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While the influence of surface melt on Antarctic ice shelf stability can be large, the duration and affected area of melt events are often small. Therefore, melt events are difficult to capture with remote sensing, as satellite sensors always face the trade-off between spatial and temporal resolution. To overcome this limitation, we developed UMelt: a surface melt record for all Antarctic ice shelves with a high spatial (500 m) and high temporal (12 h) resolution for the period 2016–2021. Our approach is based on a deep learning model, specifically a U-Net, which was developed in Google Earth Engine. The U-Net combines microwave remote sensing observations from three sources: Sentinel-1, Special Sensor Microwave Imager/Sounder (SSMIS), and Advanced Scatterometer (ASCAT). The U-Net was trained on the Shackleton Ice Shelf for melt seasons 2017–2021, using the fine-scale melt patterns of Sentinel-1 as reference data and SSMIS, ASCAT, a digital elevation model, and multi-year Sentinel-1 melt fraction as predictors. The trained U-Net performed well on the Shackelton Ice Shelf for test melt season 2016–2017 (accuracy: 91.3%; F1-score: 86.9%), and the Larsen C Ice Shelf, which was not considered during training (accuracy: 91.0%; F1-score: 89.3%). Using the trained U-Net model, we have successfully developed the UMelt record. UMelt allows Antarctic-wide surface melt to be detected at a small scale while preserving a high temporal resolution, which could lead to new insights into the response of ice shelves to a changing atmospheric forcing., Physical and Space Geodesy, Mathematical Geodesy and Positioning

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., Physical and Space Geodesy