PaperlayerView exact revision on arXiv

Source-linked AI summary

Optimizing Geoengineering Interventions Using Differentiable Climate Models

Pulkit Dubey, Dorian S. Abbot, Ashesh Chattopadhyay

arXiv:2609.12528v1physics.ao-phcs.AImath.OCnlin.CD

TL;DR

Existing geoengineering-design approaches rely on linear response or extra simulations as forcing parameters are added. The paper uses short-horizon gradients in a differentiable climate model to steer a warmed simulation toward its unwarmed target, and reports that a land-temperature pattern objective also restores hydrological variables outside the loss.

  • Problem

    Existing climate-intervention design approaches assume linear response or require an additional simulation for each added forcing parameter.

    Source: §1 · p. 1

  • Method

    The authors optimize SST-forcing amplitudes over short segments with gradients, apply each segment, and repeat to steer the simulation toward its target.

    Source: §1 · p. 2, §2.1 · p. 4

  • Results

    A land-temperature pattern objective restores hydrological variables near their unwarmed profiles even though those variables are absent from the loss.

    Source: §3 · pp. 8–9

  • Takeaways & Limitations

    The authors conclude that intervention objectives should be evaluated on out-of-loss variables as well as the quantities they optimize.

    Source: §3 · p. 9

    The moving-horizon strategy is feasible rather than provably optimal, and prescribed SST cooling omits ocean adjustment, radiative forcing, aerosol microphysics, energy-budget closure, and deployment constraints.

    Source: §3 · p. 11

Abstract

from arXiv · show

The deployment of a geoengineering program to cool Earth's climate may be imminent. It is crucial that tools be developed to ensure that such a program would achieve its objectives while minimizing disruption. Here we exploit recently developed differentiable atmospheric models to demonstrate a novel geoengineering control strategy. In the differentiable primitive-equation atmospheric model JAX-GCM we impose a uniform $+4$\,K ocean warming and ask what pattern of sea-surface temperature cooling -- in five ocean-masked zonal bands of prescribed SST forcings whose amplitudes are free -- returns land near-surface air temperature closest to the model's own unwarmed climatology. This idealized set-up represents a cooling pattern that could be delivered physically either by marine cloud brightening or stratospheric aerosol injection. Gradients through chaotic dynamics decorrelate from the true sensitivity beyond the Lyapunov horizon, so we optimize greedily over segments of 8 to 14 days, following receding-horizon control. The learned strategy removes $92.3 \pm 0.4\%$ of the realized land warming across a ten-member ensemble of two-year rollouts, and a three-year run sustains it. If we use the spatial pattern of land temperature as the optimization objective, the distributions of precipitation, evaporation, and specific humidity over land are restored as well, even though they are not included in the objective function. The learned strategy from JAX-GCM replayed in the AI emulators LUCIE and NeuralGCM without re-optimization is successful, suggesting robustness. These promising results demonstrate a strategy for designing optimal climate interventions that can be applied broadly for geoengineering scenarios under consideration.

1 Introduction

Climate intervention is an inverse-design problem: choose a spatiotemporal forcing pattern that restores a target climate. The paper uses short-horizon gradients in a differentiable climate model to design forcing that steers a simulation toward an unwarmed target.

1 Introduction

  • Existing intervention designs superpose precomputed linear responses, tune a few zonal moments, invert response operators, or search by sampling; these approaches assume linearity or require another simulation per added parameter.The paper frames this as an inverse-design problem: selecting the spatiotemporal forcing pattern that best restores a target climate.Source: §1 · p. 1
  • Earlier gradient-based climate-model studies target observed histories or maximum error growth; the authors say none had designed forcing to steer a simulation to a prescribed counterfactual target and hold it there for years.ECCO forcing fields are constrained to remain near observed reanalysis forcing rather than being designed.Source: §1 · p. 2
  • Because gradients through chaotic dynamics lose usable signal beyond a few Lyapunov horizons, the authors optimize each short forcing segment, apply it, and repeat without gradients crossing segment boundaries.The method provides sensitivities to every forcing parameter in one backward pass, without a precomputed response library or a linear-superposition assumption.Source: §1 · p. 2
  • In JAX-GCM, the authors test five time-varying Gaussian SST bands under +4 K warming, targeting the model’s unwarmed land near-surface temperature climatology.They also run the optimization in LUCIE and NeuralGCM.Source: §1 · p. 2
  • The experiments test gradient sensitivity, long-horizon control, hydrological responses under two land-temperature objectives, comparisons with flat and linear-response baselines, and transfer to other models.Precipitation, evaporation, and specific humidity are measured despite being absent from both objectives.Source: §1 · pp. 3–4

2 Results

Segmented SST control tracks the unwarmed land-temperature target for years. The spatial-pattern objective also better restores hydrological variables than land-mean control, performs well against baselines, and transfers to other models without re-optimization.

2.1 Gradient-based intervention design sustains multi-year control

  • The optimizer holds five ocean-masked Gaussian-band SST amplitudes constant within each 8-day segment, optimizing them successively against land-temperature bias, spatial residual structure, and forcing regularizers.Applied forcing weights prescribed amplitudes by ocean fraction and latitude-dependent area, so prescribed amplitude and delivered forcing can differ.Source: §2.1 · p. 4
  • Over two years, 8-day control converges toward the target within about 10 segments, then tracks its seasonal cycle, removing over 90% of realized land-mean warming.The 14-day-segment, three-year ensemble removes a comparable fraction of warming; gradient accuracy and precision degrade beyond 14 days and fail by about 28 to 30 days.Source: §2.1 · p. 5

2.2 A temperature pattern objective restores precipitation and evaporation as well

  • Both objectives remove comparable land-mean warming, but pattern control spreads cooling beyond the equator and better restores out-of-loss hydrological fields than land-mean control.Pattern control leaves zonal-mean precipitation, evaporation, and specific-humidity residuals near zero; land-mean control produces equatorial drying.Source: §2.2 · pp. 5–6, Figure 3 · p. 7

2.3 Optimization performance compared with baselines

  • At equal effort, pattern control beats the matched-effort baseline on T2m (G = 27.4 against 20.8), evaporation (49.2 against 23.6), specific humidity (74 against 34), and precipitation (9.8 ± 1.7 against 6.9 ± 0.7).The constant-in-time matched-pattern baseline reproduces learned gains within ensemble scatter, so time variation is not resolved by these time-mean metrics.Source: §2.3 · p. 8

2.4 Cross-model agreement and transfer

  • Replayed without re-optimization, the JAX-GCM strategy outperforms the uniform −4 K baseline on temperature and precipitation pattern restoration in JAX-GCM, LUCIE, and NeuralGCM.Runs are limited to one year because NeuralGCM becomes unstable beyond roughly a year; each model’s scores use its own unwarmed control.Source: §2.4 · p. 8

3 Discussion

The discussion presents differentiable climate control as an inverse-design method and shows that the choice of temperature objective matters: matching land-temperature patterns also restores hydrological variables outside the loss. It highlights the value and limits of learned forcing patterns, including their model dependence and the idealized scope of the demonstration.

Objective choice

  • Matching the full land-temperature pattern also restores precipitation, evaporation, and specific humidity over land, although these variables are absent from the loss.The authors suggest evaluating intervention objectives on variables outside the loss as well as on the optimized quantities.Source: §3 · pp. 8–9

Forcing structure

  • The learned strategy and its constant-in-time matched-pattern baseline achieve the highest gain on every variable and beat flat forcing at the same effort.This indicates that the spatial structure of the forcing contributes beyond the amount of cooling.Source: Figure 4 · p. 9

Higher-dimensional forcing

  • A 30-dimensional patch-forcing gradient costs nearly the same to compute as a five-band gradient, but the patch basis restores less skill, potentially reflecting a more complex optimization landscape.Reverse-mode differentiation returns sensitivities to all forcing parameters in one backward pass.Source: §3 · p. 10

Model dependence

  • Under the pattern objective, LUCIE places its deepest cooling on subtropical bands, whereas JAX-GCM and NeuralGCM place theirs at 45°N; this is consistent with a reported emulator failure mode under out-of-distribution forcing [34].The authors note that the objectives act on land temperature under out-of-training-distribution forcing.Source: §3 · p. 10

Seasonality

  • Seasonal variation in learned amplitudes adds little gain over their time-mean values because the loss is shallow near its minimum and weather noise is larger than the segment-level loss change.The loss change is about 0.007 K2 per segment, against 0.5 K2 of weather noise per segment.Source: §3 · pp. 10–11

Scope and future work

  • The moving-horizon strategy is feasible but not provably optimal, and prescribed SST cooling omits ocean adjustment, aerosol microphysics, energy-budget closure, and deployment constraints.The authors characterize this as an idealized algorithmic demonstration, with future work including multi-segment model predictive control and higher-dimensional forcing.Source: §3 · p. 11

4 Materials and Methods

The methods use differentiable climate models to optimize ocean-masked zonal SST cooling against each model’s own unwarmed climate. They define a greedy segment-wise optimization procedure, restoration and effort measures, and a cross-model replay without re-optimization.

Models

  • JAX-GCM, LUCIE, and NeuralGCM are differentiable models run at different resolutions and with different physics; each is evaluated against its own unwarmed control and temperature diagnostic.JAX-GCM couples a spectral primitive-equation core to SPEEDY physics, LUCIE is an ERA5-trained spherical Fourier neural operator, and NeuralGCM uses learned physics.Source: Models · p. 12

Warming, forcing, and target

  • The experiment imposes uniform +4 K SST warming and optimizes five ocean-masked Gaussian zonal cooling bands toward the model’s own unwarmed land-temperature climatology.The bands are centered at 45°N, 20°N, 0°, 20°S, and 45°S, with width 10°.Source: Warming, forcing, and target · p. 12

Greedy optimization

  • Each greedy segment optimizes band amplitudes by exact backpropagation through time, applies the converged forcing, and initializes the next segment from the resulting model state.Production runs use 91 eight-day segments; no gradient crosses a segment boundary.Source: Greedy optimization · p. 12

Skill and effort

  • Restoration skill compares time-mean land fields with the target and uncontrolled warmed run, while effort measures the global-area and time mean of prescribed cooling magnitude.The fields are scored over the final 364 days; effort measures what the controller prescribes, not what the ocean receives or what deployment would cost.Source: Skill and effort · pp. 12–13

Cross-model replay

  • The JAX-GCM strategy is replayed in LUCIE and NeuralGCM without re-optimization, using each model’s own implementation of the cooling bands and evaluating gain over the final 300 days.In LUCIE, the SST perturbation is smoothed before entry.Source: Cross-model replay · p. 13

Competing Interests

The authors declare no competing interest.

S1 Gradient validation

Backpropagated gradients track finite-difference sensitivities and weather-ensemble means at short segment lengths, but become unreliable around 28–30 days. A 1 K differencing step balances weather noise, while strong cooling can persist even when gradient noise exceeds signal.

Accuracy against finite differences

  • At 7 and 14 days, backpropagated gradients agree with finite differences (R = 0.91 and 0.87); at 28 days they decorrelate (R = 0.49).The 7- and 14-day gradients are 8–17% smaller in magnitude; at 28 days median gradient-vector angles rise to 45° and 41° for the pattern and land-mean objectives.Source: Accuracy against finite differences · p. 15, Figure S1 · p. 16

Choice of the finite-difference step

Dependence on the weather realization

Noise-to-signal ratio in the production runs

  • At 7 and 14 days, every production segment has a noise-to-signal ratio below one; at 30 days, noise exceeds signal in 20 of 24 segments.The median ratio is 0.03 and 0.07 at 7 and 14 days, versus 1.2 at 30 days.Source: Noise-to-signal ratio in the… · p. 17, Figure S4 · p. 18
  • Over the final 364 days, the optimizer removes 95% of land-mean warming at both 14 and 30 days, while a 50-day run removes 46%.The 7-day run removes 89%, but its β = 0.5 differs from β = 0.05 and 0.1 in the 14- and 30-day runs, so the fraction is not directly comparable.Source: Noise-to-signal ratio in the… · p. 18

S2 Validation in LUCIE and NeuralGCM

LUCIE and NeuralGCM can optimize their own band amplitudes under the pattern objective. Both reduce land warming, although their learned cooling profiles differ substantially.

S2 Validation in LUCIE and NeuralGCM

S3 Cross-model transfer of the learned strategy

A frozen JAX-GCM strategy replayed in three models restores zonal profiles of temperature, precipitation, and evaporation. The comparison uses each host’s own controls, though temperature diagnostics differ across models.

S4 Optimizer variants and baseline construction

Optimizer variants trade off actuator structure, segment length, and regularization, while the baselines separate spatial-structure and time-variation effects from effort. Added patch degrees of freedom do not improve skill, while more zonal bands can.

  • Restoration gain G compares restoration against prescribed cooling effort E, while each variable’s gain is derived from reduced land-field mean-square error.Source: S4 Optimizer variants and baseline… · p. 21
  • Matched-effort and matched-pattern baselines isolate spatial forcing structure and time variation, respectively; flat baselines vary spin-up length under identical forcing.The matched-effort baseline uses −3.72 K on each band and matches the learned ensemble at E = 3.44 K.Source: S4 Optimizer variants and baseline… · p. 21
  • The linear baseline estimates a response operator from central-difference forward runs, then inverts it for fixed band amplitudes rather than optimizing the nonlinear model.Its response is not linear across the perturbation range, so it serves as a reference rather than a converged optimum.Source: S4 Optimizer variants and baseline… · p. 21
  • The 8-day variant has the highest four-variable mean restoration skill and leads consistently across variables; 14- and 28-day segments do nearly as well on 2 m temperature but fall off elsewhere.Source: S4 Optimizer variants and baseline… · pp. 21–22
  • A much stronger amplitude regularizer shrinks both prescribed effort and restoration gain toward zero; at µ = 0.5, effort is E = 1.1 K and gains are 2.2 for 2 m temperature and precipitation.Source: S4 Optimizer variants and baseline… · p. 22
  • The 30-patch actuator has less skill than the five-band basis across all variables, despite similar computational cost.The authors suggest objective design or convergence to a local solution as possible explanations.Source: S4 Optimizer variants and baseline… · p. 22
  • Seven bands raise 2 m temperature gain by a factor of 2.7 and specific humidity gain by 1.3; three bands reduce precipitation gain to 1 while removing about three quarters of land-mean warming.With three bands, evaporation and humidity gains fall to 3.5 and 5, respectively.Source: S4 Optimizer variants and baseline… · p. 22
  • Across tested optimizer choices near the adopted operating point, the five-band amplitude structure and ensemble-mean restoration skill remain similar within member-to-member scatter.This robustness claim does not extend to arbitrary parameter values.Source: S4 Optimizer variants and baseline… · p. 22

S5 Learned amplitudes and seasonality

The learned strategy uses unequal band amplitudes and produces distinct delivered forcings because bands cover different ocean areas. Its gains over uniform cooling are attributed to spatial structure, while the measured seasonal effect is unresolved against weather noise.

  • The 45°N band maintains an amplitude about 1–2 K larger than every other band, yet has the lowest applied forcing; the 45°S band has the highest applied forcing.Source: S5 Learned amplitudes and seasonality · p. 22
  • Constant-in-time mean amplitudes restore temperature and auxiliary variables as well as the time-varying strategy; seasonal effects are unresolved beyond weather noise.The seasonal displacement changes segment loss by about 0.007 K2, below 0.5 K2 weather noise per segment and 0.04 K2 after ten members and a year.Source: S5 Learned amplitudes and seasonality · pp. 22–23
  • The 45°N and 45°S bands have clear anti-phase seasonal cycles, but the measured gains over uniform cooling come from spatial structure rather than time variation.Source: S5 Learned amplitudes and seasonality · p. 22
  • Figure S8 compares restoration gain with prescribed effort across segment lengths, objectives, and actuator variants, with markers and bars showing ensemble means and standard deviations where available.Source: Figure S8 · p. 23

S6 Prior approaches to the intervention inverse problem

Earlier inverse-intervention approaches use response patterns, tuned feedback, response-operator inversion, or sampling, while prior gradient methods target other objectives or shorter horizons. Area-weighted forcing distinguishes prescribed band amplitudes from the intervention delivered over the global area.

S6 Prior approaches to the intervention inverse problem

  • The three-year JAX-GCM control uses a ten-member ensemble and 14-day optimization segments; its figures show land-mean and zonal temperature, band-amplitude variations, and time-averaged cooling.Source: Figure S9 · p. 24, Figure S10 · p. 25
  • Prior inverse methods include superposed linear-response patterns, feedback on zonal moments, Green’s-function operator inversion, and reinforcement-learning searches.In one cited aerosol-injection setting, temperature objectives based on a few zonal moments did not restore precipitation, which had to be targeted explicitly.Source: S6 Prior approaches to the… · pp. 23–24
  • Earlier gradient applications target observed-history fit, short-range error growth, or initial states, rather than multi-year intervention forcing.ECCO extends adjoint windows to decades but treats forcing as a nuisance parameter regularized toward a prior.Source: S6 Prior approaches to the… · pp. 24–25

S7 Area weighting of the band forcing

S8 Control-run statistics

The 8-day control ensemble removes 92.3 ± 0.4% of land warming, while a replayed strategy outperforms uniform −4 K baselines on temperature and precipitation scores. The replay does not always best restore land-mean bias, and land responses to +4 K warming differ across model classes.

S8 Control-run statistics

  • 92.3 ± 0.4% of realized land warming was removed by the ten-member 8-day ensemble.The ensemble used 91 segments per member and a movement penalty λ = 0.1.Source: S8 Control-run statistics · p. 26
  • 94.6 ± 1.1% of land warming was removed by the 14-day-segment ensemble over three years.Its median in-run noise-to-signal ratio was 0.24, versus 0.075 for the 8-day run.Source: S8 Control-run statistics · p. 26
  • The land-mean objective removed 93.2 ± 0.3% of land-mean warming versus 92.3 ± 0.4% for the pattern objective, with T2m gains of 11.9 ± 0.5 versus 27.4 ± 3.8.Source: S8 Control-run statistics · p. 26

S9 Replay scores and out-of-distribution warming

  • T2m replay scores were G = 25.3, 2.3, and 21.8 versus uniform −4 K baselines of 16.9, 0.8, and 10.7 across JAX-GCM, LUCIE, and NeuralGCM, advantages of 1.5× to 2.7×.Source: S9 Replay scores and… · p. 26
  • Precipitation replay scores were 7.2, 1.8, and 2.0 versus uniform −4 K baselines of 5.2, 1.0, and 1.1, advantages of 1.4× to 1.8× across the same models.Source: S9 Replay scores and… · p. 26
  • Uniform −4 K better restored land-mean bias in JAX-GCM and NeuralGCM but was less effective for pattern and out-of-loss variables; +4 K land responses were +3.8 K and +3.9 K versus LUCIE’s +1.8 K.Source: S9 Replay scores and… · p. 27

S10 Decomposition of the temperature loss

The segment-mean land-weighted temperature loss separates mean bias from spatial residual variance. Its coefficients select whether optimization targets land-mean temperature or the spatial pattern as well.

Loading 2609.12528v1…