[Paper Review] Simulating Atmospheric Processes in Earth System Models and Quantifying Uncertainties with Deep Learning Multi-Member and Stochastic Parameterizations

Gunnar Behrens, Tom Beucler+6 more|arXiv (Cornell University)|Feb 5, 2024

Atmospheric and Environmental Gas Dynamics4 citations

TL;DR

This paper proposes deep learning ensemble and stochastic parameterizations with calibrated uncertainty quantification to improve subgrid atmospheric processes in Earth System Models (ESMs), using multi-member neural networks and variational autoencoders to simulate convection, turbulence, and radiative fluxes. The method enables stable, long-term online simulations (>5 months) and significantly improves extreme precipitation and diurnal cycle representation compared to deterministic models.

ABSTRACT

Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated uncertainty quantification to learn subgrid convective and turbulent processes and surface radiative fluxes of a superparameterization (SP) embedded in an Earth System Model (ESM). We explore three methods to construct stochastic parameterizations: 1) a single Deep Neural Network (DNN) with Monte Carlo Dropout; 2) a multi-member parameterization; and 3) a Variational Encoder Decoder with latent space perturbation. We show that the multi-member (MM) parameterization improves the representation of convective processes, especially in the planetary boundary layer, compared to individual DNNs. The respective uncertainty quantification illustrates that methods 2) and 3) are advantageous compared to a dropout-based DNN parameterization regarding the spread of convective processes. Hybrid simulations with our best-performing MM parameterizations remained challenging and crash within the first days. Therefore, we develop a pragmatic partial coupling strategy relying on the SP for condensate emulation. Partial coupling reduces the computational efficiency of hybrid Earth-like simulations but enables model stability over 5 months with our MM parameterizations. However, our hybrid simulations exhibit biases in thermodynamic fields and differences in precipitation patterns. Despite this, the MM parameterizations enable improvements in reproducing tropical extreme precipitation compared to a traditional convection parameterization. Despite these challenges, our results indicate the potential of a new generation of MM machine learning parameterizations leveraging uncertainty quantification to improve the representation of stochasticity of subgrid effects.

Motivation & Objective

• To address persistent biases in Earth System Models (ESMs), particularly the double ITCZ bias, caused by inadequate subgrid-scale convection parameterizations.
• To develop machine learning-based parameterizations that capture subgrid variability and uncertainty, moving beyond deterministic deep neural networks (DNNs).
• To enable stable, long-term online coupling of deep learning parameterizations with a full ESM, including surface and radiative fluxes, by sidestepping challenges in condensate tendency emulation.
• To quantify uncertainty in subgrid processes using stochastic deep learning approaches, improving trustworthiness and realism of climate simulations.
• To demonstrate that ensemble-based machine learning parameterizations outperform deterministic counterparts in simulating extreme precipitation and diurnal cycles.

Proposed method

• Three stochastic parameterization methods are developed: (1) a single DNN with Monte Carlo Dropout, (2) a multi-network ensemble, and (3) a Variational Autoencoder-Decoder (VAE) with latent space perturbations.
• The multi-network ensemble uses multiple independent DNNs to generate diverse predictions from the same input, enhancing representation of subgrid variability.
• A novel partial coupling strategy is introduced to decouple condensate tendency emulation, enabling stable online integration with the ESM for over 5 months.
• Uncertainty quantification is achieved through ensemble spread and probabilistic outputs, with the VAE-based method showing superior spread characteristics compared to dropout-based DNNs.
• Offline evaluation uses hold-out datasets to compare subgrid tendency predictions; online evaluation assesses precipitation extremes and diurnal cycles in coupled simulations.
• All models are trained on data from a superparameterized Community Atmosphere Model (SPCAM) in an aquaplanet setup, then embedded into the SPCESM2 ESM for online testing.

Figure 1: We compare three stochastic parameterization strategies for reproducing the superparameterization (SP), which simulates SP subgrid variables ( $\boldsymbol{Y}$ ) based on large-scale Community Atmosphere Model (CAM) variables ( $\boldsymbol{X}$ ): 1) Applying Monte-Carlo dropout to a singl

Experimental results

Research questions

• RQ1 Can deep learning ensemble parameterizations improve the representation of subgrid convective and turbulent processes in the planetary boundary layer compared to deterministic DNNs?
• RQ2 How do different stochastic parameterization techniques—Monte Carlo Dropout, multi-network ensembles, and VAE-based perturbations—compare in terms of uncertainty spread and predictive skill?
• RQ3 Can stable, long-term online simulations (>5 months) be achieved with machine learning parameterizations when fully coupled to an ESM, including surface and radiative fluxes?
• RQ4 To what extent do ensemble-based parameterizations improve the simulation of extreme precipitation and the diurnal cycle of precipitation compared to traditional schemes?
• RQ5 Can uncertainty quantification from ensemble methods be meaningfully linked to subgrid process variability in realistic, coupled Earth system simulations?

Key findings

• The multi-network ensemble parameterization significantly improves the representation of convective processes in the planetary boundary layer compared to individual DNNs, both offline and online.
• Online simulations using the ensemble approach remain stable for over 5 months, whereas simulations with individual DNNs crash within days due to instability in condensate tendency emulation.
• The VAE-based stochastic parameterization produces a more realistic spread of convective process predictions than the dropout-based DNN ensemble, indicating better uncertainty quantification.
• The ensemble parameterizations improve the simulation of extreme precipitation and the diurnal cycle of precipitation, bringing them closer to the reference superparameterization than the traditional parameterization.
• Despite improvements, faithful representation of mean precipitation patterns remains challenging, indicating ongoing limitations in large-scale circulation simulation.
• The proposed partial coupling strategy successfully sidesteps issues in condensate tendency emulation, enabling stable online integration of machine learning parameterizations with a comprehensive ESM.

Figure 2: Vertical profiles of median coefficient of determination R 2 for specific humidity tendency (a), $\boldsymbol{\dot{q}}$ ), temperature tendency (b) $\boldsymbol{\dot{T}}$ ) of DNN-dropout (solid navy blue); $\mathrm{\overline{DNN}}$ and DNN-ensemble (solid and dashed black), $\mathrm{\over