Estimating the ice thickness of mountain glaciers with a shape optimization algorithm using surface topography and mass-balance

We present a shape optimization algorithm to estimate the ice thickness distribution within a two-dimensional, non-sliding mountain glacier, given a transient surface geometry and a mass-balance distribution. The approach is based on the minimization of the surface topography misfit at the end of the glacier's evolution in the shallow ice approximation of ice flow. Neither filtering of the surface topography where its gradient vanishes nor interpolation of the basal shear stress is involved. Novelty of the presented shape optimization algorithm is the use of surface topography and mass-balance only within a time-dependent Lagrangian approach for moving-boundary glaciers. On real-world inspired geometries, it is shown to produce estimations of even better quality in smaller time than the recently proposed steady and transient inverse methods. A sensitivity analysis completes the study and evinces the method's higher susceptibility to perturbations in the surface topography than in surface mass-balance or rate facto

Bedrock topography reconstruction of glaciers from surface topography and mass-balance data

Three methods based on the three-dimensional shallow ice approximation of glacier flow are devised that infer a glacier's subglacial topography from the observation of its time-evolving surface and mass balance. The quasi-stationary inverse method relying on the apparent surface mass-balance description of the glacier's evolution is first exposed. Second, the transient inverse method that iteratively updates the bedrock topography with the surface topography discrepancy is formulated. Third, a shape optimization algorithm is presented. The aim of the paper is to collect these methods, analyze their differences, and identify what brings the sophistication of shape optimization for reconstructing subglacial topographies. The three methods are compared to the ice thickness estimation method (ITEM) on direct measurements on Gries glacier, Swiss Alps. The paper concludes with a detailed discussion on the sensitivity of the shape optimization method to the model parameters

Estimating the Ice Thickness of Mountain Glaciers from Surface Topography and Mass-Balance Data

The question addressed is the determination of a glacier’s subglacial topography, given surface topography and mass-balance data. The input data can be obtained relatively easily for a large number of glaciers. Several methods essentially based on the shallow ice approximation are proposed, some of which are extended to Stokes ice flows. Two gradient-free, iterative methods are first introduced, namely the quasi-stationary inverse method, that relies on the apparent surface mass-balance description of glacier dynamics, and the transient inverse method, consisting in the iterative update of the bedrock topography proportionally to the surface topography misfit at the end of the glacier’s considered evolution. Then, an optimal control algorithm is suggested that calculates the bedrock topography and some model parameters from surface observations through the minimization of a regularized misfit functional by means of a Lagrangian method. Numerical validations, along with sensitivity analyses and applications to real-world data are presented for each method

Constraints on the Dynamic Contribution to 21st-Century Sea Level Rise from Greenland Outlet Glaciers

Numerical models currently in use for projections of future ice sheet mass balance lack a mechanistic description of iceberg calving, introducing uncertainty in the future glaciological contribution to global sea level. Constraining dynamic mass loss associated with particular future scenarios can help us parse that uncertainty. We have modified the plastic approximation of Nye (1952) to apply to ocean- terminating glaciers (published derivation: Ultee & Bassis, 2016) and generate physically consistent constraints on dynamic mass loss. Our approach accounts for the interaction of multiple glacier tributary branches (published methods: Ul- tee & Bassis, 2017) and their contribution to sea level. For four large Greenland outlet glacier catchments—Sermeq Kujalleq (Jakobshavn Isbræ), Koge Bugt, Hel- heim, and Kangerlussuaq Glaciers—we find an upper bound of 29 mm on dy- namic contribution to sea level after 100 years of warming. This bound accounts for dynamic loss only and can be summed with surface mass balance projections to bound the total glaciological contribution to sea level from those catchments. The convergence of upper bounds derived from our two strongest forcing scenar- ios agrees with studies that suggest surface mass balance will dominate future mass loss from Greenland. Although our work is motivated by coastal communities’ exposure to rising seas, the constraints we produce here are unlikely to be immediately usable for coastal adaptation. Intermediaries such as extension agents, climate consultants, or re- gional science-policy boundary organizations may be able to tailor our results for use in local adaptation contexts (published commentary: Ultee, Arnott, Bassis, & Lemos, 2018). Understanding the landscape of science intermediation, as well as working directly with stakeholders, can help researchers produce more usable sea level information.PhDAtmospheric, Oceanic & Space ScienceUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145794/1/ehultee_1.pd

The use of Frequency domain Electro-magnetometer for the characterization of permafrost and ice layers.

openSince the industrial revolution human activities caused a record-breaking increase in the Earth’s average temperature due to the extensive use of greenhouse gases. [1] As global temperatures increase; glaciers have undergone a significant retreat in the past few decades.[2] The Ice Memory project aims to preserve ice cores from glaciers worldwide, as a record of Earth's past climate. It involves drilling deep into glaciers, extracting ice cores, and storing them in a dedicated facility in Antarctica. This is to prevent the potential loss of valuable climate archives due to glacier retreat which provides future scientists with valuable information for studying historical climate patterns and understanding the role of human activity in climate change. geophysical investigations are typically required to determine the most suitable drilling positions for ice coring. the most common technique for this purpose is the so-called GPR. (Snow cover of several meters limits the use of ERT and active seismic methods.) While each geophysical technique has certain advantages and limitations, combining them can provide a more detailed picture of changes within rock glaciers. In the present study, electromagnetic prospecting in the frequency domain (FDEM) was performed together with the ground penetration radar (GPR). The former is not a commonly used method for studying glacier environments as FDEM has a lower resolution in the study of glaciers with respect to the GPR. However, as we will see in this study, it is a quick and convenient method to study this type of environment, as it provides a large coverage area in a cost-efficient manner, although with a lower resolution with respect to the GPR. Combining these two techniques provide a more detailed map of the glaciers. comparing the GPR and borehole data with the inverted FDEM datasets (CMD-DUO, GF-Instruments) confirms the effectiveness and applicability of FDEM methodology for investigating glacial bodies in mountainous regions.Since the industrial revolution human activities caused a record-breaking increase in the Earth’s average temperature due to the extensive use of greenhouse gases. [1] As global temperatures increase; glaciers have undergone a significant retreat in the past few decades.[2] The Ice Memory project aims to preserve ice cores from glaciers worldwide, as a record of Earth's past climate. It involves drilling deep into glaciers, extracting ice cores, and storing them in a dedicated facility in Antarctica. This is to prevent the potential loss of valuable climate archives due to glacier retreat which provides future scientists with valuable information for studying historical climate patterns and understanding the role of human activity in climate change. geophysical investigations are typically required to determine the most suitable drilling positions for ice coring. the most common technique for this purpose is the so-called GPR. (Snow cover of several meters limits the use of ERT and active seismic methods.) While each geophysical technique has certain advantages and limitations, combining them can provide a more detailed picture of changes within rock glaciers. In the present study, electromagnetic prospecting in the frequency domain (FDEM) was performed together with the ground penetration radar (GPR). The former is not a commonly used method for studying glacier environments as FDEM has a lower resolution in the study of glaciers with respect to the GPR. However, as we will see in this study, it is a quick and convenient method to study this type of environment, as it provides a large coverage area in a cost-efficient manner, although with a lower resolution with respect to the GPR. Combining these two techniques provide a more detailed map of the glaciers. comparing the GPR and borehole data with the inverted FDEM datasets (CMD-DUO, GF-Instruments) confirms the effectiveness and applicability of FDEM methodology for investigating glacial bodies in mountainous regions

How accurate are estimates of glacier ice thickness? Results from ITMIX, the Ice Thickness Models Intercomparison eXperiment

© Author(s) 2017. Knowledge of the ice thickness distribution of glaciers and ice caps is an important prerequisite for many glaciological and hydrological investigations. A wealth of approaches has recently been presented for inferring ice thickness from characteristics of the surface. With the Ice Thickness Models Intercomparison eXperiment (ITMIX) we performed the first coordinated assessment quantifying individual model performance. A set of 17 different models showed that individual ice thickness estimates can differ considerably - locally by a spread comparable to the observed thickness. Averaging the results of multiple models, however, significantly improved the results: on average over the 21 considered test cases, comparison against direct ice thickness measurements revealed deviations on the order of 10 ± 24% of the mean ice thickness (1σ estimate). Models relying on multiple data sets - such as surface ice velocity fields, surface mass balance, or rates of ice thickness change - showed high sensitivity to input data quality. Together with the requirement of being able to handle large regions in an automated fashion, the capacity of better accounting for uncertainties in the input data will be a key for an improved next generation of ice thickness estimation approaches

Modelling the 20th and 21st century evolution of Hoffellsjökull glacier, SE-Vatnajökull, Iceland

The Little Ice Age maximum extent of glaciers in Iceland was reached about 1890 AD and most glaciers in the country have retreated during the 20th century. A model for the surface mass balance and the flow of glaciers is used to reconstruct the 20th century retreat history of Hoffellsjökull, a south-flowing outlet glacier of the ice cap Vatnajökull, which is located close to the southeastern coast of Iceland. The bedrock topography was surveyed with radio-echo soundings in 2001. A wealth of data are available to force and constrain the model, e.g. surface elevation maps from ~1890, 1936, 1946, 1989, 2001, 2008 and 2010, mass balance observations conducted in 1936–1938 and after 2001, energy balance measurements after 2001, and glacier surface velocity derived by kinematic and differential GPS surveys and correlation of SPOT5 images. The approximately 20% volume loss of this glacier in the period 1895–2010 is realistically simulated with the model. After calibration of the model with past observations, it is used to simulate the future response of the glacier during the 21st century. The mass balance model was forced with an ensemble of temperature and precipitation scenarios derived from 10 global and 3 regional climate model simulations using the A1B emission scenario. If the average climate of 2000–2009 is maintained into the future, the volume of the glacier is projected to be reduced by 30% with respect to the present at the end of this century. If the climate warms, as suggested by most of the climate change scenarios, the model projects this glacier to almost disappear by the end of the 21st century. Runoff from the glacier is predicted to increase for the next 30–40 yr and decrease after that as a consequence of the diminishing ice-covered area

Parameter and state estimation with a time-dependent adjoint marine ice sheet model

To date, assimilation of observations into large-scale ice models has consisted predominantly of time-independent inversions of surface velocities for basal traction, bed elevation, or ice stiffness, and has relied primarily on analytically derived adjoints of glaciological stress balance models. To overcome limitations of such "snapshot" inversions – i.e., their inability to assimilate time-dependent data for the purpose of constraining transient flow states, or to produce initial states with minimum artificial drift and suitable for time-dependent simulations – we have developed an adjoint of a time-dependent parallel glaciological flow model. The model implements a hybrid shallow shelf–shallow ice stress balance, solves the continuity equation for ice thickness evolution, and can represent the floating, fast-sliding, and frozen bed regimes of a marine ice sheet. The adjoint is generated by a combination of analytic methods and the use of algorithmic differentiation (AD) software. Several experiments are carried out with idealized geometries and synthetic observations, including inversion of time-dependent surface elevations for past thicknesses, and simultaneous retrieval of basal traction and topography from surface data. Flexible generation of the adjoint for a range of independent uncertain variables is exemplified through sensitivity calculations of grounded ice volume to changes in basal melting of floating and basal sliding of grounded ice. The results are encouraging and suggest the feasibility, using real observations, of improved ice sheet state estimation and comprehensive transient sensitivity assessments

Bayesian methods in glaciology

Thesis (Ph.D) University of Alaska Fairbanks, 2017The problem of inferring the value of unobservable model parameters given a set of observations is ubiquitous in glaciology, as are large measurement errors. Bayes' theorem provides a unified framework for addressing such problems in a rigorous and robust way through Monte Carlo sampling of posterior distributions, which provides not only the optimal solution for a given inverse problem, but also the uncertainty. We apply these methods to three glaciological problems. First, we use Markov Chain Monte Carlo sampling to infer the importance of different glacier hydrological processes from observations of terminus water flux and surface speed. We find that the opening of sub-glacial cavities due to sliding over asperities at the glacier bed is of a similar magnitude to the opening of channels due to turbulent melt during periods of large input flux, but also that the processes of turbulent melting is the greatest source of uncertainty in hydrological modelling. Storage of water in both englacial void spaces and exchange of water between the englacial and subglacial systems are both necessary to explain observations. We next use Markov Chain Monte Carlo sampling to determine distributed glacier thickness from dense observations of surface velocity and mass balance coupled with sparse direct observations of thickness. These three variables are related through the principle of mass conservation. We develop a new framework for modelling observational uncertainty, then apply the method to three test cases. We find a strong relationship between measurement uncertainty, measurement spacing, and the resulting uncertainty in thickness estimates. We also find that in order to minimize uncertainty, measurement spacing should be 1-2 times the characteristic length scale of variations in subglacial topography. Finally, we apply the method of particle filtering to compute robust estimates of ice surface velocity and uncertainty from oblique time-lapse photos for the rapidly retreating Columbia Glacier. The resulting velocity fields, when averaged over suitable time scales, agree well with velocity measurements derived from satellites. At higher temporal resolution, our results suggest that seasonal evolution of the subglacial drainage system is responsible for observed changes in ice velocity at seasonal scales, and that this changing configuration produces varying degrees of glacier flow sensitivity to changes in external water input