Aims. Although the time of the Maunder minimum (1645-1715) is widely known as a period of extremely low solar activity, it is still being debated whether solar activity during that period might have been moderate or even higher than the current solar cycle #24. We have revisited all existing evidence and datasets, both direct and indirect, to assess the level of solar activity during the Maunder minimum. Methods. We discuss the East Asian naked-eye sunspot observations, the telescopic solar observations, the fraction of sunspot active days, the latitudinal extent of sunspot positions, auroral sightings at high latitudes, cosmogenic radionuclide data as well as solar eclipse observations for that period. We also consider peculiar features of the Sun (very strong hemispheric asymmetry of the sunspot location, unusual differential rotation and the lack of the K-corona) that imply a special mode of solar activity during the Maunder minimum.Results. The level of solar activity during the Maunder minimum is reassessed on the basis of all available datasets. Conclusions. We conclude that solar activity was indeed at an exceptionally low level during the Maunder minimum. Although the exact level is still unclear, it was definitely lower than during the Dalton minimum of around 1800 and significantly below that of the current solar cycle #24. Claims of a moderate-to-high level of solar activity during the Maunder minimum are rejected with a high confidence level.

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

Abstract. In the concluding paper of this tetralogy, we here use the different geomagnetic activity indices to reconstruct the near-Earth interplanetary magnetic field (IMF) and solar wind flow speed, as well as the open solar flux (OSF) from 1845 to the present day. The differences in how the various indices vary with near-Earth interplanetary parameters, which are here exploited to separate the effects of the IMF and solar wind speed, are shown to be statistically significant at the 93% level or above. Reconstructions are made using four combinations of different indices, compiled using different data and different algorithms, and the results are almost identical for all parameters. The correction to the aa index required is discussed by comparison with the Ap index from a more extensive network of mid-latitude stations. Data from the Helsinki magnetometer station is used to extend the aa index back to 1845 and the results confirmed by comparison with the nearby St Petersburg observatory. The optimum variations, using all available long-term geomagnetic indices, of the near-Earth IMF and solar wind speed, and of the open solar flux, are presented; all with ±2σ uncertainties computed using the Monte Carlo technique outlined in the earlier papers. The open solar flux variation derived is shown to be very similar indeed to that obtained using the method of Lockwood et al. (1999).

Southward interplanetary magnetic field (IMF) in the geocentric solar magnetospheric (GSM) reference frame is the key element that controls the level of space weather disturbance in Earth's magnetosphere, ionosphere, and thermosphere. We discuss the relation of this geoeffective IMF component to the IMF in the geocentric solar ecliptic (GSE) frame, and using the almost continuous interplanetary data for 1996–2015 (inclusive), we show that large geomagnetic storms are always associated with strong southward, out‐of‐ecliptic field in the GSE frame: Dipole tilt effects, which cause the difference between the southward field in the GSM and GSE frames, generally make only a minor contribution to these strongest storms. The time‐of‐day/time‐of‐year response patterns of geomagnetic indices and the optimum solar wind coupling function are both influenced by the timescale of the index response. We also study the occurrence spectrum of large out‐of‐ecliptic field and show that for 1 h averages it is, surprisingly, almost identical in ICMEs (interplanetary coronal mass ejections), around CIRs/SIRs (corotating and stream interaction regions) and in the “quiet” solar wind (which is shown to be consistent with the effect of weak SIRs). However, differences emerge when the timescale over which the field remains southward is considered: for longer averaging timescales the spectrum is broader inside ICMEs, showing that these events generate longer intervals of strongly southward average IMF and consequently stronger geomagnetic storms. The behavior of out‐of‐ecliptic field with timescale is shown to be very similar to that of deviations from the predicted Parker spiral orientation, suggesting the two share common origins.

Near-Earth solar-wind conditions, including disturbances generated by coronal mass ejections (CMEs), are routinely forecast using three-dimensional, numerical magnetohydrodynamic (MHD) models of the heliosphere. The resulting forecast errors are largely the result of uncertainty in the near-Sun boundary conditions, rather than heliospheric model physics or numerics. Thus ensembles of heliospheric model runs with perturbed initial conditions are used to estimate forecast uncertainty. MHD heliospheric models are relatively cheap in computational terms, requiring tens of minutes to an hour to simulate CME propagation from the Sun to Earth. Thus such ensembles can be run operationally. However, ensemble size is typically limited to 10 1 to 10 2 members, which may be inadequate to sample the relevant high-dimensional parameter space. Here, we describe a simplified solarwind model that can estimate CME arrival time in approximately 0.01 seconds on a modest desktop computer and thus enables significantly larger ensembles. It is a one-dimensional, incompressible, hydrodynamic model, which has previously been used for the steady-state solar wind, but it is here used in time-dependent form. This approach is shown to adequately emulate the MHD solutions to the same boundary conditions for both steady-state solar wind and CME-like disturbances. We suggest it could serve as a "surrogate" model for the full three-dimensional MHD models. For example, ensembles of 10 5 to 10 6 members can be used to identify regions of parameter space for more detailed investigation by the MHD models. Similarly, the simplicity of the model means it can be rewritten as an adjoint model, enabling variational data assimilation with MHD models without the need to alter their code. The model code is available as an Open Source download in the Python language. B M. Owens 5 Met Office, Exeter, UK 43 Page 2 of 17 M. Owens et al.Figure 1 An example of a three-dimensional numerical MHD solution of the solar wind, using the MAS coronal model and the HelioMAS heliospheric model. The photospheric magnetic field for Carrington Rotation 1833 (spanning September 1990) was used, as it results in both fast and slow wind in the equatorial plane. (a) Latitude-time plot at Earth longitude of V r at the corona-heliosphere interface (30 R ) from MAS. (Note if the solar-wind structure is time stationary, this is an exact mirror image of a Carrington map.) The white line shows the Heliographic Equator. (b) The associated time series of V r at the sub-Earth point. (c) Latitude-time plot at Earth longitude of V r at Earth orbit (215 R ) from HelioMAS. (d) The associated time series of V r at Earth from HelioMAS (black) and HUXt (red). See text for details of the HelioMAS and HUXt models.Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a lin...

We study the semi-annual variation in geomagnetic activity, as detected in the geomagnetic indices am, aaH, AL, Dst and the four aσ indices derived for 6-hour MLT sectors (around noon, dawn, dusk and midnight). For each we compare the amplitude of the semi-annual variation, as a fraction of the overall mean, to that of the corresponding variation in power input to the magnetosphere, Pα, estimated from interplanetary observations. We demonstrate that the semi-annual variation is amplified in the geomagnetic data compared to that in Pα, by a factor that is different for each index. The largest amplification is for the Dst index (factor ~ 10) and the smallest is for the aσ index for the noon MLT sector (aσ-noon, factor ≈ 1.1). By sorting the data by the prevailing polarity of the Y-component (dawn-dusk) of the Interplanetary Magnetic Field (IMF) in the Geocentric Solar Equatorial (GSEQ) reference frame, we demonstrate that the Russell-McPherron (R-M) effect, in which a small southward IMF component in GSEQ is converted into geoeffective field by Earth’s dipole tilt, is a key factor for the semi-annual variations in both Pα and geomagnetic indices. However, the variability in the southward component in the IMF in the GSEQ frame causes more variability in power input to the magnetosphere Pα than does the R-M effect, by a factor of more than two. We show that for increasingly large geomagnetic disturbances, Pα delivered by events of large southward field in GSEQ (known to often be associated with coronal mass ejections) becomes the dominant driver and the R-M effect declines in importance and often acts to reduce geoeffectiveness for the most southward IMF in GSEQ: the semi-annual variation in large storms therefore suggests either preconditioning of the magnetosphere by average conditions or an additional effect at the equinoxes. We confirm that the very large R-M effect in the Dst index is because of a large effect at small and moderate activity levels and not in large storms. We discuss the implications of the observed “equinoctial” time-of-year (F) – Universal Time (UT) pattern of geomagnetic response, the waveform and phase of the semi-annual variations, the differences between the responses at the June and December solstices and the ratio of the amplitudes of the March and September equinox peaks. We also confirm that the UT variation in geomagnetic activity is a genuine global response. Later papers will analyse the origins and implications of the effects described.

This article reviews atmospheric changes associated with 44 solar eclipses, beginning with the first quantitative results available, from 1834 (earlier qualitative accounts also exist). Eclipse meteorology attracted relatively few publications until the total solar eclipse of 16 February 1980, with the 11 August 1999 eclipse producing the most papers. Eclipses passing over populated areas such as Europe, China and India now regularly attract scientific attention, whereas atmospheric measurements of eclipses at remote locations remain rare. Many measurements and models have been used to exploit the uniquely predictable solar forcing provided by an eclipse. In this paper, we compile the available publications and review a subset of them chosen on the basis of importance and novelty. Beyond the obvious reduction in incoming solar radiation, atmospheric cooling from eclipses can induce dynamical changes. Observations and meteorological modelling provide evidence for the generation of a local eclipse circulation that may be the origin of the 'eclipse wind'. Gravity waves set up by the eclipse can, in principle, be detected as atmospheric pressure fluctuations, though theoretical predictions are limited, and many of the data are inconclusive. Eclipse events providing important early insights into the ionization of the upper atmosphere are also briefly reviewed.This article is part of the themed issue 'Atmospheric effects of solar eclipses stimulated by the 2015 UK eclipse'.

This is the second in a series of papers that investigate the semi-annual, annual and Universal Time (UT) variations in the magnetosphere. We present a varied collection of empirical results that can be used to constrain theories and modelling of these variations. An initial study of two years’ data on transpolar voltage shows that there is a semi-annual variation in magnetospheric flux circulation; however, it is not as large in amplitude as that in geomagnetic activity, consistent with the latter showing a non-linear (quadratic) variation with transpolar voltage. We find that during the persistent minimum of the UT variation in geomagnetic activity, between about 2 and 10 UT, there is also a persistent decrease in observed transpolar voltage, which may be, in part, caused by a decrease in reconnection voltage in the nightside cross-tail current sheet. We study the response of geomagnetic activity to estimated power input into the magnetosphere using interplanetary data from 1995 onwards, an interval for which the data are relatively free of data gaps. We find no consistent variation in the response delay with time-of-year F and, using the optimum lag, we show that the patterns of variation in F-year spectrograms are very similar for geomagnetic activity and power input into the magnetosphere, both for average values and for the occurrence of large events. The Russell–McPherron (R–M) mechanism is shown to be the central driver of this behaviour. However, the (R–M) effect on power input into the magnetosphere is small and there is a non-linear amplification of the semi-annual variation in the geomagnetic response, such that a very small asymmetry in power input into the magnetosphere Pα between the “favourable” and “unfavourable” polarities of the IMF BY component generates a greatly amplified geomagnetic response. The analysis strongly indicates that this amplification is associated with solar wind dynamic pressure and its role in squeezing the near-Earth tail and so modulating the storage and release of energy extracted from the solar wind. In this paper, we show that the equinoctial pattern is found in the residuals of fits of Pα to the am index and that the amplitude of these equinoctial patterns in the am fit residuals increases linearly with solar wind dynamic pressure. Similarly, the UT variation in am is also found in these fit residuals and also increases in amplitude with solar wind dynamic pressure.