glacier subsurface heat flux characterizations for energy balance modelling in the donjek range southwest yukon canada we apply a point scale energy balance model to a small polythermal glacier in the st elias mountains of canada in order to investigate the applicability and limitations of different treatments of the glacier surface temperature and subsurface heat flux these treatments range in complexity from a multilayer subsurface model that simulates snowpack evolution to the assumption of a constant glacier surface temperature equal to 0 c the most sophisticated model includes dry densification of the snowpack penetration of shortwave radiation into the subsurface internal melting refreezing of percolating meltwater and generation of slush layers measurements of subsurface temperature and surface lowering are used for model validation and highlight the importance of including subsurface penetration of shortwave radiation in the model using an iterative scheme to solve for the subsurface heat flux as the residual of the energy balance equation results in an overestimation of total ablation by 18 while the multilayer subsurface model underestimates ablation by 6 by comparison the 0 c surface assumption leads to an overestimation of ablation of 29 in this study where the mean annual air temperature is about 8 c

a distributed temperature index ice and snowmelt model including potential direct solar radiation hourly melt and discharge of storglaciaren a small glacier in sweden were computed for two melt seasons applying temperature index methods to a 30 m resolution grid for the melt component the classical degree day method yielded a good simulation of the seasonal patient of discharge but the pronounced melt induced daily discharge cycles were not captured modelled degree day factors calculated for every hour and each gridcell from melt obtained from a distributed energy balance model varied substantially both diurnally and spatially a new distributed temperature index model is suggested attempting to capture both the pronounced diurnal melt cycles and the spatial variations in melt due to the effects of surrounding topography this is accomplished by including a radiation index in terms of potential clear sky direct solar radiation and thus without the need for other data besides air temperature this approach improved considerably the simulation of diurnal discharge fluctuations and yielded a more realistic spatial distribution of melt rates the incorporation of measured global radiation to account for the reduction in direct solar radiation due to cloudiness did not lead to additional improvement in model performance

retreating alpine glaciers increased melt rates due to accumulation of dust vadret da morteratsch switzerland the automatic weather station aws on the snout of the vadret da morteratsch switzerland has delivered a unique 12 year meteorological dataset from the ablation zone of a temperate glacier this dataset can be used to study multi annual trends in the character of the surface energy budget since 2003 there has been a substantial darkening of the glacier tongue due to the accumulation of mineral and biogenic dust the typical surface albedo in summer has dropped from 0 32 to 0 15 we have analysed the implications of the lowered albedo for the energy balance and the annual ablation for the 4 year period 2003 06 the decreased albedo caused an additional removal of about 3 5 m of ice calculations with an energy balance model show that the same increase in ablation is obtained by keeping the ice albedo fixed to 0 32 and increasing the air temperature by 1 7 k our analysis confirms that for retreating glaciers the deposition of dust from exposed side moraines on the glacier surface constitutes an important feedback mechanism the mineral dust stimulates the growth of algae lowers the surface albedo enhances the melt rates and thereby facilitates the further retreat of the glacier snout

modelling the long term mass balance and firn evolution of glaciers around kongsfjorden svalbard we analyse the long term 1961 2012 distributed surface mass balance and firn evolution of the kongsvegen and holtedahlfonna glacier systems in northwestern svalbard we couple a surface energy balance model to a firn model with forcing provided from regional climate model output in situ observational data are used to calibrate model parameters and validate the output the simulated area averaged surface mass balance for 1961 2012 is slightly positive 0 08 m w e a 1 which only fractionally compensates for mass loss by calving refreezing of percolating water in spring summer 0 13 m w e a 1 and stored water in fall winter 0 18 m w e a 1 provides a buffer for runoff internal accumulation i e refreezing below the previous year s summer surface in the accumulation zone peaks up to 0 22 m w e a 1 and is unaccounted for by stake observations superimposed ice formation in the lower accumulation zone ranges as high as 0 25 m w e a 1 a comparison of the periods 1961 99 and 2000 12 reveals 21 higher annual melt rates since 2000 and a 31 increase in runoff which can only in part be ascribed to recent warmer and drier conditions in response to firn line retreat both albedo lowering snow ice albedo feedback and lower refreezing rates refreezing feedback further amplified runoff

positive degree day factors for ablation on the greenland ice sheet studied by energy balance modelling ice ablation is related to air temperature by the positive degree day factor variations of the positive degree day factor in west greenland are studied using an energy balance model to simulate ablation under different conditions degree day factors for simulated and measured ice ablation at nordbogletscher and qaman rssup sermia agree well with values around 8 mm d 1 c 1 degree day factors for snow are less than half those for ice energy balance modelling shows that degree day factors vary with summer mean temperature surface albedo and turbulence but there is only evidence of large positive degree day factors at lower temperatures and with low albedo 0 3 the greatest effect of albedo variations 0 3 0 7 is at lower temperatures while variations in turbulence have greater effect at higher temperatures current models may underestimate runoff from the greenland ice sheet by several tenths because they use a degree day factor for melting ice that is too small for the colder parts of the ice sheet i e the upper ablation area and the northerly margin

mass balance model parameter transferability on a tropical glacier we explore the small scale spatial and temporal transferability of model parameters between two points in the ablation zone of tropical glaciar shallap cordillera blanca peru 9 s 77 w 4800 m a s l in order to provide a robust assessment of the performance of a process based glacier mass balance model relative surface height change is calculated at hourly time steps and cumulative values are compared to surface height measurements made at irregular intervals 14 64 days over the course of two continuous hydrological years august 2006 august 2008 best performing parameter combinations were determined for each point from the outcome of 1000 model simulations for which parameters were varied randomly within a defined range with these parameter combinations measurements for a specific location and time span are well reproduced transferring the parameter combination as optimized for one location to the other location in the ablation zone increases the errors of modeled cumulative mass balance by 5 1326 mm ice eq a 1 transferring the parameter combinations as optimized for one year to the other year increases the modeled errors in cumulative mass balance by 18 3179 mm ice eq a 1 model errors generally increase during periods with frequent snowfall and snow cover this could reflect either the inherent difficulty of modeling complex snow processes or the inability of the model to correctly capture the pattern of albedo evolution at this site the magnitude of errors associated with parameter transfer in space and time highlights the need for improving model performance for robust climatological and or hydrological analyses on tropical glaciers

transmission of solar radiation through clouds on melting glaciers a comparison of parameterizations and their impact on melt modelling we explore the robustness and transferability of parameterizations of cloud radiative forcing used in glacier melt models at two sites in the swiss alps we also look at the rationale behind some of the most commonly used approaches and explore the relationship between cloud transmittance and several standard meteorological variables the 2 m air temperature diurnal range is the best predictor of variations in cloud transmittance however linear and exponential parameterizations can only explain 30 50 of the observed variance in computed cloud transmittance factors we examine the impact of modelled cloud transmittance factors on both solar radiation and ablation rates computed with an enhanced temperature index model the melt model performance decreases when modelled radiation is used the reduction being due to an underestimation of incoming solar radiation on clear sky days the model works well under overcast conditions we also seek alternatives to the use of in situ ground data however outputs from an atmospheric model 2 2 km horizontal resolution do not seem to provide an alternative to the parameterizations of cloud radiative forcing based on observations of air temperature at glacier automatic weather stations conversely the correct definition of overcast conditions is important

areal melt and discharge modelling of storglaciaren sweden a grid based glacier melt and discharge model was applied to storglaciaren a small valley glacier 3 km 2 in northern sweden for the melt seasons of 1993 and 1994 the energy available for melt was estimated from a surface energy balance model using meteorological data collected by automatic weather stations on the glacier net radiation and the turbulent heat fluxes were calculated hourly for every grid point of a 30 m resolution digital terrain model using the measurements of temperature humidity wind speed and radiative fluxes on the glacier two different bulk approaches were used to calculate the turbulent fluxes and compared with respect to their impact on discharge simulations discharge of storglaciaren was simulated from calculated meltwater production and precipitation by three parallel linear reservoirs corresponding to the different storage properties of firn snow and ice the performance of the model was validated by comparing simulated discharge to measured discharge at the glacier snout depending on which parameterization of the turbulent fluxes was used the timing and magnitude of simulated discharge was in good agreement with observed discharge or simulated discharge was considerably underestimated in one year

revisiting bulk heat transfer on peyto glacier alberta canada in light of the og parameterization a scheme for katabatic turbulent heat transfer proposed by oerlemans and grisogono 2002 here referred to as the og parameterization is compared with bulk heat transfer estimates on peyto glacier alberta canada automatic weather stations awss provide off glacier data to drive the parameterization and glacier data for bulk estimates micrometeorological datasets are used to assess two schemes that employ the monin obukhov stability parameter z l to modify logarithmic or neutral bulk heat transfer equations to allow for stability both schemes fail at 1 m above the surface where the aws sensors are located unless a modified approach is used in which the stability correction is constant for z l 1 3 then the bulk sensible heat flux density falls to 0 93 of its neutral estimate at all measurement levels thus providing a basis for comparison with the parameterization the results of the comparison are very good indicating that a one to one relationship between bulk and parameterized values can be achieved by optimizing the fit with a background exchange coefficient and because there is only one off glacier aws using a sinusoidal function to model the diurnal variation of the potential temperature lapse rate

solar radiation cloudiness and longwave radiation over low latitude glaciers implications for mass balance modelling broadband radiation schemes parameterizations are commonly used tools in glacier mass balance modelling but their performance at high altitude in the tropics has not been evaluated in detail here we take advantage of a high quality 2 year record of global radiation g and incoming longwave radiation l measured on kersten glacier kilimanjaro east africa at 5873 m a s l to optimize parameterizations of g and l we show that the two radiation terms can be related by an effective cloud cover fraction neff s og or l can be modelled based on neff derived from measured l or g respectively at neff 1 g is reduced to 35 of clear sky g and l increases by 45 65 depending on altitude relative to clear sky l validation for a 1 year dataset of g and l obtained at 4850 m on glaciar artesonraju peruvian andes yields a satisfactory performance of the radiation scheme whether this performance is acceptable for mass balance studies of tropical glaciers is explored by applying the data from glaciar artesonraju to a physically based mass balance model which requires among others g and l as forcing variables uncertainties in modelled mass balance introduced by the radiation parameterizations do not exceed those that can be caused by errors in the radiation measurements hence this paper provides a tool for inclusion in spatially distributed mass balance modelling of tropical glaciers and or extension of radiation data when only g or l is measured

constraining turbulent heat flux parameterization over a temperate maritime glacier in new zealand the turbulent sensible and latent heat fluxes are important components of the surface energy balance over glaciers in the southern alps of new zealand contributing over half the energy available for ablation during large melt events to calculate these terms confidently in glacier mass balance models it is essential to use appropriate parameterizations for surface roughness and atmospheric stability eddy covariance measurements at brewster glacier were obtained over an ice surface to help facilitate an assessment of the calculation of the turbulent heat fluxes the roughness length for momentum was found to be 3 6 x 10 3 m while the roughness lengths for temperature and humidity were two orders of magnitude smaller in agreement with surface renewal theory a monte carlo approach was used to assess the uncertainty in turbulent heat fluxes calculated using the bulk aerodynamic method it was found that input data and roughness length uncertainty could not explain underestimates of observed sensible heat fluxes during periods with low wind speed and large temperature gradients during these periods a katabatic wind speed maximum alters the formulation of the turbulent exchange coefficient to that typically observed in a neutral atmosphere and this has implications for glacier mass balance sensitivity

integrated simulation of snow and glacier melt in water and energy balance based distributed hydrological modeling framework at hunza river basin of pakistan karakoram region 2015 american geophysical union all rights reserved energy budget based distributed modeling of snow and glacier melt runoff is essential in a hydrologic model to accurately describe hydrologic processes in cold regions and high altitude catchments we developed herein an integrated modeling system with an energy budget based multilayer scheme for clean glaciers a single layer scheme for debris covered glaciers and multilayer scheme for seasonal snow over glacier soil and forest within a distributed biosphere hydrological modeling framework model capability is demonstrated for hunza river basin 13 733km2 in the karakoram region of pakistan on a 500m grid for 3 hydrologic years 2002 2004 discharge simulation results show good agreement with observations nash sutcliffe efficiency 0 93 flow composition analysis reveals that the runoff regime is strongly controlled by the snow and glacier melt runoff 50 snowmelt and 33 glacier melt pixel by pixel evaluation of the simulated spatial distribution of snow covered area against moderate resolution imaging spectroradiometer derived 8day maximum snow cover extent data indicates that the areal extent of snow cover is reproduced well with average accuracy 84 and average absolute bias 7 the 3year mean value of net mass balance nmb was estimated at 0 04myr 1 it is interesting that individual glaciers show similar characteristics of nmb over 3years suggesting that both topography and glacier hypsometry play key roles in glacier mass balance this study provides a basis for potential application of such an integrated model to the entire hindu kush karakoram himalaya region toward simulating snow and glacier hydrologic processes within a water and energy balance based distributed hydrological modeling framework

how stable are twentieth century calibration models a high resolution summer temperature reconstruction for the eastern swiss alps back to ad 1580 derived from proglacial varved sediments we found a significant positive correlation between local summer air temperature may september and the annual sediment mass accumulation rate mar in lake silvaplana 46 n 9 e 1800 m a s l during the twentieth century r 0 69 p 0 001 for decadal smoothed series sediment trap data 2001 2005 confirm this relation with exceptionally high particle yields during the hottest summer of the last 140 years in 2003 on this base we developed a decadal scale summer temperature reconstruction back to ad 1580 surprisingly the comparison of our reconstruction with two other independent regional summer temperature reconstructions based on tree rings and documentary data revealed a significant negative correlation for the pre 1900 data ie late little ice age this demonstrates that the correlation between mar and summer temperature is not stable in time and the actualistic principle does not apply in this case we suggest that different climatic regimes modern little ice age lead to changing state conditions in the catchment and thus to considerably different sediment transport mechanisms therefore we calibrated our mar data with gridded early instrumental temperature series from ad 1760 1880 r 0 48 p 0 01 for decadal smoothed series to properly reconstruct the late lia climatic conditions we found exceptionally low temperatures between ad 1580 and 1610 0 75 c below twentieth century mean and during the late maunder minimum from ad 1680 to 1710 0 5 c below twentieth century mean in general summer temperatures did not experience major negative departures from the twentieth century mean during the late little ice age this compares well with the two existing independent regional reconstructions suggesting that the lia in the alps was mainly a phenomenon of the cold season

a comparison of landslide rates following helicopter and conventional cable based clear cut logging operations in the southwest coast mountains of british columbia abstract a comparison of landslide rates following helicopter and conventional cable based clear cut logging was carried out using results from two independent terrain attribute studies in the eldred and lois river watersheds in the southwest coast mountains of british columbia landslides initiating from directly within a road prism were excluded from the study in order to focus the comparison on landslides related primarily to conventional versus helicopter yarding methods a landslide rate of 0 02 landslides ha was observed in 162 terrain polygons logged by helicopter 8 years prior to this study landslide rates in 38 gullied polygons were 0 06 landslides ha no landslides were observed in 124 open slope polygons over a similar 8 year average period 0 03 landslides ha were observed in 142 cable yarded terrain polygons 0 06 and 0 02 landslides ha occurred in gullied and open slope polygons respectively t tests indicate that total landslide rates are not significantly different following helicopter and conventional logging however a dichotomy exists between gullied and open slope terrain polygons landslide rates are not significantly different in gullied terrain but are significantly higher on open slopes following conventional cable logging consequently landslides appear to have a greater potential to occur in open slope terrain following conventional logging but differences in gullied polygons are less likely increased post logging landslide rates in conventionally logged open slopes are more likely the result of undetected road related drainage changes than differences between helicopter and conventional yarding related ground disturbance

on the role of subsurface heat conduction in glacier energy balance modelling we discuss the inclusion of the subsurface heat conduction flux into the calculation of the energy balance and ablation at the glacier atmosphere interface data from automatic weather stations are used to force an energy balance model at several locations on alpine glaciers and at one site in the dry andes of central chile the heat conduction flux is computed using a two layer scheme assuming that 36 of the net shortwave radiation is absorbed by the surface layer and that the rest penetrates into the snowpack we compare simulations conducted with and without subsurface heat flux results show that assuming a surface temperature of zero degrees leads to a larger overestimation of melt at the sites in the accumulation area 10 4 13 3 than in the ablation area 0 5 2 8 due to lower air temperatures and the presence of snow the difference between simulations with and without heat conduction is also high at the beginning and end of the ablation season up to 29 for the first 15 days of the season when air temperatures are lower and snow covers the glacier surface while they are of little importance during periods of sustained melt at all the locations investigated

measuring glacier surface roughness using plot scale close range digital photogrammetry glacier roughness at sub metre scales is an important control on the ice surface energy balance and has implications for scattering energy measured by remote sensing instruments ice surface roughness is dynamic as a consequence of spatial and temporal variation in ablation to date studies relying on singular and or spatially discrete two dimensional profiles to describe ice surface roughness have failed to resolve common patterns or causes of variation in glacier surface morphology here we demonstrate the potential of close range digital photogrammetry as a rapid and cost effective method to retrieve three dimensional data detailing plot scale supraglacial topography the photogrammetric approach here employed a calibrated consumer grade 5 mpix digital camera repeatedly imaging a plot scale 25 m2 ice surface area on midtre lovenbreen svalbard from stereo pair images digital surface models dsms with sub centimetre horizontal resolution and 3 mm vertical precision were achieved at plot scales 4 m2 extraction of roughness metrics including estimates of aerodynamic roughness length z 0 was readily achievable and temporal variations in the glacier surface topography were captured close range photogrammetry with appropriate camera calibration and image acquisition geometry is shown to be a robust method to record sub centimetre variations in ablating ice topography while the dsm plot area may be limited through use of stereo pair images and issues of obliquity emerging photogrammetric packages are likely to overcome such limitations

spatial and temporal variability of air temperature on a melting glacier atmospheric controls extrapolation methods and their effect on melt modeling juncal norte glacier chile 1 temperature data from three automatic weather stations and twelve temperature loggers are used to investigate the spatiotemporal variability of temperature over a glacier its main atmospheric controls the suitability of extrapolation techniques and their effect on melt modeling we use data collected on juncal norte glacier central chile during one ablation season we examine temporal and spatial variability in lapse rates lrs together with alternative statistical interpolation methods the main control over the glacier thermal regime is the development of a katabatic boundary layer kbl katabatic wind occurs at night and in the morning and is eroded in the afternoon lrs reveal strong diurnal variability with steeper lrs during the day when the katabatic wind weakens and shallower lrs during the night and morning we suggest that temporally variable lrs should be used to account for the observed change they tend to be steeper than equivalent constant lrs and therefore result in a reduction in simulated melt compared to use of constant lrs when extrapolating from lower to higher elevations in addition to the temporal variability the temperature elevation relationship varies also in space differences are evident between local lrs and including such variability in melt modeling affects melt simulations extrapolation methods based on the spatial variability of the observations after removal of the elevation trend such as inverse distance weighting or kriging do not seem necessary for simulations of gridded temperature data over a glacier

interannual variability in the spatial distribution of winter accumulation at a high arctic glacier finsterwalderbreen svalbard and its relationship with topography glacier mass balance and hydrology are strongly influenced by the distribution of snow accumulation at the start of the melt season two successive end of winter snow cover surveys at finsterwalderbreen svalbard are here used to investigate the interannual variability in the spatial distribution of accumulation and its relationship with topography 40 62 of the variance in snow depth was not determined by elevation assessed by linear regression of snow depth on surface elevation which could not therefore necessarily be used as a sole predictor of the spatial distribution of accumulation here principal components pc analysis of the topographic variables elevation slope north south and east west aspects shows that only two of six pcs determined for 2 years sampling locations had maximum loadings on altitude aspect was more important with maximum loadings on four pcs hierarchical cluster analysis was then applied to these pcs significant correlations with accumulation in each of two terrain clusters were given by 1 elevation and slope 2 east west aspect only 1999 1 elevation only 2 no significant correlations 2000 there is strong interannual variability not only in the magnitude of winter accumulation 0 41 m w e in 1999 0 58 m w e in 2000 but also in its spatial distribution and its relationship with topography

model study of the spatial distribution of the energy and mass balance of morteratschgletscher switzerland to investigate the spatial distribution of the energy and mass balance fluxes of a glacier a two dimensional mass balance model was developed and applied to morteratschgletscher switzerland the model is driven by meteorological input from four synoptic weather stations located in the vicinity of morteratschgletscher the model results were compared to observations made on the glacier the calculated mean specific mass balance is 0 47 m w e for 1999 and 0 23 m w e for 2000 net shortwave radiation shows a minimum at around 3350 m a s l due to the effects of shading slope aspect reflection from the slopes and obstruction of the sky ignoring these effects results in a 37 increase in the annual incoming shortwave radiation on the glacier causing 0 34 m w e more ablation a 1 c change in the air temperature results in a shift of 0 67 m w e in the mean specific mass balance while altering the precipitation by 10 causes a change of 0 17 m w e

a distributed surface energy balance model for a small valley glacier i development and testing for haut glacier d arolla valais switzerland this paper describes the development and testing of a distributed surface energy balance model used to calculate rates of surface melting at haut glacier d arolla valais switzerland the model uses a digital elevation model dem of the glacier surface and surrounding topography together with meteorological data collected at a site in front of the glacier to determine hourly or daily totals of the energy balance components and hence of melting over the entire surface of the glacier with a spatial resolutio of 20 m the model can also be used to determine temporal and spatial variations in snow depth snow line position and glacier surface albedo calculations from the model are compared with observations made along the glacier centre line in 1990 and in general the model performs very well the correlation coefficients between calculated and measured snow line elevation albedo and ablation are 0 99 0 85 and 0 81 respectively the main source of error between modelled and measured values of these variables is probably inadequacies in the parameterization of albedo used in the model

melt and surface sublimation across a glacier in a dry environment distributed energy balance modelling of juncal norte glacier chile previous estimates of melt and surface sublimation on glaciers of the subtropical semiarid andes 29 34 s have been obtained at few specific locations but it is not clear how ablation components vary across the entire extent of a glacier in this dry environment here we simulate the distributed energy and mass balance of juncal norte glacier 33 s during a 2 month summer period forcing fields of near surface air temperature and wind speed are generated using two methods accounting for the main physical processes that shape their spatial variations simulated meteorological variables and ablation agree well with observations on the glacier tongue and reveal complex patterns of energy and mass fluxes ablation decreases from 70 mm w e d 1 at the low albedo glacier terminus 3000 m where almost 100 of total ablation corresponds to melt to 75 of total ablation our simulations provide the first glacier scale estimates of ablation components on a glacier in the study region and better reproduce the observed and expected spatial variations of melt and surface sublimation in comparison with more simple assumptions such as linear gradients and uniform wind speeds

hintereisferner austria mass balance reconstruction and numerical modelling of the historical length variations in this study an attempt is made to simulate the historical length variations of hintereisferner austria key elements in the model are 1 reconstruction of the local climate vent 2 multiple linear regression analysis between measured climate and mass balance variations 3 reconstruction of the mass balance with 1 and 2 4 a one dimensional numerical ice flow model forced by the mass balance history

surface mass balance of glaciers in the french alps distributed modeling and sensitivity to climate change a new physically based distributed surface mass balance model is presented for alpine glaciers based on the crocus prognostic snow model it resolves both the temporal 1 hour time step and spatial 200 m grid step variability of the energy and mass balance of glaciers mass balance reconstructions for the period 1981 2004 are produced using meteorological reconstruction from the safran meteorological model for glacier de saint sorlin and glacier d argentiere french alps both glaciers lost mass at an accelerated rate in the last 23 years the spatial distribution of precipitation within the model grid is adjusted using field mass balance measurements this is the only correction made to the safran meteorological input to the glacier model which also includes surface atmospheric temperature moisture wind and all components of downward radiation independent data from satellite imagery and geodetic measurements are used for model validation with this model glacier sensitivity to climate change can be separately evaluated with respect to a full range of meteorological parameters whereas simpler models such as degree day models only account for temperature and precipitation we provide results for both mass balance and equilibrium line altitude ela using a generic alpine glacier the sensitivity of the ela to air temperature alone is found to be 125 m c 1 or 160 m c 1 if concurrent stefan boltzmann longwave radiation change is taken into account

comparison of mass balances for vernagtferner oetzal alps as obtained from direct measurements and distributed modeling the direct comparison of modeled glacier mass balance distribution with field measure ments could be problematic as the methodology of determination and the processes considered at the point or catchment scale could differ strongly moreover direct measurements cover only small parts of a glacier and model performance is thus difficult to assess outside these regions remaining opportunities for model validation include comparison of snowlines as derived from remote sensing data and maps of the mass balance distribution as interpreted by observers with local knowledge this study compares such hand drawn maps of the vernagtferner oetzal alps mass balance with the modeled pattern as obtained from a distributed energy mass balance model of intermediate complexity the model is driven by measured daily values of temperature global radiation and precipitation from a nearby climate station and grids of mean daily potential global radiation and climatologic annual precipitation sums compared with the direct measurements the calculated mean mass balance and equilibrium line altitude agreed very well in both balance years although the spatial pattern of the mass balance distribution displayed larger deviations in regions influenced by snowdrift or local topographic undulations however compared with the remaining snow as visible on a satellite image from 1999 the modeled snowline pattern for a larger sample of glaciers is in very good agreement

catchment scale reconstruction of glacier mass balance using observations and global climate data case study of the hailuogou catchment south eastern tibetan plateau summary debris covered glaciers are common in the tibetan plateau where ablation zones are mantled in a supraglacial debris cover that influences glacier mass balance runoff and response to climate change by affecting the melt rate of the underlying ice the impact of debris cover has not yet been taken into account in regional or global scale assessments of glacier mass balances and freshwater resources by using physically based numerical models here a surface energy mass balance model that accounts for the significance of debris cover and its effect on the ice melt rate is applied to reconstruct the glacier mass balance of hailuogou catchment which is located in the south eastern tibetan plateau and contains three debris covered and four debris free monsoonal maritime glaciers according to our calculations the glaciers in hailuogou catchment show a mean annual balance of 0 42 m water equivalent w e per year for a total mass loss of 24 3 m w e over the period 1952 2009 a comparison of summer temperature and precipitation mass balance equilibrium line altitude ela relations indicates that the glaciers in the catchment are much more sensitive to temperature change than to precipitation change in the last 20 yrs increasing summer temperature is the main cause of rapid wasting of the glacier mass in the catchment meanwhile the presence of supraglacial debris markedly accelerates glacier mass loss resulting in the unstable termini of debris covered glaciers in hailuogou catchment this highlights the importance of debris cover for understanding glacier mass balance and hydrology in the tibetan plateau

2 m temperatures along melting mid latitude glaciers and implications for the sensitivity of the mass balance to variations in temperature in calculations of the variation in the 2 m temperature along glaciers the lapse rate is generally assumed to be constant this implies that the ratio of changes in the 2 m temperature above a glacier to changes in the temperature outside the thermal regime of that glacier climate sensitivity is equal to 1 however data collected during the ablation season on several mid latitude glaciers show that this sensitivity is smaller than 1 the lowest measured value 0 3 was obtained on the tongue of the pasterze a glacier in austria the measured temperature distribution along the pasterze cannot be described by a constant lapse rate either however there is almost a linear relationship between potential temperature and the distance along die glacier this paper introduces a simple analytical thermodynamic glacier wind model which can be applied to melting glaciers and which explains the observed climate sensitivities and temperature distributions much better than calculations based on a constant lapse rate this way of modelling the 2 m temperatures has implications for the sensitivity of the surface mass balance to atmospheric warming outside the thermal regime of the glacier the magnitude of this sensitivity is computed with a surface energy balance model applied to the pasterze when a constant lapse rate is used instead of the proposed glacier wind model to compute changes in the 2 m temperature along the glacier the negative change in mass balance due to 1 c warming is overestimated by 22

climate sensitivity of glaciers in southern norway application of an energy balance model to nigardsbreen hellstugubreen and alfotbreen three glaciers in southern norway with very different massbalance characteristics are studied with an energy balance model of the ice snow surface the model simulates the observed mass balance profiles in a satisfactory way and can thus be used with some confidence in a study of climate sensitivity calculated changes in equilibrium line altitude for a 1 k temperature increase are 110 108 and 135 in for nigardsbreen hellstugubreen and alfotbreen respectively the corresponding changes in mass balance averaged over the entire glacier area are 0 88 0 715 and 1 11 in year water equivalent runs with an ice flow model for nigardsbreen to which calculated mass balance profiles are imposed predict that the front will advance by 3 km for a 1 k cooling and will retreat by as much as 6 5 km for a 1 k warming the response to a 10 increase in precipitation would be a 2 km advance of the snout whereas a 4 km retreat is predicted for a 10 decrease this large sensitivity as compared to many other glaciers is to a large extent due to the geometry of nigardsbreen

rapid calculation of terrain parameters for radiation modeling from digital elevation data digital elevation models are widely used to calculate terrain parameters to determine incoming solar and longwave radiation for use in surface climate models interpretation of remote sensing data and parameters in hydrologic models because of the large number of points in an elevation grid fast algorithms are useful to save computation time a description is given of rapid methods for calculating slope and azimuth solar illumination angle horizons and view factors for radiation from sky and terrain calculation time is reduced by fast algorithms and lookup tables

statistical modelling of the surface mass balance variability of the morteratsch glacier switzerland strong control of early melting season meteorological conditions in this study we analyse a 15 year long time series of surface mass balance smb measurements performed between 2001 and 2016 in the ablation zone of the morteratsch glacier complex engadine switzerland for a better understanding of the smb variability and its causes multiple linear regressions analyses are performed with temperature and precipitation series from nearby meteorological stations up to 85 of the observed smb variance can be explained by the mean may june july temperature and the total precipitation from october to march a new method is presented where the contribution of each month s individual temperature and precipitation to the smb can be examined in a total sample of 2 24 16 8 million combinations more than 90 of the observed smb can be explained with particular combinations in which the may june july temperature is the most recurrent followed by october temperature the role of precipitation is less pronounced but autumn winter and spring precipitation are always more important than summer precipitation our results indicate that the length of the ice ablation season is of larger importance than its intensity to explain year to year variations the widely used june july august temperature index may not always be the best option to describe smb variability through statistical correlation

effects of digital elevation model spatial resolution on distributed calculations of solar radiation loading on a high arctic glacier high resolution airborne lidar data are used to produce digital elevation models dems of an arctic valley glacier midre lovenbreen svalbard at resolutions of 2 5 2000 m using three different interpolation schemes these data are used in a distributed model of solar radiation loading for glaciers when the mean of all lidar measurements within a dem cell is used to calculate cell height the differences between the finest 2 5 m and coarsest resolution 2000 m dems for the calculated annual whole glacier spatial means of total potential direct beam solar radiation potential duration of direct beam solar radiation and intensity of potential direct beam solar radiation are 20 56 and 23 of the 2 5 m dem values respectively a resolution change from 2 5 m to 200 m affects the whole glacier spatial mean summer net solar radiative flux by an average of 5 and the summer melt production from the glacier by an average of 3 compared with the 2 5 m dem values for the years 2001 03 these changes are largely driven by underestimation of shading by surrounding topography at coarser dem resolutions this dependency is reduced in the second and third interpolation schemes especially at resolutions finer than 50 m which use the maximum lidar height measurement in some or all dem cells these results suggest that resolutions of 50 m are the coarsest that should be adopted in high resolution glacier surface energy balance models for glaciers of similar size and in similar topographic situations to midre lovenbreen and that the impact of dem resolution on calculated solar radiation receipts can be reduced by an appropriate choice of dem interpolation scheme

evaluation of lateglacial temperatures in the southern alps of new zealand based on glacier modelling at irishman stream ben ohau range abstract climate proxy records from the middle to high latitude southern hemisphere indicate that a lateglacial 15 000 11 500 years ago climate reversal approximately coeval with the antarctic cold reversal acr interrupted a warming trend during deglaciation in new zealand some palaeoclimate proxy records indicate a cool episode during the acr ca 14 500 12 500 years ago while others do not express a significant change in climate recently published moraine maps and ages present an opportunity to improve the palaeoclimate interpretation through numerical modelling of glaciers we use a coupled energy balance and ice flow model to quantify palaeoclimate from past glacier extent constrained by mapped and dated moraines in the headwaters of irishman stream a high elevation catchment in the southern alps first a suite of steady state model runs is used to identify the temperature and precipitation forcing required to fit the modelled glacier to well dated lateglacial moraine crests second time dependent glacier simulations forced by a nearby proxy temperature record derived from chironomids are used to assess the fit with the glacial geomorphic record steady state experiments using an optimal parameter set demonstrate that the conditions under which the 13 000 year old moraine formed were 2 3 3 2 c colder than present with the range in temperature corresponding to a 20 variance in precipitation relative to the present day this reconstructed climate change relative to the present day corresponds to an equilibrium line altitude of ca 2000 40 m above sea level asl which is ca 400 m lower than present time dependent simulations of glacier length produce ice advance to within 100 m of the 13 000 year old terminal moraine indicating that the chironomid based temperature forcing and moraine record provide consistent information about past climate our results together with other climate proxy reconstructions from pollen records and marine sediment cores support the notion that temperatures during the acr in new zealand were 2 3 c cooler than today

a 1 year record of global radiation and albedo in the ablation zone of morteratschgletscher switzerland we analyse data on solar radiation measured with an automatic weather station on morteratschgletscher switzerland for the period 1 october 1995 30 september 1996 the station is in the lower ablation zone due to shading by surrounding mountains and atmospheric attenuation only 49 of the annual extraterrestrial irradiance mean 292 w m 2 reaches the glacier surface about 48 of this is absorbed at the surface mean 79 w m 2 annual albedo of 0 53 we present a simple albedo scheme for use in glacier mass balance models we fit the model to the 1 year dataset by optimizing five control parameters optimal values in brackets albedo of snow 0 75 albedo of firn 0 53 albedo of ice 0 34 e folding constant for effect of ageing on snow albedo 21 9 days and e folding constant for effect of snow depth on albedo 3 2 cm the input consists of daily albedo snow depth and dates of snowfall events the correlation coefficient between observed and simulated albedo is 0 931 the corresponding rms difference being 0 067

a new approach to resolving climate cryosphere relations downscaling climate dynamics to glacier scale mass and energy balance without statistical scale linking 1 we present a novel combination of methods to quantify the local mass response of mountain glaciers to large scale circulation previously such multiscale approaches bypassed the mesoscale processes of the mountain induced atmospheric flow by statistical transfer functions or subgrid parameterizations and included simplified glacier mass balance mb models here we show on the basis of kilimanjaro east africa as a test case that a limited area atmospheric model lam and a process resolving mb model can be linked without statistical corrections at their interface this is evident from robust energy and mb patterns at the glacier surface regardless of whether the mb model is forced by 1 in situ meteorological measurements or 2 uncorrected output from the high resolution lam grid over the glacier area the latter is achieved by multiple grid nesting in the land atmosphere ocean domain of the lam since this setup resolves the mesoscale process space we also show the potential to increase knowledge of how dynamical thermodynamic and microphysical phenomena of the mountain induced flow affect glacier mb all these results are encouraging for future research because they demonstrate that a dynamical system which operates on very different space time scales can be quantified in a fully physical way if dynamic meteorology and glaciology are exploited in a complementary sense this will enhance the process understanding of forward problems glacier response to climate forcing and backward problems climate signal extraction from past extents of mountain glaciers

sensitivity of rhonegletscher switzerland to climate change experiments with a one dimensional flowline model a one dimensional time dependent flowline model of rhonegletscher switzerland has been used to test the glacier s response to climatic warming mass balance variations over the last 100 years are obtained from observations of the equilibrium line altitude ela and a reconstruction of the ela based on a statistical correlation between temperature and ela for the period prior to ad 1882 for which no reliable climate data exist we chose equilibrium line altitudes that enabled us to simulate accurately the glacier length from ad 1602 the model simulates the historical glacier length almost perfectly and glacier geometry very well it underestimates glacier surface velocities by 1 18 following these reference experiments we investigated the response of rhonegletscher to a number of climate change scenarios for the period ad 1990 2100 for a constant climate equal to the 1961 90 mean the model predicts a 6 decrease in glacier volume by ad 2100 rhonegletscher will retreat by almost 1 km over the next 100 years at this scenario at a warming rate of 0 04 k a 1 only 4 of the glacier volume will be left by ad 2100

elevational changes in meteorological variables along a midlatitude glacier during summer during the summer of 1994 a glaciometeorological experiment was carried out on the pasterze a glacier in austria this paper reports on the data from six energy balance stations ranging in altitude from 2075 to 3225 m above sea level asl the wind regime was dominated by the glacier wind on the tongue directional constancies ranged between 0 94 and 0 97 mean 2 m wind speed and specifie humidity were almost constant along the glacier the variation in the 2 m temperature along the glacier cannot be described by the usually assumed constant decrease with elevation on the tongue the 2 m temperature even increased with elevation a much better description of the temperature distribution is given by a linear relation between the potential temperature and the distance along the flow line this can be understood from a simple thermodynamic analysis of the glacier wind layer it is further shown that changes in clear sky global radiation with elevation are due mainly to changes in local albedo and relief and hardly at all to changes in absolute optical path length and atmospheric water vapor and aerosol content on the tongue the laterally averaged ice albedo is almost constant with elevation the flux of incoming long wave radiation during clear sky conditions at u2 2310 m asl was 48 w m2 higher than the flux at u5 3225 m asl on average more than half of the difference was due to systematic differences in the shape of the temperature profile probably the inversion depth is larger at u2 the rest can be ascribed to higher 2 m temperatures and larger amounts of upper hemisphere slopes at u2 the distributions of the meteorological variables and the parameterizations described in this paper might be incorporated in surface energy balance models designed to simulate the surface mass balance

an energy balance model for debris covered glaciers including heat conduction through the debris layer extensive covers of supraglacial debris are often present in glacier ablation areas and it is essential to assess exactly how the debris affects glacier melt rates this paper presents a physically based energy balance model for the surface of a debris covered glacier the model is driven by meteorological variables and was developed using data collected at miage glacier italy during the ablation seasons of 2005 2006 and 2007 the debris surface temperature is numerically estimated by considering the balance of heat fluxes at the air debris interface and heat conduction through the debris is calculated in order to estimate melt rates at the debris ice interface the predicted hourly debris surface temperatures and debris internal temperatures provide a good fit to temperatures measured on rock covered miage glacier r 2 0 94 and the tephra covered glacier on villarrica volcano chile r 2 0 82 the model can also be used to reproduce observed changes in melt rates below debris layers of varying types and thicknesses an important consideration for the overall mass balance of debris covered glaciers

idealized models of fault behavior prior to dynamic rupture we present a theoretical model based on fracture mechanics concepts of the behavior of an earthquake source prior to the occurrence of the earthquake to understand under what conditions precursory slip may occur on a fault and to determine realistic initial conditions for the dynamic problem of faulting we consider a two dimensional fault consisting of in plane periodic shear cracks and unbroken zones in an infinite homogeneous elastic medium between the cracks of length 2a and the unbroken zones are intermediate zones in which the stress drop occurs when a critical shear displacement csd is reached panasyuk dugdale model at the crack tip the unbroken zones can also be interpreted in terms of friction as regions where the stress is lower than the static frictional stress so that our model can be interpreted from the point of view of fracture or friction let the period of this system be 2d as the load at infinity is slowly increased the intermediate zones grow quasi statically with a small amount of associated slip in the broken regions of the fault plane it is found that when the cracks are very small or very large or the csd is large the intermediate zones will coalesce before the csd is reached i e the entire fault is ruptured and additional preseismic slip occurs the initial conditions for dynamic rupture occurring at a later time on the fault is then a stress condition thus for the initial stages of the dynamic problem not studied here one need not solve a mixed boundary value problem but only the much simpler stress boundary problem the rupture velocity of the dynamic rupture on such a fault which is entirely broken may have any value up to the p wave velocity in principle the average slip on the fault at the point of coalescence increases with crack size from zero at zero crack length up to a d 0 67 and then decreases to zero at a d 1 the displacement distribution on the crack and the shear stress distribution around the crack as a function of increasing load and increasing crack size a d are studied it is shown that strain accumulation occurs not only at the ends of a griffith crack but also in broad regions off the crack in the normal direction corresponding to the unbroken zone there is a similar zone but of strain release off the crack this zone becomes more and more pronounced for large cracks and high loads for very long cracks the increase in shear stress off the crack becomes very very small but the decrease off the initially unbroken zone becomes very pronounced interaction between cracks is correctly accounted for in our method

integrated monitoring of mountain glaciers as key indicators of global climate change the european alps the internationally recommended multi level strategy for monitoring mountain glaciers is illustrated using the example of the european alps where especially dense information has been available through historical times this strategy combines in situ measurements mass balance length change with remote sensing inventories and numerical modelling it helps to bridge the gap between detailed local process oriented studies and global coverage since the 1980s mass balances have become increasingly negative with values close to 1 m w e a 1 during the first 5 years of the 21st century the hot dry summer of 2003 alone caused a record mean loss of 2 45 m w e roughly 50 above the previous record loss in 1998 more than three times the average between 1980 and 2000 and an order of magnitude more than characteristic long term averages since the end of the little ice age and other extended periods of glacier shrinkage during the past 2000 years it can be estimated that glaciers in the european alps lost about half their total volume roughly 0 5 a 1 between 1850 and around 1975 another 25 or 1 a 1 of the remaining amount between 1975 and 2000 and an additional 10 15 or 2 3 a 1 in the first 5 years of this century

a 5 year record of surface energy and mass balance from the ablation zone of storbreen norway a 5 year record of data from an automatic weather station aws operating in the ablation zone of storbreen norway has been used to calculate the local surface energy and mass balance the aws observations cover five mass balance years with an unusually strong mass deficit on storbreen the average energy flux q contributing to melt for the period 2001 06 is 113wm 2 of this the net shortwave radiation flux is the dominant contributor 92wm 2 followed by the sensible heat flux 20 wm 2 and the latent heat flux 9 w m 2 the net longwave radiation 6w m 2 and the subsurface heat flux 2 w m 2 contribute negatively to the budget net radiation thus produces 76 of the melt while the turbulent fluxes and the subsurface heat flux produce 24 of the total melt the seasonal mean incoming shortwave radiation is remarkably constant between the years whereas variations in temperature and reflected shortwave radiation albedo explain most of the interannual variation in melt the modelled ablation compares well with the measured ablation from stake readings the sensitivity of the energy balance model was examined by varying the surface roughness length of momentum and the sensitivity of the calculated melt by perturbations of temperature wind speed and relative humidity

effect of summer snowfall on glaciermass balance it has been postulated that heavy summer snowfalls have a large impact on the mass balance of mid latitude glaciers because they simultaneously add mass to the glacier and reduce the amount of absorbed solar radiation an automatic weather station aws on the snout of morteratschgletscher switzerland registered a large summer snowfall event on 10 11 july 2000 sonic rangers recorded about 20 cm of new snow on the snout and about 50 cm near the equilibrium line we have used data fromthe aws to study the impact on themelt process the data show that in the ablation zone of the glacier the snow has melted and the effect on the albedo has disappeared after about 5 days the suppression of themelt by the high albedo of the fresh snow is an important effect for the ablation zone we find a feedback factor of about four that is the total effect of the snowfall event on the annual specific balance is about four times the amount of mass added during the event we have also used a mass balance model with 25m spatial resolution to assess the impact of the snowfall on the net balance of the entire glacier we find the strongest effects just below the equilibrium line averaged over the glacier the amount of snow deposited was 224mmw e the calculated effect on the total mass balance of the glacier is 354mmw e

analysis of a 3 year meteorological record from the ablation zone of morteratschgletscher switzerland energy and mass balance since 1 october 1995 an automatic weather station has been operated on the tongue of morteratschgletscher switzerland the station stands freely on the ice and sinks with the melting glacier surface it is located at 2100 m a s l and measures air temperature wind speed and direction incoming and reflected solar radiation pressure and snow temperature a sonic ranger mounted to stakes drilled into the ice measures surface height from which melt rates and snow accumulation can be derived in this paper the data for the period 1 october 1995 to 30 september 1998 are used to evaluate the surface energy balance the turbulent energy fluxes are calculated with the bulk method the turbulent exchange coefficient c h is used as a control parameter with c h 0 00127 the calculated melt equals the observed melt which is 17 70 m w e over the 3 years when averaged over the time when melting occurs i e 35 of the time the mean surface heat flux equals 191 w m 2 net shortwave radiation contributes 177 w m 2 net longwave radiation 25 w m 2 the sensible heat flux 31 w m 2 and the latent heat flux 8 w m 2