EVALUATION OF GRIDDED PRECIPITATION FOR NORWAY USING GLACIER MASS‐BALANCE MEASUREMENTS

The service seNorge ( http://senorge.no ) provides gridded temperature and precipitation for mainland Norway. The products are provided as interpolated station measurements on a 1 × 1 km grid. Precipitation gauges are predominantly located at lower elevations such as coastal areas and valleys. Therefore, there are large uncertainties in extrapolating precipitation data to higher altitudes, both due to sparsity of observations as well as the large spatial variability of precipitation in mountainous regions. Using gridded temperature and precipitation data from seNorge, surface mass balance was modeled for five Norwegian glaciers of different size and climate conditions. The model accounts for melting of snow and ice by applying a degree‐day approach and considers refreezing assuming a snow depth depended storage. Calculated values are compared to point measurements of glacier winter mass balance. On average for each glacier, modeled and measured surface mass‐balance evolutions agree well, but results at individual stake locations show large variability. Two types of problems were identified: first, grid data were not able to capture spatial mass balance variability at smaller glaciers. Second, a significant increase in the bias between model and observations with altitude for one glacier suggested that orographic enhancement of precipitation was not appropriately captured by the gridded interpolation.     

Annual Mass Balance of Blue Glacier, USA: 1955–97

Mass changes of Blue Glacier, USA are calculated from topographic maps made from vertical aerial photography in late summer of 1939, 1952, 1957, and 1987, along with laser altimetry flown in June 1996. Changes in elevation between maps were adjusted for seasonal variations in the snow cover, and to account for the ablation between the date of photography and 1 October. Topography obtained from the laser altimetry was adjusted for snow thickness and glacier motion to estimate topography of 1 October 1995. The mass of Blue Glacier has changed less than 7 m (water equivalent) during this 56 year period which is minor compared with other glaciers in the region and elsewhere in the world. Glacier-average annual mass balances, beginning in 1956, have been calculated either from stake measurements and probing of late-season snow, or from a regression analysis using late-season measurements of the equilibrium line altitude. A comparison with the changes derived from surface maps shows values obtained from field measurements are too positive by about 0.4 m a^?1 , indicating that considerable caution is needed when interpreting time series of mass balance. Two alternative time series of mass balance consistent with the long-term mass changes are created by making simple adjustments: (1) a single constant is subtracted from each value so that the series is consistent with the 1957–95 mass change; (2) one constant is subtracted from each value over 1957–87 and another is subtracted from each value over 1987-95 so that the series is consistent with both the 1957–87 and 1987–95 mass changes. The mass balance of Blue Glacier was generally positive until the mid-1970s and negative since. The fluctuations of mass balance closely resemble those of snowfall on the glacier as estimated from the joint distribution of temperature and precipitation. The climate in western Washington was cooler and wetter during the decade before the mid-1970s, but the trend since has been towards warmer and drier conditions.     

Using Vertical Aerial Photography to Estimate Mass Balance at a Point

The mass balance distribution over a 0.5 km² area of the lower part of South Cascade Glacier is obtained from remotely sensed measurements of its geometry and velocity field over two periods, 1992–93 and 1993–94. Vertical aerial photography from late summer 1992, 1993, and 1994 is analyzed photogrammetrically to get surface topography of South Cascade Glacier on a 100-meter square grid. The known bed topography is subtracted from the surface topography to get the ice thickness, and the surface topographies are subtracted from each other to get the thickness change. Annual displacement vectors, determined at points where natural features could be tracked from one year to the next, are contoured by hand and interpolated to the grid. Assuming that the ice follows Glen's flow law with exponent n = 3, and that 10% of the ice flow is due to sliding at the bed, the surface velocity is scaled by 0.82 to get the average velocity in the vertical ice column. The average velocities are combined with the thicknesses to calculate the flux divergence at each of 46 gridpoints on a 100-m square grid, where it is subtracted from the thickness change to get the mass balance.
Use of the same control points from year to year makes any systematic error in photogrammetric coordinates temporally constant, so such error has no effect on the mass balance estimate. Random error in coordinates is assumed to be uncorrelated from coordinate to coordinate, from point to point, from year to year; the standard error is estimated to be 1 m, resulting in a standard error in coordinate differences of about 1.5 m. A 1 m error in a vertical coordinate has nearly twice the effect on the estimated balance that one in a horizontal coordinate has and more than ten times the effect that one in ice thickness has. Compared with measurements at a stake, the estimated balances are about 1 m too negative.     

Snow accumulation, melt, mass loss, and the near-surface ice temperature structure of Irenebreen, Svalbard

This study examines the mass balance, accumulation, melt, and near-surface ice thermal structure of Irenebreen, a 4.1 km² glacier located in northwest Spitsbergen, Svalbard. Traditional glaciological mass balance measurements by stake readings and snow surveying have been conducted annually at the glacier since 2002, yielding a mean annual net mass balance of −65 cm w.e. for the period 2002–2009. In 2009, the annual mass balance of Irenebreen was −63 cm w.e. despite above-average snow accumulation in winter. The near-surface ice temperature in the accumulation area was investigated with automatic borehole thermistors. The mean annual surface ice temperatures (September–August) of the accumulation area were −3.7 °C at 1 m depth and −3.3 °C at 10 m depth. Irenebreen is potentially polythermal, with cold ice and a temperate surface layer during summer. This temperate surface layer is influenced by seasonal changes in temperature. In winter, the temperature of all the ice is below the melting point and temperate layers are probably present in basal sections of the glacier. This supposition is supported by the presence of icings in the forefield of Irenebreen.     

Effective Sample Size for Glacier Mass Balance

Correlograms from multiple time series of point mass balance, measured on White Glacier (Axel Heiberg Island, Canada) and Abramov Glacier (Alai Range, Kirgizia), show that the correlation decreases with the difference in elevation between the points. The correlogram is used to calculate an integral spatial scale or effective sample area which, when divided into the area of the glacier, yields an estimate of the number of degrees of freedom in a stake-based estimate of the whole-glacier balance. This number – the 'effective sample size'– is a small fraction of the number of point measurements; indeed, it is independent of the number of measurements. Estimates of average balance for elevation bands are at one remove from raw stake measurements, but they are amenable to a principal component analysis which confirms that the effective sample size is very small. The small effective sample size means that uncertainty in a typical measurement of whole-glacier mass balance cannot be much less than the large value implied by the conservative assumption that stakes are perfectly correlated. One way around this difficulty would be to increase the role of prior physical understanding by seeking to model the spatial variability of mass balance. A successful model would need only a few parameters, and would allow for the joint estimation of both magnitude and uncertainty; the uncertainty in mass balance could be derived objectively from the uncertainty in the parameters. This, however, would require good estimates of the variability of mass balance at the elevation-band scale, which might in turn require that many measurement networks be redesigned.     

Constraining basin thermal history and petroleum generation using palaeoclimate data in the Piceance Basin,Colorado

Careful assessment of basin thermal history is critical to modelling petroleum generation in sedimentary basins. In this paper, we propose a novel approach to constraining basin thermal history using palaeoclimate temperature reconstructions and study its impact on estimating source rock maturation and hydrocarbon generation in a terrestrial sedimentary basin. We compile mean annual temperature (MAT) estimates from macroflora assemblage data to capture past surface temperature variation for the Piceance Basin, a high‐elevation, intermontane, sedimentary basin in Colorado, USA. We use macroflora assemblage data to constrain the temporal evolution of the upper thermal boundary condition and to capture the temperature change with basin uplift. We compare these results with the case where the upper thermal boundary condition is based solely upon a simplified latitudinal temperature estimate with no elevation effect. For illustrative purposes, 2 one‐dimensional (1‐D) basin models are constructed using these two different upper thermal boundary condition scenarios and additional geological and geochemical input data in order to investigate the impact of the upper thermal boundary condition on petroleum source rock maturation and kerogen transformation processes. The basin model predictions indicate that the source rock maturation is very sensitive to the upper thermal boundary condition for terrestrial basins with variable elevation histories. The models show substantial differences in source rock maturation histories and kerogen transformation ratio over geologic time. Vitrinite reflectance decreases by 0.21%Ro, source rock transformation ratio decreases 10.5% and hydrocarbon mass generation decreases by 16% using the macroflora assemblage data. In addition, we find that by using the macroflora assemblage data, the modelled depth profiles of vitrinite reflectance better matches present‐day measurements. These differences demonstrate the importance of constraining thermal boundary conditions, which can be addressed by palaeotemperature reconstructions from palaeoclimate and palaeo‐elevation data for many terrestrial basins. Although the palaeotemperature reconstruction compiled for this study is region specific, the approach presented here is generally applicable for other terrestrial basin settings, particularly basins which have undergone substantial subaerial elevation change over time.     

Measurements and Models of the Mass Balance of Hintereisferner

This paper summarizes the methods applied to determine the mass balance of Hintereisferner and several other glaciers in the Tyrolean Alps since 1952. On an annual basis the direct glaciological method was applied with fixed date measurements on 10–15 accumulation pits and 30–90 ablation stakes on 9 km².
Indirect mass balance determination from equilibrium line altitude, accumulation area ratios or representative stakes, yield fair results and some exceptions could be related to anomalous meteorological conditions.
Monthly or more frequent stake readings supplied time series of ablation at various altitudes and slope aspects that served as basis for the calibration of energy and mass balance models. Of various models developed, two are presented in this paper. Both are based on degree days, one using daily values from a valley station to predict the mean annual balance of the entire glacier, while the other calculates day-to-day changes at 50-m grid points on the glacier.
The geodetic method has been applied for longer periods and yields results consistent with those of the glaciological method. The balance velocity calculated from recent ice thickness soundings and accumulation measurements is significantly less than observed velocity.     

How many Stakes are Required to Measure the Mass Balance of a Glacier?

Glacier mass balance is estimated for South Cascade Glacier and Maclure Glacier using a one-dimensional regression of mass balance with altitude as an alternative to the traditional approach of contouring mass balance values. One attractive feature of regression is that it can be applied to sparse data sets where contouring is not possible and can provide an objective error of the resulting estimate. Regression methods yielded mass balance values equivalent to contouring methods. The effect of the number of mass balance measurements on the final value for the glacier showed that sample sizes as small as five stakes provided reasonable estimates, although the error estimates were greater than for larger sample sizes. Different spatial patterns of measurement locations showed no appreciable influence on the final value as long as different surface altitudes were intermittently sampled over the altitude range of the glacier. Two different regression equations were examined, a quadratic, and a piecewise linear spline, and comparison of results showed little sensitivity to the type of equation. These results point to the dominant effect of the gradient of mass balance with altitude of alpine glaciers compared to transverse variations. The number of mass balance measurements required to determine the glacier balance appears to be scale invariant for small glaciers and five to ten stakes are sufficient.     

Ablation Rate Estimates over the Greenland Ice Sheet from Microwave Radiometric Data

Scanning Multichannel Microwave Radiometer (SMMR) data are used to estimate the annual melt duration (number of days with melt) for elevation transects over the Greenland ice sheet during the period from 1979-1986. The annual melt duration is used to estimate the number of positive degree days (PDDs), which are used in a degree-day mass balance model to determine ablation rates and the equilibrium line altitude (ELA). The annual melt duration along two transects estimated with SMMR data compares favorably, particularly above the ELA, to melt duration calculated from surface temperature data for the same locations. The mass balance estimates and ELA locations along eight transects agree reasonably well with measurements reported in previous studies using surface temperature data. ELAs were within 10m of published values along two transects, and the root mean square error of SMMR-derived versus surface mass balance measurements was 43mm yr^?1. The estimated error in SMMR-derived ablation is between ±15% and ±50%, but could be reduced substantially by using daily microwave data available from the Special Sensor Microwave/Imager (SSM/I). This research shows the feasibility of using passive microwave data to estimate the ablation rate in order to determine ELA, which can be used to monitor the mass balance of the ice sheet.     

Ablation Rate Estimates over the Greenland Ice Sheet from Microwave Radiometric Data

Scanning Multichannel Microwave Radiometer (SMMR) data are used to estimate the annual melt duration (number of days with melt) for elevation transects over the Greenland ice sheet during the period from 1979‐1986. The annual melt duration is used to estimate the number of positive degree days (PDDs), which are used in a degree‐day mass balance model to determine ablation rates and the equilibrium line altitude (ELA). The annual melt duration along two transects estimated with SMMR data compares favorably, particularly above the ELA, to melt duration calculated from surface temperature data for the same locations. The mass balance estimates and ELA locations along eight transects agree reasonably well with measurements reported in previous studies using surface temperature data. ELAs were within 10m of published values along two transects, and the root mean square error of SMMR‐derived versus surface mass balance measurements was 43mm yr^?1. The estimated error in SMMR‐derived ablation is between ±15% and ±50%, but could be reduced substantially by using daily microwave data available from the Special Sensor Microwave/Imager (SSM/I). This research shows the feasibility of using passive microwave data to estimate the ablation rate in order to determine ELA, which can be used to monitor the mass balance of the ice sheet.     

Comparison of theoretical and observed temperature profiles in Devon Island ice cap, Canada

Summary. A non-steady-state theoretical model is used to predict the present variation of temperature with depth in two boreholes in the Devon Island ice cap, Arctic Canada. The boreholes are 300 m apart and one of them reaches bedrock. The heat transfer equation is solved numerically with the record of past temperatures obtained from measurements of the variations of oxygen—isotope ratio with depth in the cores as surface boundary condition. The effects of ice advection, refreezing of meltwater percolating from the surface (the amount of which is recorded in the cores), heating due to firn compaction and ice deformation, and heat flow in the bedrock below the ice sheet are all included in the model. The free parameters are geothermal heat flux, present surface temperature and heat loss at the surface which depends on the depth of meltwater penetration and other factors. Agreement between observed and predicted temperature—depth profiles is very close. Latent heat released by percolating meltwater is the predominating factor in determining the temperature distribution in the upper half of each borehole. The temperature distribution is insensitive to the value of the factor used to convert oxygen—isotope ratio to temperature.     

SURFACE MASS BALANCE AND ITS VARIATION ON THE MIZUHO PLATEAU, ANTARCTICA IN 1987-1988

From the surface mass accumulation data in year of 1987/88, the distribution and variation of annual mass balance on Mizuho Plateau are discussed. The authors also analyze the effects of shortterm climatic and topographical variations on the mass balance. It is found that there are some differences in spatial distribution and annual average state in the year of 1987/88 and other years. Ia the area at elevation lower than 550 m near the coast, the mass balance appears to be negative. The annual mass balance over 80 km distance from S_(16) to inland is 0.84m snow depth. A low mass balance zone from 80 km site to Mizuho Station, is considered to be only 0.14 m snow depth. It is found from the comparison of mass balances that the mass-balance level on the glaciers in West China is 9 times higher than that on Mizuho Plateau, where the massbalance level appears to be low accumulative and low expensive, but inverse in middle and low latitude regions, such as on glaciers in West China. The effects of short-term     

Changes of Snow Cover Thickness Measured by Conventional Mass Balance Methods and by Global Positioning System Surveying

The most labour-intensive and time-consuming part of many mass balance programmes is the acquisition of snow depth data. The standard technique, which involves probing the snow cover at intervals along a series of profiles, generally by an individual on skis, may involve more than 300 discrete measurements along a total of more than 20 km of profiling at a single glacier. Kinematic surveying with a global positioning system (GPS) in differential mode provides much more information about changes of glacier surface level and snow thickness between surveys. The positions of a large number of points can be fixed in a relatively short time by GPS surveying, and the technique is usable in adverse weather conditions. With real-time kinematic GPS surveying, it is possible to return to the same positions (longitude, latitude) during successive field programmes, and a previously followed route can be retraced precisely. GPS surveying facilitates the production of accurate glacier maps for mass balance programmes. Data obtained by snow depth probing and GPS surveying in 1995 at Austre Okstindbreen, the largest glacier of the Okstindan area, Norway (66°N), indicate that repeated GPS surveys are likely to provide a large amount of information on withinyear and between-year changes of surface topography and are not subject to the errors in mass balance calculations which arise from probing snow depths along selected profiles. Kinematic GPS surveying of several glaciers within an area would overcome the difficulties arising when mass balance studies are confined to a single glacier within a particular area.     

Effect of Uncertainties in Measured Variables on the Calculated Mass Balance of storglaciären

Detailed mass balance measurements have been carried out on Storglaciären since 1945, adhering to a fixed system of measurements since the 1960s. Using a geographical information system approach, the effect of parameters such as density conversion model, systematic snow probing error and ablation gradient calculation on the mass balance of the glacier can be investigated. It is evident that the measure of total mass balance of Storglaciären is not sensitive to variations in these parameters. This means that reasonable estimates of the mass balance of a glacier can be made with very little information, given that measurements are distributed over the glacier surface. However, the uncertainty that may result from varying the parameters is c . 0.1 m water equivalent. Hence, reporting mass balance to centimetre or even millimetre resolution is questionable. When considering mass balance measurements as input for flow models, for example, i.e. requiring a distributed balance, the detail necessary in the measurements becomes significantly greater. At this level careful attention must be made to all parameters entering the mass balance calculation. From this it seems evident that any measurements at intermediate complexity do not increase the accuracy of the mass balance in relation to the extra work required and that the choice of method determines the scientific problems to which the data is applicable.     

A long-term Arctic snow depth record from Abisko, northern Sweden, 1913–2004

A newly digitized record of snow depth from the Abisko Scientific Research Station in northern Sweden covers the period 1913-present. Mean snow depths were taken from paper records of measurements made on a profile comprising 10 permanent stakes. This long-term record yields snow depths consistent with two other shorter term Abisko records: measurements made at another 10-stake profile (1974-present) and at a single stake (1956-present). The measurement interval is variable, ranging from daily to monthly, and there are no data for about half of the winter months in the period 1930-1956. To fill the gaps, we use a simple snowpack model driven by concurrent temperature and precipitation measurements at Abisko. Model snow depths are similar to observed; differences between the two records are comparable to those between profile and single stake measurements. For both model and observed snow depth records, the most statistically significant trend is in winter mean snow depths, amounting to an increase of about 2 cm or 5 % of the mean per decade over the whole measurement period, and 10% per decade since the 1930-40s, but all seasonal means of snow depth show positive trends on the longest timescales. However, the start, end, and length of the snow season do not show any statistically significant long-term trends. Finally, the relation between the Arctic Oscillation index and Abisko temperature, precipitation and snow depth is positive and highly significant, with the best correlations for winter.     

南极瑞穗高原1987—1988年度表面物质平衡及其变化

根据1987/1988年度表面物质积累资料,对Mizuho(瑞穗)高原该年度物质平衡的分布规律及其变化进行了讨论,同时还对年内短期天气过程及地形变化对物质平衡的影响进行了分析。研究发现1987/1988年度物质平衡的空间分布与多年平均状况存在较大区别:海拔550m以下的沿海地带表现为负物质平衡状态。从S_16点向内陆80km范围内为高值物质平衡区。年平均净物质平衡量达0.84m雪层深;80km到瑞穗高原内陆的瑞穗站之间为低值物质平衡区,年平均物质平衡量仅0.14m雪层深。在瑞穗高原,表面物质平衡水平表现为低积累,低支出的特征。此外,年内短期气候和地形变化对物质平衡的影响均大于多年平均状态,在高值物质平衡区,气候变化对物质平衡的影响大于地形变化的影响;而在低值物质平衡区,地形变化对物质平衡的影响则大于气候变化对物质平衡的影响。     

Local Extremes in the Lidar‐Derived Snow Cover of Alpine Glaciers

Snow deposition and redistribution are major drivers of snow cover dynamics in mountainous terrain and contribute to the mass balance of alpine glaciers. The quantitative understanding of inhomogeneous snow distribution in mountains has recently benefited from advances in measuring technologies, such as airborne laser scanning (ALS). This contribution further advances the quantitative understanding of snow distribution by analysing the areas of maximum surface elevation changes in a mountain catchment with large and small glaciers. Using multi‐annual ALS observations, we found extreme surface elevation changes on rather thin borders along the glacier margins. While snow depth distribution patterns in less extreme terrain have presented high inter‐annual persistence, there is little persistence of those extreme glacier accumulations between winters. We therefore interpret the lack of persistence as the result of a predominance of gravity‐driven redistribution, which has an inherently higher random component because it does not occur with all conditions in all winters. In highly crevassed zones, the lidar‐derived surface elevation changes are caused by a complex interaction of ice flux divergence, the propagation of crevasses and snow accumulation. In general, the relative contribution of gravitational mass transport to glacier snow cover volume was found to decrease for glaciers larger than 5 km² in the investigated region. We therefore suggest that extreme accumulations caused by gravitational snow transport play a significant role in the glacier mass balance of small to medium‐size glaciers and that they may be successfully parameterized by simple mass redistribution algorithms, which have been presented in the literature.     

Assessment of the importance of moderate spatial resolution cloud climatology data in solar radiation modeling

Improving solar radiation models is critical for supporting the increase in solar energy usage and modeling ecosystem dynamics. However, coarse spatial resolutions of solar radiation models overlook the impacts resulting from spatial variability of clouds at meso- and micro-scales. To address this problem, Moderate Resolution Imaging Spectroradiometer (MODIS) cloud climatology developed by the National Severe Storms Laboratory was used to relate cloudiness to surface solar radiation observations. We developed a linear regression model between the surface solar radiation and MODIS cloud climatology and used the model to estimate average radiation across Oklahoma. Furthermore, the study compared the average error and coefficient of determination to measured ground radiation. Error analysis of the regression model showed that the differences between observed radiation and estimated radiation were spatially autocorrelated for the Aqua MODIS satellite scan. This suggests cloudiness alone is not sufficient to predict surface solar radiation. This study found that simple cloud datasets alone can account for approximately 50% of the variation in observed solar radiation at 250-m spatial resolution, but additional datasets such as optical depth, elevation, and slope are needed to accurately explain spatial distributions of incoming shortwave radiation.     

Mass Balance Methods on Kongsvegen, Svalbard

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.