Temporal Evolution of the Petermann Glacier Surface Elevation with Implicit Neural Representation in High Spatiotemporal Resolution using CryoSat-2 Data

Global warming threatens to cause irreversible planetary changes and is accelerated in the polar regions, warming at nearly four times the global average. Warmer temperature exacerbates ice sheet ice loss, increasing the freshwater discharge into oceans and contributing to rising sea levels and regional changes in ocean salinity, threatening a collapse of ocean currents. The number of humans living below sea level is projected to rise by 73% by the turn of the century. Therefore, accurately determining the ice loss and the freshwater discharge is paramount to enable decision-makers to take necessary actions.

 

Ice sheet ice loss can be estimated using a satellite altimeter, measuring the spatial ice sheet surface height at many time instances. The apparent elevation change can be converted into mass change by accounting for bedrock movement and snow/firn processes. An obstacle in utilising satellite altimeter data is the unstructured nature of the data points resulting from elevation observations at different time instances. We propose to treat these altimeter data as cloud points in the space-time domain and utilise implicit neural representation (INR) to encode the target field as a continuous function varying both in time and space. Compared to traditional interpolation methods such as trilinear interpolation or kriging, the INR method can capture non-linearities and long-term trends while providing a compact encoding of the target field, allowing for scalable dissemination of the product.

 

We present a feasibility study of utilising INR to reconstruct the surface elevation of the Petermann glacier, northwest Greenland, from CryoSat-2 radar altimeter elevation observations. We carried out many model training experiments, consisting of ablation studies on additional loss terms as well as model architectures (SIREN, RFF, KAN and MFN) and hyperparameters (number and width of layers and loss term weights), to find the best combination. The main difficulty is correctly capturing the glacier temporal dynamics. In addition, we trained models with varying quantities of data (5 months, 1 year, 2 years and 12.5 years) to investigate whether more data improved the model performance. Results are evaluated using Operation IceBridge (OIB) LIDAR, and GeoSAR elevation measurements. OIB allows for evaluation of model elevation over a large temporal and geographical area, whereas GeoSAR allows for comparing high resolution elevation data on a single day over a small area.

 

Results indicate that we achieve the best performance using the SIREN INR architecture coupled with high temporal and spatial loss weights. In addition, models perform best when using CryoSat-2 data from the entire 12.5 year time frame. The models perform particularly well in regions with high data point density but struggle at the outer rims of the ice sheet where the point density is low. The feasibility study presents a promising direction in modelling the spatiotemporal evolution of the ice sheet at a sub kilometre resolution with a daily temporal time step using INR. We foresee these methods being applicable to many geoscience applications with irregular data sampling in space and time.