cs.AIOct 2, 2026

REACT: Physically and Chemically Consistent Reconstruction of Marine Active Tracers

Authors: Wenbin Dai, Hao Zheng, Shiyu Liang, Chaofan Sun, Xueying Zhang, Hanbo Huang, Xuan Gong, Yiran Zhang, 

Organizations: Shanghai Jiao Tong University Shanghai, China

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Abstract

Reconstructing global sea surface pH from sparse observations is critical for monitoring ocean acidification and understanding marine carbon cycling. Traditional assimilation and inverse models are physically grounded but costly for large-scale reconstruction. Recent black-box and physics-guided AI models improve efficiency, but are mainly designed for passive tracers, where the reconstructed variable is also the transported inventory. In contrast, pH is an active carbonate tracer: it is the prediction target, while dissolved inorganic carbon (DIC) is the conserved carbon inventory. This mismatch can produce low pH error while violating carbonate closure and source-free carbon conservation. To address this, we introduce REACT, a carbon-first reconstruction framework that decouples transport, active correction, and chemical decoding. REACT transports a latent carbonate state with a conservative advection--diffusion solver, captures non-conservative carbon-cycle variations with a source module, decodes the corrected state into pH, and constrains the output through carbonate equilibrium. This design keeps pH as the target while enforcing consistency on the underlying carbon state. On simulation data, REACT reduces pH NRMSE by (14.7%) and chemical consistency error by (24.0%) over the best baseline. Cross-temporal-scale evaluations show robustness against error accumulation from coarse to fine temporal scales, and ablation studies validate the effectiveness of each component.

Figures & tables

Figure 1: Conservation-aware transport of pH in the carbonate system. (a) Passive tracers are transported as conserved physical inventories and therefore obey conservation laws. (b) In contrast, pH is an equilibrium-dependent chemical coordinate coupled to carbonate variables such as DIC and pCO2p\mathrm{CO}_{2} . (c) Treating pH as a passive tracer preserves only the transported pH field and does not generally conserve the associated carbon inventory, while introducing a latent conserved state that decodes to both pH and DIC enables transport consistent with DIC conservation.
Figure 2: Overview of REACT . REACT initializes a carbon-related state from sparse observations and physical drivers, propagates it through a conservative transport module, adds learned active source corrections, and decodes the corrected state into pH. The reconstructed pH is checked by carbonate chemistry, while the source-free branch is constrained to conserve represented DIC mass.
TaskTrainVal.Test
Month →\to Week1971–20101965–1970; 2011–20161959–1964; 2017–2022
Week →\to Day1988–20031987; 20041986; 2005
WOD1982–20182019–20202021–2022
Table 1: Overview of dataset divisions by year.
MethodsParamsMonth →\to WeekWeek →\to Day
0.11%1%10%0.11%1%10%
pHChem.pHChem.pHChem.pHChem.pHChem.pHChem.
Krig-Exp–50.6 {}_{\scalebox{0.70}{\scriptstyle\pm 0.91}}10.1 {}_{\scalebox{0.70}{\scriptstyle\pm 0.34}}37.0 {}_{\scalebox{0.70}{\scriptstyle\pm 0.84}}7.06 {}_{\scalebox{0.70}{\scriptstyle\pm 0.26}}23.3 {}_{\scalebox{0.70}{\scriptstyle\pm 0.72}}4.56 {}_{\scalebox{0.70}{\scriptstyle\pm 0.23}}51.2 {}_{\scalebox{0.70}{\scriptstyle\pm 0.86}}9.95 {}_{\scalebox{0.70}{\scriptstyle\pm 0.29}}37.1 {}_{\scalebox{0.70}{\scriptstyle\pm 0.82}}6.94 {}_{\scalebox{0.70}{\scriptstyle\pm 0.27}}22.2 {}_{\scalebox{0.70}{\scriptstyle\pm 0.68}}4.22 {}_{\scalebox{0.70}{\scriptstyle\pm 0.17}}
Krig-Sph–50.9 {}_{\scalebox{0.70}{\scriptstyle\pm 0.89}}10.2 {}_{\scalebox{0.70}{\scriptstyle\pm 0.20}}41.2 {}_{\scalebox{0.70}{\scriptstyle\pm 0.88}}7.83 {}_{\scalebox{0.70}{\scriptstyle\pm 0.27}}33.8 {}_{\scalebox{0.70}{\scriptstyle\pm 0.81}}6.11 {}_{\scalebox{0.70}{\scriptstyle\pm 0.28}}52.2 {}_{\scalebox{0.70}{\scriptstyle\pm 0.83}}10.2 {}_{\scalebox{0.70}{\scriptstyle\pm 0.33}}39.4 {}_{\scalebox{0.70}{\scriptstyle\pm 0.84}}7.35 {}_{\scalebox{0.70}{\scriptstyle\pm 0.30}}26.9 {}_{\scalebox{0.70}{\scriptstyle\pm 0.66}}5.04 {}_{\scalebox{0.70}{\scriptstyle\pm 0.19}}
4D-Var.0.27M6.92 {}_{\scalebox{0.70}{\scriptstyle\pm 0.03}}2.09 {}_{\scalebox{0.70}{\scriptstyle\pm 0.03}}7.14 {}_{\scalebox{0.70}{\scriptstyle\pm 0.04}}2.00 {}_{\scalebox{0.70}{\scriptstyle\pm 0.02}}5.99 {}_{\scalebox{0.70}{\scriptstyle\pm 0.06}}1.90 {}_{\scalebox{0.70}{\scriptstyle\pm 0.04}}5.93 {}_{\scalebox{0.70}{\scriptstyle\pm 0.07}}1.86 {}_{\scalebox{0.70}{\scriptstyle\pm 0.03}}6.02 {}_{\scalebox{0.70}{\scriptstyle\pm 0.05}}1.88 {}_{\scalebox{0.70}{\scriptstyle\pm 0.03}}7.40 {}_{\scalebox{0.70}{\scriptstyle\pm 0.05}}2.05 {}_{\scalebox{0.70}{\scriptstyle\pm 0.04}}
Marble0.83M25.7 {}_{\scalebox{0.70}{\scriptstyle\pm 0.03}}5.65 {}_{\scalebox{0.70}{\scriptstyle\pm 0.10}}25.8 {}_{\scalebox{0.70}{\scriptstyle\pm 0.03}}5.71 {}_{\scalebox{0.70}{\scriptstyle\pm 0.07}}25.2 {}_{\scalebox{0.70}{\scriptstyle\pm 0.02}}5.51 {}_{\scalebox{0.70}{\scriptstyle\pm 0.07}}26.9 {}_{\scalebox{0.70}{\scriptstyle\pm 0.04}}5.51 {}_{\scalebox{0.70}{\scriptstyle\pm 0.06}}26.9 {}_{\scalebox{0.70}{\scriptstyle\pm 0.02}}5.55 {}_{\scalebox{0.70}{\scriptstyle\pm 0.03}}27.0 {}_{\scalebox{0.70}{\scriptstyle\pm 0.03}}5.51 {}_{\scalebox{0.70}{\scriptstyle\pm 0.05}}
Table 2: Main results. Sea surface pH reconstruction on Month →\to Week and Week →\to Day tasks under different sampling ratios. pH NRMSE is reported in units of 10−410^{-4} , and Chem. is reported in units of 10−210^{-2} . Best and second-best results are shown in bold and underline , respectively. Subscript values denote standard errors over three independent sparse-observation samplings. Params denotes model size. U-Net 2 denotes a two-level U-Net variant. Gain denotes relative improvement over the strongest baseline. Decomposed pCO2sp\mathrm{CO}_{2}^{s} and DIC errors are reported in Appendix Table 8 .
Figure 3: Qualitative error maps. Spatial reconstruction errors on MOM6, computed as prediction minus ground truth. Additional qualitative results are provided in Appendix E.2 .
Figure 4: Real-observation results. pH NRMSE and Chem. measure are reported in units of 10−310^{-3} and 10−110^{-1} , respectively. Lower is better. Decomposed pCO2sp\mathrm{CO}_{2}^{s} and DIC results are provided in Appendix E.3 .
  REACT (Month →\to Week)REACT (Week →\to Day)U-Net (Month →\to Week)
SourceLmass\mathcal{L}_{\mathrm{mass}}Lchem\mathcal{L}_{\mathrm{chem}}pHChem.Drift localDrift globalpHChem.Drift localDrift globalpHChem.Drift localDrift global
–––40.8Div.––11.82.73––7.742.12––
✓––5.791.938.84‰Div.4.031.651.11‰Div.7.752.1421.2‰17.3‰
✓✓–5.681.942.26‰9.73‰4.271.690.57‰7.41‰7.782.034.24‰3.34‰
✓✓✓5.841.592.21‰10.3‰4.641.350.63‰7.68‰7.921.655.53‰4.88‰
Table 3: Component analysis. Ablation of the source module, DIC mass constraint, and carbonate chemical constraint. We report results for REACT on both reconstruction tasks and repeat the constraint ablation on U-Net for month-to-week reconstruction at 0.11%0.11\% sampling. pH NRMSE is in units of 10−410^{-4} , Chem. is in units of 10−210^{-2} , and drift is reported in per mille. Div. denotes divergent long-range drift. Decomposed pCO2sp\mathrm{CO}_{2}^{s} and DIC errors are provided in Appendix Table 9 .
Figure 5: Effect of mass-conservation training on DIC drift.
Figure 6: Uncertainty estimation of REACT.
(a) Interval Length. case pH Chem. Drift local Drift global 1 5.85 1.57 2.10‰ Div. 2 6.52 1.51 2.90‰ Div. 4 5.84 1.59 2.21‰ 10.3‰ 8 6.09 1.58 2.44‰ 10.2‰(b) Depth of State Initializer. depth pH Chem. Drift local Drift global 4 6.73 1.59 2.98‰ 11.0‰ 6 6.16 1.60 2.30‰ 8.62‰ 12 5.84 1.59 2.21‰ 10.3‰ 24 5.98 1.59 8.75‰ 19.5‰(c) Depth of pH Decoder/Source Module. depth pH Chem. Drift local Drift global 2 5.75 1.54 8.41‰ 19.1‰ 3 5.88 1.54 7.91‰ 18.4‰ 4 5.84 1.59 2.21‰ 10.3‰ 5 7.51 1.85 2.75‰ 11.4‰
(d) State Initializer Structure. case pH Chem. Drift local Drift global ViT 6.58 1.53 3.74‰ Div. 2D CNN 5.96 1.67 8.81‰ 537‰ 3D CNN 36.6 462 8.44‰ Div. ViViT 5.84 1.59 2.21‰ 10.3‰(e) Auxiliary Variables. Task Metric pCO2sp\mathrm{CO}_{2}^{s} pCO2ap\mathrm{CO}_{2}^{a} Chl. SSH MLD Salt Temp. uu vv Monthly to Weekly pH 21.7 6.98 5.97 6.18 5.93 5.95 6.05 6.17 6.32 Chem. 4.97 1.55 1.73 1.58 1.57 1.70 1.61 1.60 1.73 Weekly to Daily pH 11.9 4.81 4.79 4.76 4.88 4.69 4.77 4.78 4.75 Chem. 2.57 1.33 1.30 1.26 1.25 1.40 1.29 1.26 1.31
Table 4: Ablation Study . (a) Evaluation of reconstruction interval length; (b) analysis of state initializer depth; (c) analysis of pH decoder/source-module depth; (d) comparison of state initializer architectures; (e) quantification of the impact of auxiliary input variables. All experiments follow the default setting: Conducted on the Monthly-to-Weekly task under sampling ratio of 0.11%0.11\% , using a 12-layer ViViT [ 25 ] as state initializer, pH decoder/source module of depth 4 and interval length set to 4 and 2 for Monthly-to-Weekly and Weekly-to-Daily, respectively. Details are provided in Table 10 and Table 11
Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Observation-guided sampling strategy. Red points show historical observation footprints, defined as grid locations with at least one valid observation over the observational period. Blue points show sampled locations at one randomly selected time step under the target sampling ratios. pH is sampled at 0.11%0.11\% , 1%1\% , and 10%10\% , while pCO2sp\mathrm{CO}_{2}^{s} is sampled at 1.67%1.67\% .
Hyper-param.MeaningValue
ttTemporal tubelet size in the ViViT initializer1
p,qp,qSpatial patch size in the ViViT initializer12, 12
DDEmbedding dimension in the ViViT initializer768
# LayersNumber of transformer layers in the ViViT initializer12
# HeadsNumber of attention heads in each transformer layer12
MLP ratioExpansion ratio of the MLP layers4.0
Appendix
Table 5: Model hyperparameters used for REACT.
BaselineHyper-param.MeaningValue
NUTSttTubelet size in the initializer2
 p,qp,qPatch size in the transformer layers18, 36
 DEmbedding dimension768
 # Coarse layerNumber of transformer layers in the initializer12
 # Refine layerNumber of transformer layers in the refinement module6
 # HeadsNumber of attention heads in each transformer layer16
Appendix
Table 6: Hyper-parameters used for all baseline models.
MethodsParamsTimeTrain\text{Time}_{\text{Train}}VRAMTrain\text{VRAM}_{\text{Train}}TimeInfer\text{Time}_{\text{Infer}}VRAMInfer\text{VRAM}_{\text{Infer}}pH NRMSEChem.
(s/epoch)(GB)(s)(GB)
4D-Var.0.27M4.6545.4440.5130.8216.92 {}_{\scalebox{0.70}{\scriptstyle\pm 0.03}}2.09 {}_{\scalebox{0.70}{\scriptstyle\pm 0.03}}
Marble0.83M1.2370.5630.2130.27425.7 {}_{\scalebox{0.70}{\scriptstyle\pm 0.03}}5.65 {}_{\scalebox{0.70}{\scriptstyle\pm 0.10}}
FNO8.42M2.7110.7570.2540.38016.7 {}_{\scalebox{0.70}{\scriptstyle\pm 0.07}}3.88 {}_{\scalebox{0.70}{\scriptstyle\pm 0.07}}
U-Net31.1M1.5441.1730.1900.6127.78 {}_{\scalebox{0.70}{\scriptstyle\pm 0.04}}2.17 {}_{\scalebox{0.70}{\scriptstyle\pm 0.08}}
ViT0.11B8.8052.3190.2981.0939.56 {}_{\scalebox{0.70}{\scriptstyle\pm 0.10}}2.51 {}_{\scalebox{0.70}{\scriptstyle\pm 0.01}}
Appendix
Table 7: Parameter, efficiency, and performance comparison of different models on MOM6 monthly-to-weekly task under the 0.11% sampling ratio. pH NRMSE is reported in units of 10−410^{-4} , and Chem. is reported in units of 10−210^{-2} .
MethodsParamsMonth →\to WeekWeek →\to Day
0.11%1%10%0.11%1%10%
pCO2sp\mathrm{CO}_{2}^{s}DICpCO2sp\mathrm{CO}_{2}^{s}DICpCO2sp\mathrm{CO}_{2}^{s}DICpCO2sp\mathrm{CO}_{2}^{s}DICpCO2sp\mathrm{CO}_{2}^{s}DICpCO2sp\mathrm{CO}_{2}^{s}DIC
Kriging (Exp.)–10.39.827.336.784.864.2610.29.737.166.724.453.99
Kriging (Sph.)–10.39.998.007.656.415.8210.49.917.527.185.304.77
4D-VarNet0.27M2.281.912.181.822.061.741.931.791.951.812.121.98
Marble0.83M5.955.365.995.425.775.255.665.355.675.445.645.39
Appendix
Table 8: Decomposed chemical errors for the main reconstruction results in Table 2 . The table reports the two components of the chemical consistency metric, i.e., pCO2sp\mathrm{CO}_{2}^{s} and DIC errors, under different sampling ratios for monthly-to-weekly and weekly-to-daily sea surface pH reconstruction. Both errors are reported in units of 10−210^{-2} . All values are rounded to three significant digits. Params denotes model size. U-Net 2 denotes a two-level U-Net variant.
Figure 8: Qualitative field comparison. Ground-truth and reconstructed sea surface pH, pCO2sp\mathrm{CO}_{2}^{s} , and DIC fields from different methods at one randomly selected MOM6 test time slice.
Figure 9: Qualitative error maps. Reconstruction errors of different methods for sea surface pH, pCO2sp\mathrm{CO}_{2}^{s} , and DIC at the same time slice, computed as prediction minus ground truth.
Figure 10: Decomposed real-observation results. NRMSE of pCO2sp\mathrm{CO}_{2}^{s} and DIC for different methods on real WOD observations. Both metrics are reported in units of 10−110^{-1} .
  REACT (Month →\to Week)REACT (Week →\to Day)U-Net (Month →\to Week)
SourceLmass\mathcal{L}_{\mathrm{mass}}Lchem\mathcal{L}_{\mathrm{chem}}pCO2sp\mathrm{CO}_{2}^{s}DICpCO2sp\mathrm{CO}_{2}^{s}DICpCO2sp\mathrm{CO}_{2}^{s}DIC
–––8.94Div.2.842.622.271.98
✓––2.061.801.711.592.282.00
✓✓–2.061.821.761.622.171.89
✓✓✓1.731.451.441.271.771.53
Appendix
Table 9: Decomposed chemical errors for the source module and constraint ablations. We report pCO2sp\mathrm{CO}_{2}^{s} and DIC errors for the ablation variants in Table 3 , covering REACT on Month →\to Week and Week →\to Day reconstruction under the 0.11% sampling ratio, and the U-Net baseline ablation on Month →\to Week reconstruction under the 0.11% sampling ratio. Both metrics are reported in units of 10−210^{-2} . All values are rounded to three significant digits.
FactorSettingpCO2sp\mathrm{CO}_{2}^{s}DIC
Interval length11.711.44
21.661.36
41.731.45
81.701.46
Initializer depth41.731.46
61.741.46
Appendix
Table 10: Decomposed chemical errors for the monthly-to-weekly ablation study in Table 4 . The table reports pCO2sp\mathrm{CO}_{2}^{s} and DIC errors in units of 10−210^{-2} for interval length, state initializer depth, pH decoder/source-module depth, state initializer architecture, and auxiliary-variable ablations. The default setting uses interval length 44 , state initializer depth 1212 , pH decoder/source-module depth 44 , a ViViT state initializer, all auxiliary variables, and both mass and chemistry constraints. All values are rounded to three significant digits.
FactorSettingpHpCO2sp\mathrm{CO}_{2}^{s}DICChem.Drift localDrift global
Interval length14.891.471.291.380.61‰Div.
24.641.441.271.350.63‰7.68‰
35.371.591.501.540.85‰8.35‰
44.791.351.191.270.77‰3.59‰
Initializer depth44.741.351.201.270.63‰8.21‰
64.801.331.181.260.60‰7.96‰
Appendix
Table 11: Weekly-to-daily counterpart of the ablation study in Table 4 under the 0.11%0.11\% sampling ratio. The table reports full metrics for interval length, state initializer depth, pH decoder/source-module depth, and state initializer architecture, with auxiliary-variable ablations shown separately using decomposed chemical errors. The default setting uses interval length 22 , state initializer depth 1212 , pH decoder/source-module depth 44 , a ViViT state initializer, all auxiliary variables, and both mass and chemistry constraints. pH NRMSE is reported in units of 10−410^{-4} , while pCO2sp\mathrm{CO}_{2}^{s} , DIC, and Chem. are reported in units of 10−210^{-2} . Drift values are reported in per mille. All values are rounded to three significant digits. Div. denotes divergent results.
Figure 11: Uncertainty estimation of REACT for pCO2sp\mathrm{CO}_{2}^{s} and DIC. The predictive means are shown with one- and two-standard-deviation intervals.

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