Climate Intervention Analysis using AI Model Guided by Statistical Physics Principles

The study addresses how to estimate a system’s response to external forcings when labeled training data or targeted simulations are scarce or computationally prohibitive—particularly acute in climate science, where Earth System Models (ESMs) can take weeks to months per scenario. The paper proposes AiBEDO, an AI framework guided by the Fluctuation-Dissipation Theorem (FDT), to infer forced climate responses from internal variability, enabling rapid scenario analysis of Marine Cloud Brightening (MCB), a solar radiation management technique with regionally heterogeneous effects. The context spans prior successes of ML in scientific domains (e.g., weather prediction, medical imaging, astronomy, drug discovery) and the rise of surrogate models, but highlights the gap in predicting outcomes under external forcings that fall outside training distributions. The purpose is to build an AI emulator of time-lagged mappings between cloud radiative perturbations and surface climate responses and then time-integrate these with an FDT-like operator to estimate mean forced responses. Importance lies in accelerating exploration of vast MCB scenario spaces to assess efficacy and potential risks, including regional tipping points, without incurring the high costs of ESM simulations. Contributions include: (1) a novel FDT-guided AI approach trained on noise (internal variability) to predict forced responses, (2) mapping cloud perturbations to climate responses across multiple lags, (3) extensive evaluation against targeted CESM2 simulations showing high-fidelity emulation at orders-of-magnitude speedup, and (4) an interactive platform for rapid what-if analysis and tipping-point assessment.

Problem formulation: The framework estimates regional climate impacts of user-specified MCB cloud perturbations through two phases. Phase 1 trains a suite of AI emulators to learn simultaneous and time-lagged mappings between input cloud/clear-sky radiative anomaly fields x(t) and output surface climate anomaly fields y(t+τ) across lags τ ∈ {0,…,6} months. Inputs (cin=7 channels) include cres, crel, cresSurf, crelSurf, netTOAcs, netSurfcs, and land-sea mask; outputs (cout=3 channels) include ps, tas, pr. Phase 2 applies an FDT-like time-integration, replacing the linear operator L with learned operators Aτ and computing the mean response to a perturbation δf via averaging over randomly sampled internal variability states and integrating over lags until responses decay to noise; testing used lags up to 6 months, and full integration used up to 48 months (with Simpson’s rule in some analyses).

Data: Training/validation/testing use CESM2 Large Ensemble (CESM2-LE) historical simulations (50 members, monthly, nominal 1-degree) providing nearly 100,000 months of internal variability. Data are preprocessed by subtracting the ensemble mean at each month and grid point, removing seasonal cycles and externally forced trends across time scales (including volcanic and anthropogenic aerosol signals). For MCB response validation, new CESM2 simulations perturb cloud droplet number concentrations (CDNC=600 cm−3) in three regions—NEP, SEP, SEA—separately and jointly, under SSP2-4.5. Effective radiative forcing (ERF) perturbation fields for AiBEDO are computed from fixed-SST Year-2000 simulations as annual mean anomalies (cres, crel, cresSurf, crelSurf, netTOAcs, netSurfcs) between MCB-perturbed and control runs.

Spherical sampling: To address non-uniform area and rotational symmetry issues on latitude-longitude grids, ESM fields are resampled to a geodesy-aware icosahedral spherical mesh (level-5; N=10×2^(2g)+2=10242 points; ~220 km resolution) using PyGSP. The process builds an icosahedral graph backbone, assigns geographic coordinates, and applies bilinear interpolation from the original lat-lon grid to uniform-density spherical points, producing 1-D vectors over the sphere suitable for graph/spherical operations.

Models (Aτ): Pixel-wise regression from input tensors R^{d×cin} to outputs R^{d×cout} at each τ. Three architectures were implemented and compared:

• Spherical Multilayer Perceptron (S-MLP): Fully connected DNN on spherical-sampled vectors; four hidden layers, 1024 units each; LayerNorm and GeLU activations; AdamW optimizer, lr=2e-4 with exponential decay 1e-6/epoch; 15 epochs, batch size 10; ~108M parameters; ~1 min/epoch on NVIDIA V100 16GB.
• Spherical U-Net (S-Unet): Graph-based spherical U-Net (DeepSphere-inspired) with six Chebyshev graph convolution layers in encoder and decoder, spherical Chebyshev pooling/convolutions; kernels ~[64,128,256,512,512,512]; softmax output; AdamW, lr=5e-4 with exponential decay 1e-6/epoch; 30 epochs; ~5.8M parameters; ~1.5 min/epoch.
• Spherical Adaptive Fourier Neural Operator (S-AFNO): Transformer with AFNO token mixing; entire 1-D spherical samples projected as tokens with positional encodings; 4 transformer layers, token embedding size 384; GeLU, LayerNorm; AdamW, lr=5e-4 with exponential decay 1e-6/epoch; 50 epochs; ~9M parameters; ~12 min/epoch.

FDT-like integration: Classical Gaussian FDT computes δy = L^{-1} δf = ∫0^∞ C(τ)C(0)^{-1} dτ δf. AiBEDO generalizes this by replacing L with learned Aτ to include nonlinearities and relax Gaussianity: δy(t) = Σ{τ=0}^{Tmax} (1/N) Σ_{i=1}^N [Aτ(x_i + δf(t−τ)) − Aτ(x_i)], where x_i are samples of internal variability, N the sample size (e.g., N=480 months), and Tmax the maximum lag (testing: 6 months; full: up to 48 months). For MCB tests, perturbation responses are computed as differences in AiBEDO outputs with and without δf, averaged over internal variability samples per lag, then integrated over lag with Simpson’s rule for selected lag sets (1–6, 12, 24, 36, 48 months).

Evaluation protocol: Phase I evaluates emulation skill (RMSE, spatial correlation) versus CESM2-LE at lags 0–6, benchmarking against persistence. Phase II compares AiBEDO lag-integrated responses to MCB-like forcing against fully coupled CESM2 simulations for NEP, SEP, SEA, and all regions combined, focusing on tas, pr, ps patterns and teleconnections. An interactive visualization platform enables specification of regions, variables, magnitudes of perturbations, model runs, geospatial visualizations, out-of-distribution checks, and tipping point indicators.

• Emulation performance (Phase I): Across lags 0–6 months, all models outperform persistence; accuracy degrades with longer lags as expected. S-MLP consistently achieves the best spatial correlation and qualitative fidelity, particularly for time-lagged responses. S-MLP’s fully connected architecture and larger parameter count likely capture long-range interactions better. S-Unet underperforms due to loss of global pattern information during spherical convolutions/pooling; S-AFNO performs better than S-Unet but below S-MLP, likely requiring more data and compute.
• Quantitative comparisons: In MCB response validation (Phase II), S-MLP reproduces CESM2 response patterns with correlation scores of approximately 0.68 for temperature (tas), 0.51 for precipitation (pr), and 0.47 for surface pressure (ps). Correlation improves with increased time integration, though response magnitudes can differ due to missing/limited lags in integration.
• Teleconnections and spatial skill: S-MLP captures key remote teleconnections—for example, La Niña-like Pacific cooling under SEP forcing—and regional signals like drying in northeast Brazil, central Africa, southern North America and Europe, and wetting in the Sahel, south/southeast Asia, Australia, and Central America. Performance is stronger over the tropics and oceans than high latitudes and land, mirroring emulation skill distributions.
• Regional perturbations: AiBEDO performs best for SEP forcing, followed by SEA, with NEP responses overestimated (potential overweighting of ENSO-like variability). Nonetheless, AiBEDO correctly differentiates region-specific impacts (e.g., SEP → La Niña-like cooling; SEA → tropical Pacific warming and Amazon drying).
• Computational gains: AiBEDO reproduces targeted ESM results with high fidelity at roughly three orders of magnitude less computational cost, enabling rapid screening of vast scenario spaces.
• Practical tools: A post-hoc interactive platform supports what-if scenario prototyping, visualization, out-of-distribution assessment, and monitoring of selected regional tipping-point indicators.

The central question—can an AI model trained on internal variability infer forced responses to external perturbations—was addressed by embedding FDT principles into AiBEDO’s design. By learning lagged mappings from cloud radiative anomalies to surface climate responses and integrating over time in an FDT-like manner, AiBEDO produces plausible forced-response patterns that agree with fully coupled CESM2 simulations across multiple variables and regions. This demonstrates that internal variability encodes information sufficient to approximate linear and some nonlinear components of the forced response when augmented with AI.

Significance: The approach circumvents the scarcity of targeted scenario simulations and the prohibitive computational cost of ESMs, accelerating exploration of spatially heterogeneous interventions like MCB. The accurate capture of teleconnections (e.g., ENSO-like responses) is crucial for assessing downstream risks and benefits, including potential tipping points. The method is generalizable to other scientific domains where system responses to external forcings are needed but training data are limited to unforced variability.

Relevance and refinement: While pattern correlations are strong, magnitude discrepancies highlight sensitivity to the completeness of lag integration and model architecture. Performance heterogeneity (better in tropics/oceans than high latitudes/land) guides where predictions are more reliable and where additional model development or data are needed. The FDT-like framework, paired with AI, offers a tractable path to scenario analysis and decision support, with the visualization tool enabling expert scrutiny, OOD diagnostics, and rapid iteration on intervention designs.

This work presents AiBEDO, an AI framework guided by the Fluctuation-Dissipation Theorem that learns from internal climate variability to estimate forced responses to external radiative perturbations. Applied to Marine Cloud Brightening, AiBEDO reproduces key aspects of coupled ESM responses—including teleconnections—while operating roughly three orders of magnitude faster, enabling rapid prototyping of extensive what-if scenarios. Methodological contributions include geodesy-aware spherical resampling, comparative analysis of spherical ML architectures, and an interactive visualization platform for explainable, post-hoc analysis and tipping-point assessment.

Future directions include: (1) extending lag coverage and integration schemes to improve response magnitude fidelity; (2) enhancing high-latitude and land performance (e.g., architecture changes, additional training data); (3) inverse design for optimization—querying AiBEDO to propose spatiotemporal MCB perturbations that achieve specific regional climate targets or avoid tipping points while imposing constraints to minimize unintended consequences; and (4) broader application to other scientific systems requiring rapid forced-response estimation under limited training data.

• FDT assumptions and lag coverage: Classical FDT captures linear responses and assumes Gaussian or quasi-Gaussian statistics; AiBEDO relaxes this via learned operators but still relies on finite lag models. Limited lag integration (e.g., 0–6 months for testing; selected lags up to 48 months) can lead to magnitude biases in the integrated response.
• Spatial performance heterogeneity: Lower skill at high latitudes and over land reduces confidence for cryospheric tipping-point analyses (e.g., permafrost, ice sheets) relative to tropics/oceans.
• Architectural/data constraints: S-Unet loses global context via pooling/convolutions; S-AFNO may be data-hungry and computationally heavier. S-MLP’s strong performance comes with high parameter counts. Additional data or architectural refinements may be needed for further gains.
• Training data scope: Models are trained on internal variability (noise) from CESM2-LE; forced-signal generalization depends on how well internal variability spans relevant response modes. Overemphasis on dominant modes (e.g., ENSO) can bias regional responses (e.g., NEP overestimation).
• Out-of-distribution risks: Perturbation fields (especially near-zero outside forcing regions) can be unlike training inputs, producing artifacts unless mitigated by the differential protocol used. Careful OOD diagnostics are necessary.
• Model evaluation breadth: Validation focuses on selected regions (NEP, SEP, SEA) and variables (tas, pr, ps); broader variable sets and regions may exhibit different skill profiles.