Modulation of UK lightning by heliospheric magnetic field polarity

Observational studies have reported solar magnetic modulation of terrestrial lightning on a range of time scales, from days to decades. The proposed mechanism is two-step: lightning rates vary with galactic cosmic ray (GCR) flux incident on Earth, either via changes in atmospheric conductivity and/or direct triggering of lightning. GCR flux is, in turn, primarily controlled by the heliospheric magnetic field (HMF) intensity. Consequently, global changes in lightning rates are expected. This study instead considers HMF polarity, which doesnʼt greatly affect total GCR flux. Opposing HMF polarities are, however, associated with a 40–60% difference in observed UK lightning and thunder rates. As HMF polarity skews the terrestrial magnetosphere from its nominal position, this perturbs local ionospheric potential at high latitudes and local exposure to energetic charged particles from the magnetosphere. We speculate as to the mechanism(s) by which this may, in turn, redistribute the global location and/or intensity of thunderstorm activity.


Introduction
The electrification of thunderclouds is generally accepted to result from strong updrafts in the mixed-phase region (e.g., [4]), where the presence of both a downward flux of graupel and and upward flux of ice crystals can produce charge transfer and separation by collisions [24]. Indeed, parameterization of these processes [8] in numerical weather prediction models has led to successful forecasts of lightning flash rates [30]. A number of observational studies, however, suggest lightning flash rates may also be modulated to some degree by external factors such as solar magnetic activity [25], though the mechanism(s) and even sign of response are still under debate. On solar-cycle timescales, both positive [27] and negative [21] correlations have been found between sunspot number and thunderstorm activity. On shorter time scales, lightning over the USA has been found to decrease following impulsive reductions in galactic cosmic ray (GCR) flux by strong heliospheric magnetic field (HMF) enhancements [6]. Conversely, smaller, recurrent HMF structures appear to increase UK lightning and thunder rates, possibly via lower energy solar particles compensating for the GCR decrease [26]. These thunderstorm trends have all been linked with changes in energetic charged particle flux incident on Earth and hence changes in global atmospheric conductivity [9] and/or global lightning trigger rates [22].
The HMF is formed by the solar wind dragging coronal magnetic loops anti-sunward while both magnetic foot points remain rooted on the rotating solar surface [19]. Thus the large-scale HMF forms an Archimedean spiral, making an angle of approximately 45°to the Earth-Sun line in near-Earth space. If the overall polarity of the HMF is pointing toward ( Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. scale T or A 'sectors' in Earthʼs orbital plane, meaning the Earth is embedded in a given sector for an average of 7-14 days (e.g., [18]). This study investigates the effect of HMF polarity on lightning occurrence.

Data
There are a number of methods for detecting thunderstorm activity, but long-term studies at mid-to-high geomagnetic latitudes are best performed by radio networks, which detect radio sferics from lightning strokes. In this study, lightning stroke rates, R L , were obtained from the UK Met Officeʼs arrival time difference (ATD) network of radio receivers in Western Europe [15]. It detects the VLF component of broadband emission ('sferics') from lightning and uses the relative timing to determine location. The ATD system is primarily sensitive to cloud-to-ground (CG) lightning over Europe, but can detect lightning worldwide with reduced sensitivity. In order to ensure uniformity of the lightning measurements and enable more direct comparison with the UK-based thunderday data described below, lightning data are limited to events within a radius of 500 km of central England. Ongoing development of lightning detection systems makes long-term thunderstorm activity studies problematic. However, between September 2000 and May 2005 the ATD system was not subject to any modifications affecting its sensitivity. After this period the radio network was expanded and increased in sensitivity to form ATDnet, which detects a larger number of smaller sferics. During May 2005 to 2007, this increase was only moderate, with the annual mean of R L increasing by around 50%. We include these data in the study by normalizing R L after May 2005 by 0.64, though accept that this results in the inclusion of smaller lightning events than in the initial period. (We note that our results are largely unchanged whether these later data are included or not.) Post May 2007, further developments to ATDnet meant the sensitivity increased by around 400%. Without any means to discriminate between CG lightning and smaller, inter-cloud lightning, these data are dominated by qualitatively different lightning events from pre-2007. In order to not preferentially emphasize any one season, we only consider whole years of data, 2001 through 2006 inclusive. Data are converted to daily mean lightning stroke rates to remove any diurnal variations and to enable direct comparison with R TH data.
Audible thunder records from UK Met Office manned observing sites can serve as an independent, if low fidelity, validation of radio observations. This observation is subject to false positives (such as vehicle noise or explosions) and is of a lower time resolution compared with the ATD lightning data, but crucially its detection efficiency is not subject to the ionospheric effects which could potentially affect R L . We compute a 'thunder day rate', R TH , defined as the fraction of UK manned stations which reported thunder on a given day. Any stations which did not report a single instance of thunder in a given year were assumed to not be logging such information and excluded from the study. Note that R TH will be affected by the mean altitude, and hence audibility, of thunderstorms over the UK and thus may be sensitive to somewhat different forms/intensities of thunderstorm activity than R L . Figures 1(b) and (c) show the R L and R TH time series, respectively, further averaged to 27 day means for clarity (all analysis, however, is performed on daily means). As expected, there is general agreement between these two thunderstorm measurements, particularly in the seasonal trends. We find linear correlations in daily data of r = 0.573 (sample size, N, of 2134) and 27 day mean data of r = 0.817 (N = 80). These correlations and sample sizes result in 'p-values' of effectively zero, meaning the null hypothesis (that the correlation occurred by chance) can be rejected at almost 100% confidence, as one would expect. On the other hand, perfect correlation (i.e., r = 1) should not be expected, as the dynamic ranges of the two time series are vastly different (e.g., thunder days, as a binary measure, will measure the same value for days with 1 or 1000 lightning flashes). Furthermore, R L and R TH may be sensitive to slightly different properties and/or magnitudes of thunderstorm activity.
Heliospheric magnetic sector structure is determined using hourly OMNI data [12], which collates various near-Earth spacecraft measurements and propagates them to the nose of the magnetosphere. Simple daily means of B X and B Y can be heavily skewed by short 'spikes' in field magnitude and could therefore be unrepresentative of the resulting largescale ionospheric potential patterns, which generally vary over longer timescales. Instead, each hour of data is flagged as  heliospheric magnetic field sectors. (b) R L , the daily UK lightning stroke rate from the ATD radio network (black) and its mean seasonal variation (green). (c) R TH , UK thunder day rate (black) and its mean seasonal variation (green). All data have been 27 day averaged for purposes of plot clarity, but all analysis in this study is performed on daily data. in which the 24 hour mean is >  1(a)) and almost no seasonal trend (figure 2(a)) in sector occurrence, reducing the likelihood of systematic aliasing between sector occurrence and thunderstorm activity. Note, however, that this is not always the case, for example during the solar minimum of 2008-2009, when the quasidipolar nature of the HMF combines with inclination of the Earthʼs orbit to preferentially produce near-Earth T sectors in the first half of the year and A sectors in the latter half.

Results
Taking the 2001 through 2006 datasets as a whole, < > R L = 25.1 day −1 and < > R TH = 0.0210 day −1 . Days associated with T (A) sectors result in < > R L = 30.6 (18.5) day −1 and < > R TH = 0.0240 (0.0175) day −1 . Clearly T sectors are associated with substantially more (around 40-60%) UK thunderstorm activity than A sectors. These trends are also seen in the temporal correlations of lightning/thunder rates with HMF sector structure. Assigning T, A and undefined sectors values of −1, 1 and 0, respectively, we find a correlation coefficient of −0.0683 (−0.0724) with R L (R TH ), with a sample size of N = 2134. While these correlations are small, as meteorological effects dominate the occurrence of thunder/lightning, the p-value is such that the null hypothesis (that the observed correlation occurred by chance) can be rejected above the 99.8%, or approximately the 3-sigma, confidence level.
In order to verify this is not simply the result of aliasing between the lightning seasonality and sector occurrence, we now consider the data relative to the seasonal mean. Seasonal mean variations in R L and R TH , shown as green lines in figures 1(b) and (c), are computed by taking the day-of-year average across the 6 years of data, then applying a 27 day running mean through these daily means. (Results are essentially unchanged for a wide range of smoothing time scales, from 5 to 50 day running means.) From these curves, we compute ΔR L and ΔR TH , daily deviations from the seasonal mean. Figures 2(b) and (c) show monthly means of ΔR L and ΔR TH , respectively, which are also clearly enhanced in T sectors and reduced in A sectors, particularly during the nonwinter months.
The statistical significance of the difference between T and A means of ΔR L and ΔR TH is tested in two ways. Firstly, a Monte Carlo method is used. If there are N T (N A ) days of T (A) sectors in a given subset of data (e.g., in JJA across the 6 years), 10 000 sets of N T (N A ) daily values of ΔR L and ΔR TH are randomly selected from the same subset of data. These random samplings are used to create 10 000 T and A means and hence 10 000 random values of Δ < > R L T and Δ < > R L A . The null hypothesis (that the observed value of Δ Δ < > − < > R R L T L A occurred by chance sampling) can be rejected at a confidence level equal to the percentage of random values of Δ Δ < > − < > R R L T L A below that observed. The second method of significance testing is the Kolmogorov-Smirnov (K-S) test (e.g., [31]), which assesses the difference in the T and A cumulative distributions of ΔR L or ΔR TH and hence determines the probability at which the null hypothesis can be dismissed, that the T and A distributions are two sub-samples of the same underlying distribution.
Taken over the whole year, ΔR L (ΔR TH ) for T exceeds that for A such that the null hypothesis, that the means are the same within sampling uncertainty, can be rejected at the 99.8% (99.96%) confidence level using a Monte Carlo selection of the same data, and 98.8% (98.4%) level using the Kolmogorov-Smirnov test of the two distributions. These confidence levels are approximately at the 3 sigma level. Dividing the data into seasons, Δ < > R L T exceeds Δ < > R L A at the 99% confidence level for JJA and SON, while at the 99% confidence level for MAM and JJA. Figures 3(a) and (b) show that this is not the result of aliasing annual trends in thunderstorm activity with sector occurrence, as Δ < > R L T exceeds Ground-based neutron count rates serve as a proxy for the intensity of ionizing GCRs penetrating to the lower atmosphere. Applying the same sector analysis to data from Thule (Greenland), Newark (USA), McMurdo (Antarctica) and South Pole stations (e.g., [2]) for the 2001 through 2006 period does reveal a weak but significant trend for higher neutron counts in A than T sectors [28]. The expected solar cycle trends in GCR flux and the weak annual trends in T and A occurrence make this analysis problematic and it is not clear whether the neutron count rate trend is a result of changing GCR fluxes at the top of the atmosphere or changing magnetic access of energetic charged particles to the atmosphere. Most importantly for this study, the sector trend in GCR flux is only present in 3 of the 6 individual years and is only significant during JJA, meaning it is less prevalent than the lightning-HMF trends. Thus observed magnetic sector trends in UK thunderstorm activity cannot be explained by changes in near-Earth GCR flux alone.

Discussion
Heliospheric magnetic sector structure is known to have a number of effects on magnetospheric and ionospheric structure [7] which may in turn affect local thunderstorm activity. (We note that magnetic sector control of the atmospheric electric circuit has also been proposed as the mechanism [3,14] by which the HMF influences polar and mid-latitude surface pressure [13,16,29]). Figures 4(a) and (b) show how the HMF is essentially 'superimposed' on the Earthʼs dipole, offsetting the magnetic axis from its nominal position. For T (A) sectors, the northern hemisphere ionospheric system is shifted a few degrees dusk-ward and antisunward (dawn-ward and sunward) [11]. Figures 4(c) and (d) show that the net effect is A sectors increase ionospheric potential at dawn, while T sectors decrease ionospheric potential at dusk [10]. At the (nominally sub-auroral) geomagnetic latitude of the UK, this is likely to be a small effect, of order 10% of the total ionospheric potential relative to the ground [23]. Shifting the magnetosphere will also change the atmospheric foot point at which various energetic charged particle populations may precipitate down into the atmosphere, particularly ring current particles, which approximately track the outer boundary of the zero ionospheric potential line. Figure 4 is sketched such that T sectors result in UK latitudes encountering ring current particles for a much greater fraction of the day than A sectors, particularly in the post-noon and dusk sectors, when most thunderstorm activity occurs. In reality, however, the position of ionospheric features will be highly sensitive to a range of effects, particularly the size of the ionospheric polar cap, geomagnetic and geographic latitude, longitude and local time, as well as seasonal trends in the HMF-magnetosphere connectivity. This complexity may, in part, explain the opposing decadal [21,27] and short-term [5,26] responses observed in solar modulation of lightning. Preliminary analysis of global Met Office land surface weather records suggests a very complex response of lightning to HMF sector with geographic location, though the suitability of these proxy data for thunderstorm activity has still to be established via comparison with local radio networks and true thunder day records, and hence those data are not discussed further here.
Of course, it is necessary to quantify local changes in ionospheric potential and energetic charged particle flux with sector structure, in order to determine if they are of sufficient amplitude to explain the observed trends in thunderstorm activity. There are, however, qualitative arguments for both ionospheric potential and particle fluxes influencing lightning through the local atmospheric electric circuit: reduced ionospheric potential would extend down into the sub-ionospheric atmosphere [1], whereas increased charged particle flux at high altitudes would enhance atmospheric conductivity in the sub-ionospheric gap, both effects influencing cloud-to- Annual means of (a) UK lightning rate relative to the seasonal mean, ΔR L , and (b) UK thunder day rate relative to the seasonal mean, ΔR TH , for all data (black), away (red) and toward (blue) heliospheric magnetic field sectors. Grey shaded areas show 90% of the variations over the whole dataset.
ionosphere current which allows thunder clouds to discharge via sprites and blue jets (e.g., [20] and references therein). Enhanced conductivity down to cumulonimbus cloud top height [17] could also enhance weaker intra-cloud discharge, which is both harder to detect with the ATD network and less audible. It is not presently clear, however, how cloud-toground lightning rates respond to these effects. In addition to atmospheric electric circuit effects, sufficiently energetic charged particles may be able to provide narrow ionization channels that trigger cloud-to-ionosphere, intra-cloud or CG discharges, which may or may not be important for the observed trends. Differentiating between the proposed mechanisms will require full characterization of the global relation of thunderstorm activity to HMF, which will require careful analysis of long-term global lightning networks and thunder day records. It may also be necessary to comprehensively characterize the vertical charged particle distribution and ionospheric potential, at a range of geomagnetic latitudes and longitudes, and under differing HMF regimes. This would require coordinated observational campaigns beyond those currently performed.

Summary
The large-scale HMF consists of sectors of toward (T ) and away (A) polarity, which are known to skew the Earthʼs magnetic field in opposing manners. In this study, UK lightning and thunder rates are shown to be significantly different when the Earth is embedded in T or A sectors, with 40-60% more thunderstorm activity in T sectors than A sectors. This result persists even when the strong seasonal variation in thunderstorm activity is removed. Comparing with global neutron monitor measurements, this does not seem to be solely the result of changes in the global top-of-theatmosphere energetic charged particle flux, which is the mechanism by which previous studies have suggested solar modulation of lightning. Instead, we propose a redistribution of lightning, rather than a global change in the lightning rate. The T/A-sector skewing of the Earthʼs magnetic field relative to a fixed geographic position will change both the local ionospheric potential and the atmospheric footprints of various energetic charged particle populations. This, in turn, may change the discharge processes in electrified storm clouds, though the mechanisms have yet to be established.