Data-Driven Integration Kernels for Interpretable Nonlocal Operator Learning

Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it makes learned relationships difficult to interpret and prone to overfitting as the extent of nonlocal information grows. We address this challenge by introducing data-driven integration kernels, a framework that adds structure to nonlocal operator learning by explicitly separating nonlocal information aggregation from local nonlinear prediction. Each spatiotemporal predictor field is first integrated using learnable kernels (defined as continuous weighting functions over horizontal space, height, and/or time), after which a local nonlinear mapping is applied only to the resulting kernel-integrated features and any optional local inputs. This design confines nonlinear interactions to a small set of integrated features and makes each kernel directly interpretable as a weighting pattern that reveals which horizontal locations, vertical levels, and past timesteps contribute most to the prediction. We demonstrate the framework for South Asian monsoon precipitation using a hierarchy of neural network models with increasing structure, including baseline, nonparametric kernel, and parametric kernel models. Across this hierarchy, kernel-based models achieve near-baseline performance with far fewer trainable parameters, showing that much of the relevant nonlocal information can be captured through a small set of interpretable integrations when appropriate structural constraints are imposed.

Multidata Causal Discovery for Statistical Hurricane Intensity Forecasting

Improving statistical forecasts of Atlantic hurricane intensity is limited by complex nonlinear interactions and difficulty in identifying relevant predictors. Conventional methods prioritize correlation or fit, often overlooking confounding variables and limiting generalizability to unseen tropical storms. To address this, we leverage a multidata causal discovery framework with a replicated dataset based on Statistical Hurricane Intensity Prediction Scheme (SHIPS) using ERA5 meteorological reanalysis. We conduct multiple experiments to identify and select predictors causally linked to hurricane intensity changes. We train multiple linear regression models to compare causal feature selection with no selection, correlation, and random forest feature importance across five forecast lead times from 1 to 5 days (24 to 120 hours). Causal feature selection consistently outperforms on unseen test cases, especially for lead times shorter than 3 days. The causal features primarily include vertical shear, mid-tropospheric potential vorticity and surface moisture conditions, which are physically significant yet often underutilized in hurricane intensity predictions. Further, we build an extended predictor set (SHIPS+) by adding selected features to the standard SHIPS predictors. SHIPS+ yields increased short-term predictive skill at lead times of 24, 48, and 72 hours. Adding nonlinearity using multilayer perceptron further extends skill to longer lead times, despite our framework being purely regional and not requiring global forecast data. Operational SHIPS tests confirm that three of the six added causally discovered predictors improve forecasts, with the largest gains at longer lead times. Our results demonstrate that causal discovery improves hurricane intensity prediction and pave the way toward more empirical forecasts.

Taking the Garbage Out of Data-Driven Prediction Across Climate Timescales

Artificial intelligence (AI) -- and specifically machine learning (ML) -- applications for climate prediction across timescales are proliferating quickly. The emergence of these methods prompts a revisit to the impact of data preprocessing, a topic familiar to the climate community, as more traditional statistical models work with relatively small sample sizes. Indeed, the skill and confidence in the forecasts produced by data-driven models are directly influenced by the quality of the datasets and how they are treated during model development, thus yielding the colloquialism "garbage in, garbage out." As such, this article establishes protocols for the proper preprocessing of input data for AI/ML models designed for climate prediction (i.e., subseasonal to decadal and longer). The three aims are to: (1) educate researchers, developers, and end users on the effects that preprocessing has on climate predictions; (2) provide recommended practices for data preprocessing for such applications; and (3) empower end users to decipher whether the models they are using are properly designed for their objectives. Specific topics covered in this article include the creation of (standardized) anomalies, dealing with non-stationarity and the spatiotemporally correlated nature of climate data, and handling of extreme values and variables with potentially complex distributions. Case studies will illustrate how using different preprocessing techniques can produce different predictions from the same model, which can create confusion and decrease confidence in the overall process. Ultimately, implementing the recommended practices set forth in this article will enhance the robustness and transparency of AI/ML in climate prediction studies.

Improving Predictions of Convective Storm Wind Gusts through Statistical Post-Processing of Neural Weather Models

Issuing timely severe weather warnings helps mitigate potentially disastrous consequences. Recent advancements in Neural Weather Models (NWMs) offer a computationally inexpensive and fast approach for forecasting atmospheric environments on a 0.25{\deg} global grid. For thunderstorms, these environments can be empirically post-processed to predict wind gust distributions at specific locations. With the Pangu-Weather NWM, we apply a hierarchy of statistical and deep learning post-processing methods to forecast hourly wind gusts up to three days ahead. To ensure statistical robustness, we constrain our probabilistic forecasts using generalised extreme-value distributions across five regions in Switzerland. Using a convolutional neural network to post-process the predicted atmospheric environment's spatial patterns yields the best results, outperforming direct forecasting approaches across lead times and wind gust speeds. Our results confirm the added value of NWMs for extreme wind forecasting, especially for designing more responsive early-warning systems.

Distilling Machine Learning's Added Value: Pareto Fronts in Atmospheric Applications

While the added value of machine learning (ML) for weather and climate applications is measurable, explaining it remains challenging, especially for large deep learning models. Inspired by climate model hierarchies, we propose that a full hierarchy of Pareto-optimal models, defined within an appropriately determined error-complexity plane, can guide model development and help understand the models' added value. We demonstrate the use of Pareto fronts in atmospheric physics through three sample applications, with hierarchies ranging from semi-empirical models with minimal tunable parameters (simplest) to deep learning algorithms (most complex). First, in cloud cover parameterization, we find that neural networks identify nonlinear relationships between cloud cover and its thermodynamic environment, and assimilate previously neglected features such as vertical gradients in relative humidity that improve the representation of low cloud cover. This added value is condensed into a ten-parameter equation that rivals the performance of deep learning models. Second, we establish a ML model hierarchy for emulating shortwave radiative transfer, distilling the importance of bidirectional vertical connectivity for accurately representing absorption and scattering, especially for multiple cloud layers. Third, we emphasize the importance of convective organization information when modeling the relationship between tropical precipitation and its surrounding environment. We discuss the added value of temporal memory when high-resolution spatial information is unavailable, with implications for precipitation parameterization. Therefore, by comparing data-driven models directly with existing schemes using Pareto optimality, we promote process understanding by hierarchically unveiling system complexity, with the hope of improving the trustworthiness of ML models in atmospheric applications.

Lightning-Fast Thunderstorm Warnings: Predicting Severe Convective Environments with Global Neural Weather Models

The recently released suite of AI weather models can produce multi-day, medium-range forecasts within seconds, with a skill on par with state-of-the-art operational forecasts. Traditional AI model evaluation predominantly targets global scores on single levels. Specific prediction tasks, such as severe convective environments, require much more precision on a local scale and with the correct vertical gradients between levels. With a focus on the convective season of global hotspots in 2020, we assess the skill of three top-performing AI models (Pangu-Weather, GraphCast, FourCastNet) for Convective Available Potential Energy (CAPE) and Deep Layer Shear (DLS) at lead-times of up to 10 days against the ERA-5 reanalysis and the IFS operational numerical weather prediction model. Looking at the example of a US tornado outbreak on April 12 and 13, 2020, all models predict elevated CAPE and DLS values multiple days in advance. The spatial structures in the AI models are smoothed in comparison to IFS and ERA-5. The models show differing biases in the prediction of CAPE values, with GraphCast capturing the value distribution the most accurately and FourCastNet showing a consistent underestimation. In seasonal analyses around the globe, we generally see the highest performance by GraphCast and Pangu-Weather, which match or even exceed the performance of IFS. CAPE derived from vertically coarse pressure levels of neural weather models lacks the precision of the vertically fine resolution of numerical models. The promising results here indicate that a direct prediction of CAPE in AI models is likely to be skillful. This would open unprecedented opportunities for fast and inexpensive predictions of severe weather phenomena. By advancing the assessment of AI models towards process-based evaluations we lay the foundation for hazard-driven applications of AI-based weather forecasts.

Identifying Three-Dimensional Radiative Patterns Associated with Early Tropical Cyclone Intensification

Cloud radiative feedback impacts early tropical cyclone (TC) intensification, but limitations in existing diagnostic frameworks make them unsuitable for studying asymmetric or transient radiative heating. We propose a linear Variational Encoder-Decoder (VED) to learn the hidden relationship between radiation and the surface intensification of realistic simulated TCs. Limiting VED model inputs enables using its uncertainty to identify periods when radiation has more importance for intensification. A close examination of the extracted 3D radiative structures suggests that longwave radiative forcing from inner core deep convection and shallow clouds both contribute to intensification, with the deep convection having the most impact overall. We find that deep convection downwind of the shallow clouds is critical to the intensification of Haiyan. Our work demonstrates that machine learning can discover thermodynamic-kinematic relationships without relying on axisymmetric or deterministic assumptions, paving the way towards the objective discovery of processes leading to TC intensification in realistic conditions.

Lessons Learned: Reproducibility, Replicability, and When to Stop

While extensive guidance exists for ensuring the reproducibility of one's own study, there is little discussion regarding the reproduction and replication of external studies within one's own research. To initiate this discussion, drawing lessons from our experience reproducing an operational product for predicting tropical cyclogenesis, we present a two-dimensional framework to offer guidance on reproduction and replication. Our framework, representing model fitting on one axis and its use in inference on the other, builds upon three key aspects: the dataset, the metrics, and the model itself. By assessing the trajectories of our studies on this 2D plane, we can better inform the claims made using our research. Additionally, we use this framework to contextualize the utility of benchmark datasets in the atmospheric sciences. Our two-dimensional framework provides a tool for researchers, especially early career researchers, to incorporate prior work in their own research and to inform the claims they can make in this context.

Next-Generation Earth System Models: Towards Reliable Hybrid Models for Weather and Climate Applications

We review how machine learning has transformed our ability to model the Earth system, and how we expect recent breakthroughs to benefit end-users in Switzerland in the near future.

Systematic Sampling and Validation of Machine Learning-Parameterizations in Climate Models

Progress in hybrid physics-machine learning (ML) climate simulations has been limited by the difficulty of obtaining performant coupled (i.e. online) simulations. While evaluating hundreds of ML parameterizations of subgrid closures (here of convection and radiation) offline is straightforward, online evaluation at the same scale is technically challenging. Our software automation achieves an order-of-magnitude larger sampling of online modeling errors than has previously been examined. Using this, we evaluate the hybrid climate model performance and define strategies to improve it. We show that model online performance improves when incorporating memory, a relative humidity input feature transformation, and additional input variables. We also reveal substantial variation in online error and inconsistencies between offline vs. online error statistics. The implication is that hundreds of candidate ML models should be evaluated online to detect the effects of parameterization design choices. This is considerably more sampling than tends to be reported in the current literature.