Thickness of the upper cold ice layer in the ablation area of the polythermal glacier Grønfjordbreen (Spitsbergen) was estimated by means of numerical modeling. The results were compared with data of radio-echo sounding of the same glacier obtained in 1979 and 2012. Numerical experiments with changing water content in the lower layer of temperate ice and surface snow cover thickness made possible to compare calculated and modeled cold ice thicknesses and to estimate their changes for 33‑year period caused by regional climate change. According to data of radio-echo sounding, thickness of the cold ice layer decreased, on average, by 34 m. Numerical modeling shown similar results: the cold ice layer became thinner by 31 m and 39 m at altitudes 100–300 a.s.l. under the snow cover thickness of 1 m and 2 m. We explain this by rising of annual mean air temperature by 0,6 °С as compared to data of the nearest meteorological station Barentsburg in the same period. We believe that changes in cold ice layer thickness in polythermal glaciers can be used for estimation of changes in such regional climatic parameter as mean air temperature at different altitudes of the glacier surface in the ablation area.
Data on thickness and area of 16 glaciers on the Nordenskiöld Land (Svalbard) were obtained in 1999 and 2010–2013. These data were used to determine volume of the glaciers and to establish statistical local relationship between the volume V and the area A (V–A scaling) in the form of the power function V = cAγ, and then to calculate the total ice volume of all 202 glaciers in this area and its changes during the period since 1936 to 2002–2008. The total area of 16 glaciers was 129.9±0.35 km2, 14 of which had areas from 0.2 to 8.1 km2. The two largest ones, the Fridtjof and the West Grenfjord, had the areas 17.5 and 47.3 km2, respectively, and thus occupied about 50% (64.8 km2) of the total area of 16 glaciers. These two glaciers account for 67% of the total measured volume (10,034 km3) of the 16 glaciers. A nonlinear least-squares method was used to estimate ice reserves in all 202 glaciers from data on the volume and area of 16 glaciers. The relation between volume V and area A of the glaciers (V–A scaling) was obtained as the ratio V = 0.03637A1,283 with 95%‑th confidence intervals of the coefficients с and γ, (0.02303–0,4971) and (1.184–1.381), respectively. This made possible to calculate total volume of 202 glaciers as of 2002-2008 state using data from RGI v.6.0, and that prove to be equal to 32.89 (16.75–56.63) km3. To verify this estimation, we applied the bootstrapping method for chosen 43 glaciers and calculated the volume by means of sequential use of data for large and smaller glaciers. According to this estimate, the total volume of 202 glaciers amounted to 30.34 km3 with a 95% confidence interval of 15.42–44.27 km3, that turned out to be slightly smaller than the volume calculated by nonlinear least squares method basing on measurements on 16 glaciers. Despite the large error (on the average, from −49% to +84%) in estimating the total volume of 202 glaciers in the Nordenskiöld Land, the data obtained were used for assessment of relative changes in the total volume of glaciers in this area over different time intervals. During the period from 1936 to1990 (54 years), the total area of all glaciers reduced from 738.1 to 546.7 km2, and the total volume decreased from 49,205 to 34,857 km3. Similar results for the period 1990–2002–2008 (~15 years) are the total area changes from 546.7 to 507.9 km2 and their total volume - from 34.857 to 32.890 km3. The rate of decrease of the volume for the period 1936–1990 was equal to −0.266 km3/year, for the period 1990–2002–2008 – minus 0.131 km3/year, and as a whole for the studied period (since 1936 to 2002–2008) – minus 0.236 km3/year. The average mass balance in the first period was equal to −0.372 m w.e./year, in the second one −0.224 m w.e./year, and for the whole time −0.342 m w.e./year.
In 1967‑2015, Institute of Geography of the USSR/Russian Academy of Sciences together with other organizations carried out field expeditions in different areas of mountain and polar glaciations in many regions: the Polar Urals, Caucasus, Pamir, Zailiysky and Jungar Alatau, Tien‑Shan, Pamir‑Alai, the Kamchatka Peninsula, the Pyrenees, the Arctic – Spitsbergen, Novaya Zemlya, Franz Josef and Severnaya Zemlya, and Antarctica – on the ice flow B, and in the sub‑Antarctic – Islands King George, Galindez, and Livingston. The gravimetric and ground and aerial radar observations were made in these expeditions. About 300 glaciers of different morphological types and sizes with cold, subpolar and temperate thermal regime were studied. Basic results of these studies are the following: (1) the new data on the ice thicknesses, ice volumes, subglacial relief, internal structure, and thermal state of the glaciers were obtained; (2) the two‑layered (polythermal) glaciers consisting of the upper layer of cold ice and the lower layer of temperate water‑filled ice had been revealed in Svalbard for the first time; spatial distribution of cold, polythermal and temperate glaciers had been determined; (3) the evidences were obtained that measured changes in thickness of the upper cold ice layer in polythermal glaciers can be used to estimate the long‑period variations of regional climates and serve as regional paleothermometers; (4) methods for estimating the water content in temperate and polythermal glaciers from the RES data were developed; and its space‑time variations in temperate ices of the Svaldbald glaciers were estimated since even small water content inside of them can noticeably change their dynamic behavior; (5) methods for estimating the ice volume within glaciers in large regions of mountain and polar glaciations had been created; the ice storages were estimated in Svalbard, Franz Josef Land, Dzhungrsky Alatau, the Great Caucasus, and Mt. Elbrus; (6) detailed data on the ice thicknesses and the subglacial relief had been obtained for 40 glaciers in framework of different national and international programs and projects; the data can be used to solve a wide range of practical and theoretical problems, including numerical modeling. These studies demonstrated the following: (1) the use of monopulse radars VIRL‑6 and VIRL‑7 of decameter range (the central frequency is 20 MHz) with digital recording of the radar and GPS data is quite efficient for ground‑based and airborne (from helicopters) radio‑echo sounding of mountain and polar glaciers with their ice thicknesses up to 500–600 m; (2) it was found that thicknesses of glaciers in the Caucasus and Tien Shan can reach 330–430 m, while in regions of mountain, ice‑sheet and transitional glaciation on the Spitsbergen Archipelago – 300, 560 and 600 m, respectively, on the ice caps of the Franz‑Josef Land and Severnaya Zemlya – 450 and 813 m, and on King George and Livingston Islands (Sub‑Antarctica) – 330 and 500 m; (3) large parts of ice caps and outlet glaciers in Svalbard, Franz Josef Land, Severnaya Zemlya which beds were located below the sea level were found. Precisely these parts can be undergone quick shortening due to climate warming, and, thus, cause formation of icebergs making threats for ships and gas‑oil marine platforms in the Barents and Kara seas; (4) data of the measurements made possible to calculate volumes of a number of investigated glaciers and ice caps and to estimate the ice storages in large areas of mountain and polar glaciations (the Jungar Alatau, Great Caucasus, Spitsbergen, Franz Josef Land); (5) decreasing of glacier volumes on the Franz Josef Land and some Spitsbergen glaciers for the last decades had been estimated. Analysis of the data obtained had shown that considerable part of polythermal glaciers in Spitsbergen belong to type of surging glaciers; they have the winter englacial runoff and form the near‑glacier icings. It allows considering such glaciers as dynamically unstable, predisposed to surges as well as possible sources of winter water supply and additional sources of paleoinformation about long‑period variations of regional climate.
Статья принята к печати 15 августа 2012 г.Горный ледник, определение объёма ледника, оценка запасов льда. Glacier volume estimation, ice storage assessment, mountain glacier.Имеющиеся данные по измерению толщины и объёма горных ледников, а также существующие расчётные методы не позволяют достаточно точно установить запасы льда в горно-ледниковых системах. Обсуждаются существующие методы определения объёма горных ледников и запасов льда в горно-ледниковых системах, а также способы их более точной оценки на основе ограниченных данных о толщине и объёме отдельных ледников. Оценивается ошибка определения объёма отдельных ледников при ограниченном числе измерений.
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