The Development of a Space Climatology: 2. The Distribution of Power Input Into the Magnetosphere on a 3‐Hourly Timescale

Abstract

Paper 1 in this series (Lockwood et al., 2018a, https://doi.org/10.1029 showed that the power input into the magnetosphere P α is an ideal coupling function for predicting geomagnetic "range" indices that are strongly dependent on the substorm current wedge and that the optimum coupling exponent α is 0.44 for all averaging timescales, τ, between 1 min and 1 year. The present paper explores the implications of these results. It is shown that the form of the distribution of P α at all averaging timescales τ is set by the interplanetary magnetic field orientation factor via the nature of solar wind-magnetosphere coupling (due to magnetic reconnection in the dayside magnetopause) and that at τ = 3 hr (the timescale of geomagnetic range indices) the normalized P α (divided by its annual mean, that is, <P α > τ=3hr /<P α > τ=1yr ) follows a Weibull distribution with k of 1.0625 and λ of 1.0240. This applies to all years to a useful degree of accuracy. It is shown that exploiting the constancy of this distribution and using annual means to predict the full distribution gives the probability of space weather events in the largest 10% and 5% to within uncertainties of magnitude 10% and 12%, respectively, at the one sigma level.Plain Language Summary This is another step 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. Previous work has showed that the probability of an event of a given magnitude occurring in any 1 year can be predicted from average activity levels in that year. This is an approximate but extremely valuable result that helps us understand the occurrence of events before the space age-however, it is a result that would be more valuable and could be used with greater confidence if we understood why it applies. This paper provides us with that understanding.

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 .…”

“…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, ).…”

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

“…In addition, the optimum form of the IMF orientation factor at F θ was found not change with timescale, although the noise in the analysis is greater at low τ (largely caused by the increased importance of the variable response lag of am) and at large τ the distribution of F θ narrows to an almost constant value, as shown in Figure 2 of Lockwood et al, 2017). At high time resolution (1 min) the distribution of the optimum F θ has an unexpected form with a great many samples in a narrow spike at F θ = 0 (see explanation in Figure 9 of Lockwood, et al, 2019a). Figure 8…”

“…At high time resolution (1 min) the distribution of the optimum F θ has an unexpected form with a great many samples in a narrow spike at F θ = 0 (see explanation in Figure 9 of Lockwood, et al, ). Figure 8 of Lockwood, et al () and Figure 4 of Lockwood et al () show that it is the variability and distribution of F θ that sets the distribution of power input to the magnetosphere at high resolutions (1 min) and that averaging causes these distributions to evolve toward a lognormal form at τ = 1 day, which matches closely that in the am and ap geomagnetic indices. For timescales τ up to the response lag d t ~ 60 min, the geomagnetic response closely follows the average of the IMF orientation factor because during substorm growth phases the effects the storage of energy integrate, and hence average out, the effects of the rapid fluctuations in power input to the magnetosphere.…”

“…Journal of Geophysical Research: Space Physics 1 and then plotted as a function of θ. As discussed by Lockwood, et al (2019a), the exponent n in sin n (θ/2) has been proposed to be between 2 and 6. In Figure 9 we also test the frequently used function U(θ) cos (θ) where U(θ) = 1 for southward IMF (θ > 90°) and U(θ) = 0 for northward IMF (θ ≤ 90°).…”