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Physics-Knowledge-Guided Hybrid Neural Learning for Arctic Sea Ice Concentration Evolution and Short-Range Prediction

Maqun Zhang, Feng Gao, Wankun Chen, Hui Yu, Yanhai Gan, Junyu Dong

arXiv:2608.21767v1cs.AI

TL;DR

Accurate SIC evolution modeling matters because Arctic ice changes reflect interacting transport and thermodynamic processes that are difficult to represent. PIHIM organizes a differentiable hybrid model around the continuity equation, and the reported evaluations show improved reanalysis-forced stability with retained forecast-forced short-range skill.

  • Problem

    SIC evolution is difficult to model because transport, thermodynamic phase changes, and unresolved processes interact, while numerical and end-to-end data-driven approaches have complementary limitations.

  • Method

    PIHIM decomposes daily SIC evolution into dynamical transport, thermodynamics-guided areal change, and residual compensation within a differentiable hybrid framework.

  • Results

    PIHIM improves ice-edge preservation, error-growth control, and areal stability in reanalysis-forced simulation while retaining consistent short-range advantages under GLORYS and OSI SAF verification.

  • Takeaways & Limitations

    The process-decomposed formulation provides a lightweight alternative to purely end-to-end SIC sequence models while preserving measurable forecast-forced prediction skill.

  • Takeaways & Limitations

    PIHIM does not explicitly resolve sea ice thickness, snow cover, melt ponds, albedo, or fine-scale energy-budget processes, and forecast-forced performance depends on external forecast quality.

Abstract

from arXiv · show

Accurate modeling of sea ice concentration (SIC) evolution is essential for polar climate assessment and short?range sea ice prediction. Numerical and data-driven approaches constitute major foundations for SIC modeling, but the former often require complex parameterizations and substantial compu?tation, whereas the latter rarely encode physical dependencies explicitly. This study presents the Physics-Informed Hybrid Ice Model (PIHIM), a differentiable data-driven hybrid ice model for daily SIC evolution that organizes its network structure according to the physical dependencies encoded in the sea ice continuity equation and explicitly accounts for dynamical transport, ther?modynamically driven areal growth and loss, and unresolved local processes. PIHIM preserves the representation capacity of deep learning while providing a process-decomposed formulation of ice displacement, freeze-melt areal change, and local error closure. Two evaluation settings are adopted: reanalysis-forced simulation examines SIC evolution stability under reanalysis forcing, and forecast-forced prediction assesses short-range performance un?der forecast-forced conditions, with reanalysis and observational SIC serving as verification references. Results indicate enhanced ice-edge preservation and error-growth control in reanalysis?forced simulation, while PIHIM retains measurable short-range prediction skill under forecast-forced conditions. Our code will be made publicly available after the paper is accepted.

I. INTRODUCTION

SIC evolution is difficult to model because multiple nonlinear physical processes shape ice concentration, while existing numerical and data-driven approaches have complementary limitations. PIHIM addresses this gap by organizing learnable components around physical dependencies and evaluating stability and short-range prediction separately.

  • Motivation: SIC evolution reflects atmospheric and oceanic forcing, sea ice transport, and thermodynamic phase changes across nonlinear, seasonal, and heterogeneous conditions.These interactions complicate ice-edge displacement and low-concentration sea ice characterization.
  • Existing approaches: Numerical models represent sea ice dynamics and thermodynamics but depend on unresolved-process parameterizations and can remain computationally demanding at high resolution.
  • Existing approaches: Purely data-driven models often treat SIC evolution as an opaque end-to-end mapping whose internal states do not correspond clearly to transport, thermodynamic change, or residual closure.
  • PIHIM motivation: The continuity equation motivates separating horizontal transport from source-sink changes while using learnable residual closure for simplified physics, discretization, and unresolved processes.
  • Evaluation: The study distinguishes reanalysis-forced simulation for evolution stability from forecast-forced prediction for short-range performance under forecast-product boundary conditions.
  • PIHIM: PIHIM decomposes daily SIC evolution into dynamical transport, thermodynamics-guided source terms, and residual compensation within a differentiable hybrid framework.Its thermodynamic representation uses area-fraction-weighted freeze/melt branches and avoids the computational burden of a full thermodynamic model.

C. Physics-guided and Constrained Deep Learning Models

PIHIM formulates daily SIC prediction around the continuity equation, linking model inputs and outputs to transport, thermodynamic change, and residual local effects. Its autoregressive structure supports multi-step prediction and process diagnosis.

  • Problem formulation: Given current SIC, sea ice drift velocity, and atmospheric-oceanic forcings, PIHIM learns a one-day evolution operator and feeds each prediction into the next step autoregressively.Reanalysis and forecast forcings change the evaluation setting but not the model structure.
  • Physics-guided formulation: The continuity-equation decomposition separates velocity-driven horizontal redistribution from the thermodynamic area source-sink term associated with freezing and melting.
  • Physics-guided formulation: PIHIM implements dynamical transport, estimates freeze/melt areal change from external forcings, and learns remaining local errors through differentiable modules.This structure supports module diagnosis, ablation analysis, and long-term autoregressive evaluation.

B. Physics-guided SIC Evolution Framework

The framework combines differentiable drift-driven transport with a lightweight, constrained thermodynamic source term and residual correction. Together, these modules represent redistribution, freeze/melt areal change, and errors left by simplified process modeling.

  • Dynamical Transport Module: The dynamical module represents SIC redistribution driven by horizontal sea ice drift using a conservative continuity-equation formulation.The transport operator is differentiable and uses semi-Lagrangian integration with temporal substepping for daily stability.
  • Dynamical Transport Module: PIHIM uses 24 transport substeps per day, backtracking departure points, interpolating SIC, and applying a divergence correction before thermodynamic processing.
  • Thermodynamic Source Term: The thermodynamic module estimates potential freezing and melting tendencies from near-surface air temperature, sea surface temperature, and scalar wind speed.It uses separate freezing and melting branches rather than solving a full thermodynamic sea ice model.
  • Thermodynamic Source Term: Freezing contributes non-negative change weighted by available open-water fraction, whereas melting contributes non-positive change weighted by existing ice-covered fraction.This produces a sign-constrained, area-weighted decomposition of thermodynamic areal change.

3) Residual Compensation and State Update:

PIHIM first forms a physics-guided SIC state from dynamical and thermodynamic updates, then adds a learned residual correction for remaining local errors. The final state is constrained through masking and clipping, while residual initialization limits early override of the process-based baseline.

  • The physics-guided intermediate state combines dynamical transport with the thermodynamic source-term update through explicit time integration.
  • A residual network estimates the remaining SIC increment after unresolved deformation, ice-edge fragmentation, forcing mismatch, interpolation, and discretization errors.
  • The residual module receives velocity information to compensate for numerical errors from the discretized dynamical-transport step, while thermodynamic forcing enters indirectly through the intermediate state.
  • Adyn, Athermo, and the final prediction are clipped to [0, 1] and multiplied by the valid ocean mask during implementation.
  • Zero-initializing the residual network's last layer keeps its initial correction near zero, reducing early dominance over the dynamical and thermodynamic baseline.
  • Overall, the dynamical, thermodynamic, and residual modules respectively represent horizontal transport, freeze/melt areal change, and remaining errors.

C. Training Strategy and Loss Function

PIHIM uses staged optimization and autoregressive rollout to preserve its process-decomposed structure and improve multi-step stability. Its composite loss combines pixel-level accuracy with regional area-bias control.

  • Training Strategy: The residual pathway is staged because its representational capacity could otherwise dominate error gradients before the thermodynamics-guided module learns stable freeze/melt tendencies.
  • Training Strategy: Staged optimization first trains the thermodynamics-guided source-term module, then jointly fine-tunes it with the residual module to learn remaining errors.
  • Training Strategy: Autoregressive rollout reuses each predicted SIC field as the next input for T consecutive steps, with T = 14 during training.
  • Loss Function: The composite loss combines pixel-wise mean squared error with a regional area-bias term because local accuracy alone may not penalize systematic regional SIC drift.
  • Loss Function: The regional area-bias term penalizes the squared difference between predicted and reference mean SIC over the valid ocean region.
  • Loss Function: The main rollout loss is averaged across rollout steps to constrain both step-wise spatial accuracy and multi-step regional stability.

IV. EXPERIMENTS

The experiments evaluate PIHIM separately under reanalysis-forced simulation and forecast-forced prediction. Baselines use matched evaluation protocols, and performance is assessed with spatial, correlation, ice-edge, area, and extent metrics.

  • Evaluation settings: Reanalysis-forced simulation examines SIC evolution under prescribed reanalysis forcing, whereas forecast-forced prediction assesses D1-D9 short-range performance under forecast-forced conditions.
  • Evaluation settings: Reanalysis-forced simulation supplies ERA5/GLORYS forcings at each valid time, while forecast-forced prediction uses AIFS/RTOFS forecast forcings after initialization.
  • Evaluation protocol: Trainable baselines use the same data splits, input variables, evaluation windows, and verification references as PIHIM within each setting.
  • Evaluation metrics: Evaluation metrics include MAE, RMSE, ACC, Integrated Ice Edge Error, sea ice area, and sea ice extent.

B. Reanalysis-forced Simulation

Under reanalysis-forced simulation, PIHIM is evaluated from 14-day accuracy through multi-year autoregressive stability. It shows strong short-range metrics, controlled error growth, stable annual evolution, and limited areal drift, with some diagnostics remaining forcing- and period-dependent.

  • Fourteen-day benchmark: PIHIM attains the lowest MAE, RMSE, and IIEE and the highest ACC among evaluated models in the 14-day benchmark.
  • Fourteen-day benchmark: 41% and 61%: PIHIM reduces MAE and IIEE relative to Persistence, respectively, while IceNet remains the closest baseline.
  • Seasonal-scale and long-term stability: Through Day 90, MAE remains near 0.026-0.027, RMSE near 0.068-0.071, ACC above 0.87, and IIEE near 0.27-0.30 × 10^6 km2 without apparent error divergence.These are endpoint averages over seasonal cases rather than cumulative averages along one error sequence.
  • Seasonal-scale and long-term stability: Across 2022-2024 calendar-year integrations, PIHIM reproduces the main annual SIA/SIE phases, with MAE around 0.026-0.028 and IIEE around 0.27-0.30 × 10^6 km2.The lower ACC and higher IIEE in 2022 indicate sensitivity to interannual ice-edge conditions and external forcing states.
  • Seasonal-scale and long-term stability: PIHIM reproduces the reference multi-year SIA trend direction with a trend error of 0.0125 × 10^6 km2 yr−1, indicating limited areal drift under prescribed reanalysis forcings.This 2022-2024, forcing-dependent diagnostic should not be interpreted as evidence of climate-scale trend prediction capability.

C. Mechanistic Interpretation

The diagnostics examine component contributions through inference-time ablations, seasonal-regional error attribution, and thermodynamic source-term behavior. Results indicate that the full model benefits from complementary dynamical, thermodynamic, and residual modules.

  • C. Mechanistic Interpretation: The diagnostic analysis tests coupled process modules, regional-seasonal error patterns, and thermodynamic source-term responses.Inference-time ablations use the same trained PIHIM rather than independently retrained architectures.
  • C. Mechanistic Interpretation: The full model attains the lowest errors and highest ACC among the diagnostic variants.Dynamic + Thermo, Dynamic + compensation, and Thermo + compensation all remain below full PIHIM.
  • C. Mechanistic Interpretation: Dynamical transport, thermodynamic source terms, and residual compensation provide complementary contributions to SIC evolution accuracy.Explicit process terms alone do not close all SIC evolution errors.

2) Seasonal and Regional Error Attribution:

Errors are concentrated in the marginal ice zone, while the thermodynamic source term exhibits seasonal phase and forcing-perturbation responses. The forecast-forced evaluation uses defined test sets and excludes forecast sea ice velocity.

  • Seasonal and Regional Error Attribution: MIZ MAE reaches 0.1192-0.1384 across seasons, whereas open-water MAE is near 0.006 and pack-ice errors remain relatively low.The MIZ combines low-concentration ice, contour displacement, and freeze-melt phase changes.
  • Thermodynamic Source-term Diagnostics: The thermodynamic source term uses sign-constrained freezing and melting branches weighted by open-water and ice-covered fractions.Freezing contributes non-negative increments, while melting contributes non-positive increments.
  • Thermodynamic Source-term Diagnostics: The net source is negative during melting, positive during freezing, and intermediate during transition seasons.Warming Tair and SST perturbations shift the net source toward melting, with a stronger SST response.
  • Forecast-forced Prediction: Forecast sea ice velocity is excluded because short-range drift forecasts are sensitive to multiple forcing and assimilation factors.Incorporating reliable forecast sea ice velocity and recalibrating the dynamical module are left for future work.
  • Evaluation Design: The forecast-forced evaluation reports a 99-case overall set and a 25-case SEAS5-intersection set verified against GLORYS and OSI SAF.The 25-case set provides same-date contextual comparison.

1) 99-case Forecast-forced Prediction Results:

Across the 99-case forecast-forced evaluation, PIHIM performs best under both GLORYS and OSI SAF verification. The contextual 25-case comparison extends this pattern to selected learning baselines and SEAS5 ensemble summaries.

  • 99-case Forecast-forced Prediction Results: PIHIM obtains the lowest MAE, RMSE, and IIEE and the highest ACC under both GLORYS and OSI SAF verification.All models show larger errors under OSI SAF than under GLORYS, but PIHIM retains a consistent advantage.
  • SEAS5-intersection 25-case Contextual Comparison: The 25-case results are consistent with the 99-case evaluation.The comparison uses initialization dates common to SEAS5 and PIHIM.
  • SEAS5-intersection 25-case Contextual Comparison: PIHIM outperforms selected learning baselines and SEAS5 ensemble summaries under both verification references.SEAS5 remains a contextual numerical reference rather than part of the full 99-case comparison.
  • Spatial Comparison: Spatial cases supplement global statistics by comparing 15% SIC ice-edge contours and local morphology under forecast-forced conditions.The supplied figure passages identify GLORYS- and OSI SAF-verified cases across D3, D6, and D9.

1) Rapid Retreat and Expansion Cases in Reanalysis-forced Simulation:

Rapid retreat and expansion cases assess 15% SIC ice-edge preservation in reanalysis-forced simulation, while forecast-forced cases examine short-range spatial stability. These case studies support the broader conclusion of improved ice-edge preservation and controlled error growth.

  • Rapid Retreat and Expansion Cases in Reanalysis-forced Simulation: PIHIM keeps the 15% SIC contour closer to GLORYS than the baselines during both rapid retreat and rapid expansion.The cases correspond to the fastest 14-day retreat and expansion diagnostics.
  • Forecast-forced Spatial Cases: PIHIM remains comparatively stable from D3 to D9 in the May 22, 2024 forecast-forced case under GLORYS and OSI SAF verification.The case is consistent with the 99-case forecast-forced statistics.
  • SEAS5 Contextual Comparison: Under both verification references, PIHIM shows smaller ice-edge displacement than SEAS5 EnsMean in the 25-case contextual comparison.The comparison uses the April 1, 2026 initialization.
  • Conclusion: Overall, PIHIM improves ice-edge preservation and error-growth control in reanalysis-forced simulation while retaining short-range advantages under forecast-forced prediction.The conclusion also attributes complementary roles to transport, thermodynamic change, and residual compensation.
  • Conclusion: PIHIM remains a lightweight data-driven model rather than a full numerical sea ice model.Its thermodynamic module does not explicitly resolve thickness, snow cover, melt ponds, albedo, or fine-scale energy-budget processes.
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