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Spatially Extended Tests of a Neural Network Parametrization Trained by Coarse-graining
Noah D Brenowitz, Christopher S Bretherton
TL;DR
Coarse-resolution models cannot resolve important moist processes, while coarse-grained neural-network parametrizations had not been shown stable in fully coupled spatially extended simulations. The paper couples such a parametrization to a GCM, analyzes its instability, and modifies its inputs. The modified network runs stably and forecasts more accurately than the base coarse-grid simulation, although its mean state drifts slowly.
Problem
Coarse-resolution models cannot resolve important moist processes, and coarse-grained neural-network parametrizations had not been tested in fully coupled spatially extended GCM simulations.
Method
The study couples a neural network trained from coarse-grained cloud-system resolving data to a GCM dynamical core and analyzes the network's linearized response to stabilize the coupling.
Results
Removing upper-atmospheric humidity-related inputs stabilizes the coupled simulations, which have higher forecast skill and lower bias than the base coarse-grid simulation.
Takeaways & Limitations
The modified neural-network parametrization can run stably in spatially extended simulations and improve forecasts relative to the unparameterized coarse-grid reference.
Takeaways & Limitations
The stabilization required a crude human intervention because the network exploited a correlation rather than a causal mechanism.
Abstract
from arXiv · showhide
General circulation models (GCMs) typically have a grid size of 25--200 km. Parametrizations are used to represent diabatic processes such as radiative transfer and cloud microphysics and account for sub-grid-scale motions and variability. Unlike traditional approaches, neural networks (NNs) can readily exploit recent observational datasets and global cloud-system resolving model (CRM) simulations to learn subgrid variability. This article describes an NN parametrization trained by coarse-graining a near-global CRM simulation with a 4~km horizontal grid spacing. The NN predicts the residual heating and moistening averaged over (160 km)^2 grid boxes as a function of the coarse-resolution fields within the same atmospheric column. This NN is coupled to the dynamical core of a GCM with the same 160 km resolution. A recent study described how to train such an NN to be numerically stable when coupled to specified time-evolving advective forcings in a single column model, but feedbacks between NN and GCM components cause spatially-extended simulations to crash within a few days. Analyzing the linearized response of such an NN reveals that it learns to exploit a strong synchrony between precipitation and the atmospheric state above 10 km. Removing these variables from the NN's inputs stabilizes the coupled simulations, which predict the future state more accurately than a coarse-resolution simulation without any parametrizations of sub-grid-scale variability, although the mean state slowly drifts.
1 Introduction
Coarse-resolution climate and weather models struggle to represent important moist processes and tropical variability because subgrid convection and cloud variability remain unresolved. The section motivates machine-learning parametrizations and extends a coarse-grained neural-network approach from single-column experiments to spatially extended GCM simulations.
- Coarse-resolution models cannot explicitly resolve many important physical processes, including cumulus convection, turbulence, and subgrid cloud variability.
- Cumulus convection is dynamically important but difficult to parameterize because of the multiscale nature of moist flows.
- Climate models exhibit mean-state biases and struggle with tropical variability, including continental precipitation's diurnal cycle and the Madden–Julian Oscillation.
- Cloud-system resolving models can represent subgrid processes more explicitly, but centennial-scale global simulations remain infeasible, leaving improved coarse-resolution parametrizations important.
- Neural networks can use high-resolution datasets to learn parametrizations, and prior work found stable, accurate single-column simulations when training optimized performance over multiple time steps.
- This study extends the neural-network parametrization to a GCM dynamical core, targeting accurate multiple-day forecasts in spatially extended simulations.
2 Review of Machine Learning Parametrization
Machine-learning parametrization can exploit realistic high-resolution simulations, but coarse-graining removes the clear input–target hierarchy available in emulation tasks. The section identifies numerical stability in fully coupled three-dimensional GCMs as the unresolved challenge beyond earlier single-column work.
- Existing parametrizations can lack flexibility, and tuning a few parameters may improve mean-state bias while harming variability.
- Many earlier machine-learning parametrizations emulate existing radiation, convection, or super-parametrization schemes using atmospheric states and known outputs.
- Coarse-graining a cloud-system resolving model is harder because it lacks the hierarchical input–output structure of conventional emulation datasets.
- The coarse-graining approach leaves the target tendency unclear, with prior work defining outputs as residual heating and moistening but not presenting prognostic simulations.
- Brenowitz and Bretherton used near-global CRM data and obtained stable single-column simulations by minimizing loss accumulated over several predicted time steps.
- Their stability method had not been tested in a full three-dimensional GCM where the dynamics interact with the neural-network parametrization.
3 Training Data and Atmospheric Model Configuration
The study trains and evaluates neural-network parametrizations using a near-global 4 km cloud-system resolving simulation and a matched 160 km coarse model. The configuration includes numerical modifications and compares coupled neural-network simulations with a base coarse-resolution model over 10-day forecasts.
- Training data: The training data come from a near-global aquaplanet SAM simulation with 4 km horizontal spacing, 34 vertical levels, and a 20 480 km by 10 240 km tropical-channel domain.
- Coarse-resolution model: The coarse model uses the same geometry, dry dynamics, and vertical grid as the training simulation and is run at 160 km resolution.
- Coarse-resolution model: Hyper-diffusion was added to suppress grid-scale oscillations and blow-up, while simplified momentum damping replaced SAM's default turbulence closure.
- Coarse-resolution model: The momentum-damping difference from NG-Aqua causes cSAM simulations to drift away from NG-Aqua over a few days.
- Experiments: The experiments compare NN-coupled cSAM with a base cSAM using grid-scale mean thermodynamics for microphysics and radiation, targeting 10-day evolution from a common initial state.
4 Machine Learning Parametrization
The parametrization represents coarse-grid heating and moistening residuals with a deterministic neural network driven by column state and external surface inputs. Linear-response analysis reveals that upper-atmospheric inputs create physically implausible sensitivities and feedbacks that destabilize coupled simulations, while removing them improves stability and retains useful lower-tropospheric predictions.
- 4 Machine Learning Parametrization: The NN parameterizes unresolved heating Q1 and moistening Q2 as deterministic functions of coarse-resolution column variables, SST, and downwelling insolation.Q1 and Q2 are budget residuals containing unresolved physics including latent heating, turbulent mixing, and radiation.
- 4 Machine Learning Parametrization: MSPE-trained NNs can spin up more slowly than the cSAM timestep, making them unsuitable for spatially extended coupling.The GCM couples to the NN every 120 s, whereas the relevant spin-up occurs over a longer timescale.
- 4.3 Coupled Numerical Instability: Upper-level moisture sensitivity creates a positive feedback in which moisture raises precipitation and heating, increases upward velocity, and supplies more moisture aloft.The feedback can ultimately produce grid-scale storms, similarly to moisture-convergence closures.
5 Results
Spatially extended simulations show that NN-Lower is numerically stable and generally more accurate than the base simulation, especially for thermodynamic variables and precipitation patterns. However, it produces overly smooth tropical precipitation, and circulation biases and mean-state drift grow over time.
- Simulation configurations: NN-Lower uses humidity below level 16 and temperature below level 19, whereas NN-All uses all atmospheric levels as inputs.The simulations are initialized with NG-Aqua data and evaluated over the first 10 forecast days against training data and a base simulation.
- Simulation stability: NN-Lower is numerically stable for five days, while NN-All develops moist tropical grid-scale storms and the base simulation blows up after 9 days.NN-Lower retains reasonable precipitable-water predictions but loses some large-scale tropical moisture variability.
- Weather prediction accuracy: 50% lower errors in both sL and qT make NN-Lower the most accurate configuration across regions and variables.Vorticity improves less because the parametrization does not represent the momentum source Q3.
- Precipitation structure: NN-Lower reproduces the extra-tropical precipitation pattern but underestimates tropical variability, while the base simulation produces excessively strong and noisy precipitation.The NN-Lower prediction is smoother even when evaluated on the true coarse-grained state, indicating that the smoothness is not solely caused by coupled evolution.
- Precipitation prediction: NN-Lower predicts net precipitation more accurately than the base simulation, with higher pattern correlations and correlation remaining at 0.5 through day 101.5 in the tropics.In the extratropics and subtropics, correlation remains above 0.5 beyond day 102.5, while the base simulation has little tropical predictive skill.
- Mean-state evolution: NN-Lower’s tropical mean net precipitation is 40% weaker than NG-Aqua despite similar mean precipitable water.Reduced net-precipitation variance accompanies reduced precipitable-water variance and is proposed as a target for mitigating circulation biases.
6 Conclusions
The study extends a coarse-grained neural-network unified-physics parametrization from single-column tests to spatially extended GCM simulations. Removing upper-atmospheric humidity and temperature stabilizes the coupled model and improves short-term forecast skill, but long-term circulation and climate biases remain.
- Approach: The neural network predicts diabatic heating and moistening tendencies from a coarse-grained high-resolution simulation for application in a coarse-grid model.The training data are coarse-grained from a 4 km simulation, and the parametrization targets unresolved subgrid processes.
- Approach: The study extends earlier single-column results to a spatially extended 160 km dynamical-core simulation over the 46S–46N domain.The model uses the same anelastic atmospheric core as the training dataset and includes additional damping for stable operation.
- Stability: A preliminary coupled network caused model blow-up because it exploited a noncausal correlation between upper-atmospheric humidity and precipitation.The correlation was associated with the short lifetime of water vapor at those heights rather than a causal mechanism.
- Stability: Removing upper-atmospheric humidity and temperature from the inputs produced spatially extended simulations that ran stably indefinitely.The authors characterize this stabilization as a crude human intervention and call for automatic discovery of causal relationships in dynamically coupled settings.
- Results and limitations: The modified parametrization improved forecast skill and reduced bias relative to the base coarse-grid simulation, but long-term climate and circulation biases persisted.Temperature and humidity biases were small during the first 10 days, while the Hadley circulation weakened because tropical heating was insufficient; enhanced moisture and precipitation variance is proposed as one possible remedy.
- Results and limitations: A fairer comparison requires implementing the machine-learning parametrization in a global model alongside the traditional suite of physical parametrizations.The coarse-graining approach also lacks the natural hierarchical structure present in super-parametrization datasets.