Bayesian Inference of Subglacial Topography Using Mass Conservation

Brinkerhoff, Douglas; Aschwanden, Andy; Truffer, Martin

doi:10.3389/feart.2016.00008

Cited by 43 publications

(49 citation statements)

References 45 publications

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“…This would allow for propagating the thickness uncertainties into our model results in a more sophisticated way than is done currently. Sophisticated approaches for ice thickness derivation exist (e.g., Brinkerhoff et al, 2016), however, their application benefits substantially from high quality ice velocity fields, which we do not possess currently for Black Rapids Glacier. WRF-downscaled climate data with higher spatial resolution would be ideal to mitigate potential problems arising from our simple statistical downscaling, which, for example, fails to conserve mass and energy.…”

Section: Resultsmentioning

confidence: 99%

Mass Balance Evolution of Black Rapids Glacier, Alaska, 1980–2100, and Its Implications for Surge Recurrence

et al. 2017

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Surge-type Black Rapids Glacier, Alaska, has undergone strong retreat since it last surged in [1936][1937]. To assess its evolution during the late Twentieth and Twenty-first centuries and determine potential implications for surge likelihood, we run a simplified glacier model over the periods 1980-2015 (hindcasting) and 2015-2100 (forecasting). The model is forced by daily temperature and precipitation fields, with downscaled reanalysis data used for the hindcasting. A constant climate scenario and an RCP 8.5 scenario based on the GFDL-CM3 climate model are employed for the forecasting. Debris evolution is accounted for by a debris layer time series derived from satellite imagery (hindcasting) and a parametrized debris evolution model (forecasting). A retreat model accounts for the evolution of the glacier geometry. Model calibration, validation and parametrization rely on an extensive set of in situ and remotely sensed observations. To explore uncertainties in our projections, we run the glacier model in a Monte Carlo fashion, varying key model parameters and input data within plausible ranges. Our results for the hindcasting period indicate a negative mass balance trend, caused by atmospheric warming in the summer, precipitation decrease in the winter and surface elevation lowering (climate-elevation feedback), which exceed the moderating effects from increasing debris cover and glacier retreat. Without the 2002 rockslide deposits on Black Rapids' lower reaches, the mass balances would be more negative, by ∼ 20% between the 2003 and 2015 mass-balance years. Despite its retreat, Black Rapids Glacier is substantially out of balance with the current climate. By 2100, ∼ 8% of Black Rapids' 1980 area are projected to vanish under the constant climate scenario and ∼ 73% under the RCP 8.5 scenario. For both scenarios, the remaining glacier portions are out of balance, suggesting continued retreat after 2100. Due to mass starvation, a surge in the Twenty-first century is unlikely. The projected retreat will affect the glacier's runoff and change the landscape in the Black Rapids area markedly.

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Section: Resultsmentioning

confidence: 99%

Mass Balance Evolution of Black Rapids Glacier, Alaska, 1980–2100, and Its Implications for Surge Recurrence

et al. 2017

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“…Several methods that estimate ice thickness from characteristics of the surface have therefore been presented (e.g. Farinotti et al, 2009;Morlighem et al, 2011;Linsbauer et al, 2012;Brinkerhoff et al, 2016;Fürst et al, 2017) (Gaertner-Roer et al, 2014;Farinotti et al, 2017), but direct measurements remain pivotal for both the assessment of their performance and their calibration (Farinotti et al, 2017). It is still under debate, moreover, whether such approaches do indeed outperform a simple interpolation schemes when direct measurements are available.…”

Section: Introductionmentioning

confidence: 99%

The bedrock topography of Gries- and Findelengletscher

et al. 2018

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Abstract. Knowledge of the ice thickness distribution of glaciers is important for glaciological and hydrological applications. In this contribution, we present two updated bedrock topographies and ice thickness distributions for Gries-and Findelengletscher, Switzerland. The results are based on ground-penetrating radar (GPR) measurements collected in spring 2015 and already-existing data. The GPR data are analysed using ReflexW software and interpolated by using the ice thickness estimation method (ITEM). ITEM calculates the thickness distribution by using principles of ice flow dynamics and characteristics of the glacier surface. We show that using such a technique has a significance advantage compared to a direct interpolation of the measurements, especially for glacier areas that are sparsely covered by GPR data. The uncertainties deriving from both the interpretation of the GPR signal and the spatial interpolation through ITEM are quantified separately, showing that, in our case, GPR signal interpretation is a major source of uncertainty. The results show a total glacier volume of 0.28±0.06 and 1.00 ± 0.34 km 3 for Gries-and Findelengletscher, respectively, with corresponding average ice thicknesses of 56.8 ± 12.7 and 56.3 ± 19.6 m.

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“…Physics is incorporated by solving for the steady state solution with a finite element method (FEM) solver, given the system state. In Brinkerhoff et al (2016) velocities. Gaussian process priors are used for all unknowns, and the Metropolis-Hastings algorithm is used to fit the model.…”

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confidence: 99%

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

Gopalan¹,

Hrafnkelsson²,

Ađalgeirsdóttir³

et al. 2018

Preprint

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Abstract. Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). 5A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation 10 of numerical errors between the dome, interior, and margin of a glacier.

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Bayesian Inference of Subglacial Topography Using Mass Conservation

Cited by 43 publications

References 45 publications

Mass Balance Evolution of Black Rapids Glacier, Alaska, 1980–2100, and Its Implications for Surge Recurrence

Mass Balance Evolution of Black Rapids Glacier, Alaska, 1980–2100, and Its Implications for Surge Recurrence

The bedrock topography of Gries- and Findelengletscher

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

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