FDTransformer: A firn density prediction framework combining a self-attention transformer network with firn densification physics

Accurate firn density estimation is essential for assessing glacier mass balance. However, the accuracy of existing firn densification models (FDMs) is limited by an incomplete understanding of firn compaction dynamics, particularly as firn structure alters in warming conditions. This study proposes the firn density prediction transformer (FDTransformer), a deep learning framework that combines firn densification physics to improve density estimation. By employing the transformer network with sequential self-attention mechanisms, the FDTransformer learns a nonlinear mapping between physical firn parameters input and observed firn density, enabling physics-to-density sequence transformation. These physically constrained parameters are estimated by applying physics-based FDMs. Evaluated using <i>in situ</i> measurements from three Greenland sites (Dye-2, KAN_U, and Summit) with varying firn evolution patterns, the FDTransformer reduces mean absolute error by 30%, 42%, and 24%, respectively, compared to the physics-based FDMs. This study demonstrates that combining deep learning techniques with firn densification physics can improve firn density assessment.