Solar Wind—Magnetosphere Coupling Functions: Pitfalls, Limitations, and Applications

Abstract

Coupling functions are widely used constructs in space physics designed to quantify the effect of given set of solar wind conditions incident upon the near-Earth space environment, the magnetosphere. They do not try to allow for every physical mechanism involved explicitly, rather they attempt to capture and amalgamate the key drivers and explain a large fraction of the variance of a terrestrial space weather index or indicator. Correlations between interplanetary parameters and terrestrial disturbance indices became possible after the first spacecraft to visit interplanetary space had acquired sufficient data (e.g., Arnoldy, 1971) and the concept of combining parameters into a coupling function that allows for the different influences on terrestrial space-weather disturbance was first introduced in the PhD thesis of Perreault (1974). This led to the much-used "epsilon factor" coupling function, ε (Perreault & Akasofu, 1978). Unfortunately, there was an error in the theoretical basis for ε (Lockwood, 2019) which causes it to perform significantly less well, on all timescales, than other coupling functions (Finch & Lockwood, 2007). A large number of alternative formulations have been proposed since (see reviews by Newell et al. [2007], McPherron, et al. [2015], and Lockwood and McWilliams [2021b). Some of these coupling functions are based on theory, others are empirical fits to observations. In reality, most are a mixture of both approaches, with theory guiding the selection of parameters for empirical coupling functions (and the mathematical formulation used to combine them), whereas theoretically -derived coupling functions often use coefficients, branching ratios or exponents that are taken from observations. Coupling functions have also been derived and/or tested using global numerical MHD simulations of the magnetosphere (e.g., Wang et al., 2014). For all coupling functions, correlation with one or more terrestrial space weather disturbance index has traditionally been used as the metric by which their merit and performance is evaluated. In the past, not much attention was paid to the effects of this choice of performance metric, nor the effects of averaging timescale, nor the fact that different parts, features and indices of the coupled magnetosphere-ionosphere-thermosphere system respond differently to a given set of conditions. In addition, when building a space weather climatology, we will need to know the form of the occurrence probability distributions of indicators of space weather phenomena in order to predict probabilities of certain conditions, events and integrated effects (Lockwood et al., 2019b(Lockwood et al., , 2019c. However, little attention has been given to matching the distributions of a proposed coupling functions to those of the space weather indicator that they are designed to predict. Studies of coupling between the solar wind and the magnetosphere are now increasingly applying systems analysis and machine-learning techniques (e.g.

Magnetosphere-Ionosphere Coupling: Implications of Non-Equilibrium Conditions

“…Secondly am has the most uniform response in terms of time-ofday and and time-of-year of all geomagnetic indices (Lockwood et al, 2019a) and is genuinely planetary: however, it has the disadvantage that it is has only a 3-hourly cadence. The best-fit exponent b for the SML and AL indices was found to be essentially identical by Lockwood and McWilliams (2021b) and Lockwood (2022a). These values for b are very similar to those found in other studies using AL (e.g., McPherron et al, 2015).…”

“…There is very little data pertaining to such an effect and much of it of only quite distant relevance. Walsh et al (2019) and Lockwood (2022a) have studied the correlations (at optimum propagation lags) between L1 values of interplanetary parameters and coupling functions and those evaluated from near-Earth observations by spacecraft in the magnetosheath and undisturbed solar wind. There are distributions of correlations because the solar wind that passes over the L1 spacecraft may miss the near-Earth craft and/or because conditions can change during the transit between the two and/or there are variations in the propagation delay.…”

Regression Bias in Using Solar Wind Measurements

“…Random uncertainties in the solar wind drivers are not just limited to spatial and temporal uncertainty in the solar wind measurements and instrumental errors (Lockwood, 2022). (Though these are likely the primary source of uncertainties in ACE and WIND measurements used in this manuscript.)…”

The Joined-up Magnetosphere

“…In the past, these have been used in correlative studies with combinations of interplanetary parameters ("coupling functions", designed to quantify solar wind control of the magnetosphere; see reviews by Lockwood and McWilliams (2021b) and Lockwood (2022)) and one index or indicator which was tacitly taken to quantify the state of the whole magnetosphere. The corollary that one index can do this is that the coupling function should predict all magnetospheric indices and indicators equally well.…”

“…Alternatively, or additionally, time-integral correlations may appropriate in some or all cases (Lockwood et al, 2016;Borovsky, 2017). These steps should mean that the prediction schemes can allow for one of the biggest limitations of coupling functions, namely preconditioning by the existing state of the magnetosphere (Lockwood and McWilliams, 2021b;Lockwood, 2022). This should allow us to make more reliable and accurate forecasts of space weather systems, with better defined uncertainties.…”