Cosmic ray flux variations, modulated by the solar and earth’s magnetic fields, and climate changes. 1. Time interval from the present to 10–12 ka ago (the Holocene Epoch)

Direct and indirect data on variations in cosmic rays, solar activity, geomagnetic dipole moment, and climate from the present to 10–12ka ago (the Holocene Epoch), registered in different natural archives (tree rings, ice layers, etc.), have been analyzed. The concentration of cosmogenic isotopes, generated in the Earth’s atmosphere under the action of cosmic ray fluxes and coming into the Earth archives, makes it possible to obtain valuable information about variations in a number of natural processes. The cosmogenic isotopes ¹⁴C in tree rings and ¹⁰Be in ice layers, as well as cosmic rays, are modulated by solar activity and geomagnetic field variations, and time variations in these concentrations gives information about past solar and geomagnetic activities. Since the characteristics of natural reservoirs with cosmogenic ¹⁴C and ¹⁰Be vary with climate changes, the concentrations of these isotopes also inform about climate changes in the past. A performed analysis indicates that cosmic ray flux variations are apparently the most effective natural factor of climate changes on a large time scale.     

Long-term solar cycles according to data on the cosmogenic beryllium concentration in ice of central Greenland

Data on the concentrations of the cosmogenic ¹⁰Be isotope and Na⁺ and Ca²⁺ ions, as well as on ice accumulation rates in central Greenland, obtained by the GISP2 collaboration were studied in a time interval spanning about 40 000 recent years. Joint analysis of the indicated glacial and chemical paleoseries demonstrated that in a period from 12 008 to 24 008 years ago, the ¹⁰Be flux variations were most free of influence of climate and changes in the geomagnetic dipole moment. As a consequence, this time interval is most suitable for studying periodicities of purely solar nature. Statistical analysis of the ¹⁰Be flux data has revealed significant variations with periods of 500–800 years and 1300–1600 years in the time interval from 12 008 to 17 008 years ago. This evidence favors the existence of the appropriate cycles of solar activity in the mentioned epoch. Similar periodicities are also revealed in the time interval from 3288 to 8008 years ago.     

Paleomagnetism of some mafic intrusions in the South Carolina Piedmont. I. Magnetic systems with single characteristic directions

Four mafic and two dioritic igneous bodies intruding along the flanks of the Charlotte belt, within the King's Mountain belt and near the Slate-Kiokee-Charlotte belt boundaries in the South Carolina Piedmont, were studied paleomagnetically. The results suggest that these mafic rocks with a single characteristic magnetization are broadly contemporaneous. A mean paleomagnetic pole position of 38.9°N 120.8°E has been calculated for the six bodies. This pole position falls near the 300 Ma old point of Irving's apparent polar wander path (APWP) for North America. The α95 circle of confidence (10.2°) includes points on the APWP between 250–360 Ma. Anomalously old KAr apparent ages, greater than one billion years, are suggestive of excess ⁴⁰Ar contamination for the mafic Buffalo pluton, whereas apparent ages in the range of 360–395 Ma old are interpreted as a maximum age for the other bodies, due to the possibility of small amounts of excess ⁴⁰Ar being present. A 10° westerly tilt correction suggested by Dooley and Smith for early Mesozoic diabase brings the mafic pole position of this study to more nearly coincide with the 350 Ma virtual geomagnetic position of Irving's curve, but the test is inconclusive, awaiting better definition of radiometric ages. The simplest interpretation of the data is that the mafic pole position reflects the direction of the geomagnetic field in late Devonian Carboniferous times. The similarity of this pole position with the points on the APWP for North America provides little evidence for displaced terrains and, with the precision of this pole position, horizontal displacements on the order of that suggested by the Consortium for Continental Reflection Profile (COCORP) results, or by subsequent studies, are not detectable. This and other pole positions from granitic rocks in the southern Appalachian orogen suggest that if displaced terrains exist, the evidence must be found in older rocks, or in other geologic belts.     

Cosmogenic isotopes and their role in present-day solar paleoastrophysics

Present-day data on ¹⁴C and ¹⁰Be concentration in natural archives have been statistically analyzed. It has been established that it is difficult to extract information about solar activity variations on long (several Myr and longer) and, especially, short (to 30 years) time scales using radiocarbon data. It has been indicated that beryllium series bear reliable information about short-term, secular, and, probably, 1000-year variations in solar activity. Moreover, ¹⁰Be concentration in polar ice can also be used to study the internal dynamics of solar activity. It has been concluded that beryllium data are more promising than radiocarbon ones from the viewpoint of solar paleoastrophysics.     

In-phase anomalies in Beryllium-10 production and palaeomagnetic field behaviour during the Iceland Basin geomagnetic excursion

Increases in the production rate of cosmogenic radionuclides associated with geomagnetic excursions have been used as global tie-points for correlation between records of past climate from marine and terrestrial archives. We have investigated the relative timing of variations in ¹⁰Be production rate and the corresponding palaeomagnetic signal during one of the largest Pleistocene excursions, the Iceland Basin (IB) event (ca. 190 kyr), as recorded in two marine sediment cores (ODP Sites 1063 and 983) with high sedimentation rates. Variations in ¹⁰Be production rate during the excursion were estimated by use of ²³⁰Th_xs normalized ¹⁰Be deposition rates and authigenic ¹⁰Be/⁹Be. Resulting ¹⁰Be production rates are compared with high-resolution records of geomagnetic field behaviour acquired from the same discrete samples. We find no evidence for a significant lock-in depth of the palaeomagnetic signal in these high sedimentation-rate cores. Apparent lock-in depths in other cores may sometimes be the result of lower sample resolution. Our results also indicate that the period of increased ¹⁰Be production during the IB excursion lasted longer and, most likely, started earlier than the corresponding palaeomagnetic anomaly, in accordance with previous observations that polarity transitions occur after periods of reduced geomagnetic field intensity prior to the transition. The lack of evidence in this study for a significant palaeomagnetic lock-in depth suggests that there is no systematic offset between the ¹⁰Be signal and palaeomagnetic anomalies associated with excursions and reversals, with significance for the global correlation of climate records from different archives.     

Be in a deep-sea core: implications regardingBe production changes over the past 420 ka

The influx of¹⁰Be into a globigerinid ooze core (CH72-02) from the eastern North Atlantic has been studied. This core contains a depositional record of the first 11 δ¹⁸O stages covering the last 423 ka. It is shown that the marine deposition of¹⁰Be is strongly influenced by the sedimentation of clays. Clay particles appear 10 times more efficient than the carbonate component as a carrier in bringing¹⁰Be to the bottom sediments. In core CH72-02, the deposition rates of¹⁰Be averaged over each oxygen-isotope stage for the past 11 stages show a scatter of ±40% about the mean value of 6.6 × 10⁸ atoms cm⁻² ka⁻¹. However, after correction for changes in lithology, the data show that the production rate of¹⁰Be over the same period has varied no more than ±25%, and the variations are not systematic in that high or low¹⁰Be production appear to be associated with either cold or warm climates. On the time scale of this investigation (intervals of ca. 50 ka over the last 420 ka, with resolutions as fine as 10 ka for portions of the record), it is unlikely that the shielding effect of the solar wind has deviated by more than ±25% or the geomagnetic field intensity has deviated by more than a factor of 1.6 from their long-term averages.     

A simple model for reconstructing geomagnetic field intensity with <Superscript>10</Superscript>Be production rate and its application in Loess studies

A simple model for reconstructing the paleomagnetic field intensity with ¹⁰Be production rate was used for the first time in Loess ¹⁰Be studies of Luochuan profile. Using the LGM (Last Glacial Maxmium) method, the climatic effects and geomagnetic modulation effects on loess ¹⁰Be was separated and in turn the 80 ka geomagnetic excursion sequence reconstructed, of which the globally remarkable geomagnetic excursion events such as the Laschamp (42 ka), Mono Lake (32 ka) during the Last Glacial period were revealed and the paleo-geomagnetic intensity curve from Loess ¹⁰Be over the past 80 ka was quantitatively reconstructed. The reconstructed paleo-intensity fits well with the paleo-intensity curves (SINT200 and NAPIS75), which indicates the significance of global criterion of the ¹⁰Be paleo-intensity curve and the future direction of loess ¹⁰Be tracing studies. Results show the irregular variability of the East Asian monsoon precipitation in Loess Plateau is the main cause that has resulted in the ambiguity of the geomagnetic modulation of the ¹⁰Be record in the loess, and the intrinsic source component of the loess ¹⁰Be and inherited fraction of magnetic susceptibility (SUS) are characterized by the “quasi-homogeneous distribution” manner. Supported by the Key Innovation Project of the Chinese Academy of Sciences (Grant No. KZCX2-YW-118), the National Natural Science Foundation of China (Grant Nos: 40531003, 40121303, 40523002) and State Key Laboratory of Loess and Quaternary Geology in the Institute of Earth Environment of Chinese Academy of Sciences (Grant No. SKLLQG0712)     

Cosmic ray flux variations,modulated by the solar and terrestrial magnetic fields,and climate changes. Part 2: The time interval from ∼10000 to ∼100000 years ago

A joint analysis of paleodata on variations in cosmic ray fluxes, solar activity, geomagnetic field, and climate during the period from ～10000 to ～100000 years ago has been performed. Data on the time variations in the concentration of ¹⁴C and ¹⁰Be cosmogenic isotopes, which are generated in the Earth’s atmosphere under the action of cosmic ray fluxes modulated by solar activity and geomagnetic field variations, were used to detect variations in solar activity and the geomagnetic dipole. Information about climate changes has been obtained mainly from variations in the concentration of stable isotopes in the natural archives. A performed analysis indicates that the variations in cosmic ray fluxes under the action of variations in the geomagnetic field and solar activity are apparently one of the most effective natural factors of long-term climate changeability on a large time scale.     

Aerosol deposition velocities on the Pacific and Atlantic oceans calculated from7Be measurements

The concentrations of⁷Be have been measured in Pacific and Atlantic ocean water for the past several years to determine the deposition velocity of aerosol particles on the ocean surface.⁷Be is produced at a relatively constant rate in the atmosphere by spallation reactions of cosmic rays with atmospheric nitrogen and oxygen. Immediately after its formation⁷Be becomes attached to aerosol particles, and therefore can serve as tracers of the subsequent behavior of these particles. Isopleths of⁷Be surface water concentrations,⁷Be inventory in the ocean, and deposition velocity have been prepared for the Pacific Ocean from 30°S to 60°N and for the Atlantic Ocean from 10°N to 55°N. The concentrations, inventories and deposition velocities tended to be higher in regions where precipitation was high, and generally increased with latitude. The average flux of⁷Be across the ocean surface was calculated to be 0.027 atoms cm^?2 s^?1 which is probably not significantly greater than the worldwide average⁷Be flux across land and ocean surfaces of 0.022 atoms cm^?2 s^?1 calculated by Lal and Peters. The average deposition velocity was calculated to be 0.80 cm s^?1. This value may be 10–50% too low, since it was calculated using atmospheric⁷Be concentrations which were measured at continental stations. Measurements of atmospheric⁷Be concentrations at ocean stations suggest that the concentrations at the continental stations averaged 10–50% higher than the concentrations over the ocean.     

Paleosecular variation and absolute geomagnetic paleointensity records retrieved from the Early Cretaceous Posadas Formation (Misiones,Argentina)

The Early Cretaceous may be considered a key period for understanding the evolution of the Earth’s magnetic field. Some still unsolved problems are related to the mode of paleosecular variation (PSV) of the Earth’s magnetic field before and during the Cretaceous Normal Superchron. We report here a detailed rock-magnetic, paleomagnetic and paleointensity investigation from 28 lava flows (331 standard paleomagnetic cores) collected in the Argentinean part of the Parana Flood Basalts (Formation Posadas) in order to contribute to the study of PSV during the early Cretaceous and to obtain precise Cretaceous paleomagnetic pole positions for stable South America. The average paleofield direction is precisely determined from 26 sites, which show small within-site dispersion and high directional stability. Five sites show evidences for the self-reversal of thermoremanent magnetization. 23 sites yielded normal polarity magnetization and only 3 are reversely magnetized. Moving windows averages were used to analyze the sequential variation of virtual geomagnetic pole’s (VGP) axial positions. Interestingly, the axial average VGP path traces an almost complete cycle around the geographical pole and passes near the location of all previously published Paraná Magmatic Province poles. Both paleomagnetic poles and average VGP paths are significantly different from the pole position suggested by fixed hotspot reconstructions, which may be due to true polar wander or the hotspot motion itself. Only 15 samples from 5 individual basaltic lava flows, yielded acceptable paleointensity estimates. The site mean paleointensities range from 25.2 ± 2.2 to 44.0 ± 2.2 μT. The virtual dipole moments (VDMs) range from 4.8 to 9.9 × 10²² Am². This correspond to a mean value of 7.7 ± 2.1 × 10²² Am² which is 96% of the present day geomagnetic field strength. These intensities agree with the relatively high values already reported for Early Cretaceous, which are consistent with some inferences from computer simulations previously published.     

Meteoric 10Be speciation in subglacial sediments of East Antarctica

A sequential chemical extraction procedure was developed and tested to investigate the utility of meteoric ¹⁰Be as a tracer for authigenic mineral formation beneath the East Antarctic Ice Sheet. Subglacial meltwater is widely available under the Antarctic Ice Sheet and dissolved gases within it have the potential to drive chemical weathering processes in the subglacial environment. Meteoric ¹⁰Be is a cosmogenic nuclide with a half-life of 1.39·10⁶ years that is incorporated into glacier ice, therefore its abundance in the subglacial environment in Antarctica is meltwater dependent. It is known to adsorb to fine-grained particles in aqueous solution, precipitate with amorphous oxides/hydroxides, and/or be incorporated into authigenic clay minerals during chemical weathering. The presence of ¹⁰Be in chemical weathering products derived from beneath the ice therefore indicates chemical weathering processes in the subglacial environment. Freshly emerging subglacial sediments from the Mt. Achernar blue ice moraine were subject to chemical extractions where these weathering phases were isolated and ¹⁰Be concentrations therein quantified. Optimization of the phase isolation was developed by examining the effects of each extraction on the sample mineralogy and chemical composition. Experiments on ¹⁰Be desorption revealed that pH 3.2–3.5 was optimal for the extraction of adsorbed ¹⁰Be. Vigorous disaggregation of the samples before grain size separations and acid extractions is crucial due to the incorporation of the nuclide in clay minerals and its preferential absorption to clay-sized particles. ¹⁰Be concentrations of 2–22·10⁷ atoms·g⁻¹ measured in oxides and clay minerals in freshly emerging sediments strongly indicate subglacial chemical weathering in the catchment of the Mt. Achernar moraine. Based on total ¹⁰Be sample concentrations, local basal melt rates, and ¹⁰Be ice concentrations, sediment-meltwater contact in the subglacial environment is on the order of thousands of years per gram of underlying fine sediment. Strong correlation (R = 0.97) between ¹⁰Be and smectite abundance in the sediments supports authigenic clay formation in the subglacial environment. This suggests meteoric ¹⁰Be is a useful tool to characterize subglacial geochemical weathering processes under the Antarctic Ice Sheet.     

The geochemical cycle of 9Be: a reconnaissance

An initial survey has been made of the geochemistry of ⁹Be in natural waters with a view to utilizing the isotope with the cosmogenic species ¹⁰Be (t_1/2 = 1.5 m.y.) in geochronological studies of sedimentary accumulation. The mobility of⁹Be in continental waters is a strong function of pH with acid streams (pH < 6) being strongly enriched as compared to alkaline carbonate rivers. Large-scale scavenging of beryllium occurs in the estuaries of rivers containing more than about 200 pM of the element. In alkaline systems of lower concentration the element appears to behave conservatively. The net flux of beryllium to the ocean is estimated as that equivalent to an average effective river concentration of about 150 pM. Beryllium is strongly enriched in ridge crest hydrothermal solutions over ambient seawater. The flux is approximately 70% of that from the continents. The deep water concentrations of ⁹Be vary by only 20% between the North Atlantic and North Pacific demonstrating that the “chemical saltation” produced by scavenging from the deep water column and release from the sediments predominates over simple advective concentration along flow lines. Isotopic homogenization of ¹⁰Be and ⁹Be is probably achieved in the ocean. The situation in continental waters appears much less promising.     

Variations of angular elements of the geomagnetic field in Europe during the last 24 centuries

The analysis of variations in angular elements of the geomagnetic field during the period since 350 B.C. to the present day according to the findings from the study of thermal magnetization of baked archaeological samples from England, France, and East Europe showed that the key feature in the behavior of the geomagnetic inclination in all three regions is a millennial variation. The trend in the behavior of the inclination of the geomagnetic field can be regarded as a manifestation of a variation with a characteristic time scale of several thousand years. Despite the general likeness of variations in inclination and declination of the ancient geomagnetic field, they also exhibit a noticeable dissimilarity. The paths of the virtual geomagnetic pole reconstructed from the variations of angular elements of the geomagnetic field in East Europe indicate that the geomagnetic polar motion is quasi-cyclic. The duration of the first cycle was about 1000 years, while the second cycle has not been completed due to the change of the motion to the opposite direction in the middle of the XVII century.     

Late Holocene seacliff retreat recorded by 10Be profiles across a coastal platform: Theory and example from the English Channel

We explore a new method for documenting the long-term retreat rate of seacliffs based on measurements and modeling of ¹⁰Be concentration transects across present-day shore platforms. The proposed forward numerical model relies on a scenario of sea-level rise since the last deglaciation, and predicts the shape of ¹⁰Be concentration transects as a function of prescribed cliff recession and vertical coastal platform downwearing rates. Two independent transect features allow fitting the long-term recession rate model to field observations: a sharp ¹⁰Be concentration drop predicted at the former stationary location of the cliff during the last glacial period ∼100 ka ago, and a characteristic dome shape whose magnitude is directly related to the recession rate of the cliff. A retreating chalk cliff site from the English Channel coast of France, at Mesnil-Val, where the 7 m tidal range broadly exposes the shore platform, was selected to test the proposed method. Although retreat rates were too high to pinpoint the predicted ¹⁰Be concentration drop at the last glacial cliff position, the ¹⁰Be concentration of the flints sampled across the shore platform is consistent with the expected dome shape. When modeled using the proper tidal range and proposed Holocene sea-level rise history, the ¹⁰Be data yield a cliff retreat rate since the mid-Holocene of 11–13 cm/yr. This is consistent with a 30-year-long measurement record, strongly supporting the utility of the ¹⁰Be method.     

Motion of the Earth’s magnetic poles in the last decade

Based on vector magnetic data from the CHAMP German satellite, average daily spherical harmonic models of the main geomagnetic field to n = m = 10 have been constructed for the period from May 2001 to the end of 2009 at an interval of 4 days. The obtained 16 models, which were averaged over half a year, have been used to calculate the coordinates of the north and south magnetic poles (the points where magnetic field lines are vertical). The changes in these coordinates during these eight and a half years have been traced. Both poles continue moving northward and westward. The north magnetic pole has traveled 400 km during this period. The velocity of its motion has increased up to the year 2003, reaching 62.5 km yr⁻¹, and then started decreasing and reached 45 km yr⁻¹ by the end of 2009. In addition, the direction of motion changed from north-northwestward to northwestward; i.e., the pole started turning slightly towards Canada. The south magnetic pole moved slower by an order of magnitude and has traveled 42 km during this period. The coordinates of the geomagnetic (dipole) poles and the eccentric dipole parameters have also been calculated. The dynamics of these poles has been traced.     

Rates of rockwall slope erosion in the upper Bhagirathi catchment,Garhwal Himalaya

Rockwall slope erosion is defined for the upper Bhagirathi catchment using cosmogenic Beryllium-10 (¹⁰Be) concentrations in sediment from medial moraines on Gangotri glacier. Beryllium-10 concentrations range from 1.1 ± 0.2 to 2.7 ± 0.3 × 10⁴ at/g SiO₂, yielding rockwall slope erosion rates from 2.4 ± 0.4 to 6.9 ± 1.9 mm/a. Slope erosion rates are likely to have varied over space and time and responded to shifts in climate, geomorphic and/or tectonic regime throughout the late Quaternary. Geomorphic and sedimentological analyses confirm that the moraines are predominately composed of rockfall and avalanche debris mobilized from steep relief rockwall slopes via periglacial weathering processes. The glacial rockwall slope erosion affects sediment flux and storage of snow and ice at the catchment head on diurnal to millennial timescales, and more broadly influences catchment configuration and relief, glacier dynamics and microclimates. The slope erosion rates exceed the averaged catchment-wide and exhumation rates of Bhagirathi and the Garhwal region on geomorphic timescales (10³−10⁵ years), supporting the view that erosion at the headwaters can outpace the wider catchment. The ¹⁰Be concentrations of medial moraine sediment for the upper Bhagirathi catchment and the catchments of Chhota Shigri in Lahul, northern India and Baltoro glacier in Central Karakoram, Pakistan show a tentative relationship between ¹⁰Be concentration and precipitation. As such there is more rapid glacial rockwall slope erosion in the monsoon-influenced Lesser and Greater Himalaya compared to the semi-arid interior of the orogen. Rockwall slope erosion in the three study areas, and more broadly across the northwest Himalaya is likely governed by individual catchment dynamics that vary across space and time. © 2019 The Authors. Earth Surface Processes and Landforms Published by John Wiley & Sons, Ltd.     

Geomagnetic field variations in southeastern Europe between 6500 and 100 years B.C.

Results from joint work between the Geophysical Institute (Sofia, Bulgaria), and the Geomagnetic Institute (Grocka, Yugoslavia) on the geomagnetic field variation in the prehistoric past are presented. Preliminary curves of variation of the three geomagnetic elements: declination, inclination and intensity are presented. The movement of the virtual pole position for the 6500 years time period B.C. is derived. The curves and the virtual pole positions provide a dating tool for archaeological purposes and determination of the periodicities in the geomagnetic secular variations in southeastern Europe.     

Changes in the geomagnetic field and solar wind — causes of changes of climate and atmospheric circulation

Summary The analyses of various types of geomagnetic and atmospheric manifestations have disclosed certain associations. The agreement in the occurrence of the increased spectral densities as regards geomagnetic activity and the variations of atmospheric pressure over the geomagnetic pole proves the relation between their periodicities. The results imply that the changes in the intensity of corpuscular radiation, indicated by geomagnetic activity, affect the pressure patterns over the geomagnetic pole and polar region significantly, so that a pronounced modification of the general circulation may take place, as shown schematically in Figs 14a,b.Dedicated to Prof. RNDr. Emil Buchar, DrSc., Corresponding Member of the Czechoslovak Academy of Sciences, on the Occasion of His 75^th Birthday     

The impact of storm-triggered landslides on sediment dynamics and catchment-wide denudation rates in the southern Central Range of Taiwan following the extreme rainfall event of Typhoon Morakot

Extreme erosion events can produce large short-term sediment fluxes. Such events complicate erosion rates estimated from cosmogenic nuclide concentrations in river sediment by providing sediment with a concentration different from the long-term basin average. We present a detrital ¹⁰Be study in southern Taiwan, with multiple samples obtained in a time sequence bracketing the 2009 Typhoon Morakot, to assess the impact of landslide sediment on ¹⁰Be concentrations (N¹⁰Be) in river sediment. Sediment samples were collected from 13 major basins, two or three times over the last decade, to observe the temporal variation of N¹⁰Be. Landslide inventories with time intervals of 5–6 years were used to quantify sediment flux changes. A negative correlation between N¹⁰Be and landslide areal density indicates dilution of N¹⁰Be by landslide sediment. Denudation rates estimated from the diluted N¹⁰Be can be up to three times higher than the lowest rate derived from the same basins. Observed increases imply that, 3 years after the passage of Typhoon Morakot, fluvial channels still contain a considerable amount of sediment provided by hillslope landslides during the event. However, higher N¹⁰Be in 2016 samples indicate that the contribution from landslide sediment at the sampled grain size has decreased with time. The correlation between changes in N¹⁰Be and landslide area and volume is not strong, likely resulting from the stochastic and complex nature of sediment transport. To simultaneously evaluate the volume of landslide-derived sediment and estimate the background denudation rate, associated with less impulsive sediment supply, we constructed a sediment-mixing model with the time series of N¹⁰Be and landslide inventories. The spatial pattern of background erosion rate in southern Taiwan is consistent with the regional tectonic framework, indicating that the landscape is evolving mainly in response to the tectonic forcing, and this signal is modified, but not obscured by impulsive sediment supply. © 2019 John Wiley & Sons, Ltd.     

Greenland iceBe concentrations and average precipitation rates north of 40°N to 45°N

A model of¹⁰Be deposition within the subarctic and arctic is developed based on the behavior of⁹⁰Sr in the troposphere. Measured¹⁰Be fluxes, based on analyses of¹⁰Be in one year's snow fall (1979–1980) from the Dye-3 site in southwest Greenland and on published data, and predicted¹⁰Be fluxes, based on the¹⁰Be deposition model, agree. These results indicate that with regard to¹⁰Be, the troposphere north of 40°N to 45°N presently behaves as if it is well-mixed and that the average precipitation rate within that reservoir controls in large part the concentration of¹⁰Be in Greenland ice. Inversion of the Greenland ice core¹⁰Be concentration record with the aid of the model indicates: (1) that the average precipitation rate in the subarctic and arctic was lower than the present rate during the Maunder minimum of solar activity, and higher than the present rate during the Wolf and Sporer solar activity minimums; and (2) that during the Wisconsin-Holocene transition the average precipitation rate in the subarctic and arctic was about one third the present precipitation rate.