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Learning Subglacial Bed Topography from Sparse Radar with Physics-Guided Residuals

Bayu Adhi Tama, Jianwu Wang, Vandana Janeja, Mostafa Cham

TL;DR

This paper tackles the challenge of mapping subglacial bed topography from sparse radar by predicting bed-thickness residuals relative to a BedMachine prior using a DeepLabV3+ decoder. It couples a residual-over-prior formulation with lightweight physics regularizers—mass conservation, flow-aligned smoothing, Laplacian damping, and a non-negativity constraint—along with a radar data term and a ramped prior pull to handle radar-sparse interiors. A leakage-safe evaluation protocol with vertical and horizontal block-wise hold-outs ensures robust generalization to unseen regions, and the approach outperforms U-Net, FPN, and plain CNN baselines in both quantitative and structural metrics across two Greenland sub-regions. The resulting beds are spatially coherent and physically plausible, enabling operational mapping under domain shift, with strong potential for extension to Antarctica and for incorporating uncertainty quantification in future work.

Abstract

Accurate subglacial bed topography is essential for ice sheet modeling, yet radar observations are sparse and uneven. We propose a physics-guided residual learning framework that predicts bed thickness residuals over a BedMachine prior and reconstructs bed from the observed surface. A DeepLabV3+ decoder over a standard encoder (e.g.,ResNet-50) is trained with lightweight physics and data terms: multi-scale mass conservation, flow-aligned total variation, Laplacian damping, non-negativity of thickness, a ramped prior-consistency term, and a masked Huber fit to radar picks modulated by a confidence map. To measure real-world generalization, we adopt leakage-safe blockwise hold-outs (vertical/horizontal) with safety buffers and report metrics only on held-out cores. Across two Greenland sub-regions, our approach achieves strong test-core accuracy and high structural fidelity, outperforming U-Net, Attention U-Net, FPN, and a plain CNN. The residual-over-prior design, combined with physics, yields spatially coherent, physically plausible beds suitable for operational mapping under domain shift.

Learning Subglacial Bed Topography from Sparse Radar with Physics-Guided Residuals

TL;DR

This paper tackles the challenge of mapping subglacial bed topography from sparse radar by predicting bed-thickness residuals relative to a BedMachine prior using a DeepLabV3+ decoder. It couples a residual-over-prior formulation with lightweight physics regularizers—mass conservation, flow-aligned smoothing, Laplacian damping, and a non-negativity constraint—along with a radar data term and a ramped prior pull to handle radar-sparse interiors. A leakage-safe evaluation protocol with vertical and horizontal block-wise hold-outs ensures robust generalization to unseen regions, and the approach outperforms U-Net, FPN, and plain CNN baselines in both quantitative and structural metrics across two Greenland sub-regions. The resulting beds are spatially coherent and physically plausible, enabling operational mapping under domain shift, with strong potential for extension to Antarctica and for incorporating uncertainty quantification in future work.

Abstract

Accurate subglacial bed topography is essential for ice sheet modeling, yet radar observations are sparse and uneven. We propose a physics-guided residual learning framework that predicts bed thickness residuals over a BedMachine prior and reconstructs bed from the observed surface. A DeepLabV3+ decoder over a standard encoder (e.g.,ResNet-50) is trained with lightweight physics and data terms: multi-scale mass conservation, flow-aligned total variation, Laplacian damping, non-negativity of thickness, a ramped prior-consistency term, and a masked Huber fit to radar picks modulated by a confidence map. To measure real-world generalization, we adopt leakage-safe blockwise hold-outs (vertical/horizontal) with safety buffers and report metrics only on held-out cores. Across two Greenland sub-regions, our approach achieves strong test-core accuracy and high structural fidelity, outperforming U-Net, Attention U-Net, FPN, and a plain CNN. The residual-over-prior design, combined with physics, yields spatially coherent, physically plausible beds suitable for operational mapping under domain shift.

Paper Structure

This paper contains 50 sections, 13 equations, 3 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Setup
  4. Domain and grid.
  5. Known fields (inputs).
  6. Sparse radar observations.
  7. Learning target (residual formulation).
  8. Predictor.
  9. Physics residual (used as a regularizer).
  10. Evaluation regions.
  11. Method
  12. Residual-over-prior predictor
  13. Training objective
  14. Data term at radar picks.
  15. Mass-conservation regularizer.
  16. ...and 35 more sections

Figures (3)

  • Figure 1: Framework overview. Inputs (surface, velocity, SMB, thickness tendency) and a BedMachine prior form a feature stack for a DeepLabV3$+$ predictor of normalized residual thickness. De-normalization and reconstruction yield thickness and bed. Training uses data, physics, and regularization losses; inference leverages EMA, test-time augmentation, and seam-free tiling. Evaluation is leakage-safe on held-out cores with distance-to-radar stratification.
  • Figure 2: Radar picks and BedMachine prior. Left: geolocated radar bed picks (colored by observed bed elevation). Right: prior bed $b_p$ (BedMachine) on the same grid. Rows show Sub-region I (top) and Sub-region II (bottom) of Upernavik Isstrøm.
  • Figure 3: RMSE vs. distance to radar on held-out test cores. For each sub-region (rows) and split (columns), RMSE is reported in three distance bins (px) from the nearest radar pick: $0\!-\!2$, $2\!-\!6$, and $6\!-\!\infty$. Lines encode methods (markers/colors in the legend). Lower is better.