Toward a Learnable Climate Model in the Artificial Intelligence Era

We are in a revolutionary era where article intelligence (AI), especially large AI models (Table 1), is redefining how we understand and address climate-related challenges. AI models have swept through most areas of the atmospheric sciences, including but not limited to weather forecasting (Table 1; Pathak et al., 2022; Bi et al., 2023; Chen et al., 2023a; Chen et al., 2023b; Lam et al., 2023), subseasonal and seasonal predictions (Ham et al., 2019, 2021; Pan et al., 2020; Kim et al., 2021; Mu et al., 2021; Ravuri et al., 2021; Ling et al., 2022; Fan et al., 2023; Hess et al., 2022; Zhang et al., 2023; Zhou and Zhang, 2023), extreme weather and climate prediction (e.g., Li et al., 2023), parameterization schemes (Rasp et al., 2018; Han et al., 2020), correction of model simulations (e.g., Pan et al., 2020), and climate detection and attribution (Labe and Barnes, 2021, 2022; Diffenbaugh and Barnes, 2023; Ham et al., 2023; Labe et al., 2023). With its ability to integrate and comprehend data from diverse sources such as satellites, weather stations, and ocean buoys, AI has delivered breakthrough advancements in numerous areas. Its strengths lie in enhancing the overall understanding of atmospheric systems, handling the complexity and nonlinearity of atmospheric dynamics, and offering rapid computational speeds.

While AI blazes forward, the role of physics, often described as the bedrock of climate science, has sometimes been overshadowed. Physical laws and climate theories provide the fundamental principles underpinning our understanding of climate systems. They form the basis of dynamical climate models, offering a comprehensible framework for climate predictions and climate simulations. These models are interpretable, and they have proved their mettle for nearly one hundred years (Bauer et al., 2015). However, in the AI era, interpretability often takes a back seat. AI models are often recognized as “black boxes”, which generate predictions and simulations without transparently explaining their involved physical processes. This opaqueness poses huge challenges when it comes to validating AI models and building trust in their generated results. Additionally, AI models lacking physical constraints often face issues such as poor generalization capabilities. This can lead to results that are inconsistent with physical properties and highly unstable, particularly in the context of extreme events.

So, where do we go from here? The answer lies in the symbiotic relationship between AI and physics. AI brings unparalleled computational power and the ability to recognize complex patterns, while physics offers transparency, interpretability, and a solid foundation for scientific understanding. The future of climate modeling is not an “either/or” scenario, and is a partnership between these two realms, leveraging AI’s computational prowess and the laws of physics’ grounding to create a learnable climate model with good interpretability.

Recently emerged large AI weather models have begun to rival or surpass traditional numerical weather predictions. This naturally raises the question of whether these AI models adhere to the principles of meteorological and climate theories. Climate theories derived from various mathematical physics equations, like quasi-geostrophic theory and quasi-steady Rossby waves, serve as the foundational structure for climate research (Hoskins and Karoly, 1981; Held et al., 2002; Held, 2019). Some might envisage a scenario where, if an AI model is complex enough, with multiple layers and variables, it might closely replicate observational data, learning and following the implied conservation laws and climate theories present in the observations. (Hakim and Masanam (2023) conducted a crucial analysis on this issue, applying perturbations to Pangu-Weather, and observed that introducing a tropical heat source in the model reproduces the Matsuno–Gill response (Matsuno, 1966; Gill, 1980) in the tropics and the associated extratropical Rossby wave train. This qualitative finding suggests that AI models seem to possess the capability to learn fundamental physical laws and atmospheric dynamics. However, the actual situation is more intricate. Quantitative analyses indicate persistent challenges, such as issues in geostrophic wind balance and the rotational and divergent wind components, despite the abundance of data and high complexity in models like Pangu and Graphcast Weather (Bonavita, 2023; Kochkov et al., 2024).

These assessment conclusions may appear contradictory but are, in fact, reflective of different degrees of evaluation perspectives. Hakim and Masanam (2023) indicated that AI models can qualitatively reproduce certain dynamic modes based on climatic dynamics. Considering that these responses are inherently embedded in the data at the weather and climate scale, learning and qualitatively reproducing such modes are reasonable. On the other hand, quantitative evaluations by Bonavita (2023) and Kochkov et al. (2024) revealed significant disparities in aspects like geostrophic wind and divergent wind compared to traditional models. The absence of these factors in the inputs and outputs of the AI model, coupled with the relatively small magnitude of the divergent winds, makes it relatively natural for such errors to occur.

While these evaluations pertain to weather models, considering the lower complexity, data volume, and parameter quantity in climate models compared to weather models, similar issues need to be addressed in the evaluation and optimization processes of AI climate models. This emphasizes the importance of dynamic diagnostic and physical constraints to AI climate models. First and foremost, a meticulous examination of climate dynamics is essential for analyzing and comprehending the performance of AI models. Current evaluation methods primarily focus on first-order and second-order statistics, but good performance in these statistics does not mean a model is good at reproducing the crucial features of targeted dynamical climate variability, such as ENSO’s seasonal phase-locking and asymmetry (Jin, 1996; Wallace et al., 1998; McPhaden et al., 2006). Consequently, there is an imperative need to reevaluate AI simulations, giving prominence not only to fundamental statistics but also to dynamic modes and physical processes. A case in point is the research conducted by Wang et al. (2024), who revealed that generative models can rectify not only climatological sea surface temperature (SST) biases but also markedly mitigate the prevalent excessive westward bias in ENSO SST anomalies, which is a common issue in climate models and has a considerable impact on the ENSO decay and the East Asian climate (Li and Xie, 2012, 2014; Tao et al., 2018, 2019; Jiang et al., 2021). Due to the complexity of the climate system, evaluating climate simulations could be a challenging task. Numerical climate model evaluations have largely relied on the Coupled Model Intercomparison Project (CMIP), allowing scientists from various research domains to thoroughly assess these models based on their climate physics knowledge. To enhance the evaluation of AI simulations, it is imperative to establish a similar comparative project, such as the AI Model Intercomparison Project (AI-MIP). This initiative should construct and release unified dynamic diagnostic tools of varying complexities and benchmarks to facilitate comprehensive assessments. AI-MIP mandates the construction of AI models on a unified and open dataset, and the evaluation and comparison of these models based on standardized metrics. Through AI-MIP, we expect to significantly reduce the costs of data acquisition, model comparison, and learning. Individuals will be able to easily compare their models with state-of-the-art models, accelerating progress in the field.

Furthermore, it is imperative to apply physical constraints informed by climate dynamics to refine AI models. Basic physical knowledge plays a crucial role in providing physical constraints to AI models (Mohan et al., 2019; Beucler et al., 2020). PINNs (Physics-Informed Neural Networks) are a groundbreaking approach where deep-learning (DL) models are informed by physical laws, integrating differential equations directly into the learning process (Raissi et al., 2019). Besides, conservation laws such as energy conservation, mass conservation, and momentum conservation, have always been essential for model development and climate diagnostics.

These constraints can be categorized as soft constraints and hard constraints. Soft constraints do not explicitly impose specific network changes but provide some representations of physical linkages, and physical equations or mathematical constraints. They may encompass connections between different regions, such as teleconnections, or interactions between different variables. One popular soft constraint uses existing physical equations to constrain the loss function (Beucler et al., 2021). Moreover, Mu et al. (2021) offered an example where a graph neural network (GNN) was designed to predict ENSO. They employed a graph structure to represent various physical variables, particularly the coupling relationships between SST and clouds. This method can be understood as a feature fusion, improving the nonlinear combination of different variables/features to better identify critical processes influencing ENSO development. Another example comes from Chen et al. (2024) who designed a GNN for precipitation prediction considering the constraints of the omega equation and moisture equation. By using this physics-constrained network, the prediction of heavy rainfall was significantly improved, and the whole prediction results were also better than those of the other DL models without constraints. Meanwhile, a hard constraint usually modifies the neural network, ensuring an expected constraint during learning and inference (González-Abad et al., 2023; Harder et al., 2024). For instance, when downscaling T_min (minimum temperature) and T_mean (mean temperature) in González-Abad et al. (2023), the activation function for T_min was configured as ReLU, whereas the activation function for T_mean/T_min was set as (1 + ReLU). This specific configuration guarantees that the results consistently adhere to the a priori relationship where T_mean is greater than T_min. Besides, there are also studies that have extended convolutional networks to accommodate a wider variety of symmetries, such as rotations, reflections, and more extensive gauge symmetry transformations (Bronstein et al., 2017; Cohen et al., 2019). This enhancement enables convolutional networks to more effectively recognize and process data patterns exhibiting these symmetries, helping models more accurately capture complex patterns and dynamics in atmospheric phenomena, thereby improving the precision and reliability of weather forecasting and climate modeling.

In the previous discussion, we emphasize the importance of dynamic diagnostics and physical constraints for AI climate models. It is essential to understand how AI can affect the field of numerical climate models. AI applications within numerical models are already underway, with a prominent example being the use of AI to construct parameterization schemes, enhancing the performance of numerical models (e.g., Rasp et al., 2018; Han et al., 2020; Zhu et al., 2022; Wang and Tan, 2023). The Fortran Torch Adaptor (Mu et al., 2023) is an adapter designed to bridge Fortran and Torch, enabling researchers to load Torch model parameters and perform forward propagation within a Fortran environment, which facilitates the coupling of AI models with numerical models.

However, challenges persist in current AI parameterization schemes. Firstly, most AI parameterization schemes are currently offline. These offline parameterization schemes, when coupled with models for long-term integration, may lead to instability, resulting in model crashes, and potentially give rise to various issues such as climate drift. Secondly, a DL optimization of a specific parameter in isolation for a given parameterization scheme aims to achieve the optimum value for that parameter. In reality, climate models have numerous parameters, and optimizing one parameter may only represent a local optimum for the entire model.

A potential solution to address these issues could involve the development of online parameterization schemes. Such a system could potentially compute losses by comparing numerical model output to observations and optimizing AI weights that are coupled to numerical models using back-propagation. Is it possible to develop this AI-driven parameterization scheme that is updated online to correct the results of the numerical model (Chen et al., 2023c)? A similar approach has been adopted in the field of hydrology, known as “differentiable models”, which couple DL parameterization schemes with hydrological models, optimizing DL parameterizations based on hydrological model outputs (Shen et al., 2023). Even though attempts have been made to determine a few model parameters to reduce the difference between the observed and simulated results through the online parameter estimation (Han et al., 2014; Wu et al., 2016), implementing such an approach, especially within complex climate or coupled models, is still considered challenging. Recently, a groundbreaking development occurred with Google’s neural general circulation model (NGCM; Kochkov et al., 2024). It represents an online AI–physics hybrid GCM, exhibiting superior performance compared to current mainstream models and demonstrating excellent adherence to physical conservation laws. This pioneering work has the potential to catalyze the application of similar paradigms in climate modeling. Despite this advancement, constructing comparable climate models remains challenging. While the NGCM employs an embedding approach to create AMIP-like experiments, there are substantial differences from climate simulations. In contrast to weather models, finding corresponding observations for climate model simulations is challenging due to the presence of internal variability, making it difficult to calculate errors for iterative optimization as demonstrated by the NGCM.

Earlier, we addressed the primary challenges faced by the integration of AI and climate studies, along with proposed potential solutions. We emphasize the crucial role of detailed dynamic diagnostics and physical constraints for AI models, along with the importance of developing online parameterization schemes for climate models. However, resolving these issues heavily relies on community culture and robust leadership. Currently, the climate-AI community lacks unified benchmarks and baselines, resulting in significant redundant efforts and making model comparisons exceptionally challenging. The principles of unified benchmarks and baselines are crucial for the advancement of the climate AI community. Wisdom can be gleaned from distant sources. Relevant experiences can be drawn from the computer science community to inform our approach.

The rapid development of the AI era is propelled by the explosion of computational power and the open nature of DL communities. For the continued advancement of climate models in the AI era, a similar condition is required, especially within the climate community, that is an open and collaborative infrastructure. It is essential to foster progress in the climate field, creating an environment where innovative models and ideas can be shared and developed collectively. We can summarize this requirement as the “Open, Comparable, Reproducible” (OCR) principle (Fig. 1).

Figure 1.  The OCR principles.

● “Open” emphasizes open-source code and open datasets of AI climate modeling.

● “Comparable” signifies the creation of unified evaluation metrics. It involves integrating climate model evaluation frameworks to conduct thorough assessments involving climate dynamic assessments and the establishment of uniform datasets, task sets, and baselines.

● “Reproducible” denotes that the results published in research papers should be reproducible.

The OCR principles have a nuanced interplay and mutual influence. “Open” serves as the foundational bedrock for the subsequent principles to materialize. “Comparable” and “Reproducible” complement each other symbiotically. The “Reproducible” part of AI model results is crucial for comparing different model outputs. This, in turn, increases scientists’ awareness and emphasis on model reproducibility, creating a harmonious framework that propels scientific research toward more reliable and enduring progress.

The OCR principles hold significant potential for expediting the application of AI in climate science, particularly in climate prediction and modeling. Regarding the latter, the success of CMIP has already demonstrated how an open-data comparison project can substantially advance the field. In accordance with the OCR principles, an AI-MIP can be established, which would greatly facilitate the evaluation, iteration, and optimization of AI models. Simultaneously, this initiative would promote the development of numerical modeling and AI–physics hybrid modeling.

Looking ahead, more comprehensive dynamic diagnostics and physical constraints can further enhance the performance of AI climate models. This progress will also stimulate the development of AI parameterization schemes. Considering the development of AI (especially unsupervised learning; physics-constrained AI) and numerical climate models, there is optimism that the challenge of discrepancies between climate model outputs and observations could be addressed. A balance between AI and numerical climate modeling may be attainable. This balance could involve using numerical methods to resolve solvable processes while employing online AI solutions to address critical parameterization schemes. As this hybrid approach advances, it becomes increasingly challenging to classify a model as purely numerical or AI-based. Ultimately, it evolves into a balanced AI–physics climate model (Fig. 2). Through the incorporation of AI-based parameterization schemes, such a model can be iteratively optimized, transforming into a learnable climate model. Furthermore, since it includes explicit computations of physical quantities and obeys physical equations, this model exhibits a high level of interpretability, guaranteeing direct climate diagnostic analyses.

Figure 2.  Schematic of the balanced AI–physics model.

Acknowledgements. This work was supported by the National Natural Science Foundation of China (Grant Nos. 42141019 and 42261144687) and STEP (Grant No. 2019QZKK0102). Yoo-Geun HAM was supported by the Korea Environmental Industry & Technology Institute (KEITI) through the “Project for developing an observation-based GHG emissions geospatial information map”, funded by the Korea Ministry of Environment (MOE) (Grant No. RS-2023-00232066). Ya WANG would like to thank Prof. Baoxiang PAN for sharing related papers and useful discussions.