surface and bed topography of trapridge glacier yukon territory canada digital elevation models and derived hydraulic geometry measurements of ice thickness and surface elevation are prerequisite to many glaci ological investigations a variety of techniques has been develo ped for inter pret ation of these data including means of constructing regularly gridded digital eleva tion models dem s for use in numcrical studies here we present a simple yet stati sti cally sound method for processing ice pe netr ating radar data and descr ibe a tech nique for interpol ating these data onto a regular grid dems generatcd fort rapridge glacier yukon territory canada are used to derive geometric quantities lhal give pre liminary insights into the underlying basin scale hydrol ogical syste m this simple geo metric analysis suggests that at low water press ures a dendrilic drainage netw ork exists that evolves into a uniaxial morphology as water pressure approaches notation these pre dictions are compared to hydraulic connection probabilities based on bore hole drilling

impacts of surface elevation on the growth and scaling properties of simulated river networks we investigate the connection between surface elevation and the growth and scaling of river networks three planar models scheidegger eden and invasion percolation are first considered these models develop aggregating networks according to stochastic rules but do not simulate erosion because the network growth is independent of the surface elevation we show that none of these planar growth models produces scaling results consistent with observations for natural river basins we then modify the models to include elevation simulating the effects of fluvial erosion by enforcing the slope area relationship the resulting configurations have scaling properties that still depend on the model scheidegger eden or invasion percolation but are closer to natural river networks when compared with those from the planar growth rules we conclude that inclusion of the vertical dimension in these three models is critical for explaining the formation and regularities of fluvial networks c 2001 elsevier science bn all rights reserved

global distributions of glacier properties a stochastic scaling paradigm many problems in global climate and earth systems science require knowledge of regional or global scale distributions of glacier properties which includes mass balance ice velocity flux thickness volume and surface area among others with roughly 160 000 glaciers worldwide obtaining information on the global probability distributions of most ice properties is expensive and often infeasible only surface area distributions are relatively easy to measure either by direct observation or remote sensing while other properties are difficult to observe this work shows that scaling relationships from the continuum dynamics of ice can link the distribution of surface areas to the global and regional distributions of any other continuum property some data inventories already exist for constructing reasonable distributions of glacier sizes and this analysis presents theoretical arguments based on glacier network topologies similar in concept to river networks to suggest a power law times an exponential distribution of surface areas in agreement with the data therefore by using existing data or the theoretical distributions of surface areas specific distributions for other glacier properties in any region of the world can be constructed as an example predictions up to a scaling constant are made for the distribution of glacier volumes characteristic thicknesses characteristic velocities and characteristic response times in the alps

a consensus estimate for the ice thickness distribution of all glaciers on earth knowledge of the ice thickness distribution of the world s glaciers is a fundamental prerequisite for a range of studies projections of future glacier change estimates of the available freshwater resources or assessments of potential sea level rise all need glacier ice thickness to be accurately constrained previous estimates of global glacier volumes are mostly based on scaling relations between glacier area and volume and only one study provides global scale information on the ice thickness distribution of individual glaciers here we use an ensemble of up to five models to provide a consensus estimate for the ice thickness distribution of all the about 215 000 glaciers outside the greenland and antarctic ice sheets the models use principles of ice flow dynamics to invert for ice thickness from surface characteristics we find a total volume of 158 41 103 km3 which is equivalent to 0 32 0 08 m of sea level change when the fraction of ice located below present day sea level roughly 15 is subtracted our results indicate that high mountain asia hosts about 27 less glacier ice than previously suggested and imply that the timing by which the region is expected to lose half of its present day glacier area has to be moved forward by about one decade the ice volume of glaciers outside the greenland and antarctic ice sheets totals about 158 000 km3 with about 27 less ice in high mountain asia than thought according to multiple models that estimate ice thickness from surface characteristics

potential risks when using seismic attributes as predictors of reservoir properties the advance of our ability to generate seismic attributes and the growing emphasis on production geophysics has led to the widespread use of seismic attributes as predictors of reservoir properties in many cases we can show using seismic modeling or rock physics a physically justifiable relationship between a seismic attribute and the reservoir property of interest when this is true we are able to greatly reduce the uncertainty of interwell predictions of reservoir properties

regional and global volumes of glaciers derived from statistical upscaling of glacier inventory data 1 very few global scale ice volume estimates are available for mountain glaciers and ice caps although such estimates are crucial for any attempts to project their contribution to sea level rise in the future we present a statistical method for deriving regional and global ice volumes from regional glacier area distributions and volume area scaling using glacier area data from 123 000 glaciers from a recently extended world glacier inventory we compute glacier volumes and their sea level equivalent sle for 19 glacierized regions containing all mountain glaciers and ice caps on earth on the basis of total glacierized area of 741 103 68 103 km2 we estimate a total ice volume of 241 103 29 103 km3 corresponding to 0 60 0 07 m sle of which 32 is due to glaciers in greenland and antarctica apart from the ice sheets however our estimate is sensitive to assumptions on volume area scaling coefficients and glacier area distributions in the regions that are poorly inventoried i e antarctica north america greenland and patagonia this emphasizes the need for more volume observations especially of large glaciers and a more complete world glacier inventory in order to reduce uncertainties and to arrive at firmer volume estimates for all mountain glaciers and ice caps

a more complete version of the world glacier inventory the world glacier inventory wgi was conceived half a century ago as an activity to be completed during the international geophysical year 1957 58 it consisted until very recently of nearly 70 000 glacier records covering slightly less than one quarter of the glacier ice outside the ice sheets a complete wgi must be a compromise if it is to be available and usable soon a more complete version called wgi xf is available and usable now and contains records for just over 131 000 glaciers and nearly half of the global extent of ice the additional glaciers come mainly from the assimilation of existing inventories but also from rescuing inventories that have been lost and from new inventories in canada and the subantarctic in wgi xf the xf stands for extended format flagging the fact that wgi xf conforms to a set of explicit specifications which enhance usefulness by eliminating low level inconsistencies two important features are nominal glaciers and glacier complexes a nominal glacier of which there are about 5000 in wgi xf is one about which little is known other than its existence and approximate location a glacier complex is one or more contiguous glaciers this term embodies the idea which is not new that inventories can be preliminary based upon vector outlines which await subdivision by trained glaciologists many regional studies have found that measurements of changes in single glaciers require accurate work and painstaking quality control wgi xf is not assuredly reliable as a source for such detailed work but there are several other subjects in which less detail would be a price worth paying for more complete coverage incomplete information about the dates of imagery and maps is a hindrance to analysis and the recovery of dates from metadata should have high priority

application of inventory data for estimating characteristics of and regional climate change effects on mountain glaciers a pilot study with the european alps a parameterization scheme using simple algorithms for unmeasured glaciers is being applied to glacier inventory data to estimate the basic glaciological characteristics of the inventoried ice bodies and simulate potential climate change effects on mountain glaciers for past and potential climate scenarios glacier changes for assumed mass balance changes are calculated as step functions between steady state conditions for time intervals that approximately correspond to the characteristic dynamic response time a few decades of the glaciers in order to test the procedure a pilot study was carried out in the european alps where detailed glacier inventories had been compiled around the mid 1970s total glacier volume in the alps is estimated at about 130 km3 for the mid 1970s strongly negative mass balances are likely to have caused a loss of about 10 20 of this total volume during the decade 1980 90 backward calculation of glacier length changes using a mean annual mass balance of 0 25m w e a 1 since the end of the little ice age around 1850 ad gives considerable scatter but satisfactory overall results as compared with long term observations the total loss of alpine surface ice mass since 1850 can be estimated at about half the original value an acceleration of this development with annual mass losses of around 1 m a 1 or more as anticipated from ipcc scenario a for the coming century could eliminate major parts of the presently existing alpine ice volume within decades

comment on the potential for sea level rise new estimates from glacier and ice cap area and volume distribution by s c b raper and r j braithwaite

the physical basis of glacier volume area scaling ice volumes are known for only a few of the roughly 160 000 glaciers worldwide but are important components of many climate and sea level studies which require water flux estimates a scaling analysis of the mass and momentum conservation equations shows that glacier volumes can be related by a power law to more easily observed glacier surface areas the relationship requires four closure choices for the scaling behavior of glacier widths slopes side drag and mass balance reasonable closures predict a volume area scaling exponent which is consistent with observations giving a physical and practical basis for estimating ice volumes glacier volume is insensitive to perturbations in the mass balance scaling but changes in average accumulation area ratios reflect significant changes in the scaling of both mass balance and ice volume

ice volume and subglacial topography for western canadian glaciers from mass balance fields thinning rates and a bed stress model abstracta method is described to estimate the thickness of glacier ice using information derived from the measured ice extent surface topography surface mass balance and rate of thinning or thickening of the ice column shear stress beneath an ice column is assumed to be simply related to ice thickness and surface slope as for an inclined slab but this calculation is cast as a linear optimization problem so that a smoothness regularization can be applied assignment of bed stress is based on the flow law for ice and a mass balance calculation but must be preceded by delineation of the ice flow drainage basin validation of the method is accomplished by comparing thickness estimates to the known thickness generated by a numerical ice dynamics model once validated the method is used to estimate the subglacial topography for all glaciers in western canada that lie south of 60 n adding the present ice volume of each glacier gives the estimated total volume as 2320 km3 equivalent to 5 8 mm of sea leve

width and length scaling of glaciers an analysis of hundreds of mountain and valley glaciers in the former soviet union and the alps shows that characteristic glacier widths scale as characteristic glacier lengths raised to an exponent of 0 6 this is in contrast to most previous analyses which implicitly or explicitly assumed scaling exponents of either 0 or 1 the exponent 0 6 implies that average glacier widths are proportional to average glacier thicknesses although this seems to suggest v shaped glacier valleys the linear width thickness relationship is not inconsistent with parabolic valley cross sections because the characteristic or average width of a glacier depends on many other aspects of channel and glacier morphology including variations in the channel width with distance up and downstream

snow patch and glacier size distributions a simple theoretical model demonstrates that some amount of randomness in snow and ice mass balance is sufficient to reproduce empirically observed power law and exponential distributions of snow patch and glacier sizes no other assumptions about the underlying topography or snow accumulation and ablation processes are necessary to extract this important spatial property the inclusion of additional geometrical and physical processes can alter the specific scaling constants of the size distributions but the fundamental behavior remains unchanged specifically for snow patch and glacier sizes less than some correlation length the size distribution is a decreasing power law and for sizes larger than the correlation length the distribution decreases rapidly as an exponential the solution is based on a mapping to a relatively well explored class of problems in percolation theory

volume area scaling vs flowline modelling in glacier volume projections volume area scaling provides a practical alternative to ice flow modelling to account for glacier size changes when modelling the future evolution of glaciers however uncertainties remain as to the validity of this approach under non steady conditions we address these uncertainties by deriving scaling exponents in the volume area relationship from one dimensional ice flow modelling we generate a set of 37 synthetic steady state glaciers of different sizes and then model their volume evolution due to climate warming and cooling as prescribed by negative and positive mass balance perturbations respectively on a century timescale the scaling exponent derived for the steady state glaciers 1 56 differs from the exponents derived for the glaciers in transient non steady state by up to 86 nevertheless volume projections employing volume area scaling are relatively insensitive to these differences in scaling exponents volume area scaling agrees well with the results from ice flow modelling in addition the scaling method is able to simulate the approach of a glacier to a new steady state if mass balance elevation feedback is approximated by removing or adding elevation bands at the lowest part of the glacier as the glacier retreats or advances if area changes are approximated in the mass balance computations in this way our results indicate that volume area scaling is a powerful tool for glacier volume projections on multi century timescales

analysis of scaling methods in deriving future volume evolutions of valley glaciers volume area scaling is a common tool for deriving future volume evolutions of valley glaciers and their contribution to sea level rise we analyze the performance of scaling relationships for deriving volume projections in comparison to projections from a one dimensional ice flow model the model is calibrated for six glaciers nigardsbreen rhonegletscher south cascade glacier sofiyskiy glacier midre lovenbreen and abramov glacier volume evolutions forced by different hypothetical mass balance perturbations are compared with those obtained from volume area v a volume length v l and volume area length v a l scaling results show that the scaling methods mostly underestimate the volume losses predicted by the ice flow model up to 47 for v a scaling and up to 18 for v l scaling by the end of the 100 year simulation period in general v l scaling produces closer simulations of volume evolutions derived from the ice flow model suggesting that v l scaling may be a better approach for deriving volume projections than v a scaling sensitivity experiments show that the initial volumes and volume evolutions are highly sensitive to the choice of the scaling constants yielding both over and underestimates however when normalized by initial volume volume evolutions are relatively insensitive to the choice of scaling constants especially in the v l scaling the 100 year volume projections differ within 10 of initial volume when the v a scaling exponent commonly assumed 1 375 is varied by 30 to 45 0 95 2 00 and the v l scaling exponent q 2 2 is varied by 30 to 45 q 1 52 3 20 this is encouraging for the use of scaling methods in glacier volume projections particularly since scaling exponents may vary between glaciers and the scaling constants are generally unknown

mountain glaciers and ice caps around antarctica make a large sea level rise contribution the intergovernmental panel on climate change ipcc estimates that the sum of all contributions to sea level rise for the period 1961 2004 was 1 1 0 5 mm a 1 leaving 0 7

the potential for sea level rise new estimates from glacier and ice cap area and volume distributions projections of sea level rise from mountain glaciers and ice caps for the next century and beyond should be based on an assessment of the ice available for melting projections to date are based on all regions except greenland and antarctica the latter are considered separately by the ipcc yet no sound estimates for the appropriate volume of ice and its potential for sea level rise are evident in the literature an ice cap data set is compiled allowing the separate treatment of glacier area coverage data glacier inventory data are comprehensive enough in some regions to allow the estimation of glacier size distributions the differences in the distributions are related to a metric of the regional topographic variability allowing glacier size distributions to be estimated on a 1 latitude longitude grid of cells containing glaciers appropriate volume area scaling for glaciers and for ice caps gives global estimates of glacier and ice cap volumes by size class this leads to an estimate of the total ice volume of 0 087 0 010 106 km3 and a sea level rise equivalent of 0 241 0 026 m the glaciers and ice caps contribute 41 and 59 to these estimates respectively these values are based on data sets compiled during several decades mainly in the second half of the 20th century we compare our results to published results that include the glaciers and icecaps at the margins of the greenland and antarctic ice sheets

sharply increased mass loss from glaciers and ice caps in the canadian arctic archipelago the canadian arctic archipelago contains one third of the global volume of land ice outside the ice sheets but its contribution to sea level change is largely unknown gardner et al use three independent techniques to reveal that mass loss from the archipelago was 92 12 gigatonnes per year in 2007 09 about three times greater than in 2004 06 and coincident with warmer summer temperatures the record is too short to allow a firm conclusion on longer term trends but it is clear that the canadian arctic archipelago is a significant contributor to sea level rise mountain glaciers and ice caps are contributing significantly to present rates of sea level rise and will continue to do so over the next century and beyond1 2 3 4 5 the canadian arctic archipelago located off the northwestern shore of greenland contains one third of the global volume of land ice outside the ice sheets6 but its contribution to sea level change remains largely unknown here we show that the canadian arctic archipelago has recently lost 61 7 gigatonnes per year gt yr 1 of ice contributing 0 17 0 02 mm yr 1 to sea level rise our estimates are of regional mass changes for the ice caps and glaciers of the canadian arctic archipelago referring to the years 2004 to 2009 and are based on three independent approaches surface mass budget modelling plus an estimate of ice discharge smb d repeat satellite laser altimetry icesat and repeat satellite gravimetry grace all three approaches show consistent and large mass loss estimates between the periods 2004 2006 and 2007 2009 the rate of mass loss sharply increased from 31 8 gt yr 1 to 92 12 gt yr 1 in direct response to warmer summer temperatures to which rates of ice loss are highly sensitive 64 14 gt yr 1 per 1 k increase the duration of the study is too short to establish a long term trend but for 2007 2009 the increase in the rate of mass loss makes the canadian arctic archipelago the single largest contributor to eustatic sea level rise outside greenland and antarctica

a method to estimate the ice volume and ice thickness distribution of alpine glaciers sound knowledge of the ice volume and ice thickness distribution of a glacier is essential for many glaciological applications however direct measurements of ice thickness are laborious not feasible everywhere and necessarily restricted to a small number of glaciers in this paper we present a method to estimate the ice thickness distribution and the total ice volume of alpine glaciers this method is based on glacier mass turnover and principles of ice flow mechanics the required input data are the glacier surface topography the glacier outline and a set of borders delineating different ice flow catchments three parameters describe the distribution of the apparent mass balance which is defined as the difference between the glacier surface mass balance and the rate of ice thickness change and two parameters define the ice flow dynamics the method was developed and validated on four alpine glaciers located in switzerland for which the bedrock topography is partially known from radio echo soundings the ice thickness along 82 cross profiles can be reproduced with an average deviation of about 25 between the calculated and the measured ice thickness the cross sectional areas differ by less than 20 on average this shows the potential of the method for estimating the ice thickness distribution of alpine glaciers without the use of direct measurements

neural networks applied to estimating subglacial topography and glacier volume abstract to predict the rate and consequences of shrinkage of the earth s mountain glaciers and ice caps it is necessary to have improved regional scale models of mountain glaciation and better knowledge of the subglacial topography upon which these models must operate the problem of estimating glacier ice thickness is addressed by developing an artificial neural network ann approach that uses calculations performed on a digital elevation model dem and on a mask of the present day ice cover because suitable data from real glaciers are lacking the ann is trained by substituting the known topography of ice denuded regions adjacent to the ice covered regions of interest and this known topography is hidden by imagining it to be ice covered for this training it is assumed that the topography is flooded to various levels by horizontal lake like glaciers the validity of this assumption and the estimation skill of the trained ann is tested by predicting ice thickness for four 50 km 50 km regions that

rapid wastage of alaska glaciers and their contribution to rising sea level we have used airborne laser altimetry to estimate volume changes of 67 glaciers in alaska from the mid 1950s to the mid 1990s the average rate of thickness change of these glaciers was 0 52 m year extrapolation to all glaciers in alaska yields an estimated total annual volume change of 52 15 km 3 year water equivalent equivalent to a rise in sea level sle of 0 14 0 04 mm year repeat measurements of 28 glaciers from the mid 1990s to 2000 2001 suggest an increased average rate of thinning 1 8 m year this leads to an extrapolated annual volume loss from alaska glaciers equal to 96 35 km 3 year or 0 27 0 10 mm year sle during the past decade these recent losses are nearly double the estimated annual loss from the entire greenland ice sheet during the same time period and are much higher than previously published loss estimates for alaska glaciers they form the largest glaciological contribution to rising sea level yet measured