Graph transformers have demonstrated remarkable capability on complex spatio-temporal tasks, yet their depth is often limited by oversmoothing and weak long-range dependency modeling. To address these challenges, we introduce GRIT -LP, a graph transformer explicitly designed for polar ice-layer thickness estimation from polar radar imagery. Accurately estimating ice layer thickness is critical for understanding snow accumulation, reconstructing past climate patterns and reducing uncertainties in projections of future ice sheet evolution and sea level rise. GRIT -LP combines an inductive geometric graph learning framework with self-attention mechanism, and introduces two major innovations that jointly address challenges in modeling the spatio-temporal patterns of ice layers: a partitioned spatial graph construction strategy that forms overlapping, fully connected local neighborhoods to preserve spatial coherence and suppress noise from irrelevant long-range links, and a long-range skip connection mechanism within the transformer that improves information flow and mitigates oversmooth-ing in deeper attention layers. We conducted extensive experiments, demonstrating that GRIT -LP outperforms current state-of-the-art methods with a 24.92% improvement in root mean squared error. These results highlight the effectiveness of graph transformers in modeling spatiotemporal patterns by capturing both localized structural features and long-range dependencies across internal ice layers, and demonstrate their potential to advance data-driven understanding of cryospheric processes. Introduction Graph transformers have proven to be highly effective for modeling complex graph-structured data, with wide-range of applications in real-world scenarios, particularly those involving spatiotemporal patterns. Their ability to capture intricate relationships and dependencies makes them highly valuable in domains such as pedestrian trajectory prediction [1] and traffic prediction [2]. Despite their success, current graph transformer architectures face notable limitations, including overfitting and over-smoothing--a phenomenon where node features become indistinguishable as layers deepen [3]. Additionally, many existing graph transformers are relatively shallow, limiting their ability to effectively capture the complex, long-range dependencies that often emerge in real-world datasets.

Understanding the thickness and variability of internal ice layers in radar imagery is crucial for monitoring snow accumulation, assessing ice dynamics, and reducing uncertainties in climate models. Radar sensors, capable of penetrating ice, provide detailed radargram images of these internal layers. In this work, we present ST-GRIT, a spatio-temporal graph transformer for ice layer thickness, designed to process these radargrams and capture the spatiotemporal relationships between shallow and deep ice layers. ST-GRIT leverages an inductive geometric graph learning framework to extract local spatial features as feature embeddings and employs a series of temporal and spatial attention blocks separately to model long-range dependencies effectively in both dimensions. Experimental evaluation on radargram data from the Greenland ice sheet demonstrates that ST-GRIT consistently outperforms current state-of-the-art methods and other baseline graph neural networks by achieving lower root mean-squared error. These results highlight the advantages of self-attention mechanisms on graphs over pure graph neural networks, including the ability to handle noise, avoid oversmoothing, and capture long-range dependencies. Moreover, the use of separate spatial and temporal attention blocks allows for distinct and robust learning of spatial relationships and temporal patterns, providing a more comprehensive and effective approach.

Gaining a deeper understanding of the thickness and variability of internal ice layers in Radar imagery is essential in monitoring the snow accumulation, better evaluating ice dynamics processes, and minimizing uncertainties in climate models. Radar sensors, capable of penetrating ice, capture detailed radargram images of internal ice layers. In this work, we introduce GRIT, graph transformer for ice layer thickness. GRIT integrates an inductive geometric graph learning framework with an attention mechanism, designed to map the relationships between shallow and deeper ice layers. Compared to baseline graph neural networks, GRIT demonstrates consistently lower prediction errors. These results highlight the attention mechanism's effectiveness in capturing temporal changes across ice layers, while the graph transformer combines the strengths of transformers for learning long-range dependencies with graph neural networks for capturing spatial patterns, enabling robust modeling of complex spatiotemporal dynamics.

Understanding spatio-temporal patterns in polar ice layers is essential for tracking changes in ice sheet balance and assessing ice dynamics. While convolutional neural networks are widely used in learning ice layer patterns from raw echogram images captured by airborne snow radar sensors, noise in the echogram images prevents researchers from getting high-quality results. Instead, we focus on geometric deep learning using graph neural networks, aiming to build a spatio-temporal graph neural network that learns from thickness information of the top ice layers and predicts for deeper layers. In this paper, we developed a novel multi-branch spatio-temporal graph neural network that used the GraphSAGE framework for spatio features learning and a temporal convolution operation to capture temporal changes, enabling different branches of the network to be more specialized and focusing on a single learning task. We found that our proposed multi-branch network can consistently outperform the current fused spatio-temporal graph neural network in both accuracy and efficiency.

Learning spatio-temporal patterns of polar ice layers is crucial for monitoring the change in ice sheet balance and evaluating ice dynamic processes. While a few researchers focus on learning ice layer patterns from echogram images captured by airborne snow radar sensors via different convolutional neural networks, the noise in the echogram images proves to be a major obstacle. Instead, we focus on geometric deep learning based on graph neural networks to learn the spatio-temporal patterns from thickness information of shallow ice layers and make predictions for deep layers. In this paper, we propose a physics-informed hybrid graph neural network that combines the GraphSAGE framework for graph feature learning with the long short-term memory (LSTM) structure for learning temporal changes, and introduce measurements of physical ice properties from Model Atmospheric Regional (MAR) weather model as physical node features. We found that our proposed network can consistently outperform the current non-inductive or non-physical model in predicting deep ice layer thickness.

As we deal with the effects of climate change and the increase of global atmospheric temperatures, the accurate tracking and prediction of ice layers within polar ice sheets grows in importance. Studying these ice layers reveals climate trends, how snowfall has changed over time, and the trajectory of future climate and precipitation. In this paper, we propose a machine learning model that uses adaptive, recurrent graph convolutional networks to, when given the amount of snow accumulation in recent years gathered through airborne radar data, predict historic snow accumulation by way of the thickness of deep ice layers. We found that our model performs better and with greater consistency than our previous model as well as equivalent non-temporal, non-geometric, and non-adaptive models.

The accurate prediction and estimation of annual snow accumulation has grown in importance as we deal with the effects of climate change and the increase of global atmospheric temperatures. Airborne radar sensors, such as the Snow Radar, are able to measure accumulation rate patterns at a large-scale and monitor the effects of ongoing climate change on Greenland's precipitation and run-off. The Snow Radar's use of an ultra-wide bandwidth enables a fine vertical resolution that helps in capturing internal ice layers. Given the amount of snow accumulation in previous years using the radar data, in this paper, we propose a machine learning model based on recurrent graph convolutional networks to predict the snow accumulation in recent consecutive years at a certain location. We found that the model performs better and with more consistency than equivalent nongeometric and nontemporal models.

In recent years, We focus on the Snow Radar [1] dataset collected by the airborne radar sensors, such as the Snow Radar, have been Center for Remote Sensing of Ice Sheets (CReSIS) as part of shown to be able to measure these internal ice layers over NASA's Operation IceBridge. The Snow Radar operates from large areas with a fine vertical resolution. In our previous 2-8 GHz and is able to track deep layers of ice with a high resolution work, we found that temporal graph convolutional networks over wide areas of an ice sheet. The sensor produces perform reasonably well in predicting future snow accumulation a two-dimensional grayscale profile of historic snow accumulation when given temporal graphs containing deep ice layer over consecutive years, where the horizontal axis represents thickness. In this work, we experiment with a graph attention the along-track direction, and the vertical axis represents network-based model and used it to predict more annual layer depth. Pixel brightness is directly proportional to snow accumulation data points with fewer input data points the strength of the returning signal.

Ice thickness estimation is an important aspect of ice sheet studies. In this work, we use convolutional neural networks with multiple output nodes to regress and learn the thickness of internal ice layers in Snow Radar images collected in northwest Greenland. We experiment with some state-of-the-art networks and find that with the residual connections of ResNet50, we could achieve a mean absolute error of 1.251 pixels over the test set. Such regression-based networks can further be improved by embedding domain knowledge and radar information in the neural network in order to reduce the requirement of manual annotations.