Source-linked AI summary
Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations
Tapio Schneider, Shiwei Lan, Andrew Stuart, João Teixeira
TL;DR
Climate projections remain uncertain because key parameterization schemes, including those for clouds, convection, and ecosystems, contain uncertain parameters and structures. The paper proposes ESMs that learn from global observations and targeted high-resolution simulations by matching statistics, illustrates the approach in a simple dynamical system, and identifies opportunities and challenges for realization.
Problem
Climate-projection uncertainty is rooted in uncertain parameterization schemes, while the traditional effort to develop globally correct process schemes in isolation has had limited success.
Method
The paper proposes embedding physical, biological, and chemical parameterization schemes in ESMs that learn from global observations and targeted high-resolution simulations using statistical objective functions.
Results
The paper outlines a learning-ESM framework and illustrates parameter learning with a simple dynamical system that mimics characteristics of the atmosphere and oceans.
Takeaways & Limitations
The framework could improve ESM reliability and predictive power while quantifying uncertainty in parameters and predictions.
Takeaways & Limitations
Realizing the framework requires innovation in how observations and targeted high-resolution simulations are combined, including how simulations are targeted and balanced against computational cost.
Abstract
from arXiv · showhide
Climate projections continue to be marred by large uncertainties, which originate in processes that need to be parameterized, such as clouds, convection, and ecosystems. But rapid progress is now within reach. New computational tools and methods from data assimilation and machine learning make it possible to integrate global observations and local high-resolution simulations in an Earth system model (ESM) that systematically learns from both. Here we propose a blueprint for such an ESM. We outline how parameterization schemes can learn from global observations and targeted high-resolution simulations, for example, of clouds and convection, through matching low-order statistics between ESMs, observations, and high-resolution simulations. We illustrate learning algorithms for ESMs with a simple dynamical system that shares characteristics of the climate system; and we discuss the opportunities the proposed framework presents and the challenges that remain to realize it.
1 Introduction
Earth system models have advanced, but climate-projection uncertainty remains rooted in uncertain parameterization schemes, especially for clouds and ecosystems. The paper proposes learning these schemes from global observations and targeted high-resolution simulations using data assimilation and machine learning.
- 1 Introduction: Parameterization schemes encode processes whose governing equations are unknown or poorly known, including ecological and biogeochemical processes.Their parameters and underlying equation structures therefore carry both parametric and structural uncertainty.
- 1 Introduction: Climate projections remain less accurate than weather forecasts despite improvements in simulating several climate phenomena.The paper links this gap to persistent uncertainty in parameterization schemes.
- 1 Introduction: Cloud parameterizations dominate uncertainties in physical processes through uncertain cloud turbulence and microphysics representations.These representations affect droplet sizes, precipitation of condensate, and liquid–ice partitioning.
- 1 Introduction: About half of emitted CO2 accumulates in the atmosphere while the remainder is taken up by oceans and land, with future terrestrial uptake uncertain.Carbon-residence times differ by O(1) factors among models and affect the biosphere’s climate response.
- 1 Introduction: The traditional strategy of developing one globally correct parameterization for each process in isolation has achieved only limited success.The approach typically relies on observations or computational process studies focused on specific regions.
- 1 Introduction: The paper proposes that parameterization schemes learn within ESMs from global observations and targeted high-resolution simulations through data assimilation and machine learning.It illustrates the approach with a simple dynamical system sharing characteristics of the atmosphere and oceans.
2 Learning from Observations and Targeted High-Resolution Simulations
The proposed framework combines global observations with targeted, local high-resolution simulations so ESM parameterizations can learn during a computationally intensive phase. It matches time-averaged statistics to reduce biases and exploit emergent constraints while addressing computational and coordination challenges.
- 2.1 Information Sources for Parameterization Schemes: Global observations provide worldwide measurements of atmospheric, physical, biogeochemical, and cryospheric variables for learning parameterization schemes.Satellite measurements include temperature, humidity, cloud and sea-ice cover, CO2 concentrations, and terrestrial photosynthesis.
- 2.1 Information Sources for Parameterization Schemes: Targeted high-resolution simulations complement observations where observational information is insufficient to obtain tight parameter estimates.They are deployed locally in entire grid columns selected using uncertainty measures, rather than globally across a small fraction of each column.
- 2.2 Computable and Non-computable Parameters: The learning phase integrates observations and nested high-resolution simulations to estimate computable and non-computable parameters in physical, biological, or chemical process models.Afterward, the ESM can be used more efficiently, like models in current use.
- 2.2 Computable and Non-computable Parameters: Using observations and high-resolution simulations in tandem creates implementation challenges but could improve ESM reliability and predictive power while quantifying uncertainty.The framework therefore requires coordinated use of both information sources during parameter learning.
- 2.3 Objectives: Bias Reduction and Exploitation of Emergent Constraints: Parameter learning must remain computationally tractable because standard approaches may require O(105) evaluations to estimate O(100) parameters.Such repeated long climate integrations are infeasible when each evaluation accumulates long-term climate statistics.
- 2.3 Objectives: Bias Reduction and Exploitation of Emergent Constraints: Objective functions can directly penalize climate-simulation biases, including precipitation and cloud-cover biases, using mean-field terms for spatially and seasonally resolved fields.Examples include precipitation, ecosystem primary productivity, and top-of-atmosphere radiative energy fluxes.
- 2.3 Objectives: Bias Reduction and Exploitation of Emergent Constraints: Emergent-constraint objectives use covariations in present-climate observables to constrain responses to perturbations such as global warming.Examples relate low-cloud cover with surface temperature and atmospheric CO2 with surface temperature.
- 2.3 Objectives: Bias Reduction and Exploitation of Emergent Constraints: Time-averaged statistics make objective functions less sensitive to atmospheric initial conditions and smoother for minimization than direct trajectory matching.Slowly evolving components such as ocean circulation or ice sheets can still retain initial-condition dependence.
3 Machine Learning Framework for Earth System Models
The framework learns Earth system model parameters by comparing model outputs with observations and nested high-resolution simulations using time-averaged statistics. It separates parameters learnable from high-resolution simulations from those requiring observations, while accounting for computational cost, non-uniqueness, normalization, and model error.
- 3.1 Models and Data: The framework represents global model states, observations, and local high-resolution simulations with linked maps for learning parameterization parameters.The global model maps parameters to states, the observing system maps states to observables, and nested simulations provide high-resolution counterparts for parameterized quantities.
- 3.1 Models and Data: Computable parameters can be learned from high-resolution simulations, whereas non-computable parameters require observational information.The local high-resolution map depends only on non-computable parameters, while the ESM column map depends on both parameter classes, enabling their mismatch to inform computable parameters.
- 3.2 Objective Functions: Objective functions compare simulated and observed data, and simulated ESM quantities with high-resolution results, using time-averaged first- and second-order statistics.Observational objectives can penalize mismatches in means and covariance components, with normalization and covariance information represented by Σy and Σz.
- 3.2 Objective Functions: Time-averaged mismatches reduce sensitivity to atmospheric initial conditions, but averages can still depend on slowly evolving ocean and ice-sheet states.Direct trajectory matching would require assimilating atmospheric initial conditions, while slowly evolving Earth-system components retain initial-condition dependence.
- 3.3 Learning Algorithms: Learning algorithms minimize observational and high-resolution mismatch objectives, but regularization is needed when parameters are correlated or underdetermined by available observations.Regularization selects among multiple possible solutions and involves trade-offs between computational expense and parameter information.
- 3.3 Learning Algorithms: Computational tractability constrains algorithm choice because standard estimation methods may require O(105) evaluations, while classical regularized least squares typically requires O(102) forward-model integrations.Bayesian MCMC methods can require many more integrations, sometimes O(105), particularly when uncertainty estimates are sought.
- 3.3 Learning Algorithms: The framework can incorporate structural uncertainty through additional learned model-error parameters, but normalization choices strongly affect parameter learning and error disentanglement.The covariance structures Σy and Σz determine weighting in the objective functions and may be addressed with hierarchical Bayesian methods or ensemble Kalman analogues.
- 3.3 Learning Algorithms: Realizing the framework requires filtering methods for strongly serially correlated averages and inexpensive sensitivity calculations for experimental design.These needs arise when averages are accumulated over increasing spans and parameters are updated between successive averages.
4 Illustration With Dynamical System
The Lorenz-96 illustration tests whether low-order statistics can support parameter learning in a multiscale system resembling an ESM. Bayesian inversion and ensemble Kalman inversion recover useful parameter information, while revealing computational and uncertainty-quantification trade-offs.
- Model setup: The Lorenz-96 model represents resolved slow variables and unresolved fast variables coupled through an interaction coefficient analogous to an ESM parameterization.The model includes nonlinearities resembling fluid advection and a multiscale coupling between slow and fast variables.
- Learning from statistics: One-point statistics constrain the interaction coefficient through the fast-variable second moment and its covariance with the slow variables.The inverse interaction coefficient is proportional to the regression coefficient of fast variables onto slow variables, providing an emergent constraint.
- Bayesian inversion: Rough potential-energy landscapes and multimodality challenge learning because one-point statistics cannot readily distinguish prograde from retrograde wave modes.Longer accumulation windows or ensembles of initial conditions could smooth sampling variability, but these remedies may be impractical for ESMs.
- Bayesian inversion: Bayesian inversion produces posterior probability mass around the true parameters, although parameter c has the largest relative uncertainty and posterior roughness contributes to that spread.The posteriors differ significantly from the priors, indicating information from the synthetic data, but they do not all peak exactly at the true values.
- Ensemble Kalman inversion: Ensemble Kalman inversion can yield reasonable parameter estimates, but its ensemble spread is not always quantitatively consistent with Bayesian posterior uncertainty and small ensembles may collapse.With perturbed data and larger ensembles, the spread is qualitatively consistent with MCMC, especially for identifying c as the most uncertain parameter.
- Ensemble Kalman inversion: Ensemble Kalman inversion typically converges within ≲5 iterations for M = 100, using substantially fewer objective-function evaluations than MCMC but providing less detailed uncertainty information.Larger ensembles produce solutions closer to the truth, while the optimal trade-off between efficiency, estimate precision, and uncertainty quantification remains unresolved.
- Fast-variable learning: Fast-variable-only Bayesian inversion under selected conditions produces posterior modes, multimodality, uncertainties, and biases similar to those from the full dynamics.The experiment uses a single grid column, illustrating potential learning from local high-resolution simulations without establishing generalization to imperfect parameterizations.
5 Outlook
The proposed ESM framework learns parameterizations from global observations and targeted high-resolution simulations, while supporting uncertainty quantification and observing-system assessment. Realizing it requires advances in equation-informed learning, algorithms, metrics, simulation targeting, and parameterization design.
- 5 Outlook: Global observations and targeted high-resolution simulations can jointly inform parameterizations through data assimilation and machine learning.The framework targets processes including clouds, convection, turbulence, and ecosystems.
- 5 Outlook: Systematic parameter learning allows parameterization uncertainty to be quantified and propagated into ensembles of climate simulations.The proposed objective matches mean values and covariance components across ESMs, observations, and targeted high-resolution simulations.
- 5 Outlook: Equation-informed machine learning can use governing equations to derive coarse-grained process models whose closure parameters are learned from diverse data.For unknown ecological or biogeochemical processes, more empirical data-driven parameterizations may be needed.
- 5 Outlook: Key challenges include improving learning algorithms, selecting informative metrics, balancing simulation cost against information, and designing refinable parameterization schemes.The paper also calls for unified treatment of subgrid-scale motions and reconsideration of column-based subgrid dynamics as resolution increases.
- 5 Outlook: Higher-resolution ESMs will require re-engineered parameterizations as grid spacings reach 1–10 km and begin resolving deep convection.This motivates designing ESMs from the outset to learn systematically from observations and targeted high-resolution simulations.
- 5 Outlook: Observing system simulators can both map model states to observables for parameter learning and support observing system simulation experiments.These experiments assess the value of new observations in terms of reduced ESM uncertainties.