We show the global dynamics of spatial cross-correlation of Pc2 wave activity can track the evolution of the 2015 St. Patrick’s Day geomagnetic storm for an 8 hour time window around onset. The global spatially coherent response is tracked by forming a dynamical network from 1 second data using the full set of 100+ ground-based magnetometer stations collated by SuperMAG and Intermagnet. The pattern of spatial coherence is then captured by a few network parameters which in turn track the evolution of the storm. At onset IMF B_z>0 and Pc2 power increases, we find a global response with stations being correlated over both local and global distances. Following onset, whilst B_z>0, the network response is confined to the day-side. When IMF B_z<0, there is a strong local response at high latitudes, consistent with the onset of polar cap convection driven by day-side reconnection. The spatially coherent response as revealed by the network grows and is maximal when both SME and SMR peak, consistent with an active electrojet and ring-current. Throughout the storm there is a coherent response both in stations located along lines of constant geomagnetic longitude, between hemispheres, and across magnetic local time. The network does not simply track the average Pc2 wave power, however is characterized by network parameters which track the evolution of the storm. This is a first study to parameterize global Pc2 wave correlation and offers the possibility of statistical studies across multiple events to detailed comparison with, and validation of, space weather models.

The Newcomb-Benford Law (NBL) prescribes the probability distribution of the first digit of variables which explore a broad range under conditions including aggregation. Long-term space weather relevant observations and indices necessarily incorporate changes in the contributing number and types of observing instrumentation over time and we find that this can be detected solely by comparison with the NBL. It detects when upstream solar wind magnetic field OMNI HRO Interplanetary Magnetic Field incorporated new data from WIND and ACE after 1995. NBL comparison can detect underlying changes in geomagnetic indices AE (activity dependent background subtraction) and SME (different station types) that select individual stations showing the largest deflection, but not where station data are averaged, as in the SMR index. As composite indices becomes more widespread across the geosciences, the NBL may provide a generic data flag to indicate changes in the constituent raw data, calibration or sampling method.

Geomagnetic indices are routinely used to characterize space weather event intensity. The DST index is well resolved, but only available over 5 solar cycles. The aa index extends over 14 cycles but is highly discretized with poorly resolved extremes. We parameterize extreme aa activity by the annual averaged top few % of observed values, show these are exponentially distributed and they track annual DST index minima. This gives a 14 cycle average ~4% chance of at least one great (DST<-500nT) storm and ~28% chance of at least one severe (DST<-250nT) storm per year. At least one DST=-809[-663,-955]nT event in a given year would be a 1:151 year event. Carrington event estimate DST~-850nT is within the same distribution as other extreme activity seen in aa since 1868 so that its likelihood can be deduced from that of more moderate events. Events with DST<-1000nT are in a distinct class, requiring special conditions.

There can be few greater scientific challenges than predicting the response of the global system to anthropogenic disruption, even with the array of sensing tools available in the “digital Anthropocene”. Rather than depend on one approach, climate science thus employs a hierarchy of models, trading off the tractability of Energy Balance Models (EBMs) [1] against the detail of Global Circulation Models. Since the 70s Hasselmann-type stochastic EBMs have allowed treatment of climate fluctuations and noise. They remain topical, e.g. their use by Cox et al to propose an emergent constraint on climate sensitivity [2]. Insight comes from exploiting a mapping between Hasselmann’s EBM and the original stochastic model in physics, the Langevin equation of 1908. However, it has recently been claimed that the wide range of time scales in the global system may require a heavy-tailed response [3,4] to perturbation, instead of the familiar exponential. Evidence for this includes long range memory (LRM) in GMT, and the success of a fractional Gaussian model in predicting GMT [5]. Our line of enquiry is complementary to [3-5] and proposes mapping a model well known in statistical mechanics, the Green-Kubo “Generalised Langevin Equation” (GLE) to generalise the Hasselmann EBM [6]. If present LRM then simplifies the GLE to a fractional Langevin equation (FLE). As well as a noise term the FLM has a dissipation term not present in [3,4], generalising Hasselmann’s damping constant. We describe the corresponding EBM [7] that maps to the FLE, discuss its solutions, and relate it to existing models. References: [1] Ghil M (2019) Earth and Space Sciences, in press. [2] Cox P et al. (2018) Nature 553: 319-322 [3] Rypdal K. (2012) JGR 117: D06115 [4] Rypdal M and Rypdal K (2014) J Climate 27: 5240-5258. [5] Lovejoy et al (2015) ESDD 6:1–22 [6] Watkins N W (2013) GRL 40:1-9 [7] Watkins et al, to be submitted.

The frequency of major solar eruptions, and their space weather impacts at earth vary with the cycle of solar activity but large amplitude events can occur at any time. Each solar cycle has a distinct amplitude and duration so that the solar cycle dependent frequency of rare, extreme space weather events is challenging to quantify. By constructing the analytic signal of daily sunspot numbers since 1818 we construct a new solar cycle phase clock which maps each of the last 18 solar cycles onto a single time-base. This clock orders solar coronal activity and extremes of the aa index, which tracks geomagnetic storms at the earth’s surface over the last 14 solar cycles. We identify and quantify the occurrence times of a geomagnetically quiet solar cycle interval of ~4.4 years (~2 pi/5 phase or 40% of the cycle) in extent centered on solar minimum within which only two severe (aa>300nT) and one extreme (aa>500nT) geomagnetic storms occurred since 1868. The solar cycle modulation of activity is such that 1-3% of severe (aa>300nT) geomagnetic storms and 4-6% of C, M and X class solar flares occurred in the solar cycle quiet phase. Terminators of solar EUV bright point activity indicate the end of this quiet interval and the ‘switch on’ of increased frequency of solar flares and geomagnetic storms. This provides quantitative support to planning resilience against space weather impacts since only a few percent of all severe storms occur in this quiet interval and its start and end are forecast-able.

The overall level of solar activity, and space weather response at earth, varies within and between successive solar cycles and can be characterized by the statistics of bursts, that is, time-series excursions above a threshold. We consider non-overlapping 1 year samples of the auroral electrojet index (AE) and the SuperMAG-based ring current index (SMR), across the last four solar cycles. These indices respectively characterize high latitude and equatorial geomagnetic disturbances. We suggest that average burst duration τ̅ and burst return period R̅ form an activity parameter, τ̅/R̅ which characterizes the fraction of time the magnetosphere spends, on average, in an active state for a given burst threshold. If the burst threshold takes a fixed value, τ̅/R̅ for SMR tracks sunspot number, while τ̅/R̅ for AE peaks in the solar cycle declining phase. Crossing theory directly relates τ̅/R̅ to the observed index value cumulative distribution function (cdf). For burst thresholds at fixed quantiles, we find that the probability density functions of τ̅ and R each collapse onto single empirical curves for AE at solar cycle minimum, maximum, and declining phase and for (-)SMR at solar maximum. Moreover, underlying empirical cdf tails of observed index values collapse onto common functional forms specific to each index and cycle phase when normalized to their first two moments. Together, these results offer operational support to quantifying space weather risk which requires understanding how return periods of events of a given size vary with solar cycle strength.