The recent decline in the open magnetic flux of the Sun heralds the end of the Grand Solar Maximum (GSM) that has persisted throughout the space age, during which the largest-fluence Solar Energetic Particle (SEP) events have been rare and Galactic Cosmic Ray (GCR) fluxes have been relatively low. In the absence of a predictive model of the solar dynamo, we here make analogue forecasts by studying past variations of solar activity in order to evaluate how long-term change in space climate may influence the hazardous energetic particle environment of the Earth in the future. We predict the probable future variations in GCR flux, near-Earth interplanetary magnetic field (IMF), sunspot number, and the probability of large SEP events, all deduced from cosmogenic isotope abundance changes following 24 GSMs in a 9300-year record.
 Geomagnetic activity records [Lockwood et al., 1999, 2009] and abundances of cosmogenic radionuclides, generated by Galactic Cosmic Rays (GCRs) and stored in terrestrial reservoirs [Steinhilber et al., 2008, 2010], have revealed and quantified centennial and millennial variations in the open solar flux and the near-Earth Interplanetary Magnetic Field (IMF), B. The agreement between the reconstructions is remarkable, given that the two techniques are independent [Lockwood and Owens, 2011]. The cosmogenic isotopes show that in recent decades the Sun has been in a Grand Solar Maximum (GSM) which has lasted longer than all others in the past 9.3 millennia and is expected to end soon [Abreu et al., 2008]. This is supported by geomagnetic and satellite observations which show a decline in mean B since 1985 [Lockwood and Fröhlich, 2007; Lockwood et al., 2009], of which the recent low and prolonged sunspot minimum is part [Lockwood, 2010]. These changes in near-Earth space influence the occurrence of space-weather phenomena, returning Earth to conditions that last prevailed around 1920 [Lockwood et al., 2009; Steinhilber et al., 2010; Lockwood and Owens, 2011], before the advent of susceptible modern operational systems, such as spacecraft, power distribution grids and aircraft [Hapgood, 2011]. McCracken and Beer  have used Monte-Carlo simulations to combine cosmogenic isotope data with observations by modern ionisation chambers and neutron monitors and shown that higher GCR intensities existed before the space age and noted that they were likely to reoccur in the future. McCracken  extended the study of McCracken and Beer  to high-fluence Solar Energetic Particle (SEP) events (sufficient to be seen as “Ground-Level Enhancements”, GLEs, in neutron monitor data) to demonstrate that SEPs were also more frequent in the past and deduced that their fluence was also likely to increase in future.
 Measurements of nitrates in ice cores has led to the identification of 15 major SEP events (fluence of >30 MeV protons exceeding 5 × 109cm−2) during 1700–1970 [Shea et al., 2006] which gives an average SEP event occurrence per century of PSEP = 5.6 for this interval. In contrast, spacecraft measurements [Barnard and Lockwood, 2011] during 1970–2009 yield just 1 equivalent event, an occurrence of PSEP = 2.6 per century. This decrease was also identified in GLE events by McCracken .
 At cruise altitudes of commercial aviation, both SEPs and GCRs pose threats through single event upsets in critical electronics and through exposure of crew and passengers to radiation [Dyer et al., 2003; Barish, 2009]. Radiation standards for avionics are based on past experience from the current GSM and there are no regulations concerning passenger exposure. Allowed radiation limits on the ground vary between nations. The International Commission on Radiological Protection (ICRP) recommends a 20 mSv limit for the annual exposure of occupational radiation workers and a 1 mSv limit for the public and prenatal annual exposure [Wrixon, 2008; Mertens et al., 2010]. Dosages during a flight depend on path, duration and altitude as well as solar activity. For example, Mertens et al.  find a commercial 8-hour polar flight during the 2003 “Halloween” SEP event would have given 0.7 mSv. Models such as QARM [Lei et al., 2006] (which can run be online at http://qarm.space.qinetiq.com/) show that a round trip of two such flights during the recent solar minimum gave a GCR dose of order 0.2 mSv and during the largest known SEP event, the “Carrington event” of 1859 [Shea et al., 2006; Hapgood, 2011], would have given 20 mSv. Some flights have already been diverted to lower latitudes and altitudes based on solar event warnings (mainly to avoid communications blackouts rather than the associated SEP hazard) with monetary and flight-time costs [Fisher and Jones, 2007]. GCRs and SEPs are also a threat to spacecraft, reducing operational lifetimes and thus returns on investment. Current engineering and business models are also based on experience gained during the current GSM and long-term solar change will impact the economics of commercial space activities. Estimates vary, but from studies of smaller events, the direct and knock-on (loss of service etc.) costs of a Carrington-scale event have been estimated at $1–2 trillion and full recovery would take 4–10 years [Odenwald et al., 2006].
 To understand how solar activity may evolve in the future, we need to study past behaviour. We here use the 9300-year record of 25-year means of the solar modulation potential ϕ compiled by Steinhilber et al.  from cosmogenic isotope and neutron monitor data: ϕ quantifies the solar shielding of the Earth from GCRs and taking ϕ ≥ 600 MV defines 24 GSMs prior to the current one. Lockwood  carried out a superposed-epoch study of ϕ around the ends of these 24 GSMs (at times t = to). Figure 1 is an updated version of that study and shows that the chance of 25-year running means, ϕ25, falling to Maunder minimum levels at (t − to) ≤ 40 years is 8%. We here take the mean ϕM and standard deviation σ of the composited ϕ25 at a given (t − to), and use upper and lower values, ϕU = ϕM + 2σ and ϕL = ϕM − 2σ (exceeded in about 5 and 95% of cases, respectively) as predictions of the range of likely behaviours after the end of the current GSM.
Figure 2 demonstrates how the solar cycle variations are added to the means shown in Figure 1, using the procedure developed by Lockwood et al.  and the reconstruction of annual values of ϕ by Usoskin et al.  for 1720 onwards. The polynomial fit is used to estimate ϕ for a predicted ϕ25 and solar cycle phase, .
2. Analogue Forecasts of the Future
Figure 3a shows past variations of ϕ (in black) and ϕ25 (in grey), from Usoskin et al.  and Steinhilber et al.  respectively, in the 110 years leading up to the end of the current GSM, taken to be at to = 2014 [Lockwood et al., 2009]. The plot also uses the composite in Figure 1 to predict ϕM, ϕU and ϕL at a given (t − to), as shown by the thick green, cyan and orange lines, respectively. The annual values for these predicted 25-year means are then computed for t > to from the polynomial fit shown in Figure 2, where is computed by assuming future solar cycles are all of the average 11-year duration (shown by the thin green, blue and red lines for ϕM, ϕU and ϕL, respectively).
Figure 3 also shows the corresponding plots for the integrated GCR flux for a geomagnetic rigidity cut-off of 1 GV, I>1GV (Figure 3b); the IMF, B (Figure 3c) and the sunspot number R (Figure 3d). The predicted ϕM, ϕL, and ϕU are converted into the corresponding values of B and I>1GV; the former using the formula by Steinhilber et al. , the latter by integrating the formula for differential GCR flux by Castagnoli and Lal  and using their model local interstellar GCR spectrum. Note that 1 GV is used here because it applies at geomagnetic latitude of about 60° and so is relevant to high-latitude aircraft flights. For R, the conversion is made using a linear regression of 25-year means of R and ϕ25 for 1700–2009. Once the 25-year running means of I>1GV, B and R have been computed, the solar cycle variation in annual means is constructed using the same procedure as was applied to ϕ in Figure 2. A grand minimum (ϕ lower than in the Maunder minimum) occurs within 40 years of to for ϕL, giving near-zero R and B and with I>1GV rising to 2.5 times the average for recent decades. On the other hand, ϕU yields only a slight and brief rise in I>1GV and ϕM gives a rise by a factor near 1.5. Additionally we calculated the integrated GCR flux for the cut-off of the Climax neutron monitor (3 GV) (not shown). We find an increase in I>3GV of about 40% for ϕL which agrees well with the Maunder minimum value derived by McCracken and Beer .
Figures 4, 5, and 3e analyse the other energetic particle hazard, SEPs. We employ the recent survey of gradual SEPs at energies >60 MeV [Barnard and Lockwood, 2011], predominantly generated at the shocks ahead of super-Alfvénic coronal mass ejections (CMEs) [Reames, 2004]. Figure 4a shows the probability distributions of annual means of measured and reconstructed B for 1968–2009 and 1700–2009, respectively. It can be seen that B in the space age has been higher (because it is within the recent GSM). Figure 4b shows the fraction of SEP events, N/No at B below the threshold given by the x-axis and 4c shows the corresponding normalised logarithm of the integrated fluence in those events, F/Fo (No is the total number of events and Fo is the logarithm of the integrated total fluence). Both decrease as the B reduces, but N/No falls more rapidly than F/Fo so the log of the fluence per event, (F/N) increases rapidly (Figure 4d). This shows that although SEP events become rarer as B decreases, the mean fluence within each event increases dramatically. This agrees with the analysis of GLE event occurrence by McCracken .
Figures 5a and 5b compare the intervals 1700–2009 and 1968–2009. The contours give the number of years with mean B falling in bins 1nT wide and with mean R in bins of width 25. In both plots, the black dots are the large SEP events (fluence of 30 MeV protons >5 × 109cm−2) as inferred from nitrates deposited in ice sheets [McCracken et al., 2001; Shea et al., 2006] and as directly measured by spacecraft. The radius of the dot is proportional to the log of the event fluence. Note that the events define a band at intermediate B values and that they cluster around a B which increases with R. It has been postulated [McCracken et al., 2001] that when B is low, the occurrence of large and fast CMEs is also low but that at large B the consequent enhanced Alfvén speed of the interplanetary medium reduces the CME shock compression ratio and hence the efficiency of SEP acceleration. Combined, these two factors could therefore explain why large events are more common in a band at intermediate B. The open flux continuity equation [Vieira and Solanki, 2010] has a production term that depends on R and CME rate and a loss term which depends on other factors such as the heliospheric current sheet tilt [Owens et al., 2011]; as a result, although B increases with R on average, a spread of B-R combinations is possible. Figure 5b shows that in the space age, B has generally been higher than the optimum combination of B and R for large SEPs to occur. This contrasts with Figure 5a in which optimum combinations were much more common. Figure 5c shows contours of the SEP rate PSEP as a function of R and B, derived from a fit to the occurrence frequency of all events. Annual (B, R) coordinates vary both over solar cycles and on longer timescales and it is found that they often move in and out of the band of high PSEP occurrence at varying phases of the cycle.
Figure 3e shows PSEP variations derived from the annual R and B means using Figure 5c. During the recent solar minimum the fall in B caused PSEP to rise. For predictions based on ϕL, the average probability of a large event continues to rise (by to up to 3 times) before falling to low values as the Sun enters the grand minimum. For ϕU, PSEP shows oscillations similar to the present solar cycle before a slow decay: peak PSEP occur for the lower B values at sunspot minimum, as was true for the interval 1900–1930 (−102 < t − to < −72 yr). The most likely exit from the current GSM is given by ϕM which yields persistently higher PSEP than we have experienced during the current GSM. The solar cycle variation is different to the other two cases, showing lowest PSEP at sunspot minima with clear peaks in both the rising and falling phases: the average PSEP remains enhanced throughout the next century.
 This analysis reveals that the risk of the space-weather radiation effects is considerably enhanced over the next century compared to the space age thus far. There is an 8% chance of the Sun falling into a grand minimum during the next 40 years [Lockwood, 2010], giving enhanced dosages of GCR radiation which is of concern for aircraft avionics, crew and passengers. The risk of large SEP events is initially enhanced in this case but then is low during the grand minimum itself. A more likely scenario is given by the mean of all previous examples and this predicts a more modest rise in the GCR fluxes but a persistently enhanced risk of a large SEP event. Lastly we note that both GCR and SEP enhancements will be amplified by the probable continuation of the decrease in the geomagnetic field, and the shielding it provides, that has been observed over the past 160 years [Gubbins et al., 2006].
 L.B. was supported by a Ph.D studentship from the UK Natural Environment Research Council, M.L., M.A.H. and C.J.D. are funded by the Science and Technology Research Council and FS by NCCR climate (Swiss climate research).
 The Editor thanks Margaret Shea and an anonymous reviewer for their assistance in evaluating this paper.