List of Figures
Figure 1:
Polecentric maps of the (left) northern and (right) southern hemispheres showing the locations of known operating magnetometer stations in 1996 (coloured dots), as compiled by the World Data Centre, C1 for Solar Terrestrial Physics, RAL Space, UK. 

Figure 2:
Simplified schematic of the currents flowing in the magnetosphereionosphere system in the northern hemisphere (southern hemisphere currents are omitted for clarity). Part (a) shows (in orange) segments of the Chapman–Ferraro currents that flow in the magnetopause and separate the geomagnetic and (shocked) interplanetary fields: the relevant segments are at the sunward edge of the magnetospheric tail and flow from dusk to dawn (see also Figure 14). These connect to the highlatitude ionosphere via the Region 1 fieldaligned (Birkeland) currents (shown in blue). The Region 2 fieldaligned currents are needed to maintain ionospheric current continuity and because of the incompressibility of the ionosphere (in the sense that the magnetic field there is essentially constant). As shown in red in (b), these Region 2 currents close via the ring current that flows westward around the Earth in the inner magnetosphere (in cyan), caused by the gradient and curvature drifts of trapped energetic particles. Part (c) shows the Region 1 and 2 currents entering and leaving the polar Eregion ionosphere and how they connect to the Pedersen currents there (in green), which flow in the direction of the electric field. The paired up and down fieldaligned currents transfer solar wind energy, momentum, and electric field down into the ionosphere as well as current (see review by Lockwood, 1997). The Hall currents (shown by black lines) flow perpendicular to the electric field (and so cause no energy dissipation) and are antiparallel to associated ionospheric flow (convection) in the overlying Fregion ionosphere. For a uniform spatial distribution of conductivities, the effects of fieldaligned and Pederson currents cancel beneath the ionosphere and only the Hall currents are detected by highlatitude magnetometers on the ground. The formation of the westward electrojet in the substorm current wedge (shown here in mauve) is described later by Figure 14. In this electrojet, a highly conducting channel is formed by ionisation generated by the associated particle precipitation and the Cowling conductivity is relevant. 

Figure 3:
Linear correlation coefficients of annual means of various geomagnetic indices with , as a function of , the exponent of the solar wind speed, ( is the IMF field strength). The primes denote the fact that data have been omitted in calculating either set of annual means if any of , or the geomagnetic index are missing because of data gaps exceeding 1 hour duration. Values of are computed hourly and then averaged. Correlograms are shown for: (red line) ; (green line) ; (blue solid line) ; (blue dashed line) the negative part of , (where is the same as but intervals when are treated as data gaps); (cyan) ; (orange) ; (black dashed) ; (black solid line) ; (mauve) ; (yellow) and (red dashed) . For indices which are increasingly negative for increasing activity (, and ) the index has been multiplied by . Image reproduced from Lockwood et al. (2013a). 

Figure 4:
Averages over Bartels 27day solar rotation intervals (coloured) and calendar years (in black) of (top) the geomagnetic index and (bottom) the index. The colours give the station(s) contributing the data to the indices at any one time. This version of the index is as stored in the World Data Centres. The data labelled Niemegk are a composite from the three nearby stations, Niemegk, Potsdam, and Seddin. 

Figure 5:
Comparison of annual means of the standard index (in red) and the modified version derived by Lockwood et al. (2006b) (in blue). The estimated maximum uncertainty, relative to modern values, is shown by the grey band. The green dots are annual means of the index. 

Figure 6:
The median index, . For each station at a given UT, the standard deviation of the hourly means of the horizontal component of the geomagnetic field is computed over a full year, . These are then correlated with, and linearly regressed against, the annual means of aa shown in Figure 4 to yield . These normalisations are needed because both the sensitivity and offset for a station have been shown to depend on its location and on the UT hour (which, for example, alters the location of the station relative to the midnightsector auroral oval) (Finch, 2008). Each stationUT is treated as an independent data series. The grey lines show the variations of the values for all stationUTs for which the correlation coefficient exceeds 0.5 and is significant at the level. The number of stationUTs meeting this criterion is shown as a function of time by the black histogram in the lower panel. The black line in the upper panel is the median of all the available data for each year and is called the “median index”, . Image reproduced from Lockwood et al. (2006b). 

Figure 7:
Annual means of the index compiled by Svalgaard and Cliver (2010). The grey curves are the variations for individual stations. The red curve is the index, defined as the arithmetic mean of the median and average values of the individual station values. A few station values were very large outliers of the distribution at any one time and those that were more than five standard deviations from the average were omitted in calculating the value for that year. The number of contributing stations, , is shown by the thin blue curve. The dashed blue line is the corresponding number of stations used by Svalgaard and Cliver (2005). Bartels’ index is considered a single station and gives the dotted line extension to before 1871 using a linear regression of 1871 – 1930 data with the index proper. Image reproduced by permission from Svalgaard and Cliver (2010), copyright by AGU. 

Figure 8:
Correlations between the geomagnetic activity index and a number of solar wind coupling functions, as a function of averaging timescale, T. Upper and lower graphs are identical, other than that the upper graph displays timescale linearly, whereas the lower graph displays it logarithmically. The coloured lines give the results for: (dark blue), (light blue), (green), (red), (olive), (magenta), and (black). Image reproduced by permission from Finch and Lockwood (2007), copyright by EGU. 

Figure 9:
The northward component of the nearEarth interplanetary magnetic field (IMF) in the GSM frame, , from the OMNI2 composite dataset. The lefthand plot shows the temporal variations of for 1966 – 2013 at different averaging timescales, T. The righthand plot shows the corresponding probability density functions over the same interval. Note the difference in the vertical scales. In both panels light blue is for T = 1 h, dark blue for T = 1 day, red for T = 27 days and black for T = 1 yr. 

Figure 10:
Scatter plots of the halfwave rectified southward component of the IMF in the GSM frame, as a function of the IMF magnitude, , for (a) hourly observations and (b) 1year averages. Panel (c) shows a histogram of the distribution of annual values of the ratio , which has a mean value of 3.251 and a standard deviation of 0.369. The thin line is the normal distribution with the same mean and standard deviation. 

Figure 11:
Scatter plots of the predicted ratio from Parker spiral theory, where is the IMF magnitude and is the modulus of its radial component, as a function of the observed value of that ratio. The lefthand plot is for hourly observations, the righthand plot for 1year averages. In the case of the annual means, the modulus of daily means of observations, i.e., , is used. 

Figure 12:
Correlation coefficients of the annual means of the coupling functions (top) IMF magnitude , (middle) , and (bottom) with indices from a variety of magnetic observatories, shown as a function of the modulus of their invariant magnetic latitude . Solid diamonds are for northern hemisphere stations and open circles for southern. Black and grey symbols are for correlations that are significant at the and levels, respectively. The vertical dashed lines show the auroral oval between absolute invariant latitudes of 60° and 82°. Image reproduced by permission from Finch et al. (2008), copyright by AGU. 

Figure 13:
MLT dependence of maximum correlations of for stations shown in Figure 12 with . In the top panel, filled circles and open diamonds show the MLT (magnetic local time) – Geographic longitude coordinates of the maximum correlation of with and , respectively. The bottom two panels show the histograms of the MLT of the maxima in the correlations for (in black) and (in white). Image reproduced by permission from Finch et al. (2008), copyright by AGU. 

Figure 14:
Schematic of Earth’s magnetospheric current systems. Parts (b) and (d) are views of the noonmidnight crosssection of the magnetosphere, ABDC, from the ecliptic on dusk side of the Earth and show current sheets in orange, interplanetary field lines in green, open geomagnetic field lines (that thread the magnetopause) in red and closed field lines (that do not) in blue. Parts (a) and (c) are views of the northernhemisphere currents in the tail and dayside magnetopause from high northern latitudes in the premidnight sector. In all panels , , and are the axes of the GSM reference frame. Parts (a) and (b) are for a substorm growth phase, whereas (c) and (d) are for a substorm expansion phase. is the undisturbed IMF and is the current in the Bow Shock. In all panels magnetic reconnection is taking place at in the dayside magnetopause. The tail lobe field is and the current in the crosstail current sheet () is disrupted in the grey areas in (c) and (d). The mauve currents in (c) are the “substorm current wedge” within which the magnetospheric field lines “dipolarise” at onset (the dashed line in (d) shows the stretched field line before onset and the arrow the associated sunward convection surge of the frozenin plasma). The “nearEarth neutral line”, , is also shown in (d). 

Figure 15:
Scatter plots and best fit regressions of annual means of (left) against and (right) against . The bestfit regression lines are derived using the Bayesian leastsquares regression fit procedure described by Rouillard et al. (2007). The correlation for with is and using the autoregressive AR1 red noise model this correlation is found to be significant at greater than the level. The correlation of with is with significance exceeding the level. Image reproduced by permission from Lockwood et al. (2009d), copyright by AAS. 

Figure 16:
Top: Correlograms showing the correlation coefficients (between and , dashed line) and (between and , solid line) as a function of the exponent . The vertical dashed lines mark the peaks at and , respectively. Middle: the significances and (dashed and solid lines, respectively) of the differences between the correlations at general and the peak values, as evaluated using the FischerZ transform and (bottom) the joint probability . Image reproduced by permission from Lockwood et al. (2009d), copyright by AAS. 

Figure 17:
A comparison of Ulysses and ACE data during the third perihelion pass of Ulysses, which took place between day 36 of 2007 and day 13 of 2008. In all panels, black lines are data from Ulysses while green lines are from ACE, which is in a halo orbit around the L1 Lagrange point. From top to bottom: (a) daily means of the solar wind speed, ; (b) The difference between successive daily values, ; (c) The 27day running means of the away and toward (red and blue lines, respectively) radial field components observed at Ulysses and averaged separately; (d) 27day running means of the normalized absolute radial field magnitude at Ulysses, (black line), and ACE, (green line); (e) The flux excess at Ulysses, defined as (grey shaded area); (f) The heliographic latitude of Ulysses (, black line) and ACE (, green line); (g) The heliocentric distance of Ulysses (, black line) and ACE (, green line). In all cases the radial field values are the asymptotic values for the averaging timescale T approaching zero. Image reproduced by permission from Lockwood et al. (2009b), copyright by AGU. 

Figure 18:
A comparison of values, as a function of (where ), computed using Equation (7) for T = 1 h and averages over Carrington rotations (i.e., is used for both the heliospheric and simultaneous nearEarth data) from 14 heliospheric spacecraft: Pioneer 6, Pioneer 7, Pioneer 10, Pioneer 11, Helios 1, Helios 2, Pioneer Venus Orbiter (PVO), International SunEarth Explorer ISEE3 (later renamed International Cometary Explorer, ICE), Ulysses, NearEarth Asteroid Rendezvous (NEAR), Solar Terrestrial Relations Observatory (STEREO) A, STEREO B, Voyager 1, and Voyager 2. The lines show the distribution of predicted from the “kinematic correction” calculated for each sample (Lockwood et al., 2009c), which are exceeded a fraction of the time, where is 0.1 (for black line), 0.25, 0.5, 0.75, and 0.9 (light gray line). Image reproduced by permission from Lockwood et al. (2009c), copyright by AGU. 

Figure 19:
Application of the “kinematic correction” to the third Ulysses perihelion pass shown in Figure 17. All three panels show 27day running means of various estimates of the absolute radial field (normalized to ) from measurements by Ulysses (thick black lines) and ACE (thin black lines). Ulysses data from the top panel are shown by the area shaded grey in all three panels to facilitate comparisons. a) the asymptotic limit of the timescale , (for ACE data, thin black line) and (for Ulysses, thick black line); (b) the same for T = 1 day, (thin black line) and (thick black line); and (c) data for T = 1 h with the kinematic correction applied to the Ulysses data to allow for heliospheric effects between and , (thin line) and (thick black line). Image reproduced by permission from Lockwood et al. (2009b), copyright by AGU. 

Figure 20:
Top: The excess flux from Equation (8) as a function of . The data points show the mean values from the spacecraft data shown in Figure 18, averaged over bins in that are 0.1 AU wide, with error bars of plus and minus one standard deviation. The lines are the same as shown in Figure 18. The data point at the lowest is the entire PFSS data set for the coronal source surface at . Bottom: The number of full Carrington rotation averages contributing to these means. The open triangle shows the number in the OMNI2 data set from . Note that is shown on a logarithmic scale. Image reproduced by permission from Lockwood et al. (2009c), copyright by AGU. 

Figure 21:
The variation of various open solar flux estimates during the space age. The grayshaded areas show annual means of the signed open solar flux from the OMNI2 data derived using and the absolute value of the radial field taken of means on timescale T: the light gray area bounded by the blue line is for T = 1 h, and successively darker gray areas are for T = 1, 2, and 3 days. The green line is the variation from solar magnetograms using the PFSS method. The red line shows the OMNI2 values for T = 1 h, minus the correction term for kinematic effects, . Image reproduced by permission from Lockwood et al. (2009c), copyright by AGU. 

Figure 22:
Scatter plot and bestfit linear regressions between the index and the IMF strength . The wide variety of regression slopes demonstrates the effect of the choice of regression method used. The light blue line is the fit by SC05, the other lines are the bestfit regressions by LEA06 for residual minimization methods of: (mauve line) Ordinary Least Squares (OLS); (green line) least median of squares (LMS); (blue line) Major Axis Analysis (MAA); (black line) Bayesian Least Squares (BLS). 

Figure 23:
Analysis by Svalgaard and Cliver (2006) of the fit residuals in the fit of against by Svalgaard and Cliver (2005). The fit residuals are plotted as a function of the fitted value, which is the correct test for homoscedasticity. Image reproduced by permission from Svalgaard and Cliver (2006), copyright by AGU. 

Figure 24:
Quantilequantile (QQ) plots for (left) OLS and (right) BLS regressions of the index and the IMF strength . These plots are used to check if the distribution of fit residuals is Gaussian, as assumed by leastsquares fitting procedures. The ordered, standardized residuals (where and is the number of samples) are shown as a function of the corresponding quantiles of a standard normal distribution. Deviations from the line of slope 1 shown reveal departures from a normal distribution of standard distribution . 

Figure 25:
Analysis of the fit residuals in the fit of against using: (left) MAA; (middle) OLS; and (right) (BLS). The fit residuals are shown as a function of , where is the observed value and is the fitted value from the index. The dashed line is the linear regression fit to the points to highlight trends. The OLS and MAA fit residuals show strong trends and so should not be used because is consistently an overestimate of when is small and consistently an underestimate of when it is large. Hence, these fits seriously underestimate the real trend in the data. In contrast, the BLS regression is free of such a trend. 

Figure 26:
Reconstructions of annual means of the nearEarth IMF field strength from geomagnetic activity data: LEA99 (orange) uses the method of Lockwood et al. (1999a) applied to ; LEA09 (red) is by Lockwood et al. (2009d) and uses and ; REA07 (blue) is by Rouillard et al. (2007) and also uses and ; SC10 (thin black line with uncertainty shown by the surrounding grey area) is by Svalgaard and Cliver (2010) and uses . Solid circles show annual means of IMF observations from the OMNI2 database. Note that Lockwood et al. (1999a) did not reconstruct and the LEA99 variation shown was generated by Lockwood and Owens (2011) who adapted the Lockwood et al. (1999a) procedure to predict . Image reproduced by permission from Lockwood and Owens (2011), copyright by AGU. 

Figure 27:
Reconstructions of annual means of the nearEarth solar wind speed from geomagnetic activity data. The upper panel is for ordinary least squares (OLS) regression, the lower panel for Bayesian least squares regression (BLS). Plots to the left are the time series, those to the right give the distribution of residuals of the fit to interplanetary insitu observations. Blue and red lines are derived using and whereas green and black are using and . Solid circles show annual means of solar wind speed observations from the OMNI2 database. Image reproduced by permission from Rouillard et al. (2007), copyright by AGU. 

Figure 28:
Reconstructions of annual means of the open solar flux from geomagnetic activity data: LEA99 (orange), LEA09 (red), REA07 (blue), SC10 (thin black line with uncertainty shown by the surrounding grey area). See text for details. The variations are as they appear in the publications except that attributed to SC10, which is their variation in , converted to using the polynomial fit shown in Figure 29. The green line (LEA99) is derived from the LEA procedure, applied to the index and to interplanetary data with the kinematic correction applied to . The solid circles are the values derived from interplanetary observations using the kinematic correction, described by Lockwood et al. (2009c). 

Figure 29:
Scatter plot of open solar flux as a function of nearEarth IMF field strength, . The solid points are from the LEA09 reconstruction and the open triangles are annual means from insitu interplanetary data (with computed using Equation (8) with T = 1 h and the kinematic correction for ). The black line is a polynomial fit to both datasets, constrained to pass through the origin , with an uncertainty given by the grey area. The dotdash line is a linear regression fit. The vertical solid line labelled SEA MM shows the value of during the Maunder minimum derived using cosmogenic isotopes by Steinhilber et al. (2010) and the vertical dashed lines bound the uncertainty in that estimate. Image reproduced by permission from Lockwood and Owens (2011), copyright by AGU. 

Figure 30:
Longterm variations in (top) reconstructed IMF, ; (middle) open solar flux, ; and (bottom) group sunspot number, . The upper two panels are as in Figures 26 and 28. In the bottom panel the orangeshaded area gives annual means of the group sunspot number and the black line their 11year running means. The black dot to the right of each panel is the maximum 12month mean seen thus far in cycle 24 at the time of writing (31 March 2013). 

Figure 31:
The distribution of fit residuals for 1966 – 2012, where and are the bestfit linear regression coefficients. The mean of the distribution is 0nT to within 5 decimal places. The standard deviation is 0.459 nT. The dashed line is the bestfit Gaussian distribution of the same mean and standard deviation. 

Figure 32:
Scatter plot of annual means (with piecewise removal of datagaps) of and IMF , showing the results of a polynomial fit of the functional form . The blue line is the median of 100 000 best polynomial fits and grey area defines the 2 uncertainty band, derived using a MonteCarlo technique, allowing for the distributions of uncertainties introduced by the IMF orientation factor and the experimental uncertainties in both and . The linear correlation coefficient of fitted and observed IMF is 0.947. The error bars on datapoints allow for the effect of the datagaps. 

Figure 33:
Reconstructions of the nearEarth IMF, , from geomagnetic data with uncertainty analysis. The black line uses the new geomagnetic activity composite, (Lockwood et al., 2013a) and the polynomial fit to . The grey area surrounding this black line is the uncertainty band associated with using this polynomial fit derived using a MonteCarlo technique (see Figure 32 and text for details) and also includes the uncertainty caused by the intercalibration of the stations. The red line shows the best reconstruction using a linear fit. The green line shows the reconstruction of Svalgaard and Cliver (2010). Blue dots show the annual means of the observed IMF (from Lockwood et al., 2013b). 

Figure 34:
Longterm variations of 25year means in the IMF derived from ^{10}Be cosmogenic isotope data by Steinhilber et al. (2010) (SEA10): the green line is the best estimate and the yellow band the estimated uncertainty. In addition, 11year running means of the reconstructions from geomagnetic activity, as presented in Figure 26, are shown using the same colour scheme as in that figure. Also shown are the SC07 and SC10 floor estimates for annual means and the Dalton and Maunder sunspot minima are labelled DM and MM. Image reproduced by permission from Lockwood and Owens (2011), copyright by AGU. 

Figure 35:
Longterm variation of unsigned open solar flux, . The grey area bounded by a black line is a model fit to the green line which is the LEA09 reconstruction. Ten year averages of cosmogenic isotope estimates of open solar flux are shown in blue (from ^{14}C) and red (from ^{10}Be), with solid and dashed lines showing linear and thirdorder fits of the heliospheric modulation potential variation to the open solar flux reconstruction from geomagnetic activity. Image reproduced by permission from Owens and Lockwood (2012), copyright by AGU. 

Figure 36:
The composite record of 25year means of the solar modulation potential, derived from ^{10}Be cosmogenic isotope abundances by Steinhilber et al. (2008). The red areas show Grand Solar Maxima (GSM) defined here as when exceeds the 600 MV level (the horizontal orange line) the blue areas are where is less than this value. The vertical lines show the end times of these GSM, . The Maunder minimum is marked MM and the minimum value of during it, , is marked by the horizontal green line. 

Figure 37:
Update of the superposed epoch plot by Barnard et al. (2011). The black lines are the 25year means of the heliospheric modulation potential derived from icecore ^{10}Be abundances by Steinhilber et al. (2008) and here interpolated to annual values using splines interpolation: these are composited around the 24 times in the 9300year record that fell below the 600 MV level. The horizontal dashed line in the Maunder minimum value, . The blue line shows 22year running means of derived from monthlymean Oulu neutron monitor data with (when fell to 600 MV). The red line shows 22year running means of the reconstruction of annual values, as derived by Usoskin et al. (2002) for the same . 

Figure 38:
Observed past and predicted future variations of (from top to bottom): sunspot number, ; interplanetary magnetic field strength at Earth, ; cosmic ray counts by the Oulu neutron monitor, ; and the geomagnetic index. The black lines are monthly averages of observations. The mauve line in the second panel is the LEA09 reconstruction of annual means of from geomagnetic data by Lockwood et al. (2009d), and that in the third panel from the reconstruction of by Usoskin et al. (2002). The redtoblue lines show predicted variations of annual means at various probabilities, made from the 9300year cosmogenic isotope composite of Steinhilber et al. (2008) using the procedure developed by Lockwood et al. (2011a) and Barnard et al. (2011). In the top panel the blue to red lines show the values of which have a probability that will be lower than the value shown. Corresponding predictions are given in the other panels. (Note that in the third panel the probability of is shown as rises as solar activity falls). Image adapted from Lockwood et al. (2012). 

Figure 39:
Solar polar fields observed by the magnetograph at Wilcox Solar Observatory (WSO) during solar cycles 21 – 24. The top panel shows the difference between the two polar fields, as a function solar cycle phase, , as determined from mean sunspot latitudes using the method described by Owens et al. (2011b), where and are the average fields seen over the north and south solar poles, respectively, and for oddnumbered cycles and for even ones. The reversals all occur within the grey band and the phases of the peak sunspot number in 12month running means are given by the vertical lines. The lower panel shows (solid lines) and (dashed lines) as a function of where and are the and data that have been passed through a 20 nHz lowpass filter. In both panels, red, blue, green and black denotes solar cycles SC21, SC22, SC23, and SC24, respectively. This plot will be updated regularly as the cycle progresses: this version was generated on 20 April 2013. 

Figure 40:
The evolution of solar cycle 24 thus far. Observed monthly means (in grey) and 12point running means of monthly data (in black) of (a) sunspot number, ; (c) Oulu neutron monitor counts, and (d) the observed nearEarth IMF field strength, . In each of these plots the coloured lines are the predicted levels at various probabilities between 95% (in red) and 5% (in mauve), as derived by Barnard et al. (2011). The value shown is that which has a chance of being exceeded in the case of and and a % chance of being exceeded in the case of the comic ray counts. Panel (b) shows the monthly mean latitudes of sunspots groups . The red line is for the southern solar hemisphere, the blue for the north and solid line is observed whereas the dashed is a linear extrapolation of the cycle 24 behaviour into the future. The circles show the mean latitude for that hemisphere at which peak sunspot number was seen in cycles 12 – 23: the number of open circles to the right of the dashed line is the number of those cycles that had not yet reached their peak sunspot number in that hemisphere for the latest shown mean latitude of spots in that hemisphere. This plot will be updated regularly as the cycle progresses: this version was generated on 20 April 2013. 

Figure 41:
Update of the solar polar field plot given in Figure 39. Plot updated on 1 August 2013. 

Figure 42:
Update of Figure 40 summarising the evolution of solar cycle 24 thus far. Plot updated on 1 August 2013. 