Cloud cover parameterizations play an important role in climate models, influencing radiative transfer, atmospheric dynamics, and hydrological cycles. However, their correct formulation remains a major challenge in climate modeling, as subgrid-scale cloud processes must be approximated. Classical and quantum Neural Networks have been proposed as potential tools for improving these parameterizations. While previous studies suggest that classical neural networks can produce physically meaningful results, it remains unclear whether quantum neural networks (QNNs) exhibit similar capabilities or rely on spurious correlations. This study begins by comparing a classical neural network and a quantum neural network to assess whether they capture comparable physical dependencies when predicting cloud cover, before exploring alternative architectures for each approach. Using explainable AI (XAI) techniques, specifically SHapley Additive exPlanations (SHAP), the learned feature dependencies in both types of models are analyzed. This approach enables us to evaluate not only predictive performance but also the extent to which each model captures the underlying physics of cloud cover. Our results show that both classical and quantum models exhibit similar learning patterns, extracting comparable relationships from the data. While the QNN does not outperform the classical network, it achieves comparable results, suggesting that quantum machine learning (QML) could be a viable approach in this domain. These findings contribute to the ongoing exploration of QML in climate science and highlight the potential of quantum methods for atmospheric modeling. More broadly, this study supports the integration of machine learning into climate science while ensuring physical consistency and interpretability.
Cloud cover parameterizations play an important role in climate models, influencing radiative transfer, atmospheric dynamics, and hydrological cycles. However, their correct formulation remains a major challenge in climate modeling, as subgrid-scale cloud processes must be approximated. Classical and quantum Neural Networks have been proposed as potential tools for improving these parameterizations. While previous studies suggest that classical neural networks can produce physically meaningful results, it remains unclear whether quantum neural networks (QNNs) exhibit similar capabilities or rely on spurious correlations. This study begins by comparing a classical neural network and a quantum neural network to assess whether they capture comparable physical dependencies when predicting cloud cover, before exploring alternative architectures for each approach. Using explainable AI (XAI) techniques, specifically SHapley Additive exPlanations (SHAP), the learned feature dependencies in both types of models are analyzed. This approach enables us to evaluate not only predictive performance but also the extent to which each model captures the underlying physics of cloud cover. Our results show that both classical and quantum models exhibit similar learning patterns, extracting comparable relationships from the data. While the QNN does not outperform the classical network, it achieves comparable results, suggesting that quantum machine learning (QML) could be a viable approach in this domain. These findings contribute to the ongoing exploration of QML in climate science and highlight the potential of quantum methods for atmospheric modeling. More broadly, this study supports the integration of machine learning into climate science while ensuring physical consistency and interpretability.
Long-term climate projections require running global Earth system models on timescales of hundreds of years and have relatively coarse resolution (from 40 to 160 km in the horizontal) due to their high computational costs. Unresolved subgrid-scale processes, such as clouds, are described in a semi-empirical manner by so called parameterizations, which are a major source of uncertainty in climate projections. Machine learning models trained on short high-resolution climate simulations are promising candidates to replace conventional parameterizations. In this work, we explore the potential of quantum machine learning (QML), and in particular quantum neural networks (QNNs), to develop cloud cover parameterizations. QNNs differ from their classical counterparts, and their potentially high expressivity turns them into promising tools for accurate data-driven schemes to be used in climate models. We perform an extensive comparative analysis between several QNNs and classical neural networks (NNs), by training both ansatzes on data coming from high-resolution simulations with the ICOsahedral Non-hydrostatic weather and climate model (ICON). Our results show that the overall performance of the investigated QNNs is comparable to that of classical NNs of similar size, i.e., with the same number of trainable parameters, with both ansatzes outperforming standard parameterizations used in climate models. Our study includes an analysis of the generalization ability of the models as well as the geometrical properties of their optimization landscape. We also investigate the effects of finite sampling noise, and show that the training and the predictions of the QNNs are stable even in this noisy setting. These results demonstrate the applicability of QML to learn meaningful patterns in climate data, and are thus relevant for a broad range of problems within the climate modeling community.
Quantum machine learning (QML) is making rapid progress, and QML-based models hold the promise of quantum advantages such as potentially higher expressivity and generalizability than their classical counterparts. Here, we present work on using a quantum neural net (QNN) to develop a parameterization of cloud cover for an Earth system model (ESM). ESMs are needed for predicting and projecting climate change, and can be improved in hybrid models incorporating both traditional physics-based components as well as machine learning (ML) models. We show that a QNN can predict cloud cover with a performance similar to a classical NN with the same number of free parameters and significantly better than the traditional scheme. We also analyse the learning capability of the QNN in comparison to the classical NN and show that, at least for our example, QNNs learn more consistent relationships than classical NNs.
Compact quantum neural networks have been explored for cloud-cover parameterization, but their predictive value depends on how physical knowledge is incorporated and which classical models provide the reference. We investigate an offline residual formulation that retains a fitted \XR\ cloud-cover estimate and learns a correction to its logit in transformed target space. Using released ICON/DYAMOND-derived data, we compare ten model variants in six- and eight-input settings, with three matched replicates and 10,000 training samples per replicate. All quantum circuits use local Z readout and noiseless exact expectation values. Under a common 30-epoch protocol, residual prediction reduced physical-space test mean squared error relative to direct QNN prediction by 54.3\% and 38.8\% for six-input XYZ and ZZXY circuits, and by 49.2\% and 38.9\% for their eight-input versions. Residual QNNs also outperformed the selected compact residual multilayer perceptron in every paired replicate. A larger, longer-trained Grundner-Q1 adaptation nevertheless achieved lower error: residual Q1 reached mean MSEs of 0.00778 and 0.00791, compared with 0.01124 and 0.01082 for residual XYZ. The results support residual prediction for compact simulated QNNs within the tested budget and establish a clear boundary set by stronger classical references. They do not establish computational quantum advantage or online climate-model skill.
Accurate representation of the atmospheric Boundary Layer Height (BLH) remains challenging in numerical weather and climate modeling, especially when turbulent processes occur at scales below the model grid resolution. This thesis investigates whether Quantum Machine Learning (QML) models can be used to build compact BLH parameterizations from coarse-grained ICON-XPP atmospheric columns. The work develops a complete offline pipeline for QML-compatible BLH prediction. Starting from high-dimensional atmospheric profiles, several dimensionality reduction and feature-engineering strategies are evaluated to obtain compact representations suitable for Quantum Neural Networks (QNNs). Two complementary 8-dimensional input representations are selected: SAE8D, a supervised autoencoder latent space optimized for predictive performance, and FtEng8D, a physically interpretable feature-engineered space based on stability, humidity-gradient and wind-shear diagnostics. Several QNN architectures are then trained and compared against parameter-matched classical Multi-Layer Perceptron (MLP) baselines. The QNN experiments analyze the effect of circuit depth, ansatz family, readout, data re-uploading and training-set size. The final full-dataset evaluation shows that the selected QNN remains competitive with a fixed MLP under the same parameter budget. The MLP achieves slightly better average RMSE, R2 and MAE, while the QNN shows lower seed-to-seed variability and a bias closer to zero. The error analysis reveals that the final QNN performs best in the dominant low and moderate BLH regimes, but systematically underestimates rare deep-boundary-layer cases. SHAP-based interpretability analysis indicates that the QNN mainly relies in physically meaningful thermodynamic, stability and humidity-gradient features, supporting the plausibility of the learned parameterization. Overall, the results do not demonstrate a systematic quantum advantage over classical machine learning. However, they show that QML-compatible BLH parameterization is feasible when high-dimensional atmospheric columns are first compressed into carefully designed low-dimensional representations. The proposed QNN therefore provides a compact and physically motivated prototype for future quantum-compatible atmospheric parameterizations, with future work focusing on richer interpretable feature spaces, rare high-BLH regimes and online testing in ICON-XPP.
Abstract As machine learning grows increasingly complex due to big data and deep learning, model explainability has become essential to fostering user trust. Quantum machine learning (QML) has emerged as a promising field, leveraging quantum computing to enhance classical machine learning methods, particularly through quantum representation learning (QRL). QRL aims to provide more efficient and powerful machine learning capabilities on noisy intermediate-scale quantum (NISQ) devices. However, interpreting QRL models poses significant challenges due to the reliance on quantum gate-based parameterized circuits, which, while analogous to classical neural network layers, operate in the quantum domain. To address these challenges, we propose an explainable QRL framework combining a quantum autoencoder (QAE) with a variational quantum classifier (VQC) and incorporating theoretical and empirical explainability for image data. Our dual approach enhances model interpretability by integrating visual explanations via local interpretable model-agnostic explanations (LIME) and analytical insights using Shapley Additive Explanations (SHAP). These complementary methods provide a deeper understanding of the model’s decision-making process based on prediction outcomes. Experimental evaluations on simulators and superconducting quantum hardware validate the effectiveness of the proposed framework for classification tasks, underscoring the importance of explainable representation learning in advancing QML towards more transparent and reliable applications.
Quantum machine learning (QML) could have the potential to leverage advantages of quantum over classical computing but still lacks strong evidence of actual improvements and scalability, partly due to phenomena such as barren plateaus. In this paper, we employ a hybrid quantum neural network (QNN) on a dataset on cloud microphysics, containing processes for phase transitions of water in the atmosphere and its related temperature changes, which are highly relevant for accurate climate predictions and projections. To reach optimal performance of our QNNs, we employ a rich and trainable frequency spectrum together with expressivity enhancing classical postprocessing. We find that our QNNs strongly benefit from extensive hyperparameter optimization and thereby demonstrate the feasibility of applying QNNs to complex physical systems. At the same time, the QNNs are outperformed by classical baselines in the form of simple fully-connected neural networks. We discuss identified bottlenecks of this class of quantum models to learn the full complexity of the cloud microphysics dataset to show that there is a need to further understand and improve variational quantum models for machine learning such that they might fill the gap where classical models fail or are inefficient.