The Development of a Space Climatology: 1. Solar Wind Magnetosphere Coupling as a Function of Timescale and the Effect of Data Gaps

Abstract

Different terrestrial space weather indicators (such as geomagnetic indices, transpolar voltage, and ring current particle content) depend on different coupling functions (combinations of near-Earth solar wind parameters), and previous studies also reported a dependence on the averaging timescale, τ. We study the relationships of the am and SME geomagnetic indices to the power input into the magnetosphere P α , estimated using the optimum coupling exponent α, for a range of τ between 1 min and 1 year. The effect of missing data is investigated by introducing synthetic gaps into near-continuous data, and the best method for dealing with them when deriving the coupling function is formally defined. Using P α , we show that gaps in data recorded before 1995 have introduced considerable errors into coupling functions. From the near-continuous solar wind data for 1996-2016, we find that α = 0.44 ± 0.02 and no significant evidence that α depends on τ, yielding P α ∝B 0.88 V sw 1.90 (m sw N sw ) 0.23 sin 4 (θ/2), where B is the interplanetary magnetic field, N sw the solar wind number density, m sw its mean ion mass, V sw its velocity, and θ the interplanetary magnetic field clock angle in the geocentric solar magnetospheric reference frame. Values of P α that are accurate to within ±5% for 1996-2016 have an availability of 83.8%, and the correlation between P α and am for these data is shown to be 0.990 (between 0.972 and 0.997 at the 2σ uncertainty level), 0.897 ± 0.004, and 0.790 ± 0.03, for τ of 1 year, 1 day, and 3 hr, respectively, and that between P α and SME at τ of 1 min is 0.7046 ± 0.0004.Plain Language Summary This is the first step of three toward constructing a climatology describing the statistics of how space weather has varied over the past 400 years. This climatology will be valuable in the design of systems vulnerable to space weather. To do this, we here investigate how best to quantify the power extracted from the solar wind by the magnetosphere. We need to do this over a range of timescales from the annual averages used to describe long-term changes (space climate) down to fluctuations over minutes and hours, which drive space weather events.A great many combinations of near-Earth interplanetary parameters (so-called coupling functions) have been proposed over many years to describe the transfer of energy, and/or mass, and/or momentum, and/or LOCKWOOD ET AL. 133

Dynamical Properties of Peak and Time‐Integrated Geomagnetic Events Inferred From Sample Entropy

“…This implies that all plotted correlation coefficients displayed in Figure are statistically significant at the level (Cohen, ). Similarly high correlations were already found by Lockwood et al (, ) between their full coupling function and auroral indices that mainly describe the directly driven response of the magnetospheric system. However, we provide here the new information that their peak and time‐integrated values are also highly correlated and that peak values of and are also tightly correlated with peak values of .…”

“…Therefore, should be sensibly more responsive to electric fields that contribute to ring current enhancement (that is, to changes) inside geosynchronous orbit during strong disturbances than or , which are measured inside the auroral oval (Rostoker, ; Thomsen, ). In addition, Lockwood et al () have noticed that saturates at high geomagnetic activity measured by (when , with a mid‐latitude index very similar to ) probably because the auroral oval then expands equatorward of the stations used to measure . This means that high and values should be much less correlated with simultaneous values during strong disturbances.…”

“…Forecasts of geomagnetic activity in the inner magnetosphere often rely on solar wind parameters, or on various solar wind‐magnetosphere coupling functions (Borovsky, ). Let us consider here a very simplified version of the best solar wind‐magnetosphere coupling function obtained by Lockwood et al (), with the solar wind velocity and the interplanetary magnetic field. We neglect the very small influence on of the ion mass ( 5%), the small influence of the IMF orientation factor, and the relatively weak dependence of on solar wind density .…”

“…Actually, the highly variable IMF orientation is not always available in the OMNI database, and using a constant IMF orientation factor in merely induces a 10% error in 27‐day means and a 42% error in 1‐day means of (Lockwood et al, ), while we use here a 10‐day moving time window. We also neglect the dependence on , because (i) it is relatively weak with a dependence with 0.166–0.246 (Lockwood et al, ), (ii) is too often (2.5% of the time in 2001–2017) unavailable in the OMNI database, and (iii) only solar wind velocity and interplanetary magnetic field values are available during the Halloween 2003 super‐storm (Skoug et al, ). Note that the measured (Skoug et al, ) is used during this Halloween 2003 event to fill a large gap in the OMNI database.…”

Does Adding Solar Wind Poynting Flux Improve the Optimum Solar Wind‐Magnetosphere Coupling Function?

“…Assuming the dayside magnetopause is in equilibrium, pressure balance at the dayside magnetopause gives and expression for L o . The power input in to the magnetosphere due to kinetic energy density of the solar wind can then be estimated (see Lockwood, Bentley, et al, ; Lockwood, et al, ; Vasyliunas et al, ): where k 1 and k 2 are constants and M E is the magnetic moment of the Earth, which can be computed for a given time using the IGRF‐15 Model ( Thébault et al, ). Because the variation of M E with time is small and approximately linear, we can treat the term in brackets as a constant that we can later cancel out by normalizing P α to its average value over the whole period P o to give P α / P o .…”