Mass Balance Rate Research Articles

Reconstruction of Dead Sea lake level and mass balance back to 237 ka BP using halite fluid inclusions

The lake level of the Dead Sea, Southern Levant, has fluctuated with an amplitude of ∼250 m in response to the last glacial-interglacial cycle. This exceptional sensitivity to climate change, and the availability of long sedimentary archives, make the Dead Sea a benchmark for long quantitative paleohydrological reconstructions. However, discontinuities and chronological uncertainties in the marginal sedimentary record have hampered the reconstruction of Dead Sea lake levels beyond the Last Glacial (70–14 ka before present, BP). Here, we apply a two-pronged methodology. First, we measure the lake water density along ICDP deep core 5017-1-A using a new method, Brillouin spectroscopy on two-phase halite fluid inclusions; we combine it with the composition of pore water and the thickness of halite layers in the core to reconstruct lake level, volume, mass balance and subsidence rate. Second, we tune the chronology of lake levels from outcrops by matching it to the chronology of the deep core. The resulting lake level reconstruction, spanning 237–70 ka BP, is validated by the excellent agreement between outcrop- and mass balance-based methodologies. It shows a long-term recession of the lake, its level decreasing from one interglacial to the other, down to a Holocene record low. There are two reasons for this lake level fall. First, with an average rate of 2.65 ± 0.15 m/ka, subsidence has outpaced sedimentation at least over the last ∼130 ka. Second, by reducing the solute inventory of the lake, massive halite precipitation events such as that of 131–116 ka BP have durably increased surface water activity and evaporation, and thus lowered the lake level, up to today. Conversely, our analysis suggests that, during 191–11 ka BP, the dissolution of Mount Sedom salt diapir and freshwater inflows provided to the lake about three times the mass of solute NaCl contained in the modern Dead Sea (in 1985). This massive solute influx, occurring mainly during glacial highstands, strongly contributed to lowering surface water activity and evaporation and, therefore, to increasing the lake volume. Our results suggest that Dead Sea lake levels are more accurately interpreted in terms of climatic change if surface water activity is taken into account.

Century-long multi-source analyses highlight decreasing vulnerability for a small, debris-covered and avalanche-fed glacier in the eastern Italian Alps

Small, debris-covered and avalanche-fed glaciers are widespread in high-relief areas of the world. However, their climatic response is poorly known because they cannot be investigated with ‘traditional’ techniques, like the glaciological mass-balance method, and long-term observations series are very rare. This work documents changes in elevation, mass balance rate and surface cover in the last century (from 1920 to 2020) for the small, debris-covered and avalanche-fed Montasio Glacier, where recent investigations show unusual response to climatic changes, but it is unclear whether this response is a short- or a long-term characteristic. Glacier response is analysed primarily through Digital Elevation Models reconstructed from different types of data sources (maps, terrestrial and aerial images, point clouds). Glacier changes are analysed jointly with trends in the most relevant climatic variables. The glacier experienced phases of rapid mass loss between 1920 and 1948 (−0.49 m w.e. y-1) and between 1982 and 2006 (−0.36 m w.e. y-1). Smaller imbalance occurred between 1948 and 1982 (−0.14 m w.e. y-1) and, remarkably, between 2006 and 2020 (−0.03 m w.e. y-1). Whereas the 1948–1982 was a favourable time-window for most glaciers in the Alps, the last fifteen years were characterized by rapid warming and show a clear divergence between the behaviour of the Montasio Glacier and of the rest of Alpine glaciers. A century-long increase in debris cover, now 2–3 m thick in the lower half of the glacier, explains largely this divergence. Snow-rich winters in recent years also played a role, because the glacier reacts sensitively to changes in solid precipitation. Even in the case of possible decreased snowfalls and increased melt associated with warming temperatures during the next decades, the glacier is not expected to vanish soon, because it will likely survive under a thick layer of debris and shadowed by the north walls of the Mount Jôf di Montasio. On the other hand, the results of this study, paired with the current distribution of permafrost in the study area, suggest that the Montasio Glacier will unlikely evolve into a rock glacier or a glacial-permafrost composite landform.

Evaluation of a helicoidal flux photoreactor applied in the dicloxacillin degradation by UV-C/H2O2 and UV-A/photo-Fenton including the effect of photon absorption

The efficiency of a helical flow photoreactor in the oxidation of the antibiotic Dicloxacillin as a function of the recirculation flow, the local volumetric rate of photon absorption (LVRPA) and photonic efficiency using oxidation processes based on UV-C/H2O2 and UV-A/photo-Fenton were evaluated in this work. Mathematical modeling of the degradation process and experiments in lab-scale helicoidal reactor were done. Mathematical evaluation was supported in function of photon flux, mass balance and reaction rate law. The LVRPA was calculated by modified Beer-Lambert Equation. The effect of the concentration of hydrogen peroxide and iron (II) on the efficiency of the oxidation of the antibiotic Dicloxacillin was evaluated by means of the photo-Fenton. In 45 min, 100% degradation of dicloxacillin was achieved using 1.5 mM H2O2 and 7.32 μM ferrous ion in the photo-Fenton experiments with the helical flow photoreactor. The optical thickness of the reaction and distribution of energy absorption confirmed the kinetic and photonic efficiency performance. The prediction of the model presented a global error less to 2.4% between experimental and simulated data.

Nonlinear sensitivity of glacier mass balance to future climate change unveiled by deep learning

Glaciers and ice caps are experiencing strong mass losses worldwide, challenging water availability, hydropower generation, and ecosystems. Here, we perform the first-ever glacier evolution projections based on deep learning by modelling the 21st century glacier evolution in the French Alps. By the end of the century, we predict a glacier volume loss between 75 and 88%. Deep learning captures a nonlinear response of glaciers to air temperature and precipitation, improving the representation of extreme mass balance rates compared to linear statistical and temperature-index models. Our results confirm an over-sensitivity of temperature-index models, often used by large-scale studies, to future warming. We argue that such models can be suitable for steep mountain glaciers. However, glacier projections under low-emission scenarios and the behaviour of flatter glaciers and ice caps are likely to be biased by mass balance models with linear sensitivities, introducing long-term biases in sea-level rise and water resources projections.

Long-term mass-balance monitoring and evolution of ice in caves through structure from motion–multi-view stereo and ground-penetrating radar techniques

This study investigates the application of a terrestrial structure from motionmulti-view stereo (SfM-MVS) approach combined with ground-penetrating radar (GPR) surveys for monitoring the surface topographic change of two permanent ice deposits in caves located in the Julian Alps (south-eastern European Alps). This method allows accurate calculation of both seasonal and annual mass balance, estimating the amount of ice inside caves. The ground-based SfM approach represents a low-cost workflow with very limited logistical problems of transportation and human resources and a fast acquisition time, all key factors in such extreme environments. Under optimal conditions, SfM-MVS allows sub-centimetric resolution results, comparable to more expensive and logistically demanding surveys such as terrestrial laser scanning (TLS). Fourteen SfM acquisitions were made between the 2017–2020 ablation seasons (i.e. July–October) while 2 GPR surveys were acquired in 2012. The obtained dense point clouds and digital terrain models (DTMs) made possible a reliable calculation of topographic changes and mass balance rates during the analysed period. The integration of SfM-MVS products with GPR surveys provided comprehensive imaging of the ice thickness and the total ice volume present in each of the caves, proving to be a reliable, low cost and multipurpose methodology ideal for long-term monitoring.

Debris Emergence Elevations and Glacier Change

Debris-covered glaciers represent potentially significant stores of freshwater in river basins throughout High Mountain Asia (HMA). Direct glacier mass balance measurements are extremely difficult to maintain on debris-covered glaciers, and optical remote sensing techniques to evaluate annual equilibrium line altitudes (ELAs) do not work in regions with summer-accumulation type glaciers. Surface elevation and glacier velocity change have been calculated previously for debris-covered glaciers across the region, but the response of debris cover itself to climate change remains an open question. In this research we propose a new metric, i.e. the debris emergence elevation (ZDE), which can be calculated from a combination of optical and thermal imagery and digital elevation data. We quantify ZDE for 975 debris-covered glaciers in HMA over three compositing periods (1985–1999, 2000–2010, and 2013–2017) and compare ZDE against median glacier elevations, modelled ELAs, and observed rates of both mass change and glacier velocity change. Calculated values of ZDE for individual glaciers are broadly similar to both median glacier elevations and modelled ELAs, but slightly lower than both. Across the HMA region, the average value of ZDE increased by 70 +/− 126 m over the study period, or 2.7 +/− 4.1 m/yr. Increases in ZDE correspond with negative mass balance rates and decreases in glacier velocity, while glaciers and regions that show mass gains and increases in glacier velocity experienced decreases in ZDE. Regional patterns of ZDE, glacier mass balance, and glacier velocities are strongly correlated, which indicates continued overall increases in ZDEE and expansion of debris-covered areas as glaciers continue to lose mass. Our results suggest that ZDE is a useful metric to examine regional debris-covered glacier changes over decadal time scales, and could potentially be used to reconstruct relative mass and ELA changes on debris-covered glaciers using historical imagery or reconstructed debris cover extents.

Mass balances of Yala and Rikha Samba glaciers, Nepal, from 2000 to 2017

Abstract. The glacier mass balance is an important variable to describe the climate system and is used for various applications like water resource management or runoff modelling. The direct or glaciological method and the geodetic method are the standard methods to quantify glacier mass changes, and both methods are an integral part of international glacier monitoring strategies. In 2011, we established two glacier mass-balance programmes on Yala and Rikha Samba glaciers in the Nepal Himalaya. Here we present the methods and data of the directly measured annual mass balances for the first six mass-balance years for both glaciers from 2011/2012 to 2016/2017. For Yala Glacier we additionally present the directly measured seasonal mass balance from 2011 to 2017, as well as the mass balance from 2000 to 2012 obtained with the geodetic method. In addition, we analysed glacier length changes for both glaciers. The directly measured average annual mass-balance rates of Yala and Rikha Samba glaciers are −0.80 ± 0.28 and −0.39 ± 0.32 m w.e. a−1, respectively, from 2011 to 2017. The geodetically measured annual mass-balance rate of Yala Glacier based on digital elevation models from 2000 and 2012 is −0.74 ± 0.53 m w.e. The cumulative mass loss for the period 2011 to 2017 for Yala and Rikha Samba glaciers is −4.80 ± 0.69 and −2.34 ± 0.79 m w.e., respectively. The mass loss on Yala Glacier from 2000 to 2012 is −8.92 ± 6.33 m w.e. The winter balance of Yala Glacier is positive, and the summer balance is negative in every investigated year. The summer balance determines the annual balance. Compared to regional mean geodetic mass-balance rates in the Nepalese Himalaya, the mean mass-balance rate of Rikha Samba Glacier is in a similar range, and the mean mass-balance rate of Yala Glacier is more negative because of the small and low-lying accumulation area. During the study period, a change of Yala Glacier's surface topography has been observed with glacier thinning and downwasting. The retreat rates of Rikha Samba Glacier are higher than for Yala Glacier. From 1989 to 2013, Rikha Samba Glacier retreated 431 m (−18.0 m a−1), and from 1974 to 2016 Yala Glacier retreated 346 m (−8.2 m a−1). The data of the annual and seasonal mass balances, point mass balance, geodetic mass balance, and length changes are accessible from the World Glacier Monitoring Service (WGMS, 2021), https://doi.org/10.5904/wgms-fog-2021-05.

SAR-derived flow velocity and its link to glacier surface elevation change and mass balance

Modern remote sensing techniques, such as Synthetic Aperture Radar (SAR), can measure the direction and intensity of glacier flow. Yet the question remains as to what these measurements reveal about glaciers' adjustment to the warming climate. Here, we present a technique that addresses this question by linking the SAR-derived velocity measurements with the glacier elevation change and the specific mass balance (i.e. mass balance per unit area). The technique computes the speckle offset tracking results from the north, east and vertical flow displacement time series, with the vertical component further split into a Surface Parallel Flow (SPF) advection component due to the motion along a glacier surface slope and a non-Surface Parallel Flow (nSPF). The latter links the glacier surface elevation change with the specific mass balance and strain rates. We apply this technique to ascending and descending Sentinel-1 data to derive the four-dimensional flow displacement time series for glaciers in southeast Alaska during 2016–2019. Time series extracted for a few characteristic regions demonstrate remarkable temporal variability in flow velocities. The seasonal signal observed in the nSPF component is modeled using the Positive Degree Day model. This method can be used for computing either mass balance or glacier surface elevation change if one of these two parameters is known from external observations.

Evolution of debris cover on glaciers of the Eastern Alps, Austria, between 1996 and 2015

AbstractDebris cover on glaciers is an important component of glacial systems as it influences climate–glacier dynamics and thus the lifespan of glaciers. Increasing air temperatures, permafrost thaw and rock faces freshly exposed by glacier downwasting in accumulation zones result in increased rockfall activity and debris input. In the ablation zone, negative mass balances result in an enhanced melt‐out of englacial debris. Glacier debris cover thus represents a clear signal of climate warming in mountain areas. To assess the temporal development of debris on glaciers of the Eastern Alps, Austria, we mapped debris cover on 255 glaciers using Landsat data at three time steps. We applied a ratio‐based threshold classification technique and analysed glacier catchment characteristics to understand debris sources better. Across the Austrian Alps, debris cover increased by more than 10% between 1996 and 2015 while glaciers retreated in response to climate warming. Debris cover distribution shows significant regional variability, with some mountain ranges being characterised by mean debris cover on glaciers of up to 75%. We also observed a general rise of the mean elevation of debris cover on glaciers in Austria. The debris cover distribution and dynamics are highly variable due to topographic, lithological and structural settings that determine the amount of debris delivered to and stored in the glacier system. Despite strong variation in debris cover, all glaciers investigated melted at increasing rates. We conclude that the retarding effects of debris cover on the mass balance and melt rate of Austrian glaciers is strongly subdued compared with other mountain areas. The study indicates that, if this trend continues, many glaciers in Austria may become fully debris covered. However, since debris cover seems to have little impact on melt rates, this would not lead to prolonged existence of debris‐covered ice compared with clean ice glaciers.

Inequality-constrained free-surface evolution in a full Stokes ice flow model (<i>evolve_glacier v1.1</i>)

Abstract. Like any gravitationally driven flow that is not constrained at the upper surface, glaciers and ice sheets feature a free surface, which becomes a free-boundary problem within simulations. A kinematic boundary condition is often used to describe the evolution of this free surface. However, in the case of glaciers and ice sheets, the naturally occurring constraint that the ice surface elevation (S) cannot fall below the bed topography (B) (S-B≥0), in combination with a non-zero mass balance rate complicates the matter substantially. We present an open-source numerical simulation framework to simulate the free-surface evolution of glaciers that directly incorporates this natural constraint. It is based on the finite-element software package FEniCS solving the Stokes equations for ice flow and a suitable transport equation, i.e. “kinematic boundary condition”, for the free-surface evolution. The evolution of the free surface is treated as a variational inequality, constrained by the bedrock underlying the glacier or the topography of the surrounding ground. This problem is solved using a “reduced space” method, where a Newton line search is performed on a subset of the problem (Benson and Munson, 2006). Therefore, the “constrained” non-linear problem-solving capabilities of PETSc's (Portable, Extensible Toolkit for Scientific Computation, Balay et al., 2019) SNES (Scalable Non-linear Equations Solver) interface are used. As the constraint is considered in the solving process, this approach does not require any ad hoc post-processing steps to enforce non-negativity of ice thickness and corresponding mass conservation. The simulation framework provides the possibility to divide the computational domain into different subdomains so that individual forms of the relevant equations can be solved for different subdomains all at once. In the presented setup, this is used to distinguish between glacierised and ice-free regions. The option to chose different time discretisations, spatial stabilisation schemes and adaptive mesh refinement make it a versatile tool for glaciological applications. We present a set of benchmark tests that highlight that the simulation framework is able to reproduce the free-surface evolution of complex geometries under different conditions for which it is mass-conserving and numerically stable. Real-world glacier examples demonstrate high-resolution change in glacier geometry due to fully resolved 3D velocities and spatially variable mass balance rate, whereby realistic glacier recession and advance states can be simulated. Additionally, we provide a thorough analysis of different spatial stabilisation techniques as well as time discretisation methods. We discuss their applicability and suitability for different glaciological applications.

Artificial intelligence in the modeling of chemical reactions kinetics

Abstract The work presents a selection of recent papers in the field of modeling chemical kinetics by the use of artificial intelligence methods. Due to the fact that kinetics of the chemical reaction is the key element of industrial reactor design and analysis, the work is focused on the presentation of the quality of modeling, the assembly of neural network systems and methods of training required to achieve acceptable results. The work covers a wide range of classes of chemical processes and modeling approaches presented by several authors. Because of the fact that the methods of neural networks training require huge amounts of data, many approaches proposed are intrinsically based on classical kinetics modeling like Monte Carlo methods, quantum ab initio models or classical Arrhenius-like approaches using mass balance rate equations. The work does not fully exhaust the area of artificial intelligence because of its very broad scope and very fast evolution, which has been greatly accelerated recently. However, it is a contribution to describing the current state of science in this field.

Ice Mass Loss in the Central Andes of Argentina Between 2000 and 2018 Derived From a New Glacier Inventory and Satellite Stereo-Imagery

Based on the recently released National Glacier Inventory (NGI), we analyzed the characteristics and the mass balance rates of ice masses in the Argentinean Central Andes (ca. 30°–37° S). The NGI provides unprecedented information on area, number and distribution of different ice masses, including debris-covered glaciers and rock glaciers. In the Central Andes, a number of 8,076 ice masses were identified covering a total area of 1767 km2. For the period 2000–2018, a general lowering of the ice surface was observed with a region-wide mass balance rate of −0.18 ± 0.19 m w.e. yr−1. Clear differences depending on the debris coverage of the different ice masses were identified, with mass balance rates ranging from −0.36 ± 0.19 m w.e. yr−1 for partly debris-covered glaciers to −0.02 ± 0.19 m w.e. yr−1 for rock glaciers. Considering different sub-periods, the region-wide mass balance rate was slightly positive (+0.12 ± 0.23 m w. e. yr−1) from 2000 to 2009 and negative (−0.21 ± 0.30 m w.e. yr−1) from 2009 to 2018. A comparison with the Randolph Glacier Inventory (RGI version 6.0) indicates that the NGI provides more detailed information regarding different type of ice masses whereas region-wide mass balance rates show limited sensitivity to the choice of the inventory. The inclusion of rock glaciers and “debris-covered ice with rock glacier” in the NGI causes mass balance rates to be slightly less negative than when using the RGI. Since the Central Andes are experiencing an unprecedented decade-long drought, our study provides crucial information to estimate current and future hydrological contribution of the different type of ice masses to river discharge in the arid subtropical Andes.

Glacier mass and area changes on the Kenai Peninsula, Alaska, 1986–2016

AbstractGlacier mass loss in Alaska has implications for global sea level rise, fresh water input into the Gulf of Alaska and terrestrial fresh water resources. We map all glaciers (>4000 km2) on the Kenai Peninsula, south central Alaska, for the years 1986, 1995, 2005 and 2016, using satellite images. Changes in surface elevation and volume are determined by differencing a digital elevation model (DEM) derived from Advanced Spaceborne Thermal Emission and Reflection Radiometer stereo images in 2005 from the Interferometric Synthetic Aperture Radar DEM of 2014. The glacier area shrunk by 543 ± 123 km2(12 ± 3%) between 1986 and 2016. The region-wide mass-balance rate between 2005 and 2014 was −0.94 ± 0.12 m w.e. a−1(−3.84 ± 0.50 Gt a−1), which is almost twice as negative than found for earlier periods in previous studies indicating an acceleration in glacier mass loss in this region. Area-averaged mass changes were most negative for lake-terminating glaciers (−1.37 ± 0.13 m w.e. a−1), followed by land-terminating glaciers (−1.02 ± 0.13 m w.e. a−1) and tidewater glaciers (−0.45 ± 0.14 m w.e. a−1). Unambiguous attribution of the observed acceleration in mass loss over the last decades is hampered by the scarcity of observational data, especially at high elevation, and by large interannual variability.

Detailed quantification of glacier elevation and mass changes in South Georgia

Most glaciers in South America and on the Antarctic Peninsula are retreating and thinning. They are considered strong contributors to global sea level rise. However, there is a lack of glacier mass balance studies in other areas of the Southern Hemisphere, such as the surrounding Antarctic Islands. Here, we present a detailed quantification of the 21st century glacier elevation and mass changes for the entire South Georgia Island using bi-static synthetic aperture radar interferometry between 2000 and 2013. The results suggest a significant mass loss since the beginning of the present century. We calculate an average glacier mass balance of −1.04 ± 0.09 m w.e.a−1 and a mass loss rate of 2.28 ± 0.19 Gt a−1 (2000–2013), contributing 0.006 ± 0.001 mm a−1 to sea-level rise. Additionally, we calculate a subaqueous mass loss of 0.77 ± 0.04 Gt a−1 (2003–2016), with an area change at the marine and lake-terminating glacier fronts of −6.58 ± 0.33 km2 a−1, corresponding to ∼4% of the total glacier area. Overall, we observe negative mass balance rates in South Georgia, with the highest thinning and retreat rates at the large outlet glaciers located at the north-east coast. Although the spaceborne remote sensing dataset analysed in this research is a key contribution to better understanding of the glacier changes in South Georgia, more detailed field measurements, glacier dynamics studies or further long-term analysis with high-resolution regional climate models are required to precisely identify the forcing factors.

An Improved Analytical Solution for the Temperature Profile of Ice Sheets

The one‐dimensional steady state analytical solution of the energy conservation equation obtained by Robin (1955, https://doi.org/10.3189/002214355793702028) is frequently used in glaciology. This solution assumes a linear change in surface velocity from a minimum value equal to minus the mass balance at the surface to zero at the bed. Here we show that this assumption of a linear velocity profile leads to large errors in the calculated temperature profile and especially in basal temperature. By prescribing a nonlinear power function of elevation above the bed for the vertical velocity profile arising from use of the Shallow Ice Approximation, we derive a new analytical solution for temperature. We show that the solution produces temperature profiles identical to numerical temperature solutions with the Shallow Ice Approximation vertical velocity near ice divides. We quantify the importance of strain heating and demonstrate that integrating the strain heating and adding it to the geothermal heat flux at the bed is a reasonable approximation for the interior regions. Our analytical solution does not include horizontal advection components, so we compare our solution with numerical solutions of a two‐dimensional advection‐diffusion model and assess the applicability and errors of the analytical solution away from the ice divide. We show that several parameters and assumptions impact the spatial extent of applicability of the new solution including surface mass balance rate and surface temperature lapse rate. We delineate regions of Greenland and Antarctica within which the analytical solution at any depth is likely within 2 K of the actual temperatures with horizontal advection.

Geodetic Mass Balances and Area Changes of Echaurren Norte Glacier (Central Andes, Chile) between 1955 and 2015

The Echaurren Norte Glacier is a reference glacier for the World Glacier Monitoring Service (WGMS) network and has the longest time series of glacier mass balance data in the Southern Hemisphere. The data has been obtained by the direct glaciological method since 1975. In this study, we calculated glacier area changes using satellite images and historical aerial photographs, as well as geodetic mass balances for different periods between 1955 and 2015 for the Echaurren Norte Glacier in the Central Andes of Chile. Over this period, this glacier lost 65% of its original area and disaggregated into two ice bodies in the late 1990s. The geodetic mass balances were calculated by differencing digital elevation models derived from several sources. The results indicated a mean cumulative glacier wide mass loss of −40.64 ± 5.19 m w.e. (−0.68 ± 0.09 m w.e. a−1). Within this overall downwasting trend, a positive mass balance of 0.54 ± 0.40 m w.e. a−1 was detected for the period 2000–2009. These estimates agree with the results obtained with the glaciological method during the same time span. Highly negative mass change rates were found from 2010 onwards, with −1.20 ± 0.09 m w.e. a−1 during an unprecedented drought in Central Andes of Chile. The observed area and the elevation changes indicate that the Echaurren Norte Glacier may disappear in the coming years if negative mass balance rates prevail.

SPATIOTEMPORAL CHANGES IN VELOCITY OF MELLOR GLACIER, EAST ANTARCTICA USING LANDSAT-8 DATA

Abstract. Glaciers all over the world are experiencing changes at varying stages due to changing climatic conditions. Minuscule changes in the glaciers in Antarctica can thus have major implications. The velocity of glaciers is important in several aspects of glaciology. A glacier’s movement is caused by different factors such as gravity, internal deformation present in the ice, pressure caused by accumulation of snow, basal sliding etc. The velocity of a glacier is an important factor governing mass balance and the stability of the glacier. A glacier which moves fast generally brings more ice towards the terminus than a slow moving glacier. Thus, the glacier velocity can determine its load carrying capacity and gives indication on the ‘health’ of the glacier. Measurement of the ice flow velocity can help model glacier dynamics and thus provide increasing insights on different glacier subtleties. However, field measurements of velocity are limited in spatial and temporal domains because these operations are manual, tedious and logistically expensive. Remote sensing is a tool to monitor and generate such data without the need for physical expeditions. This study uses optical satellite imagery to understand the mechanisms involved in the movement of a glacier. Optical image correlation method (COSI-Corr module) is chosen here as the promising method to derive displacement of a moving glacier. The principle involved in this technique is that two images acquired at different times are correlated to find the shift in the position of moving ice, which is then treated as displacement in the time interval. Employing this technique we estimated the velocity of Mellor glacier (73°30′S, 66°30′E), a tributary glacier of the Amery Ice Shelf, Antarctica, over a span of four years from 2014 to 2017. Correlation is performed using Landsat-8 panchromatic images of 15 m resolution. Optical images from Landsat 8 often have noise due to atmospheric conditions such as cloud cover, so we used only those images cloud with cloud cover less than 10%. The glacier is covered in 128 path frame and 112 by Landsat-8. The correlation frequency was calculated using the correlator engine. Window size taken here is 256 and step sizes is 64 for both x and y dimensions. Once the correlation is calculated for an image pair for a specific time-period, we obtain three different outputs. Two of them indicated displacement (one in x direction and another in y direction) and the remaining output provided signal to noise ratio. The band math tool using displacement outputs in ENVI software performed velocity calculations. This gives us a raster image showing velocity at each point or pixel. Some errors such as noise persist and their correction is performed in ArcGIS software. In order to get pure signals, we removed all the signals with a signal to noise ratio less than 0.9 and this was carried out using raster calculator tool. All the resultant velocity rasters were interpolated and bias was calculated between seasons of two consecutive years. Two maps were generated for each year, one for early summer i.e. from January to April and one from September to December using the resultant velocity raster. The mean values of velocities found for Mellor glacier from Jan-April 2014, 2015, 2016 and 2017 were 374.06 ma−1, 413.59 ma−1, 278.62 ma−1 and 406.66 ma−1, respectively. Velocities for September-December 2014, 2015, 2016 and 2017 were found to be 334.63 ma−1, 334.43 ma−1, 367.37 ma−1 and 381.31 ma−1, respectively. The biases are computed for all the seasons of four years and root mean square (RMSE) values are estimated. These RMSE values signify the season-wise variations in the velocities. RMSE values for season of Jan–April 2014–15, 2015–16 and 2016–17 were 75.92 ma−1, 147.82 ma−1, and 133.33 ma−1, respectively. Similarly, RMSE values for season of September-December 2014–15, 2015–16 and 2016–17 are 35.7 ma−1, 51.29 ma−1 and 35.84 ma−1 respectively. The results showed variations in velocities for different seasons. We plan to integrate this data with the discharge rates, to estimate mass balance and melting rates of the glacier to decipher mechanisms at work for the Mellor glacier.

Elevation change of Fedchenko Glacier, Pamir Mountains, from GNSS field measurements and TanDEM-X elevation models, with a focus on the upper glacier

ABSTRACTFedchenko Glacier experienced a large thickness loss since the first scientific investigations in 1928. As the largest glacier in the Pamir Mountains, this glacier plays an important role for the regional glacier mass budget. We use a series of Global Navigation Satellite Systems observations from 2009 to 2016 and TanDEM-X elevation models from 2011 to 2016 to investigate recent elevation changes. Accounting for radar wave penetration minimizes biases in elevation that can otherwise reach up to 6 m in dry snow on Fedchenko Glacier, with mean values of 3–4 m in the high accumulation regions. The seasonal elevation changes reach up to ±5 m. The glacier surface elevation decreased along its entire length over multi-year periods. Thinning rates increased between 2000 and 2016 by a factor of 1.8 compared with 1928–2000, resulting in peak values of 1.5 m a−1. Even the highest accumulation basins above 5000 m elevation have been affected by glacier thinning with change rates between −0.2 and −0.4 m a−1 from 2009 to 2016. The estimated glacier-wide mass-balance rates are −0.27 ± 0.05 m w.e. a−1 for 2000 to 2011 and −0.51 ± 0.04 m w.e. a−1 between 2011 and 2016.

Particle transport in a porous medium with initial deposit

Modelling of the suspended particles transport in a porous medium is used in the analysis of methods for strengthening foundations. To strengthen the porous soil, a low concentration cement-based grout is pumped into it under pressure. The suspension is filtered in a porous medium and fills the cavity of the soil. Grains of the grout are distributed along the network structure of the porous medium and strengthen the soil. The transfer of particles by a flow of a carrier fluid is accompanied by an uneven formation of a deposit on the porous medium frame.The purpose of the paper is to determine the mobile two-phase boundary between water and the particles during the injection of a suspension into a porous medium and to obtain an analytical solution of the nonlinear filtration problem for a general case of variable porosity and permeability.The mathematical model of one-dimensional deep bed filtration with size-exclusion particles retention includes the equations of mass balance and kinetic rate of a deposit and unsteady boundary conditions with unknown dimensionless concentrations of suspended and retained particles. Methods of non-linear asymptotic analysis are used to obtain the analytical solution and to construct an asymptotics near the porous medium inlet. The asymptotics is determined on the basis of a local exact solution of the problem.It is shown that the mobile two-phase boundary moves with variable speed. At the boundary of two phases, the concentration of suspended particles is discontinuous, and the concentration of retained particles is continuous and loses its smoothness. The exact explicit formula for the two-phase boundary and its asymptotics in a form convenient for calculations are obtained. An exact solution is obtained on the boundary of the porous medium and the asymptotics of the filtration problem is constructed near the porous medium inlet. Numerical calculation of the asymptotic solution is performed; graphs of the dependence of concentrations on time and coordinate are presented.In contrast to the numerical solution, analytical methods make it possible to determine the dependence of the solution of the filtration problem on the controlled external parameters. This allows the construction engineers to choose the best size of injected grout grains and the properties of the carrier fluid, optimize the filtration process and form a grouted porous soil of the required strength and density.

The challenge of monitoring glaciers with extreme altitudinal range: mass-balance reconstruction for Kahiltna Glacier, Alaska

ABSTRACTGlaciers spanning large altitudinal ranges often experience different climatic regimes with elevation, creating challenges in acquiring mass-balance and climate observations that represent the entire glacier. We use mixed methods to reconstruct the 1991–2014 mass balance of the Kahiltna Glacier in Alaska, a large (503 km2) glacier with one of the greatest elevation ranges globally (264–6108 m a.s.l.). We calibrate an enhanced temperature index model to glacier-wide mass balances from repeat laser altimetry and point observations, finding a mean net mass-balance rate of −0.74 mw.e. a−1( ± σ = 0.04, std dev. of the best-performing model simulations). Results are validated against mass changes from NASA's Gravity Recovery and Climate Experiment (GRACE) satellites, a novel approach at the individual glacier scale. Correlation is strong between the detrended model- and GRACE-derived mass change time series (R2 = 0.58 and p ≪ 0.001), and between summer (R2 = 0.69 and p = 0.003) and annual (R2 = 0.63 and p = 0.006) balances, lending greater confidence to our modeling results. We find poor correlation, however, between modeled glacier-wide balances and recent single-stake monitoring. Finally, we make recommendations for monitoring glaciers with extreme altitudinal ranges, including characterizing precipitation via snow radar profiling.