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1.
Six rock glaciers in the Southern Carpathians have been investigated by means of geoelectrical soundings in order to detect their internal stratigraphy and the existence of frozen sediments. In the case of three relict rock glaciers, the electrical resistivity measurements indicated a typical internal structure. Low resistivity values (<10 kΩm) which are typical of unfrozen fine‐grained materials were obtained, but high resistivity values (25–240 kΩm) measured in the Pietroasa, Ie?u and Pietrele rock glaciers denote the presence of sediments cemented by interstitial ice and ice lenses. Based on the moderate resistivity values, the ice content is probably low to medium in the upper portion of these rock glaciers, that is, above 2040 m. At two sites (Pietroasa and V?iuga rock glaciers), ground surface temperature (GST) evolution was monitored using digital dataloggers. Mean annual ground surface temperature and GST regime throughout the winter were extracted from the recordings and confirmed the probability of permafrost occurrence in Pietroasa rock glacier. In the Ie?u and Pietrele rock glaciers, measurements of bottom temperatures of the winter snow cover were performed in March 2012. Considering the thick active layer, the reduced ice content and the presence of scarce vegetation on their surface it could be assumed that the permafrost exists in marginal conditions in the Southern Carpathians. The ground ice in permafrost is produced by the groundwater freezing or by snow banks buried by coarse angular boulders following large rockfalls.  相似文献   

2.
The Characteristics and Formation of A High-Arctic Proglacial Icing   总被引：1，自引：0，他引：1  
Well‐known from permafrost hydrology, icings (naled or Aufeis) are also frequently encountered at the margins of high‐latitude glaciers. The morphology of a proglacial icing at Scott Turnerbreen in the Norwegian Arctic archipelago of Svalbard is described, and the process of formation is considered in detail. Ground thermal‐regime modelling indicates an equilibrium permafrost depth of at least 200 m in the studied catchment, and it appears unlikely that groundwater contributes to icing formation. Meltwater flow through ice‐marginal drainage channels is accompanied by estimated heat fluxes of up to about 190 W m?2, suggesting that stored meltwater may continue to percolate through thawed sub‐channel sediments when surface runoff is absent during winter. A hydraulic conductivity of 6.9 × 10?3 m s?1 is implied, which is consistent with other studies of glacier drainage systems. The long residence time of winter‐draining meltwater, and solute rejection by refreezing water, account for high observed concentrations of solute in interstitial water in the icing. It has often been asserted that the presence of a proglacial icing indicates that a glacier is polythermal. However, as Scott Turnerbeen is entirely non‐temperate, the presence of an icing cannot always be treated as a reliable guide to the thermal regime of a glacier.  相似文献   

3.
Storglaciären is a 3.2 km long polythermal valley glacier in northern Sweden. Since 1994 a number of small (1–2 m high) transverse debris‐charged ridges have emerged at the ice surface in the terminal zone of the glacier. This paper presents the results of a combined structural glaciological, isotopic, sedimentological and ground‐penetrating radar (GPR) study of the terminal area of the glacier with the aim of understanding the evolution of these debris‐charged ridges, features which are typical of many polythermal glaciers. The ridges originate from steeply dipping (50–70°) curvilinear fractures on the glacier surface. Here, the fractures contain bands of sediment‐rich ice between 0.2 and 0.4 m thick composed of sandy gravel and diamicton, interpreted as glaciofluvial and basal glacial material, respectively. Structural mapping of the glacier from aerial photography demonstrates that the curvilinear fractures cannot be traced up‐glacier into pre‐existing structures visible at the glacier surface such as crevasses or crevasse traces. These curvilinear fractures are therefore interpreted as new features formed near the glacier snout. Ice adjacent to these fractures shows complex folding, partly defined by variations in ice facies, and partly by disseminated sediment. The isotopic composition (δ18O) of both coarse‐clear and coarse‐bubbly glacier ice facies is similar to the isotopic composition of the interstitial ice in debris layers that forms the debris‐charged ridges, implying that none of these facies have undergone any significant isotopic fractionation by the incomplete freezing of available water. The GPR survey shows strong internal reflections within the ice beneath the debris‐charged ridges, interpreted as debris layers within the glacier. Overall, the morphology and distribution of the fractures indicate an origin by compressional glaciotectonics near the snout, either at the thermal boundary, where active temperate glacier ice is being thrust over cold stagnant ice near the snout, or as a result of large‐scale recumbent folding in the glacier. Further work is required to elucidate the precise role of each of these mechanisms in elevating the basal glacial and glaciofluvial material to the ice surface.  相似文献   

4.
Glaciological investigations of the Upper Fremont Glacier in the Wind River Range of Wyoming were conducted during 1990–1991. The glaciological data will provide baseline information for monitoring future changes to the glacier and support ongoing research utilizing glacial-ice-core composition to reconstruct paleoenvironmental records. Ice thickness, determined by radio-echo sounding, ranged from 60 to 172 m in the upper half of the glacier. Radio-echo sounding of ice thickness at one point was confirmed by drilling 159.7 m to bedrock. The difference between radio-echo sounding depth and measured drilling depth was about 4 m. Annual ablation (including snow, firn, and ice) measured for the 1990–1991 period averaged about 0.93 m/a. Densification proceeds rapidly on Upper Fremont Glacier. Measured densities in the near-surface parts of the glacier ranged from 4.4 x 105 g/m3 at the surface to larger than 8.5 x 105 g/m3 at depths exceeding 14 m. Surface ice velocity and direction were monitored from July 1990 to August 1991. Ice velocity decreased in a downslope direction. The largest measured velocity was about 3.1 m/a and the smallest was 0.8 m/a. The yearly mean air temperature of the study site during the period from July 11, 1990 to July 10, 1991 was -6.9°. Borehole temperatures from 10-m depths are 0 ± 0.4°. The warmer borehole temperatures relative to the yearly mean air temperature may be caused by the latent heat of freezing, as meltwater from the surface percolates into the glacier and refreezes. [Key words: glaciers, Wyoming, Wind River Range, ice thickness, ablation rates.]  相似文献   

5.
We present a glaciological and climatic reconstruction of a former glacier in Coire Breac, an isolated cirque within the Eastern Grampian plateau of Scotland, 5 km from the Highland edge. Published glacier reconstructions of presumed Younger Dryas‐age glaciers in this area show that equilibrium line altitudes decreased steeply towards the east coast, implying a arctic maritime glacial environment. Extrapolation of the ELA trend surface implies that glaciers should have existed in suitable locations on the plateau, a landscape little modified by glaciation. In Coire Breac, a 0.35 km2 cirque glacier existed with an equilibrium line altitude of 487 ± 15 m above present sea level. The equilibrium line altitude matches closely the extrapolated regional equilibrium line altitude trend surface for Younger Dryas Stadial glaciers. The mean glacier thickness of 24 m gives an ice volume of 7.8 × 106 m3, and a maximum basal shear stress of c. 100 kPa?1. Ablation gradient was c. –0.0055 m m?1, with a mean July temperature at the equilibrium line altitude of c. 5.1°C. The reconstruction implies an arctic maritime climate of low precipitation with local accumulation enhanced by blown snow, which may explain the absence of other contemporary glaciers nearby. Reconstructed ice flow lines show zones of flow concentration around the lower ice margin which help to explain the distribution of depositional facies associated with a former debris cover which may have delayed eventual glacier retreat. No moraines in the area have been dated, so palaeoclimatic interpretations remain provisional, and a pre‐Lateglacial Interstadial age cannot be ruled out.  相似文献   

6.
Rockfalls are dominant in the rock slopes and rock ridge morphodynamics in high mountain areas and endanger people who pass along or stay there, as well as infrastructure that host them (cable cars, refuges). Risks are probably greater now because of fast permafrost degradation and regression of surface ice, two consequences of the atmospheric warming of the last decades. These two commonly associated factors are involved in the instability of rock slopes by modifying the mechanical behaviour of often ice‐filled rock fractures and the mechanical constraints in the rock masses. This paper examines over 15 years the instability of the lower Arête des Cosmiques on the French side of the Mont Blanc massif. Its vulnerability is due to the presence of a high‐capacity refuge on its top (3613 m a.s.l.). In 1998, a part of the refuge was left without support when a collapse of 600 m3 occurred immediately below it. Since this date, reinforcement work has been carried out in this area, but the whole ridge has been affected by around 15 relatively shallow rockfalls. Through a multidisciplinary approach, this article assesses the role of the cryospheric factors in the triggering of these rockfalls.  相似文献   

7.
Hooker Glacier in the central Southern Alps of New Zealand has undergone significant downwasting and recession (～2.14 km) during the last two centuries. High retreat rates (51 m a?1 1986–2001, 43 m a?1 2001–2011) have produced a large (1.22 km2) proglacial lake. We present a retreat scenario for Hooker Glacier. A retreat scenario predicts that the glacier terminus will stabilise >3 km up‐valley of the current lake outlet after 2028 when ice velocity equals calving rate.  相似文献   

8.
Flow velocities of active rock glaciers in the Austrian Alps   总被引：1，自引：0，他引：1  
High surface flow velocities of up to 3 m a–1 were measured near the front of three active rock glaciers in the western Stubai Alps (Rei‐chenkar) and Ötztal Alps (Kaiserberg and Ölgrube) in Tyrol (Austria) using differential GPS technology. Flow velocities have increased since about 1990. The highest velocities were recorded in 2003 and 2004, but showed a slight decrease in 2005. At the Reichenkar rock glacier, flow rates are constant throughout the year, indicating that meltwater has no significant influence on the flow mechanism. At Ölgrube rock glacier, flow velocities vary seasonally with considerably higher velocities during the melt season. Meltwater is likely to influence the flow of Ölgrube rock glacier as evident by several springs near the base of the steep front. Because the high surface velocities cannot be explained by internal deformation alone on Reichenkar rock glacier, we assume that horizontal deformation must also occur along a well defined shear zone within a water‐saturated, fine‐grained layer at the base of the frozen body. The increased surface flow velocities since about 1990 are probably caused by slightly increased ice temperature and greater amounts of meltwater discharge during the summer, a product of global warming.  相似文献   

9.
A tongue‐like, boulder‐dominated deposit in Tverrbytnede, upper Visdalen, Jotunheimen, southern Norway, is interpreted as the product of a rock avalanche (landslide) due to its angular to subangular boulders, surface morphology with longitudinal ridges, down‐feature coarsening, and cross‐cutting relationship to ‘Little Ice Age’ moraines. The rock avalanche fell onto glacier ice, probably channelled along a furrow between two glaciers, and stopped on the glacier foreland, resulting in its elongated shape and long runout distance. Its distal margin may have become remobilized as a rock glacier, but a rock glacier origin for the entire landform is discounted due to lack of source debris, presence of matrix, lack of transverse ridges, and sparcity of melt‐out collapse pits. Lichenometric dating of the deposit indicates an approximate emplacement age of ad 1900. Analysis highlights the interaction of rock‐slope failures and glaciers during deglacierization in a neoparaglacial setting, with reduced slope stability due to debuttressing and permafrost degradation, and enhanced landslide mobility due to flow over a glacier and topographic channelling. Implications for the differentiation of relict landslides, moraines and rock glaciers are discussed and interrelationships between these landforms are considered in terms of an ice‐debris process continuum.  相似文献   

10.
During the deglaciation stages of the last glacial period a rock avalanche took place on the glacier that occupied the upper sector of the Cuerpo de Hombre Valley (Sierra de Béjar). The material displaced during the avalanche fell onto the ice, was transported by the glacier and later deposited as supraglacial ablation till. The cause of the avalanche was the decompression of the valley slopes after they were freed from the glacier ice (stress relaxation). Reconstruction of the ice masses has been carried out to quantify the stress relaxation that produced the collapse. The rock avalanche took place on a lithologically homogeneous slope with a dense fracture network. The avalanche left a 0.4 ha scar on the slope with a volume of displaced material of 623 ± 15 × 103 m3. The deposit is an accumulation of large, angular, heterometric boulders (1–100 m3 in volume) with a coarse pebble‐size matrix. The avalanche can be explained as a relaxation process. This implies rock decompression once the glacier retreat left the wall ice free (debuttressing). Calculations show that the avalanche took place where the decompression stresses were highest (130–170 kPa). In the Spanish Central System paleoglaciers the largest accumulation of morainic deposits occurred after the glacial maximum and the earliest stages of the ice retreat. The process described here is used as an example to formulate a hypothesis that the largest accumulations of tills were formed in relation to enhanced slope dynamics once some glacier retreat had occurred.  相似文献   

11.
Ice temperature measurements were taken from three shallow and five deep (to bedrock) boreholes on Hansbreen, Svalbard, in selected years between 1988 and 1994. In general, results show a subpolar, polythermal structure. The glacier accumulation zone is of warm ice within the entire vertical profile except the uppermost layer of seasonal temperature fluctuations where there is an upper cold ice layer in the ablation zone which varies in thickness and may even be absent in the western lateral part. The upper layer of cold ice thins along the glacier centre-line from the equilibrium line altitude down to the glacier front. The depth of the pressure melting, indicating the base of the cold ice layer, was defined at the borehole measurement sites but was not manifested as an internal reflection horizon using multi-frequency radar methods. The isotherm lies about 20 m above a radar internal reflecting horizon near the equilibrium line altitude and about 40 m above it in the frontal part of the glacier. The internal reflection horizon almost certainly reflects the high water content within temperate ice and not the cold/temperate ice interface. At 10 m depth, the temperatures are 2–3°C higher than the calculated mean annual air temperatures, demonstrating the importance of meltwater refreezing on the release of latent heat.  相似文献   

12.
Groundwater in front of warm‐based glaciers is likely to become a more integrated part of the future proglacial hydrological system at high latitudes due to global warming. Here, we present the first monitoring results of shallow groundwater chemistry and geochemical fingerprinting of glacier meltwater in front of a warm‐based glacier in Southeast Greenland (Mittivakkat Gletscher, 65° 41′ N, 37° 48′ W). The groundwater temperature, electrical conductivity and pressure head were monitored from August 2009 to August 2011, and water samples were collected in 2009 and analyzed for major ions and water isotopes (δD, δ18O). The 2 yrs of monitoring revealed that major outbursts of glacier water during the ablation season flushed the proglacial aquifer and determined the groundwater quality for the next 2–8 weeks until stable chemical conditions were reached again. Water isotope composition shows that isotopic fractionation occurs in both groundwater and glacier meltwater, but fractionation due to evaporation from near‐surface soil moisture prior to infiltration has the most significant effect. This study shows that groundwater in Low Arctic Greenland is likely to possess a combined geochemical and isotopic composition, which is distinguishable from other water sources in the proglacial environment. However, the shallow groundwater composition at a given time is highly dependent on major outbursts of glacier water in the previous months.  相似文献   

13.
Although rock glaciers in the Central and Desert Andes of Argentina and Chile have been previously studied in detail, much less attention has been paid to the occurrence of these permafrost forms in Patagonia. Recently, however, the establishment of the Argentinean Glacier Inventory program, which intends to inventory and monitor all ice masses along the Argentinean Andes, has started a large amount of new geocryological research. The project is designed to provide reliable and worldwide comparable results, supported by well established technical procedures and background information. Presented here is the first rock glacier inventory of the Monte San Lorenzo (Cerro Cochrane) region in the southern Patagonian Andes. A total of 130 intact (9.86 km2) and 47 fossil (1.45 km2) landforms were inventoried using two 2.5 m resolution ALOS Panchromatic Remote‐sensing Instruments for Stereo Mapping images. Since the Argentinean federal initiative described above legally protects all rock glaciers in the country as water reserves, and due to the little scientific knowledge concerning rock glaciers in the vast majority of the Patagonian Andes, this inventory provides an important basis for political decision‐making and opens further geocryological research avenues for the Patagonian region in general.  相似文献   

14.
This paper presents a simple analytical model for estimating rock glacier age by coupling the ratio of frontal advance to total rock glacier length and the ratio of debris volume in the rock glacier to present debris flux in the talus cone–rock glacier transition zone. The model was applied to two rock glaciers at Prins Karls Forland, Svalbard. By assuming volumetric debris contents in the deforming layer of the rock glacier of between 0.3 and 0.4, we obtained age estimates for the rock glaciers of between 12 ka and 24 ka. The corresponding average rockwall retreat rates are between 0.30 and 0.62 mm a‐1. Considering the limitations of the model, we suggest a minimum age of 13 ka for the initiation of rock glacier development. Using this age, rockwall retreat rates for the seven rock glaciers investigated at Prins Karls Forland are between 0.13 and 0.64 m ka‐1 (assuming the volumetric debris content for the whole rock glacier/talus cone is 0.35). The model requires further testing on other datasets, better field estimates of the debris content and depth of the deforming layer, and could also benefit from the inclusion of an unsteady debris supply function in order to refine age estimates.  相似文献   

15.
天山1号冰川厚度和冰下地形探测与冰储量分析   总被引：12，自引：0，他引：12       下载免费PDF全文
通过对天山乌鲁木齐河源 1号冰川的雷达回波探测 ,清晰地揭示出冰川底部冰 /岩界面的位置及其起伏变化特征 ,显示出雷达波对山地冰川良好的穿透能力和对冰下地形的高分辨能力 ,冰川雷达测厚的误差小于 1 .2 %。研究结果显示 ,1号冰川东支冰川平均厚度为 5 8.77m ,西支冰川平均厚度为 44.84m ,冰体厚度最大值发育于冰川中部趋于主流线位置。冰川冰储量计算表明 ,东支冰储量为 0 .0 5 1 868km3,西支冰储量为 0 .0 2 0 2 1 0km3。表面和底部地形有明显差异 ,主要因冰川动力过程对基岩强烈的地貌作用所致 ,意味着冰床的起伏地形对冰川浅层冰体的运动过程影响不显著。  相似文献   

16.
Surface velocities have been regularly monitored at the rock glacier in Outer Hochebenkar, Ötztal Alps, Austria since the early 1950s. This study provides an update to previously published surface velocity time series, showing mean profile velocities of four cross profiles since the beginning of the measurements (1951,1954, 1997; depending on the profile), as well as single block displacements from 1998 to 2015. Profiles P1, P2 and P3 have moved between 42 and 90 m, at mean velocities between 0.70 and 1.48 m yr–1, since they were first established in the early 1950s (1951/54). Profile P0, established in 1997, has since moved 13 m or 0.75 m yr–1. An acceleration can be observed at all profiles since the late 1990s, with a particularly sharp velocity increase since 2010. All profiles reached a new maximum velocity in 2015, with 1.98 m yr–1 at the slowest profile (P0) and 6.37 m yr–1 at the fastest profile (P1). Year‐to‐year variations in profile velocities cannot be clearly attributed to inter‐annual variations of climatic parameters like mean annual air temperature, summer temperature, positive degree days, or precipitation. However, higher correlation is found between velocities and cumulative anomalies of air temperature (mean annual air temperature and positive degree days) and summer precipitation, suggesting that these parameters play a key role for the movement of the rock glacier. The lower profiles (P0, P1) show more pronounced year‐to‐year variations than the upper profiles (P2, P3). It is considered likely that processes other than climatic forcing (e.g. sliding, topography) contribute to the different velocity patterns at the four profiles.  相似文献   

17.
Glacier mass balance and mass balance gradient are fundamentally affected by changes in glacier 3D geometry. Few studies have quantified changing mountain glacier 3D geometry, not least because of a dearth of suitable spatiotemporally distributed topographical information. Additionally, there can be significant uncertainty in georeferencing of historical data and subsequent calculations of the difference between successive surveys. This study presents multiple 3D glacier reconstructions and the associated mass balance response of Kårsaglaciären, which is a 0.89 ± 0.01 km2 mountain glacier in sub‐arctic Sweden. Reconstructions spanning 101 years were enabled by historical map digitisation and contemporary elevation and thickness surveys. By considering displacements between digitised maps via the identification of common tie‐points, uncertainty in both vertical and horizontal planes were estimated. Results demonstrate a long‐term trend of negative mass balance with an increase in mean elevation, total glacier retreat (1909–2008) of 1311 ± 12 m, and for the period 1926–2010 a volume decrease of 1.0 ± 0.3 × 10–3 km3 yr–1. Synthesising measurements of the glaciers’ past 3D geometry and ice thickness with theoretically calculated basal stress profiles explains the present thermal regime. The glacier is identified as being disproportionately fast in its rate of mass loss and relative to area, is the fastest retreating glacier in Sweden. Our long‐term dataset of glacier 3D geometry changes will be useful for testing models of the evolution of glacier characteristics and behaviour, and ultimately for improving predictions of meltwater production with climate change.  相似文献   

18.
This paper examines the occurrence of ephemeral hoarfrost crystals at funnel openings (funnel hoarfrost) detected between large blocks at the surface of the presumably relict Schöneben Rock Glacier. Field mapping on 25 November 2011 identified 51 individual funnel openings with notable hoarfrost crystals distributed over the entire rock glacier. Hoarfrost was no longer detectable a few days after the initial mapping campaign. At least in the period 20–25 November 2011 temperature conditions at the rock glacier surface were favourable for hoarfrost formation and preservation as indicated by different types of measurements. A period of 24–48 h of hoarfrost‐suitable weather conditions would have been sufficient to form the observed hoarfrost if crystal growth rates of 2–4 mm h?1 are assumed. The void systems with funnel hoarfrost seem to be rather localised and limited in horizontal (10s of metres) and vertical (some metres) extent. Presumably the observed funnel hoarfrost was caused by the so‐called chimney effect, although no larger reversible air circulation systems with warm air exhalation were identified. Continuous ground temperature data from several sites at the rock glacier surface (period November 2011–December 2012) showed that hoarfrost sites are cooler and thermally buffered compared with non‐hoarfrost sites at similar elevations. This seems to be related to the decoupling of the air above the rock glacier and the pore air during periods of atmospheric warming. Only the combination of specific micro‐climatic (temperature/humidity), geometric (open void systems) and sedimentological (grain size/sediment structure) conditions allow the formation of the ephemeral funnel hoarfrost at this rock glacier.  相似文献   

19.
Glacier Benito is a temperate outlet glacier on the west side of the North Patagonian Icefield. Rates of thinning and ablation were obtained using data collected by the British Joint Services Expedition in 1972/73 and subsequent data collected in 2007 and 2011. Ice‐front recession rates were based on dendrochronological dating for the terminal moraines and aerial and satellite imagery of the ice front in 1944, 1998 and 2002. Between the first Benito survey in 1973 and 2007, the lower glacier thinned by nearly 150 m at an average rate of 4.3 m yr?1 with the rate increasing to 6.1 m yr?1 between 2007 and 2011, a 28.7% increase during the latter period. Increases in ice movement and ablation were negligible: ice movement for 1973 and 2007 averaged 0.45 m day?1 and ablation averaged 0.05 m day?1. Ice front recession along the glacier's centre line from 1886 to 2002 was approximately 1860 m. Retreat rates between 1886 and 1944 averaged 8.9 m yr?1. Thereafter glacier asymmetry makes measurement along the glacier centre line unrepresentative of areal change until 1998 when symmetry was restored; retreat between 1944 and 1998 was 15.4 m yr?1. From 1998 to 2002 the rate increased dramatically to 127.2 m yr?1. Recession from the southern end of Benito's terminal moraine in the 1850s supports an early date for initial retreat of the Icefield's glaciers.  相似文献   

20.
Mass Balance Methods on Kongsvegen, Svalbard   总被引：3，自引：0，他引：3  
On the glacier Kongsvegen (102 km2) in northwest Spitsbergen, Svalbard, traditional mass balance measurements by stake readings and snow surveying have been conducted annually since 1987. In addition, repeated global positioning system (GPS) profiling, shallow core analysis and ground-penetrating radar (GPR) surveying have been applied. The purpose of this paper is to evaluate the input from the different methods, especially the GPS profiling, using the results from the traditional direct method as a reference. The annual flow rate on Kongsvegen is low (2 ? 3 m a?1), and the emergence velocity is almost negligible. Thus the geometry changes of the glacier, i.e. the change in altitude per distance from the head of the glacier, should reflect the change in net balance of the glacier. The mean annual altitude change from the longitudinal, centreline GPS profiles was compared to the direct stake readings and showed a very good agreement. On Kongsvegen the measured actual ice flux is so low that the mass transfer down-glacier at the mean equlibrium line altitude is less than 10% of what is needed to maintain steady-state geometry. This is clearly shown in the changing altitude profiles. GPS profiling can be used on large glaciers in remote areas to monitor geometry changes, ice flow and net mass balance changes. However, it requires that the centreline profile changes are representative for the area/altitude intervals, i.e. that the accumulation and ablation pattern is evenly distributed. For this purpose the GPR surveying quickly gave the snow distribution variability over long distances. Shallow cores drilled in different altitudes in the accumulation area were analysed to detect radioactive reference layers from the fallout after the Chernobyl accident in 1986, and showed very good agreement to the direct measured net balance. Thus older reference horizons from bomb tests in 1962 could be used to extend the net balance series backwards.  相似文献   

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