Structured Neural Modeling of Daily Arctic Sea-Ice Concentration Evolution: Physical-Trajectory-Driven Learning and Forecast-Domain Adaptation

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

physics.ao-phAug 22, 2026

Structured Neural Modeling of Daily Arctic Sea-Ice Concentration Evolution: Physical-Trajectory-Driven Learning and Forecast-Domain Adaptation

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

Organizations: State Key Laboratory of Physical Oceanography and Faculty of Information Science and Engineering, Ocean University of China, Qingdao 266100, China · School of Psychology and Neuroscience, University of Glasgow, Glasgow G12 8QQ, U.K.

Abstract

Accurate modeling of the daily evolution of sea ice concentration (SIC) is central to improving the credibility and operational forecasting capability of deep learning-based sea ice prediction. However, existing deep learning methods often couple the underlying sea ice evolution relationships and data errors within high-dimensional nonlinear mappings, making it difficult to construct a stable and verifiable evolution core and apply it reliably to practical forecasting. To address this issue, this study proposes a reanalysis-forecast dual-domain decoupled framework for learning sea ice evolution operators. The framework builds upon a lightweight physical baseline to generate daily evolution trajectories, employs a temporally constrained joint multi-lead compensation network to com?pensate for unresolved processes, and introduces an ice-mass?aware transport mechanism to suppress numerical dissipation. In the forecasting stage, the parameters of the base evolution core are fixed, while a lightweight variable-semantic adaptation mechanism calibrates inter-domain distributions and evolution responses, thereby separating forecast-domain errors from base evolution errors. Experiments show that the constructed base evolution core can accurately and stably simulate daily sea ice evolution at both short-term and annual scales under reanal?ysis forcing, and can be effectively transferred to the forecast domain through lightweight adaptation, achieving stable prac?tical forecasting capability while preserving the base evolution structure. The source code will be made publicly available at https://github.com/zhangmaqun65535/SNM upon acceptance of this manuscript.

Figures & tables

Fig. 1: Overall architecture of the proposed network. In the reanalysis domain, the model takes the initial SIC and multi-lead forcings as inputs, generates the daily state trajectory through the Lightweight Physical Trajectory Module ( $P_{\theta}$ ), and jointly estimates residuals in a single forward pass using the Temporally Prefix-Constrained Multi-Lead Compensation Module ( $C_{\phi}$ ), thereby producing the evolution-core output. During forecasting, the evolution core remains frozen. Variable-Specific Input Adaptation (VSIA) calibrates the observed initial condition and forecast forcings, while Response-Domain Semantic Correction (RDSC) further refines the output. The model thereby establishes a structured separation among physical propagation, multi-lead residual learning, and forecast-domain adaptation.

Item	Description
Input	Current SIC $A_{t}$ , relative ice mass $S_{t}$ , vector sea ice velocity $\mathbf{v}_{t}$ , and valid domain $\Omega$ .
Output	Corrected dynamical state $(A_{t+1}^{D},S_{t+1})$ .
Notation	$[x]_{+}=\max(x,0)$ , $\varepsilon>0$ is a stability constant for weight calculation, and $S_{\max}$ is the prescribed upper bound of the relative ice-mass state.
Step 1: Baseline transport	Advance SIC and relative ice mass separately through the existing dynamical transport to obtain the intermediate states $A^{\mathrm{adv}}$ and $S^{\mathrm{adv}}$ .
Step 2: Area-deficit calculation	Because the grid is equal-area, calculate the equivalent sea ice area deficit induced by transport as $\displaystyle\Delta m=\left[\sum_{p\in\Omega}A_{t,p}-\sum_{p\in\Omega}A_{p}^{\mathrm{adv}}\right]_{+}$ .
Step 3: Area-constrained redistribution	Calculate the local loss, remaining capacity, and replenishment weight as $\displaystyle\ell_{p}=[A_{t,p}-A_{p}^{\mathrm{adv}}]_{+}$ , $\displaystyle c_{p}=[1-A_{p}^{\mathrm{adv}}]_{+}$ , and $\displaystyle w_{p}=\ell_{p}c_{p}\sqrt{A_{t,p}+\varepsilon}$ . Distribute $\Delta m$ according to the normalized weights $w_{p}$ , with $c_{p}$ limiting local replenishment, to obtain $A^{\mathrm{area}}$ . If all local-loss weights are zero, determine replenishment locations solely from the remaining capacity and existing sea ice distribution.

Table 2

Task	Initial State and Target	External Forcing	Training or Adaptation Period	Evaluation Period	No. of Initializations (Training/Evaluation)	Lead Time
Reanalysis-forced simulation	GLORYS12V1 SIC [ 53 ]	GLORYS12V1 sea ice velocity and sea surface temperature [ 53 ] ; ERA5 2-m air temperature and net heat flux [ 54 ]	2015–2021	2022–2024	2459/1054	14 days
Forecast-forced prediction	OSI-430-a and OSI-401-d SIC [ 55 , 56 ]	TOPAZ5 sea ice velocity and sea surface temperature [ 57 ] ; GFS 2-m air temperature and net heat flux [ 58 ]	2023-09-01–2024-08-31	2024-09-18–2025-09-01	366/336	10 days

TABLE I: Data Sources, Temporal Splits, and Evaluation Protocols.

Model	MAE	RMSE	Bias	ACC	IIEE
PredRNN++	0.031302	0.083033	+0.002932	0.808657	0.458069
FCNet	0.029835	0.081050	+0.000717	0.814477	0.404746
VMRNN	0.029337	0.071583	+0.002563	0.855370	0.369199
SwinLSTM	0.029252	0.071281	+0.003275	0.856853	0.362219
PredRNN-v2	0.026686	0.068568	+0.000905	0.867448	0.361438
SimVP	0.024916	0.067109	+0.001198	0.874807	0.284190

TABLE II: Fourteen-Day Mean Performance Under Reanalysis Forcing.

Fig. 2: SIC MAE of all models over days 1–14.

Fig. 3: SIC IIEE of all models over days 1–14.

Fig. 4: Mean annual SIA cycle over 2022–2024.

State	MAE	RMSE	Bias	ACC	IIEE
Persistence	0.038852	0.109363	+0.000894	0.699885	0.620202
D	0.043211	0.115129	+0.000110	0.673471	0.612158
DT	0.036729	0.093969	-0.001214	0.738146	0.528937
DTC	0.020235	0.052285	+0.002911	0.925123	0.229394

TABLE III: Fourteen-Day Mean Performance of the Stagewise States.

State	Annual SIC MAE	SIA Seasonal Correlation	SIA Amplitude Ratio
D	0.189529	0.643167	0.145488
DT	0.058713	0.992654	1.144676
DTC	0.024120	0.999362	1.002461

TABLE IV: Annual Closed-Loop Performance of the Stagewise States.

Fig. 5: Lead-wise errors of Persistence, D, DT, and DTC over 14 days.

Fig. 6: Three-year mean annual SIA evolution over 2022–2024 and direct correction of physical-baseline errors by the compensation module.

Fig. 7: Ablation diagnostics of the ice-mass conservation mechanisms: (a) lead-wise SIC Bias for the complete dynamics module, without mass refilling, and without relative ice-mass storage; (b) 14-day mean MAE under the three dynamics configurations; (c) annual and three-year mean end-of-year SIA errors for the complete dynamics module and the configuration without relative ice-mass storage.

Fig. 8: Conditional-residual semantics and physical-trajectory dependence of the compensation module: (a) lead-wise error-reduction rate; (b) spatial cosine similarity between the compensation correction and the target physical-baseline error; (c) MAE increases induced by zero, climatological, and lead-reversed trajectories relative to the correct physical trajectory.

Subsequent-input replacement	H24 without temporal constraints	H24 with temporal constraints	H34 with temporal constraints
Zero forcing	0.07404	0	0
Noisy forcing	0.09715	0	0
All-zero inputs	0.09365	0	0
Repeated day-7 inputs	0.01543	0	0
Reversed tail	0.01333	0	0

TABLE V: Mean Absolute Changes in the Original Compensation Residuals Over Days 1–7 After Replacement of the Inputs for Days 8–14.

Fig. 9: Temporal influence matrices for H24 without temporal constraints, H24 with temporal constraints, and H34 with temporal constraints. The horizontal and vertical axes represent input lead $j$ and output lead $k$ , respectively, with the vertical axis increasing upward. Gray denotes exact zeros, whereas the remaining colors represent $\log_{10}M_{k,j}$ .

Structure	Parameter count	14-day MAE	Max 7-Day Residual- Prefix Drift	Max Future-Input Influence
No temporal constraint, H24 †	0.281 M	0.018878	1.897592	0.132352
Temporal constraint, H24	0.281 M	0.023708	0	0
Temporal constraint, H34 (Ours)	0.556 M	0.020235	0	0

TABLE VI: Accuracy Cost of the Temporal Constraint and Structural Verification Results.

Variable	Physical pathway	Compensation pathway	Both pathways
Sea ice velocity	+17.24% / +20.41%	+29.63% / +57.98%	+53.01% / +79.80%
Sea surface temperature	+27.05% / +15.66%	+3.12% / +5.10%	+25.66% / +12.72%
2-m air temperature	+6.41% / +14.72%	+0.42% / +0.98%	+6.32% / +13.13%
Net heat flux	+13.15% / +4.03%	+1.59% / +0.54%	+14.88% / +3.26%

TABLE VII: Relative Error Increases for Different Variable Pathways Under Daily Spatial-Climatology Replacement (MAE / IIEE).

Fig. 10: Cumulative relative increases in MAE and IIEE for different variables under daily spatial-climatology replacement. Dashed lines mark days 14 and 90, and points denote the results at day 14, day 90, and the end of the year.

Fig. 11: Annual SIA response under daily spatial-climatology replacement: (a) three-year mean seasonal cycles of the complete model and the reanalysis reference; (b) SIA differences between the variable-replacement results and the complete model.

Method	MAE	RMSE	Bias	IIEE	SIAE
Persistence	0.033642	0.090711	+0.000137	0.508404	0.310133
Direct replacement	0.125973	0.208540	-0.093977	1.245631	1.973573
Initial-domain adaptation	0.038366	0.089657	-0.010703	0.476152	0.240168
Variable-semantic adaptation	0.032689	0.078341	-0.001965	0.436107	0.125756
Dynamical–thermodynamic refinement (Ours)	0.032401	0.075930	+0.000211	0.428574	0.119582

TABLE VIII: Ten-Day Mean Performance Under Progressive Forecast-Domain Adaptation. IIEE and SIAE Are Reported in

10^{6}\ \mathrm{km}^{2}

Fig. 12: Lead-wise performance of different adaptation models: (a) SIC MAE over days 1–10; (b) IIEE over days 1–10.

Fig. 13: Forecast-domain adaptation under an equal parameter budget: (a) ten-day mean SIC MAE; (b) ten-day mean IIEE. Ours denotes the variable-semantic adaptation model under the equal-budget setting.

Adaptation configuration	MAE	RMSE	Bias	IIEE	SIAE
Initial adaptation	0.038366	0.089657	-0.010703	0.476152	0.240168
Sea-ice-velocity correction only	0.037833	0.087556	-0.011037	0.465355	0.247052
Flux correction only	0.038000	0.089564	-0.008301	0.471681	0.224860
Sea-ice velocity + flux + gating	0.037757	0.087717	-0.008534	0.455445	0.244399
Complete semantic structure	0.032689	0.078341	-0.001965	0.436107	0.125756

TABLE IX: Performance of Different Adaptation-Module Configurations. IIEE and SIAE Are Reported in

10^{6}\ \mathrm{km}^{2}

Refinement structure	MAE	RMSE	Bias	IIEE	SIAE
Variable-semantic adaptation baseline	0.032689	0.078341	-0.001965	0.436107	0.125756
Dynamical branch only	0.032823	0.077184	-0.003126	0.432103	0.125337
Freezing/melting branches only	0.033264	0.077404	+0.001256	0.432064	0.127710
Dynamical + freezing/melting	0.032401	0.075930	+0.000211	0.428574	0.119582
Dynamical + freezing/melting + interaction	0.032570	0.075874	-0.000587	0.429033	0.115946

TABLE X: Performance of Different Process-Refinement Branch Configurations Under Fixed Jointly Trained Parameters. IIEE and SIAE Are Reported in

10^{6}\ \mathrm{km}^{2}

Fig. 14: Relative sensitivity to future forecast information: (a) based on MAE; (b) based on IIEE. Percentages are normalized only over the positive error increases of the four external forcing variables and exclude the initial SIC.

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Physics-Informed ML Climate Modeling Spatiotemporal Forecasting

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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.

Abstract

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