-magnetosphere coupling mechanism, but the phase coherence (Figure 4c) slightly favours the second possibility. Through either mechanism, or both, the global circuit provides a physical linkage between the heliosphere and the lower troposphere.
 The Climax neutron monitor is supported by National Science Foundation grant ATM-0339527; data was also obtained from the UK Solar System Data Centre. M. Ambaum constructed the band pass filter.