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Geoscientific models are facing increasing challenges to exploit growing datasets coming from remote sensing. Universal differential equations (UDEs), aided by differentiable programming, provide a new scientific modelling paradigm enabling both complex functional inversions to potentially discover new physical laws and data assimilation from heterogeneous and sparse observations. We demonstrate an application of UDEs as a proof of concept to learn the creep component of ice flow, i.e. a nonlinear diffusivity differential equation, of a glacier evolution model. By combining a mechanistic model based on a two-dimensional shallow-ice approximation partial differential equation with an embedded neural network, i.e. a UDE, we can learn parts of an equation as nonlinear functions that then can be translated into mathematical expressions. We implemented this modelling framework as ODINN.jl, a package in the Julia programming language, providing high performance, source-to-source automatic differentiation (AD) and seamless integration with tools and global datasets from the Open Global Glacier Model in Python. We demonstrate this concept for 17 different glaciers around the world, for which we successfully recover a prescribed artificial law describing ice creep variability by solving ∼ 500 000 ordinary differential equations in parallel. Furthermore, we investigate which are the best tools in the scientific machine learning ecosystem in Julia to differentiate and optimize large nonlinear diffusivity UDEs. This study represents a proof of concept for a new modelling framework aiming at discovering empirical laws for large-scale glacier processes, such as the variability in ice creep and basal sliding for ice flow, and new hybrid surface mass balance models. [ABSTRACT FROM AUTHOR]

In recent years a vast amount of glacier surface velocity data from satellite imagery has emerged based on correlation between repeat images. Thereby, much emphasis has been put on the fast processing of large data volumes and products with complete spatial coverage. The metadata of such measurements are often highly simplified when the measurement precision is lumped into a single number for the whole dataset, although the error budget of image matching is in reality neither isotropic nor constant over the whole velocity field. The spread of the correlation peak of individual image offset measurements is dependent on the image structure and the non-uniform flow of the ice and is used here to extract a proxy for measurement uncertainty. A quantification of estimation error or dispersion for each individual velocity measurement can be important for the inversion of, for instance, rheology, ice thickness and/or bedrock friction. Errors in the velocity data can propagate into derived results in a complex and exaggerating way, making the outcomes very sensitive to velocity noise and outliers. Here, we present a computationally fast method to estimate the matching precision of individual displacement measurements from repeat imaging data, focusing on satellite data. The approach is based upon Gaussian fitting directly on the correlation peak and is formulated as a linear least-squares estimation, making its implementation into current pipelines straightforward. The methodology is demonstrated for Sermeq Kujalleq (Jakobshavn Isbræ), Greenland, a glacier with regions of strong shear flow and with clearly oriented crevasses, and Malaspina Glacier, Alaska. Directionality within an image seems to be the dominant factor influencing the correlation dispersion. In our cases these are crevasses and moraine bands, while a relation to differential flow, such as shear, is less pronounced on the correlation spread. [ABSTRACT FROM AUTHOR]

Icelandic glaciers have been losing mass since the Little Ice Age in the mid‐to‐late 1800s, with higher mass loss rates in the early 21st century, followed by a slowdown since 2011. As of yet, it remains unclear whether this mass loss slowdown will persist in the future. By reconstructing the contemporary (1958–2019) surface mass balance of Icelandic glaciers, we show that the post‐2011 mass loss slowdown coincides with the development of the Blue Blob, an area of regional cooling in the North Atlantic Ocean to the south of Greenland. This regional cooling signal mitigates atmospheric warming in Iceland since 2011, in turn decreasing glacier mass loss through reduced meltwater runoff. In a future high‐end warming scenario, North Atlantic cooling is projected to mitigate mass loss of Icelandic glaciers until the mid‐2050s. High mass loss rates resume thereafter as the regional cooling signal weakens. Plain Language Summary: Icelandic glaciers are currently losing mass, but with a recent slowdown in the last decade. We show that this slowdown coincides with the development of an area of regional cooling in the North Atlantic Ocean to the south of Greenland, called Blue Blob. Cooling in the Blue Blob has been mitigating atmospheric warming in Iceland since 2011, reducing glacier melt. In a future warmer climate, North Atlantic cooling is projected to persist until the mid‐2050s, further slowing down mass loss of Icelandic glaciers. High mass loss resumes thereafter as the regional cooling in the Blue Blob weakens. Key Points: We project daily surface mass balance of Icelandic glaciers at 500 m spatial resolution under a high‐end warming scenario until 2100We correlate the post‐2011 glacier mass loss slowdown with a local cooling in the North Atlantic OceanWe predict that local North Atlantic cooling will continue mitigating Icelandic glaciers mass loss until the mid‐2050s [ABSTRACT FROM AUTHOR]

Meltwater from Himalayan glaciers sustains the flow of rivers such as the Ganges and Brahmaputra on which over half a billion people depend for day-to-day needs. Upstream areas are likely to be affected substantially by climate change, and changes in the magnitude and timing of meltwater supply are expected to occur in coming decades. About 10 % of the Himalayan glacier population terminates into proglacial lakes, and such lake-terminating glaciers are known to exhibit higher-than-average total mass losses. However, relatively little is known about the mechanisms driving exacerbated ice loss from lake-terminating glaciers in the Himalaya. Here we examine a composite (2017–2019) glacier surface velocity dataset, derived from Sentinel 2 imagery, covering central and eastern Himalayan glaciers larger than 3 km 2. We find that centre flow line velocities of lake-terminating glaciers (N = 70; umedian : 18.83 m yr -1 ; IQR – interquartile range – uncertainty estimate: 18.55–19.06 m yr -1) are on average more than double those of land-terminating glaciers (N = 249; umedian : 8.24 m yr -1 ; IQR uncertainty estimate: 8.17–8.35 m yr -1) and show substantially more heterogeneity than land-terminating glaciers around glacier termini. We attribute this large heterogeneity to the varying influence of lakes on glacier dynamics, resulting in differential rates of dynamic thinning, which causes about half of the lake-terminating glacier population to accelerate towards the glacier termini. Numerical ice-flow model experiments show that changes in the force balance at the glacier termini are likely to play a key role in accelerating the glacier flow at the front, with variations in basal friction only being of modest importance. The expansion of current glacial lakes and the formation of new meltwater bodies will influence the dynamics of an increasing number of Himalayan glaciers in the future, and these factors should be carefully considered in regional projections. [ABSTRACT FROM AUTHOR]

Mountain glaciers and ice caps are contributing significantly to present rates of sea level rise and will continue to do so over the next century and beyond. The Canadian Arctic Archipelago, located off the northwestern shore of Greenland, contains one-third of the global volume of land ice outside the ice sheets, but its contribution to sea-level change remains largely unknown. Here we show that the Canadian Arctic Archipelago has recently lost 61 ± 7 gigatonnes per year (Gt yr−1) of ice, contributing 0.17 ± 0.02 mm yr−1 to sea-level rise. Our estimates are of regional mass changes for the ice caps and glaciers of the Canadian Arctic Archipelago referring to the years 2004 to 2009 and are based on three independent approaches: surface mass-budget modelling plus an estimate of ice discharge (SMB+D), repeat satellite laser altimetry (ICESat) and repeat satellite gravimetry (GRACE). All three approaches show consistent and large mass-loss estimates. Between the periods 2004-2006 and 2007-2009, the rate of mass loss sharply increased from 31 ± 8 Gt yr−1 to 92 ± 12 Gt yr−1 in direct response to warmer summer temperatures, to which rates of ice loss are highly sensitive (64 ± 14 Gt yr−1 per 1 K increase). The duration of the study is too short to establish a long-term trend, but for 2007-2009, the increase in the rate of mass loss makes the Canadian Arctic Archipelago the single largest contributor to eustatic sea-level rise outside Greenland and Antarctica. [ABSTRACT FROM AUTHOR]