A Hierarchical Spatio-Temporal Statistical Model Motivated by Glaciology

In this paper, we extend and analyze a Bayesian hierarchical spatio-temporal model for physical systems. A novelty is to model the discrepancy between the output of a computer simulator for a physical process and the actual process values with a multivariate random walk. For computational efficiency, linear algebra for bandwidth limited matrices is utilized, and first-order emulator inference allows for the fast emulation of a numerical partial differential equation (PDE) solver. A test scenario from a physical system motivated by glaciology is used to examine the speed and accuracy of the computational methods used, in addition to the viability of modeling assumptions. We conclude by discussing how the model and associated methodology can be applied in other physical contexts besides glaciology.Comment: Revision accepted for publication by the Journal of Agricultural, Biological, and Environmental Statistic

Tidal influence on Rutford Ice Stream, West Antarctica: observations of surface flow and basal processes from closely-spaced GPS and passive seismic stations

High-resolution surface velocity measurements and passive seismic observations from Rutford Ice Stream, West Antarctica, 40 km upstream from the grounding line are presented. These measurements indicate a complex relationship between the ocean tides and currents, basal conditions and ice-stream flow. Both the mean basal seismicity and the velocity of the ice stream are modulated by the tides. Seismic activity increases twice during each semi-diurnal tidal cycle. The tidal analysis shows the largest velocity variation is at the fortnightly period, with smaller variations superimposed at diurnal and semi-diurnal frequencies. The general pattern of the observed velocity is two velocity peaks during each semi-diurnal tidal cycle, but sometimes three peaks are observed. This pattern of two or three peaks is more regular during spring tides, when the largest-amplitude velocity variations are observed, than during neap tides. This is the first time that velocity and level of seismicity are shown to correlate and respond to tidal forcing as far as 40 km upstream from the grounding line of a large ice stream

The role of an interactive Greenland ice sheet in the coupled climate-ice sheet model EC-Earth-PISM

AbstractIce sheet processes are often simplified in global climate models as changes in ice sheets have been assumed to occur over long time scales compared to ocean and atmospheric changes. However, numerous observations show an increasing rate of mass loss from the Greenland Ice Sheet and call for comprehensive process-based models to explore its role in climate change. Here, we present a new model system, EC-Earth-PISM, that includes an interactive Greenland Ice Sheet. The model is based on the EC-Earth v2.3 global climate model in which ice sheet surface processes are introduced. This model interacts with the Parallel Ice Sheet Model (PISM) without anomaly or flux corrections. Under pre-industrial climate conditions, the modeled climate and ice sheet are stable while keeping a realistic interannual variability. In model simulations forced into a warmer climate of four times the pre-industrial CO2 concentration, the total surface mass balance decreases and the ice sheet loses mass at a rate of about 500 Gt/year. In the climate warming experiments, the resulting freshwater flux from the Greenland Ice Sheet increases 55% more in the experiments with the interactive ice sheet and the climate response is significantly different: the Arctic near-surface air temperature is lower, substantially more winter sea ice covers the northern hemisphere, and the ocean circulation is weaker. Our results indicate that the melt-albedo feedback plays a key role for the response of the ice sheet and its influence on the changing climate in the Arctic. This emphasizes the importance of including interactive ice sheets in climate change projections.</jats:p

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

Effect of topography on subglacial discharge and submarine melting during tidewater glacier retreat.

-We explored secular variations in subglacial discharge and submarine melting with an idealized model -Subglacial discharge increases as tidewater glaciers retreat along retrograde beds -Submarine melting depends on subglacial discharge and therefore promotes unstable retreat on retrograde bedsTo first order, subglacial discharge depends on climate, which determines precipitation fluxes and glacier mass balance, and the rate of glacier volume change. For tidewater glaciers, large and rapid changes in glacier volume can occur independent of climate change due to strong glacier dynamic feedbacks. Using an idealized tidewater glacier model, we show that these feedbacks produce secular variations in subglacial discharge that are influenced by subglacial topography. Retreat along retrograde bed slopes (into deep water) results in rapid surface lowering and coincident increases in subglacial discharge. Consequently, submarine melting of glacier termini, which depends on subglacial discharge and ocean thermal forcing, also increases during retreat into deep water. Both subglacial discharge and submarine melting subsequently decrease as glacier termini retreat out of deep water and approach new steady state equilibria. In our simulations, subglacial discharge reached peaks that were 6–17% higher than preretreat values, with the highest values occurring during retreat from narrow sills, and submarine melting increased by 14% for unstratified fjords and 51% for highly stratified fjords. Our results therefore indicate that submarine melting acts in concert with iceberg calving to cause tidewater glacier termini to be unstable on retrograde beds. The full impact of submarine melting on tidewater glacier stability remains uncertain, however, due to poor understanding of the coupling between submarine melting and iceberg calving.Funding was provided by the National Oceanic and Atmospheric Association (NA13OAR4310098) and the U.S. National Science Foundation (PLR-1504288 and PLR-1504521).Ye

Future evolution and uncertainty of river flow regime change in a deglaciating river basin

The flow regimes of glacier-fed rivers are sensitive to climate change due to strong climate–cryosphere–hydrosphere interactions. Previous modelling studies have projected changes in annual and seasonal flow magnitude but neglect other changes in river flow regime that also have socio-economic and environmental impacts. This study employs a signature-based analysis of climate change impacts on the river flow regime for the deglaciating Virkisá river basin in southern Iceland. Twenty-five metrics (signatures) are derived from 21st century projections of river flow time series to evaluate changes in different characteristics (magnitude, timing and variability) of river flow regime over sub-daily to decadal timescales. The projections are produced by a model chain that links numerical models of climate and glacio-hydrology. Five components of the model chain are perturbed to represent their uncertainty including the emission scenario, numerical climate model, downscaling procedure, snow/ice melt model and runoff-routing model. The results show that the magnitude, timing and variability of glacier-fed river flows over a range of timescales will change in response to climate change. For most signatures there is high confidence in the direction of change, but the magnitude is uncertain. A decomposition of the projection uncertainties using analysis of variance (ANOVA) shows that all five perturbed model chain components contribute to projection uncertainty, but their relative contributions vary across the signatures of river flow. For example, the numerical climate model is the dominant source of uncertainty for projections of high-magnitude, quick-release flows, while the runoff-routing model is most important for signatures related to low-magnitude, slow-release flows. The emission scenario dominates mean monthly flow projection uncertainty, but during the transition from the cold to melt season (April and May) the snow/ice melt model contributes up to 23&thinsp;% of projection uncertainty. Signature-based decompositions of projection uncertainty can be used to better design impact studies to provide more robust projections.</p

Full-depth englacial vertical ice-sheet velocities measured using phase-sensitive radar

We describe a geophysical technique to measure englacial vertical velocities through to the beds of ice sheets without the need for borehole drilling. Using a ground-based phase-sensitive radio-echo sounder (pRES) during seven Antarctic field seasons, we measure the temporal changes in the position of englacial reflectors within ice divides up to 900 m thick on Berkner Island, Roosevelt Island, Fletcher Promontory and Adelaide Island. Recorded changes in reflector positions yield 'full-depth' profiles of vertical ice velocity that we use to examine spatial variations in ice flow near the divides. We interpret these variations by comparing them to the results of a full-Stokes simulation of ice-divide flow, qualitatively validating the model and demonstrating that we are directly detecting an ice-dynamical phenomenon called the Raymond Effect. Using pRES, englacial vertical ice velocities can be measured in higher spatial resolution than is possible using instruments installed within the ice. We discuss how these measurements could be used with inverse methods to measure ice rheology, and to improve ice-core dating by incorporating pRES-measured vertical velocities into age modelling

Surface elevation change and mass balance of Icelandic ice caps derived from swath mode CryoSat-2 altimetry

We apply swath processing to CryoSat-2 interferometric mode data acquired over the Icelandic ice caps to generate maps of rates of surface elevation change at 0.5 km postings. This high-resolution mapping reveals complex surface elevation changes in the region, related to climate, ice dynamics, and subglacial geothermal and magmatic processes. We estimate rates of volume and mass change independently for the six major Icelandic ice caps, 90% of Iceland's permanent ice cover, for five glaciological years between October 2010 and September 2015. Annual mass balance is highly variable; during the 2014/2015 glaciological year, the Vatnajökull ice cap (~70% of the glaciated area) experienced positive mass balance for the first time since 1992/1993. Our results indicate that between glaciological years 2010/2011and 2014/2015 Icelandic ice caps have lost 5.8 ± 0.7 Gt a−1 on average, ~40% less than the preceding 15 years, contributing 0.016 ± 0.002 mm a−1 to sea level rise

Winter mass balance of Drangajökull ice cap (NW Iceland) derived from satellite sub-meter stereo images

Sub-meter resolution, stereoscopic satellite images allow for the generation of accurate and high-resolution digital elevation models (DEMs) over glaciers and ice caps. Here, repeated stereo images of Drangajökull ice cap (NW Iceland) from Pléiades and WorldView2 (WV2) are combined with in situ estimates of snow density and densification of firn and fresh snow to provide the first estimates of the glacier-wide geodetic winter mass balance obtained from satellite imagery. Statistics in snow- and ice-free areas reveal similar vertical relative accuracy (<  0.5 m) with and without ground control points (GCPs), demonstrating the capability for measuring seasonal snow accumulation. The calculated winter (14 October 2014 to 22 May 2015) mass balance of Drangajökull was 3.33 ± 0.23 m w.e. (meter water equivalent), with ∼ 60 % of the accumulation occurring by February, which is in good agreement with nearby ground observations. On average, the repeated DEMs yield 22 % less elevation change than the length of eight winter snow cores due to (1) the time difference between in situ and satellite observations, (2) firn densification and (3) elevation changes due to ice dynamics. The contributions of these three factors were of similar magnitude. This study demonstrates that seasonal geodetic mass balance can, in many areas, be estimated from sub-meter resolution satellite stereo images.This study was funded by the University of Iceland (UI) Research Fund. Pleiades images were acquired at research price thanks to the CNES ISIS program (http://www.isis-cnes.fr). The WV2 DEM was obtained through the ArcticDEM project. This work is a contribution to the Rannis grant of excellence project, ANATILS. Collaboration and travels between IES and LEGOS were funded by the Jules Verne research fund and the TOSCA program from the French Space Agency, CNES. This study used the recent lidar mapping of the glaciers in Iceland that was funded by the Icelandic Research Fund, the Landsvirkjun research fund, the Icelandic Road Administration, the Reykjavik Energy Environmental and Energy Research Fund, the Klima-og Luftgruppen (KoL) research fund of the Nordic Council of Ministers, the Vatnajokull National Park, the organization Friends of Vatnajokull, the National Land Survey of Iceland, the Icelandic Meteorological Office and the UI research fund. The ground-based mass balance measurements on Drangajokull have been jointly funded by Orkubu Vestfjarda (Westfjord Power Company), the National Energy Authority (2004-2009) and the Icelandic Meteorological Office (2009-2015).Peer Reviewe