1 Introduction

Variability in the near-Earth solar wind can disturb the terrestrial magnetosphere. When the orientation of the heliospheric magnetic field (HMF) is anti-parallel to that at the dayside magnetopause, magnetic reconnection can lead to efficient energization of the terrestrial system (Dungey, 1961). As the Earth’s magnetic dipole is (on average) broadly aligned with the solar rotation axis, the ambient Parker spiral HMF (Parker, 1958) and the dayside magnetopause magnetic field are (on average) closer to orthogonal than antiparallel. Additional processes that give rise to southward magnetic field, \(B_{S}\), in the terrestrial frame are needed to drive the most intense geomagnetic activity (Lockwood et al., 2016). Geomagnetic storms – periods of intense, long-duration disturbance to the magnetosphere – are driven by the arrival of a coronal mass ejection (CME) in near-Earth space (Gosling, 1993), as the internal CME magnetic field can contain a strong, sustained \(B_{S}\) component.

Moderate \(B_{S}\) can also be generated by the ambient HMF due to Earth’s axial tilt and orbit around the Sun (see Lockwood et al., 2020b; Cliver, Kamide, and Ling, 2002, for more complete overviews of this subject). There are three such geometric effects:

  • The Russell–McPherron (RM) effect (Russell and McPherron, 1973) arises from tilt of the Earth’s magnetic dipole relative to the Earth’s rotation axis, and the annual variation of the Earth’s rotation axis relative to the solar equator (Cortie, 1912, 1913). As the angle between the nominal Parker-spiral HMF and the dayside magnetopause magnetic field varies, this gives rise to peaks in geomagnetic activity at the equinoxes, in March and September, as well as systematic diurnal variations. The RM effect depends strongly on the azimuthal or Y-component of the HMF in the solar frame (\(B_{Y}\)) and gives a strong peak at about 10 UT at the September equinox for HMF \(B_{Y} > 0\) and a strong peak around 22 UT at the March equinox for HMF \(B_{Y} > 0\) (Zhao and Zong, 2012). However, because \(B_{Y}\) polarities are present with almost equal occurrence probabilities and because the response of geomagnetic activity is not just a half-wave rectification of \(B_{S}\), the RM effect for all data combined is rather weak, despite the fact it is very strong for each of the two \(B_{Y}\) polarities individually (Lockwood et al., 2020b; Lockwood and Milan, 2023).

  • The equinoctial effect also arises from the inclination of the Earth’s magnetic axis, but as it tilts towards or away from the Sun (McIntosh and Feather, 1959). This also maximises geomagnetic activity around the equinoxes, but with a different diurnal pattern than the RM effect.

  • The axial effect arises from the inclination of Earth’s orbit relative to the solar equator (Cortie, 1912, 1913). As with the previous two effects, this results in geomagnetic activity peaks at the equinoxes, but as it does not involve Earth rotation, it does not produce any diurnal variation. While not strictly a geometric effect, but when Earth is at high heliographic latitude, it can lead to preferential sampling of the HMF polarity associated with the polar field (Rosenberg and Coleman, 1969).

Note that these geometric effects are important for the mean level of geomagnetic activity and the core of the distribution of geomagnetic responses, but not of great importance for the large-event tail of the distribution: the long-lived southward HMF in the magnetospheric frame that generates major storms is also found in the southward component of the HMF in solar frames (Lockwood et al., 2016). Hence large geomagnetic storms are generated by persistent deflection of the HMF toward southward (in both the Earth and solar frames) associated with CMEs and not by large \(B_{Y}\) HMF and tilt of the Earth’s dipole (i.e. the Russell–McPherron effect).

Geometric effects and their annual variations have long been acknowledged as important to geomagnetic activity (e.g. Lockwood et al., 2019, and references therein). But the annual variation in the scalar properties of the solar wind – namely the solar wind density, speed, and HMF intensity – are not as well appreciated. It is often implicitly assumed that the near-Earth solar wind is uniformly sampled throughout the year. A number of studies have hinted that this may not be a valid assumption.

Due to the slightly elliptical orbit, Earth is approximately 3.5% closer to the Sun in northern-hemisphere winter than in summer. Due to the inverse-square variation of density with distance, this might be expected to give around 7% change in solar wind plasma density, on average. This effect has been noted in the near-Earth solar wind (Lockwood et al., 2020a). However, as will be demonstrated in this article, the reality may be more complex, due to the heliolatitude and distance variations of Earth being intrinsically coupled. Earth’s variation in heliolatitude by \(\pm 7.25\) degrees over the year can lead to systematic sampling of different solar wind types. Murayama (1974) and Orlando et al. (1993) have suggested that preferential sampling of fast wind when Earth is at high heliographic latitudes may contribute to the geomagnetic activity variation ascribed to the RM effect. This study aims to understand and quantify the annual variations in near-Earth solar wind properties.

2 Near-Earth Solar Wind Data

Solar wind observations are provided by the Advanced Composition Explorer (ACE) magnetic field and solar wind instruments (McComas et al., 1998; Smith et al., 1998). ACE was selected for its orbital position, which does not vary significantly with respect to Earth throughout the entire mission lifetime, simplifying the interpretation of the results. The data are available at 64-second resolution, which is subsequently averaged up to 1 hour. We primarily consider the scalar quantities of solar wind proton number density, \(n_{P}\), heliospheric magnetic-field intensity, \(|B|\), and radial solar wind speed, \(V_{r}\). We do not investigate the magnetic-field orientation factors, as they primarily couple to geomagnetic activity through the daily and annual variations of the orientation of the Earth’s magnetosphere, which have been well studied elsewhere (see Lockwood et al., 2020b; Cliver, Kamide, and Ling, 2002).

In order to investigate the effect of removing solar wind intervals known to result from the interplanetary coronal mass ejections (ICMEs), we use a list of manually identified ICMEs (Richardson and Cane, 2010). Both ICMEs and preceding sheath are removed for the ‘No ICMEs’ dataset, using the observed boundaries. Removing an additional day of data prior to the start of the sheath and after the ICME trailing edge does not significantly change the results presented here.

Before investigating the annual variations in solar wind parameters, it is instructive to understand the interrelation between the solar wind parameters themselves. The solar wind has long been known to have two primary states: ‘Fast’ wind tends to have lower plasma density and magnetic-field intensity than ‘slow’ wind, also referred to as streamer belt wind (e.g. McComas et al., 2003; Ebert et al., 2009; Bloch et al., 2020; Owens, 2020). Fast wind is also referred to as coronal hole wind and thus is primarily encountered at high latitudes at solar minimum when polar coronal holes dominate. In the ecliptic plane at Earth orbital distance, it is rare to encounter fast wind that has not been somewhat slowed and compressed by interaction with the more dominant slow wind (McComas et al., 2003).

Figure 1 shows median properties of the solar wind over the full ACE dataset, at 1-hour resolution. Data have been split into 25 equal-width bins and the error on the median is computed as the 95% confidence interval from a bootstrapping method (McGill, Tukey, and Larsen, 1978), wherein the original distribution is repeatedly sampled with replacement 1000 times. Varying bin sizes does not qualitatively affect these results. The scaling of solar wind speed, density, and magnetic-field intensity to account for the small radial distance variation of ACE, shown in red, is described in Section 3. It has very little effect on the trends discussed here. Figure 1a shows the expected result that high speed wind is less dense than low speed wind. However, in the ecliptic plane at Earth orbital distance, the distinct fast and slow wind populations are not readily discernible, and the relation appears to be continuous. Figure 1c shows that, in general, \(|B|\) also increases with \(n_{P}\), consistent with the typical fast and slow wind properties (Ebert et al., 2009). Though, again, there is more of a continuous variation than two distinct populations. Note also that for very low \(n_{P}\) (\(< 2\mbox{ cm}^{-3}\)), \(|B|\) increases. This is not the result of identifiable ICME material. Figure 1b shows a weak increase in \(|B|\) with \(V_{R}\). This runs counter to the fast and slow wind paradigms (Ebert et al., 2009) and the results shown in Figures 1a and 1c. This apparent contradiction is likely the result of using a single value – the median – to describe a distribution, which contains contributions from multiple populations within the solar wind. Indeed, this can be seen to some degree in the relation between \(n_{P}\) and \(|B|\) (Figure 1c): High \(|B|\) populations exist for both very high and very low \(n_{P}\). As these broad interrelations are presented here only as context for the annual variations discussed below, we do not investigate these features further in this study.

Figure 1
figure 1

The interdependence of solar wind parameters from 1-hour resolution ACE observations over the period 1998 to 2023. Lines show median values, error bars are 95% confidence intervals on the medians. Black and blue lines show the observed values over the whole dataset with and without ICMEs, respectively. Red lines show the data scaled to 215 \(r_{\odot}\) (1 AU), as described in Section 3. (a) Solar wind proton density, \(n_{P}\), as a function of solar wind radial speed, \(V_{R}\). (b) Heliospheric magnetic-field intensity, \(|B|\), as a function of \(V_{R}\). (c) \(|B|\) as a function of \(n_{P}\).

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In order to investigate solar cycle variations, we use the daily sunspot number (SSN), provided by the Sunspot Index and Long-term Solar Observations (SILSO) activity of the Solar Influences Data-analysis Center (SIDC) (Clette and Lefèvre, 2016), and available from https://www.sidc.be/silso/. While we use version 2.0 of the SILSO record, the 1998 to 2022 interval considered in this study is not subject to any of the calibration issues or corrections that are necessary for the early data (Clette et al., 2023). As the solar wind structure is expected to be primarily a function of the solar cycle phase (e.g. Owens, 2020), we also construct a solar activity index (SAI, Owens et al., 2022), aimed at characterising the progression of the solar cycle independent of the variation in sunspot cycle amplitude:

$$ SAI (t) = \frac{SSN_{13} (t)}{\max \left [ SSN_{13} (t - 5.5 \mathrm{yr}: t + 5.5 \mathrm{yr}) \right ] }, $$
(1)

where \(SSN_{13} (t)\) is the 13-month smoothed sunspot number centred on time \(t\). It is computed as a rolling average at daily intervals. This is normalised by the maximum \(SSN_{13}\) value in an 11-year window centred on \(t\). Thus, by construction, SAI has a minimum possible value of 0 and reaches a maximum value of 1 in every solar cycle. To select out periods of solar minimum and maximum, we use SAI thresholds of 0.25 and 0.67, respectively. These values are somewhat arbitrary, but give approximately equal duration intervals of minimum and maximum. The results presented here are not qualitatively sensitive to the choice of these thresholds.

3 Spaceship Earth

Figure 2 shows the orbital characteristics of Earth and ACE. In Figure 2a it can be seen that while ACE is in a halo orbit about the L1 point, the heliographic latitudes, \(\theta \), of ACE and Earth are essentially identical. Figure 2b shows that ACE, near the L1 point, is typically 1-2 solar radii (\(r_{\odot}\)) closer to the Sun than Earth and Figure 2c shows that the ACE-Earth distance, \(R_{AE}\) is an almost constant fraction (0.01) of the Earth-Sun distance, \(R_{ES}\). Thus, ACE data can be treated as representative of near-Earth solar wind over the whole period considered. Finally, Figure 2d shows the 13-month smoothed SSN and SAI variations over this interval. There are two solar cycles of observations from which we select out solar minimum and maximum intervals that comprise around a third of the dataset each.

Figure 2
figure 2

Time series of Earth and ACE orbital characteristics over 1998 – 2022. (a) The heliographic latitude of ACE (red) and Earth (black). (b) The heliocentric distance, \(R\), from the Sun. (c) The ratio of the ACE-Earth distance, \(R_{AE}\), to the Earth-Sun distance, \(R_{ES}\). (d) The 13-month smoothed sunspot number, scaled by a factor 1/200 (black) and the solar activity index, SAI (red). The red dashed lines show the SAI thresholds used to define solar minimum and solar maximum.

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Figure 3 shows the median annual variations of ACE and Earth orbital parameters as a function of fraction of calendar year, \(F\). Figure 3a shows that perihelion occurs at \(F=0.01\) (early January), while aphelion is at \(F = 0.51\) (early July). Figures 3b and c show that Earth is at the helioequator at \(F=0.43\) (early June) and \(F=0.94\) (mid-December). Thus, Earth reaches maximum \(|\theta |\) at \(F = 0.17\) (early March) and \(F=0.69\) (early September).

Figure 3
figure 3

The median orbital variations as a function of fraction of the year, \(F\). Error bars are one standard error on the median. ACE is shown in red, Earth in black. (a) The heliocentric radial distance, \(R\). (b) The heliographic latitude, \(\theta \). (c) The absolute heliographic latitude, \(|\theta |\). For reference, \(F = 0.5\) is shown as a solid vertical black line.

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The blue, black and red lines in Figure 4 show how observed solar wind parameters vary with heliocentric distance and latitude. Black and blue lines show, respectively, the observed values over all data and with ICMEs removed. There are no particularly obvious trends, though see further discussion below. However, as shown in Figure 3, \(R\) and \(\theta \) are closely interconnected, particularly with the largest and smallest \(R\) values being associated with both high and low \(|\theta |\). This makes it difficult to directly disentangle these effects on the solar wind encountered by Earth.

Figure 4
figure 4

Variations of near-Earth solar wind conditions with Earth orbital parameters, namely heliocentric distance (left), heliographic latitude (middle), and absolute latitude (right). Lines show median values, error bars are 95% confidence interval on the median. In all panels, black and blue lines show the observed values over all data and ICMEs removed, respectively, while red lines show values scaled for heliocentric distance. (a–c): Solar wind density. (d–f): Solar wind speed. (g–i): Heliospheric magnetic-field intensity.

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One means to separate the \(R\) and \(\theta \) contributions is to scale parameters for the expected \(R\) variation. By conservation of mass, the proton number density, \(n_{P}\), in a spherically expanding solar wind should fall off as \(1/R^{2}\). This ignores any dynamics – compression or rarefaction – that may occur within the few solar radii of variation in ACE heliocentric distance. The value of \(R\) at ACE (and at Earth) varies by around 7 \(r_{\odot}\) over the year, which is around a 3% variation. As the solar wind density is expected to vary as \(1/R^{2}\), we would therefore expect \(n_{P}\) to systematically vary by around 7%, if the solar wind were uniformly sampled. We therefore compute \(n_{0}\), the density at a reference distance \(R_{0}\), on the basis of \(n\) measured at some other distance \(R\), using the following expression:

$$ n_{0} = n \frac{R^{2}}{R_{0} ^{2}}. $$
(2)

We use \(R_{0} = 215 r_{\odot}\), the mean Earth-Sun distance. This \(R\)-scaled \(n_{P}\) is shown by the red lines in Figures 4a to c. While Figure 4a does appear to show a weak decline in \(n_{P}\) with \(R\), and the scaled \(n_{P}\) does slightly reduce this, the variation is not explained by \(R\) alone. There are no obvious systematic variations of \(n_{P}\) with \(\theta \) (Figures 4b and c), with or without scaling for \(R\).

In order to scale the radial solar wind speed, \(V_{r}\), for radial distance variations, we use the empirical solar wind acceleration expression from Riley and Lionello (2011):

$$ V_{0}= \frac{V}{1 + \alpha \left [ 1 - \exp (\frac{R_{0}-R}{R_{H}}) \right ] }, $$
(3)

where \(V\) is the measured solar wind speed at a distance \(R\), \(V_{0}\) is the scaled solar wind speed to a reference distance \(R_{0}\), \(\alpha = 0.15\) and \(R_{H} = 50 r_{\odot}\). As seen in Figures 4d to f, this correction has little impact, due to the large \(R\) and the small \(\Delta R\) considered here. It can be seen that the slight rising trend of \(V_{r}\) with \(R\) is not a direct result of solar wind acceleration over the heliocentric distances considered. There is no obvious trend in \(V_{r}\) with \(\theta \).

The magnetic-field magnitude, \(|B|\), can be scaled for the \(R\) variation if an ideal Parker spiral (Parker, 1958) is assumed. In this approximation, the angle of the HMF to the radial direction, \(\phi \), at distance \(R\) in a constant solar wind speed \(V\) is given by:

$$ \phi = \arctan \frac{\Omega R}{V}, $$
(4)

where \(\Omega \) is the angular rotation speed of the Sun. The magnetic-field intensity, \(|B|\), is therefore given by

$$ |B| = \frac{B_{r}}{\cos \phi }, $$
(5)

where \(B_{r}\) is the radial magnetic field component at a distance \(R\). By conservation of magnetic flux, this radial component, \(B_{r}\), will fall off as \(1/R^{2}\):

$$ B_{r0} = B_{r} \frac{R^{2}}{R_{0} ^{2}}, $$
(6)

where \(B_{r0}\) is the radial HMF intensity at a reference distance \(R_{0}\). Thus the HMF intensity at a reference distance, \(R_{0}\), can be estimated from:

$$ |B|_{0} = |B| \frac{R^{2} \cos \phi}{R_{0}^{2} \cos \phi _{0}}, $$
(7)

where \(\phi _{0}\) is the Parker spiral angle at a distance \(R_{0}\).

Figure 4g shows that scaling \(|B|\) for the \(R\) variation does reduce the observed trend of \(|B|\) generally declining with \(R\). This suggests that the observed decrease in \(|B|\) with \(R\) is largely explained by the expected \(R\) variation. A weak apparent trend between \(|B|\) and \(\theta \) (Figure 4h) is also reduced when the variation with \(R\) is removed, suggesting an interplay between the orbital parameters \(R\) and \(\theta \).

4 Time-of-Year Variations

We now consider the variations in near-Earth solar wind properties over the year. Figures 5a to c show the \(n_{P}\) variations. The median value varies by around 25% over the year, reaching a minimum value around June (\(F=0.46\)). This suggests the Earth’s heliocentric distance variation could be the cause, as it reaches a maximum value at \(F=0.51\). However, while scaling the observations for the expected \(R\) variation does slightly decrease the \(n_{P}\) variation over the year, it does not produce the 25% variation that is observed. Furthermore, the \(n_{P}\) peaks are closer to the \(|\theta |\) maxima in March and September than the \(R\) maximum in January, suggesting latitude – and hence systematic sampling of different solar wind types – may be contributing to the observed variation. Dividing the data by the solar activity level shows that the peaks are more prominent at solar minimum than maximum. At solar minimum, the timing of the density peaks is close, but not perfectly aligned, with the March and September \(|\theta |\) peaks.

Figure 5
figure 5

Variations of solar wind parameters with the time of year, \(F\). Lines show median values, error bars are 95% confidence interval on the median. Black and blue show the observed values for all data and with ICMEs removed, respectively. Red lines show values scaled for heliocentric distance. (a–c): Solar wind density. (d–f): Solar wind radial speed. (g–i): Heliospheric magnetic-field intensity. Columns from left to right show all data, solar minimum, and solar maximum, respectively. For reference, \(F = 0.5\) is shown as a solid vertical black line.

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Figures 5d to f show the median \(V_{r}\) variation over the year. Particularly during solar minimum conditions, there is an obvious \(|\theta |\) variation in the median \(V_{r}\), with peaks in March and September. This is about a 10 – 15% variation. At solar maximum, there is some evidence of a similar variation present, though the data are generally less ordered at this time.

For \(|B|\), there is also around a 5% variation over the year, peaking near the year start/end and reaching a minimum around July. This is most apparent at solar maximum. After adjusting the values for expected radial distance variation of an ideal Parker spiral, the \(|B|\) variation with \(F\) is reduced.

Next, we investigate how \(n_{P}\) and \(V_{r}\) combine in the form of the solar wind dynamic pressure, \(P_{DYN} = \rho V_{r} ^{2}\), where \(\rho \) is the mass density of the solar wind. For simplicity, we use here only the proton number density, \(n_{P}\), to compute \(\rho \). Alpha particles, the next most abundant ion in the solar wind, only constitute a few percent of the solar wind by number, but their increased mass means they contribute around 10% to \(P_{DYN}\). However, this value is approximately constant, as we find only small systematic variation of the alpha-to-proton ratio (not shown, but can be verified from the provided analysis code). Note that \(P_{DYN}\) is computed from hourly solar wind properties, not from the binned median values over the year.

Figures 6a to c show the resulting annual variations in dynamic pressure. Overall, there is about a 20% variation in \(P_{DYN}\) over the year. However, at solar maximum, this annual variation rises to around 60%. At both solar minimum and maximum, \(P_{DYN}\) reaches a minimum around \(F=0.5\) (June/July), when the Earth is farthest from the Sun. However, the peak in \(P_{DYN}\) in September suggests this is primarily due to sampling different types of solar wind, rather than an intrinsic distance effect. But the peak earlier in the year precedes the \(|\theta |\) peak in March.

Figure 6
figure 6

Variation in the solar wind dynamic pressure (\(P_{DYN}\), top) and potential power input to the magnetosphere (\(P_{\alpha}\), bottom) with fraction of the year \(F\). Lines show median values, error bars are 95% confidence interval on the median. Black and blue show the observed values for all data and with ICMEs removed, respectively. Red lines show values scaled for heliocentric distance. Columns from left to right show all data, solar minimum, and solar maximum, respectively. For reference, \(F = 0.5\) is shown as a solid vertical black line.

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To estimate the potential contribution to the annual variation in geomagnetic activity, we use the Vasyliunas et al. (1982) solar wind-magnetosphere coupling function to estimate the potential power input of the solar wind to the magnetosphere, \(P_{\alpha}\):

$$ P_{\alpha }= n^{(2/3-\alpha )} B ^{(2 \alpha )} V^{(7/3 - 2\alpha )} \sin ^{4} (\theta _{B} /2 ), $$
(8)

where \(\alpha \) is an empirically-derived constant, found to be approximately 0.3 (Lockwood et al., 2017), and \(\theta _{B}\) is the magnetic field clock angle in geocentric solar magnetic (GSM) coordinates. As we are not considering the annual variation in the orientation of Earth’s magnetic field (i.e. the transformation from heliographic to Earth-centric coordinates), we set the \(\sin ^{4} (\theta _{B}/2)\) term to unity.

Figures 6d to f show the annual variation in \(P_{\alpha}\). Patterns are generally similar to \(P_{DYN}\), owing to the common \(n_{P}\) and \(V_{r}\) factors and similar exponents. At solar maximum, there is around 30% annual variation in \(P_{\alpha}\), with peaks in mid February and September, again suggesting that preferential solar wind sampling by heliographic latitude is a significant contributing factor.

5 Conclusion

Geomagnetic activity exhibits many systematic trends over the day – as the Earth rotates – and over the year – as the Earth orbits the Sun. These variations are primarily driven by the geometric effects resulting from the changing orientation of Earth’s magnetic field relative to that of the heliospheric magnetic field. However, there is an additional contribution to time-of-year variations in geomagnetic activity which is often overlooked. It is the changing position of the Earth within the heliosphere, specifically the heliocentric distance of the Earth from the Sun, and Earth’s heliographic latitude. These two coupled variations mean the solar wind is not uniformly sampled through the year. The Sun-Earth distance varies between around 211 \(r_{\odot}\) in January and 218 \(r_{\odot}\) in July, while the heliographic latitude of Earth varies between \(-7.25^{\circ}\) in March and \(7.25^{\circ}\) in September. Using two solar cycles of ACE observations, we have demonstrated that there are systematic trends in the solar wind conditions encountered by Earth as a result.

The annual variation in solar wind speed closely follows the Earth’s heliographic latitude, reaching peak values in March and September, and minima in June and November. It is most clearly seen at solar minimum, as expected (Owens et al., 2019, 2020), but is still also present at solar maximum. The amplitude of this variation is around 10 to 15%. However, the variation does seem to persist to the tail of the speed distribution; for example, at solar minimum, analysis of the solar wind speed probability distribution (not shown) suggests there is around 50% greater probability of encountering solar wind speeds in excess of 600 km s−1 during March and September than in June or December. This could potentially result in preferential energization of the radiation belts throughout the year (Reeves, Morley, and Cunningham, 2013). Similarly, while the occurrence of magnetospheric Kelvin-Helmholtz waves over the year appears to be primarily controlled by geometric effects such as the RM effect (Kavosi et al., 2023), the annual variation in solar wind speed may also contribute.

Annual variations are also present in the solar wind density, with an amplitude of around 25%. Perhaps surprisingly, this is unlikely to be the result of the Earth’s heliocentric distance variation, which is expected to account for around a 7% variation over the year. The phase of the density variation is also inconsistent with heliocentric distance. Instead, it seems more closely related to the latitudinal variation of Earth and hence non-uniform sampling of the solar wind. Naively, we may expect the times of elevated solar wind speed to be associated with lower density, as fast coronal-hole wind is typically lower density than slower streamer-belt wind (e.g. Ebert et al., 2009). However, while this may be true for individual hours of data, in the time-averaged properties considered here, the annual variations of density and speed are not obviously anti-correlated. Indeed, if anything, there is some degree of correlation, with both speed and density reaching minima near the middle of the year and start/end of the year.

The magnetic field intensity shows a weaker annual trend, which is roughly consistent with Earth’s heliocentric distance variation, peaking around January and reaching a low value around June/July.

The density and solar wind speed variations combine to give the dynamic pressure, \(P_{DYN}\) variation. However, despite the strong annual variations of the average speed and density at solar minimum, the resulting dynamic pressure variation is rather weak at this time. There is a minimum in \(P_{DYN}\) around June/July, and some suggestion of a maximum around September, but the amplitude is only 15%. This suggests that while the annual variations of density and speed are somewhat correlated, the individual hours of data that make up these average variations are somewhat anti-correlated, as might be expected from the properties of fast and slow wind. At solar maximum, the picture is quite different. The annual speed and density variations are less ordered at this time. But the individual hourly data combine to produce a strong \(P_{DYN}\) variation over the year. This peaks in mid-February and late-October, and reaches a minimum value in June/July. These dates are suggestive of the Earth’s latitudinal variation, though not in complete agreement. The reason for such a timing offset is not known and could be insufficient sample size. The amplitude of the annual variation in \(P_{DYN}\) is around 60% at solar maximum. As the magnetopause distance at the nose scales by \(P_{DYN}^{1/6}\), this would constitute about a 10%, or 1 Earth radius, variation. This too may have implications for the radiation belts, as magnetopause shadowing can cause particle loss (Staples et al., 2022).

Finally, we considered a proxy for geomagnetic activity, in the form of power input to the magnetosphere, \(P_{\alpha}\). The dominant factor in \(P_{\alpha}\) is the angle between the heliospheric and magnetospheric magnetic fields. The variation of this orientation factor over the day and year has been well studied elsewhere (e.g. Lockwood et al., 2020b). Instead, we focus on the variation in the bulk properties, which determine the potential for geomagnetic activity for a given HMF orientation. The annual variation in \(P_{\alpha}\) is qualitatively similar to that of \(P_{DYN}\). At solar maximum, the potential power input to the magnetosphere seems to be more obviously modulated by heliographic latitude rather than heliocentric distance. The amplitude of the variation is around 30% at solar maximum, suggesting it could be a significant contribution to the overall annual variation in the base-level of geomagnetic activity.