The Development of a Space Climatology: 3. Models of the Evolution of Distributions of Space Weather Variables With Timescale

Abstract

We study how the probability distribution functions of power input to the magnetosphere P α and of the geomagnetic ap and Dst indices vary with averaging timescale, τ, between 3 hr and 1 year. From this we develop and present algorithms to empirically model the distributions for a given τ and a given annual mean value. We show that lognormal distributions work well for ap, but because of the spread of Dst for low activity conditions, the optimum formulation for Dst leads to distributions better described by something like the Weibull formulation. Annual means can be estimated using telescope observations of sunspots and modeling, and so this allows the distributions to be estimated at any given τ between 3 hr and 1 year for any of the past 400 years, which is another important step toward a useful space weather climatology. The algorithms apply to the core of the distributions and can be used to predict the occurrence rate of large events (in the top 5% of activity levels): they may contain some, albeit limited, information relevant to characterizing the much rarer superstorm events with extreme value statistics. The algorithm for the Dst index is the more complex one because, unlike ap, Dst can take on either sign and future improvements to it are suggested.Plain Language Summary This is the third in a series of three papers aimed at developing a climatology of space weather that applies to all solar conditions between grand solar minimum and grand solar maximum. We generate empirical models to enable us to predict the probability of a given level of space weather disturbance, as quantified by either the ap of the Dst geomagnetic indices, in a year with a given average level of disturbance. The models can be used with averaging/integration times anywhere between 3 hr and 1 year. , et al. (2019). The development of a space climatology: 3. Models of the evolution of distributions of space weather variables with timescale. Space Weather, 17, 180-209. https://doi.

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

“…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.…”

“…of Lockwood, et al (2019a) andFigure 4ofLockwood et al (2019b) show that it is the variability and distribution of F θ 10.1029/2019JA026639…”

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

“…Lockwood et al () have estimated the annual mean power input into the magnetosphere for all years back to 1612 from the reconstructed solar wind and interplanetary field parameters derived by Owens et al (), and from this Lockwood et al () have derived the annual means of Ap and AE back to this date. In the two subsequent papers in the present series (Lockwood, et al, , ) we begin to construct a space weather climatology by studying the distributions of space weather parameters about these averages and, in particular, how these distributions evolve with timescale. The present paper is an important first step in this because it shows that the formula for the optimum coupling function does not significantly evolve with timescale.…”

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

“…This is an extremely valuable result, but one which would have greater predictive power (and in which we could have greater confidence) if we understood why it applies and what its limitations are. In Paper 3 of this series (Lockwood et al, ), we study the evolution of the distribution of P α with τ from the 3 hr studied here up to τ = 1 year. Together, these papers supply much of the understanding of the empirical result that we are searching for.…”

“…Hence, although the use of this result can tell us about the occurrence of “large” events (in the top 5%), we should not expect it to hold well for the most extreme events. The relationship of large storms in the tail of the core distribution to extreme event “superstorms” is discussed further in Paper 3 (Lockwood et al, ).…”