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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, the existence of perennial firn aquifers in the Antarctic Peninsula (AP) has been confirmed by in situ observations. Previous studies have suggested that these subsurface aquifers, together with meltwater ponds at the surface, provide a reservoir of liquid water to feed propagating fractures, promoting hydrofracture-driven ice-shelf disintegration. This study maps perennial firn aquifers in the AP from space using C-band Synthetic Aperture Radar imagery from ESA's Sentinel-1 (S1) mission. With these observations, we detect firn aquifers at 1 km × 1 km resolution, for the period 2017 to 2020. Existing methods, that use S1 data and rely on a backscatter intensity difference threshold approach, are prone to misclassify late-melt events as aquifers, when applied to the AP. Therefore, we have developed and evaluated a new approach that is better suited to the Antarctic environment. The new method exploits the characteristic, gradual backscatter increase during the (partial) refreezing of the liquid water in the firn layer after the peak of the melt season. Most firn aquifers are detected in the north and northwest of the AP, as well as on the Wilkins and George VI ice shelves. Aquifer locations detected with the present methodology agree with in situ observations and with model simulations of firn water content. [ABSTRACT FROM AUTHOR]

The intrusion of Circumpolar Deep Water in the Amundsen and Bellingshausen Sea embayments of Antarctica causes ice shelves in the region to melt from below, potentially putting their stability at risk. Earlier studies have shown how digital elevation models can be used to obtain ice shelf basal melt rates at a high spatial resolution. However, there has been limited availability of high-resolution elevation data, a gap the Reference Elevation Model of Antarctica (REMA) has filled. In this study we use a novel combination of REMA and CryoSat-2 elevation data to obtain high-resolution basal melt rates of the Dotson Ice Shelf in a Lagrangian framework, at a 50 m spatial posting on a 3-yearly temporal resolution. We present a novel method: Basal melt rates Using REMA and Google Earth Engine (BURGEE). The high resolution of BURGEE is supported through a sensitivity study of the Lagrangian displacement. The high-resolution basal melt rates show a good agreement with an earlier basal melt product based on CryoSat-2. Both products show a wide melt channel extending from the grounding line to the ice front, but our high-resolution product indicates that the pathway and spatial variability of this channel is influenced by a pinning point on the ice shelf. This result emphasizes the importance of high-resolution basal melt rates to expand our understanding of channel formation and melt patterns. BURGEE can be expanded to a pan-Antarctic study of high-resolution basal melt rates. This will provide a better picture of the (in)stability of Antarctic ice shelves. [ABSTRACT FROM AUTHOR]

The intrusion of warm circumpolar deep water causes ice shelves in the Amundsen and Bellinghausen Sea Embayments of Antarctica to melt from below, thereby potentially putting their stability at risk. Earlier studies have shown how digital elevation models can be used to obtain high-resolution ice shelf basal melt rates. However, there has been limited availability of high-resolution elevation data, a gap the Reference Elevation Model of Antarctica (REMA) has filled. In this study we use a novel combination of REMA and CryoSat-2 elevation data to obtain high-resolution basal melt rates of the Dotson Ice Shelf in a Lagrangian framework, at a 50m spatial resolution on a 3-yearly temporal resolution. We present a novel Basal melt rates Using REMA and Google Earth Engine (BURGEE) method, which high resolution is supported through a sensitivity study assuming that the quality of the Lagrangian displacement is the main error source. The high-resolution basal melt rates show a good agreement with an earlier 500-m resolution basal melt product based on CryoSat-2, with a wide melt channel extending from the grounding line to the ice shelf front. Our high-resolution product indicates that the pathway and spatial variability of the main channel is influenced by a pinning point on the ice shelf. Additionally, it reveals a narrower coastal channel running along the western margin, which was not identified in the lower-resolution melt product, but does show up in a recent ocean modeling study. This emphasizes the importance of high-resolution basal melt rates to expand our understanding of channel formation and melt patterns. BURGEE can be expanded to a Pan-Antarctic study of high-resolution basal melt rates. This will provide a better picture of the (in)stability of Antarctic ice shelves. [ABSTRACT FROM AUTHOR]

In recent years, the existence of firn aquifers in the Antarctic Peninsula (AP) has been confirmed by in-situ observations. Given their importance for understanding the hydrology of the Antarctic ice sheet, a more spatially comprehensive assessment of AP firn aquifers is desirable. The purpose of this study is to map firn aquifers in the AP from space using C-band Synthetic Aperture Radar imagery from ESA's Sentinel-1 mission. These observations enable the detection of firn aquifers at 1 x 1 km² resolution. The method presented here is based on quantifying the characteristic, gradual backscatter increase during the (partial) refreezing of the liquid water in the firn layer after the peak melt season. When applied to the available time series, it detects perennial aquifers (existing year-round) for the period 2017 to 2020, as well as seasonal aquifers which do not persist through winter. We acknowledge that the backscatter signature in any given year is indistinguishable for seasonal and perennial aquifers. We detect seasonal firn aquifers in the north and northwest of the AP, as well as on the Wilkins and George VI ice shelves. Only in the north and northwest of the AP, aquifers are detected each year in the observation period, here taken as a proxy for perennial firn aquifers. Both distributions agree with model simulations. Further in situ and modelling studies and longer time series of satellite observations are needed to validate the results of this study. [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]

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]

We introduce an algorithm (Watta) which automatically calculates supraglacial lake bathymetry and detects potential ice layers along tracks of the ICESat-2 (Ice, Cloud, and Land Elevation Satellite) laser altimeter. Watta uses photon heights estimated by the ICESat-2 ATL03 product and extracts supraglacial lake surface, bottom, and depth corrected for refraction and (sub-)surface ice cover in addition to producing surface heights at the native resolution of the ATL03 photon cloud. These measurements are used to constrain empirical estimates of lake depth from satellite imagery, which were thus far dependent on sparse sets of in situ measurements for calibration. Imagery sources include Landsat 8 Operational Land Imager (OLI), Sentinel-2, and high-resolution Planet Labs PlanetScope and SkySat data, used here for the first time to calculate supraglacial lake depths. The Watta algorithm was developed and tested using a set of 46 lakes near Sermeq Kujalleq (Jakobshavn) glacier in western Greenland, and we use multiple imagery sources (available for 45 of these lakes) to assess the use of the red vs. green band to extrapolate depths along a profile to full lake volumes. We use Watta-derived estimates in conjunction with high-resolution imagery from both satellite-based sources (tasked over the season) and nearly simultaneous Operation IceBridge CAMBOT (Continuous Airborne Mapping By Optical Translator) imagery (on a single airborne flight) for a focused study of the drainage of a single lake over the 2019 melt season. Our results suggest that the use of multiple imagery sources (both publicly available and commercial), in combination with altimetry-based depths, can move towards capturing the evolution of supraglacial hydrology at improved spatial and temporal scales. [ABSTRACT FROM AUTHOR]

The aerodynamic roughness of heat, moisture, and momentum of a natural surface are important parameters in atmospheric models, as they co-determine the intensity of turbulent transfer between the atmosphere and the surface. Unfortunately this parameter is often poorly known, especially in remote areas where neither high-resolution elevation models nor eddy-covariance measurements are available. In this study we adapt a bulk drag partitioning model to estimate the aerodynamic roughness length (z0m) such that it can be applied to 1D (i.e. unidirectional) elevation profiles, typically measured by laser altimeters. We apply the model to a rough ice surface on the K-transect (west Greenland Ice Sheet) using UAV photogrammetry, and we evaluate the modelled roughness against in situ eddy-covariance observations. We then present a method to estimate the topography at 1 m horizontal resolution using the ICESat-2 satellite laser altimeter, and we demonstrate the high precision of the satellite elevation profiles against UAV photogrammetry. The currently available satellite profiles are used to map the aerodynamic roughness during different time periods along the K-transect, that is compared to an extensive dataset of in situ observations. We find a considerable spatio-temporal variability in z0m , ranging between 10-4 m for a smooth snow surface and 10-1 m for rough crevassed areas, which confirms the need to incorporate a variable aerodynamic roughness in atmospheric models over ice sheets. [ABSTRACT FROM AUTHOR]

We present a reconstruction of historical (1950–2014) surface mass balance (SMB) of the Greenland ice sheet (GrIS) using a high-resolution regional climate model (RACMO2; ∼11 km) to dynamically downscale the climate of the Community Earth System Model version 2 (CESM2; ∼111 km). After further statistical downscaling to 1 km spatial resolution, evaluation using in situ SMB measurements and remotely sensed GrIS mass change shows good agreement. Comparison with an ensemble of previously conducted RACMO2 simulations forced by climate reanalysis demonstrates that the current product realistically represents the long-term average and variability of individual SMB components and captures the recent increase in meltwater runoff that accelerated GrIS mass loss. This means that, for the first time, climate forcing from an Earth system model (CESM2), which assimilates no observations, can be used without additional corrections to reconstruct the historical GrIS SMB and its recent decline that initiated mass loss in the 1990s. This paves the way for attribution studies of future GrIS mass loss projections and contribution to sea level rise. [ABSTRACT FROM AUTHOR]

Rapid changes in thickness and velocity have been observed at many marine-terminating glaciers in Greenland, impacting the volume of ice they export, or discharge, from the ice sheet. While annual estimates of ice-sheet-wide discharge have been previously derived, higher-resolution records are required to fully constrain the temporal response of these glaciers to various climatic and mechanical drivers that vary in sub-annual scales. Here we sample outlet glaciers wider than 1 km (N=230) to derive the first continuous, ice-sheet-wide record of total ice sheet discharge for the 2000–2016 period, resolving a seasonal variability of 6 %. The amplitude of seasonality varies spatially across the ice sheet from 5 % in the southeastern region to 9 % in the northwest region. We analyze seasonal to annual variability in the discharge time series with respect to both modeled meltwater runoff, obtained from RACMO2.3p2, and glacier front position changes over the same period. We find that year-to-year changes in total ice sheet discharge are related to annual front changes (r2=0.59 , p=10-4) and that the annual magnitude of discharge is closely related to cumulative front position changes (r2=0.79), which show a net retreat of >400 km, or an average retreat of >2 km, at each surveyed glacier. Neither maximum seasonal runoff or annual runoff totals are correlated to annual discharge, which suggests that larger annual quantities of runoff do not relate to increased annual discharge. Discharge and runoff, however, follow similar patterns of seasonal variability with near-coincident periods of acceleration and seasonal maxima. These results suggest that changes in glacier front position drive secular trends in discharge, whereas the impact of runoff is likely limited to the summer months when observed seasonal variations are substantially controlled by the timing of meltwater input. [ABSTRACT FROM AUTHOR]

The Greenland Ice Sheet (GrIS) is currently losing ice mass. In order to accurately predict future sea level rise, the mechanisms driving the observed mass loss must be better understood. Here, we combine data from the satellite gravimetry mission Gravity Recovery and Climate Experiment (GRACE), surface mass balance (SMB) output of the Regional Atmospheric Climate Model v. 2 (RACMO2), and ice discharge estimates to analyze the mass budget of Greenland at various temporal and spatial scales. We find that the mean rate of mass variations in Greenland observed by GRACE was between -277 and -269 Gt yr-1 in 2003-2012. This estimate is consistent with the sum (i.e., -304±126 Gt yr-1) of individual contributions - surface mass balance (SMB, 216±122 Gt yr-1) and ice discharge (520±31 Gt yr-1) - and with previous studies. We further identify a seasonal mass anomaly throughout the GRACE record that peaks in July at 80-120 Gt and which we interpret to be due to a combination of englacial and subglacial water storage generated by summer surface melting. The robustness of this estimate is demonstrated by using both different GRACE-based solutions and different meltwater runoff estimates (namely, RACMO2.3, SNOWPACK, and MAR3.9). Meltwater storage in the ice sheet occurs primarily due to storage in the high-accumulation regions of the southeast and northwest parts of Greenland. Analysis of seasonal variations in outlet glacier discharge shows that the contribution of ice discharge to the observed signal is minor (at the level of only a few gigatonnes) and does not explain the seasonal differences between the total mass and SMB signals. With the improved quantification of meltwater storage at the seasonal scale, we highlight its importance for understanding glaciohydrological processes and their contributions to the ice sheet mass variability. [ABSTRACT FROM AUTHOR]

We evaluate modelled Antarctic ice sheet (AIS) near-surface climate, surface mass balance (SMB) and surface energy balance (SEB) from the updated polar version of the regional atmospheric climate model, RACMO2 (1979-2016). The updated model, referred to as RACMO2.3p2, incorporates upper-air relaxation, a revised topography, tuned parameters in the cloud scheme to generate more precipitation towards the AIS interior and modified snow properties reducing drifting snow sublimation and increasing surface snowmelt. Comparisons of RACMO2 model output with several independent observational data show that the existing biases in AIS temperature, radiative fluxes and SMB components are further reduced with respect to the previous model version. The model-integrated annual average SMB for the ice sheet including ice shelves (minus the Antarctic Peninsula, AP) now amounts to 2229 Gt with an interannual variability of 109 Gt y-1. The largest improvement is found in modelled surface snowmelt, which now compares well with satellite and weather station observations. For the high-resolution (~5.5 km) AP simulation, results remain comparable to earlier studies. The updated model provides a new, high-resolution data set of the contemporary near-surface climate and SMB of the AIS; this model version will be used for future climate scenario projections in a forthcoming study. [ABSTRACT FROM AUTHOR]

We assess the recent contribution of the Greenland ice sheet (GrIS) to sea level change. We use the mass budget method, which quantifies ice sheet mass balance (MB) as the difference between surface mass balance (SMB) and solid ice discharge across the grounding line (D). A comparison with independent gravity change observations from GRACE shows good agreement for the overlapping period 2002-2015, giving confidence in the partitioning of recent GrIS mass changes. The estimated 1995 value of D and the 1958-1995 average value of SMB are similar at 411 and 418 Gt yr-1, respectively, suggesting that ice flow in the mid-1990s was well adjusted to the average annual mass input, reminiscent of an ice sheet in approximate balance. Starting in the early to mid-1990s, SMB decreased while D increased, leading to quasi-persistent negative MB. About 60% of the associated mass loss since 1991 is caused by changes in SMB and the remainder by D. The decrease in SMB is fully driven by an increase in surface melt and subsequent meltwater runoff, which is slightly compensated by a small (<3%) increase in snowfall. The excess runoff originates from lowlying (<2000ma.s.l.) parts of the ice sheet; higher up, increased refreezing prevents runoff of meltwater from occurring, at the expense of increased firn temperatures and depleted pore space. With a 1991-2015 average annual mass loss of ~0.47±0.23 mm sea level equivalent (SLE) and a peak contribution of 1.2mm SLE in 2012, the GrIS has recently become a major source of global mean sea level rise. [ABSTRACT FROM AUTHOR]

Observations over the past 2 decades show substantial ice loss associated with the speed-up of marine-terminating glaciers in Greenland. Here we use a regional three-dimensional outlet glacier model to simulate the behaviour of Jakobshavn Isbræ (JI) located in western Greenland. Our approach is to model and understand the recent behaviour of JI with a physical process-based model. Using atmospheric forcing and an ocean parametrization we tune our model to reproduce observed frontal changes of JI during 1990-2014. In our simulations, most of the JI retreat during 1990-2014 is driven by the ocean parametrization used and the glacier's subsequent response, which is largely governed by bed geometry. In general, the study shows significant progress in modelling the temporal variability of the flow at JI. Our results suggest that the overall variability in modelled horizontal velocities is a response to variations in terminus position. The model simulates two major accelerations that are consistent with observations of changes in glacier terminus. The first event occurred in 1998 and was triggered by a retreat of the front and moderate thinning of JI prior to 1998. The second event, which started in 2003 and peaked in the summer 2004, was triggered by the final break-up of the floating tongue. This break-up reduced the buttressing at the JI terminus that resulted in further thinning. As the terminus retreated over a reverse bed slope into deeper water, sustained high velocities over the last decade have been observed at JI. Our model provides evidence that the 1998 and 2003 flow accelerations are most likely initiated by the ocean parametrization used but JI's subsequent dynamic response was governed by its own bed geometry. We are unable to reproduce the observed 2010-2012 terminus retreat in our simulations. We attribute this limitation to either inaccuracies in basal topography or to misrepresentations of the climatic forcings that were applied. Nevertheless, the model is able to simulate the previously observed increase in mass loss through 2014. [ABSTRACT FROM AUTHOR]