Accelerating Climate Model Accuracy and Reliability
Accelerated progress in climate modeling is urgently needed for proactive and effective climate change adaptation. The central challenge lies in accurately representing processes that are small in scale yet climatically important, such as turbulence and cloud formation. These processes will not be explicitly resolvable for the foreseeable future, necessitating the use of parameterizations.
We propose a balanced approach that leverages the strengths of traditional process-based parameterizations and contemporary artificial intelligence (AI)-based methods to model subgrid-scale processes. This strategy employs AI to derive data-driven closure functions from both observational and simulated data, integrated within parameterizations that encode system knowledge and conservation laws.
In addition, increasing the resolution to resolve a larger fraction of small-scale processes can aid progress toward improved and interpretable climate predictions outside the observed climate distribution. However, currently feasible horizontal resolutions are limited to O(10 km) because higher resolutions would impede the creation of the ensembles that are needed for model calibration and uncertainty quantification, for sampling atmospheric and oceanic internal variability, and for broadly exploring and quantifying climate risks.
By synergizing decades of scientific development with advanced AI techniques, our approach aims to significantly boost the accuracy, interpretability, and trustworthiness of climate predictions.
The Dual Roles of Climate Models
Climate models serve two distinct purposes. First, they encode our collective knowledge about the climate system. They instantiate theories and provide a quantitative account of climate processes – the complex interplay of causes and effects that governs how the climate system operates. In this role, they belong to the realm of episteme, or explanatory science (Russo, 2000; Parry, 2021).
Second, climate models function as practical tools that allow us to calculate how the climate system might behave under different circumstances that have not yet been directly observed. In this role, they fall under the realm of techne, or goal-oriented applied science (Russo, 2000; Parry, 2021).
The requirements for climate models differ depending on their primary role as episteme or techne. As encodings of our understanding (episteme), climate models should strive for explainability and simplicity, even if it means sacrificing a certain level of accuracy. An understanding of the climate system at different levels of description emerges through a hierarchy of models, ranging from simpler ones such as one-dimensional radiative–convective equilibrium models to more complex ones such as atmospheric general circulation models with simplified parameterizations of subgrid-scale processes (Held, 2005; Jeevanjee et al., 2017; Mansfield et al., 2023).
On the other hand, as calculation tools (techne), climate models should aim to simulate the climate system as accurately as possible under unobserved circumstances. Over the past 6 decades, climate modeling has operated under the tacit assumption that these two roles of climate models align, implying that the most complex models reflecting our understanding of the system are also the most accurate tools for predicting its behavior in unobserved conditions. This is a desirable goal, but it may not always be attainable in systems as complex as the climate system.
In this essay, we focus on the use of climate models as techne, emphasizing their role as tools for accurately calculating the behavior of the climate system in unobserved circumstances, although, as we will see, this role cannot entirely be decoupled from episteme.
Optimizing Climate Models for Accurate Predictions
The goal of calculating the behavior of the climate system is to obtain its statistics, including average temperatures at specific locations and seasons, the probability that daily precipitation in a given region exceeds some threshold, or the covariance between temperature and humidity, which can lead to potentially dangerous humid heat extremes. These calculations correspond to what Lorenz (1975) defined as predictions of the second kind, where future climate statistics are estimated given evolving boundary conditions, such as human-induced greenhouse gas emissions. This contrasts with predictions of the first kind, which focus on forecasting the future state of a system given its initial conditions ζ0, as seen in weather forecasting.
Consequently, when used as techne, climate models should aim to minimize a loss function of the form (Schneider et al., 2017a)
Here, the angle brackets ⟨⟩ indicate an appropriate time averaging, such as a seasonal average over multiple years. The vector y(t) represents time-varying observables of the climate system, including those whose time average ⟨y(t)⟩ gives rise to higher-order statistics such as the frequency of exceeding a daily precipitation threshold in a specific region. It may also include frequency-space observables, such as the amplitude and phase of the diurnal cycle of precipitation.
The climate model, denoted as G(t;θ,λ,ν;ζ0), is a mapping of parameter vectors (θ,λ,ν) and an initial condition vector ζ0 (usually important only for slowly varying components of the climate system, such as oceans and ice sheets) to time-varying simulated climate states ζ(t)=G(t;θ,λ,ν;ζ0). The observation operator H maps simulated climate states ζ(t) to the desired observables y(t). Lastly, ∥·∥_Σ^{-1}=∥Σ^{-1/2}(·)∥_2 represents a weighted Euclidean norm, or Mahalanobis distance. The weight is determined by the inverse of the covariance matrix Σ, which reflects model and observational errors and noise due to fluctuations from internal variability in the finite-time average ⟨⟩.
The weighted Euclidean norm is chosen because the climate statistics are aggregated over time, meaning that, due to the central limit theorem, it is reasonable to assume that these statistics exhibit Gaussian fluctuations (Iglesias et al., 2013; Schneider et al., 2017a; Dunbar et al., 2021). However, the specific choice of norm in the loss function is not crucial for the following discussion. The essence is that the loss function penalizes mismatches between simulated and observed climate statistics, with less-noisy statistics receiving greater weight.
This can be done for longer-term aggregate statistics or for shorter-term predictions (for example, those of El Niño and its impact on the climate system). The relatively sparse statistics available from reconstructions of past climates can additionally serve as a useful test of climate models outside the distribution of the present climate (Zhu et al., 2022).
To achieve accurate simulations of climate statistics, the objective is to minimize the loss function (Eq. 1) for unobserved climate statistics ⟨y⟩ with respect to the parameters (θ,λ,ν). Importantly, the climate statistics may fall outside the distribution of observed climate statistics, particularly in the context of global warming projections. Therefore, the ability of a model to generalize beyond the distribution of the observed data becomes essential. Merely minimizing the loss over observed climate statistics or even driving the loss to zero in an attempt to imitate observations and pass a “climate Turing test” (Palmer, 2016) is not sufficient. Instead, fundamental science and data science tools, such as cross-validation and Bayesian tools, need to be brought to bear to plausibly minimize the loss for unobserved statistics.
In the loss function, we distinguish three types of parameters:
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The parameters
θappear in process-based models of subgrid-scale processes, such as entrainment and detrainment rates in parameterizations of convection. These parameters are directly interpretable and theoretically measurable, although their practical measurement can be challenging. -
The parameters
λrepresent the characteristics of the climate model’s resolution, such as the horizontal and vertical resolution in atmosphere and ocean models. -
The parameters
νpertain to artificial intelligence (AI)-based data-driven models that capture subgrid-scale processes or correct for structural model errors, either within process-based models of subgrid-scale processes or holistically for an entire climate model (Kennedy and O’Hagan, 2001; Levine and Stuart, 2022; Bretherton et al., 2022; Wu et al., 2024). These parameters are neither easily interpretable nor directly measurable but are learned from data.
This distinction among the parameters is useful as it reflects three different dimensions along which climate models can be optimized.
Three Dimensions of Climate Model Optimization
First, optimization can be achieved by calibrating parameters and improving the structure of process-based models that represent subgrid-scale processes such as turbulence, convection, and clouds. These processes have long been identified as a dominant source of biases and uncertainties in climate simulations (Cess et al., 1989; Bony and Dufresne, 2005; Stephens, 2005; Vial et al., 2013; Schneider et al., 2017b; Zelinka et al., 2020).
Second, optimization can be accomplished by increasing the resolution of the models, which reduces the need for parameterization (Bauer et al., 2021; Slingo et al., 2022).
Finally, optimization can be pursued by integrating AI-based data-driven models. These models have the potential to replace (Gentine et al., 2018; O’Gorman and Dwyer, 2018; Yuval and O’Gorman, 2020; Yuval et al., 2021) or complement (Schneider et al., 2017a; Lopez-Gomez et al., 2022) process-based models for subgrid-scale processes. Additionally, they can serve as comprehensive error corrections for climate models (Watt-Meyer et al., 2021; Bretherton et al., 2022; Wu et al., 2024).
In the past 2 decades, efforts to optimize climate models have often focused on individual dimensions in isolation. For example, Climate Process Teams initiated under the US Climate Variability and Predictability Program have concentrated on enhancing process-based models by incorporating knowledge from observational and process-oriented studies into climate modeling (Subramanian et al., 2016).
The resolution of atmosphere and ocean models has gradually increased, albeit at a pace slower than the advances in computer performance would have allowed (Schneider et al., 2017b). More recently, there have been calls to prioritize increasing the resolution; the aim is to achieve kilometer-scale resolutions in the horizontal, with the expectation that this would alleviate the need for subgrid-scale process parameterizations, such as those for deep convection, and substantially increase the reliability of climate predictions (Bauer et al., 2021; Slingo et al., 2022).
Moreover, there is rapidly growing interest in advancing climate modeling by using AI tools, broadly understood to include tools such as Bayesian learning, deep learning, and generative AI (e.g., Schneider et al., 2017a; Reichstein et al., 2019; Chantry et al., 2021; Watson-Parris, 2021; Balaji et al., 2022; Irrgang et al., 2022; Schneider et al., 2023).
Beginning with a review of recent advances in the goodness of fit between climate simulations and observed records, here we will explore the potential benefits and challenges associated with optimizing each of the three dimensions mentioned earlier. Our analysis will highlight the importance of adopting a balanced approach that encompasses progress along each dimension, as this is likely to yield the most robust and accurate climate models and the most trustworthy and usable predictions.
Assessing Recent Progress in Climate Modeling
The climate statistics ⟨y⟩ used in the loss function (Eq. 1) can vary depending on the specific application. For example, a national climate model may prioritize minimizing the loss within a particular country. However, there are several climate statistics that are generally considered important and should be included in any comprehensive loss function.
Two such examples are the top-of-atmosphere (TOA) radiative energy fluxes and surface precipitation rates. The inclusion of TOA radiative energy fluxes is crucial because accurately simulating these fluxes is a prerequisite for accurately simulating the changes in any climate statistic. After all, radiative energy is the primary driver of the climate system. Changes in radiative energy fluxes caused by changes in greenhouse gas concentrations drive global climate change; climate models must accurately simulate changes in these energy fluxes and their effect on multiple climate system components, from oceans and land surfaces to clouds.
As a consequence, errors in radiative energy fluxes affect many aspects of a simulated climate, from wind to precipitation distributions. The balance of TOA radiative energy fluxes must also be closed to machine precision. A closed energy balance is necessary to achieve a steady climate in unforced centennial to millennial integrations in which tiny imbalances of the energy budget otherwise accumulate over 10^7 discrete time steps, leading to large-scale climate drift. The conservation requirements for climate predictions – for what John von Neumann called the “infinite forecast” (Edwards, 2010) – are more stringent than those for the short-term integrations needed for weather forecasting.
Similarly, precipitation rates are of significant importance as they are part of what closes the water balance and they directly impact human activities. Achieving accurate simulations of precipitation rates relies on accurately simulating numerous subgrid-scale processes within the climate system. Therefore, precipitation is an emergent property that serves as a holistic metric to assess the goodness of fit of a climate model.
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The rms errors are relative to climatologies from the Global Precipitation Climatology Project (GPCP) (Adler et al., 2018) and CERES-EBAF (Loeb et al., 2009) datasets over the period 2001–2020. CMIP and AMIP rms errors represent median values of the RMSE computed separately for each of the included models. Climatologies were computed as follows: for CMIP3, over 2001–2020 for the B1 scenario; for CMIP5/6, over 2001–2020 for a combination of the historical and RCP4.5/SSP2.45 scenarios; for AMIP, over 1995–2014 for models contributing to CMIP6; for HadGEM3-GC31 and MPI-ESM1-2, over 1995–2014 for the historical simulations and over 4 simulated years for the kilometer-scale nextGEMS cycle 3 simulations (Hohenegger et al., 2023; Rackow et al., 2024), which are shown together with averages over the equivalent simulation length in CMIP6. The rms error is normalized by the median across the CMIP3 and CMIP5 models for each field and across all seasons, with normalization constants shown below the color bar.
Figure 1 assesses the evolution of climate models over the past 2 decades in simulating the observed climatology of TOA radiative energy fluxes and precipitation rates, temporarily setting aside that the loss minimization should occur for unobserved records. The figure displays the median root mean square (rms) error between model seasonal climatologies and observations, with all data conservatively remapped to a common 2.5° latitude–longitude grid using Climate Data Operators (Schulzweida, 2023).
The plot includes three generations of climate models from the Coupled Model Intercomparison Project (CMIP) as well as recent higher-resolution simulations. It is evident that, over time, there has been a gradual improvement in the fidelity of models in simulating TOA radiative energy fluxes and precipitation. For example, in CMIP6 (late 2010s), the median rms error relative to CMIP3 (mid-2000s) is reduced by 15% for precipitation, 31% for TOA outgoing longwave flux, and 30% for TOA reflected shortwave flux, with all values indicating average seasonal-mean improvements (Fig. 1, upper row).
Individual modeling centers have surpassed this median rate of improvement; for example, there are rms error reductions of 30% for precipitation, 49
