Fog, a weather phenomenon near the Earth’s surface, poses significant visibility challenges, critically impacting all modes of transportation. Accurate fog prediction models are crucial for ensuring safety and reducing delays. Forecasting meteorological phenomena involves complex five-dimensional data structures, including geographical coordinates, atmospheric conditions, altitude layers, and time-series data. The challenge is to effectively learn from this data to improve visibility predictions. Recent advancements in vision transformers have revolutionized deep learning, particularly in image analysis, opening new avenues for interpreting complex spatio-temporal data in atmospheric science. This paper focuses on coastal fog forecasting with a 24-hour prediction window. We introduce and compare innovative tokenization strategies for vision transformer models aimed at enhancing the accuracy and interpretability of fog predictions. The study evaluates various sampling methods, comparing traditional 2D approaches (Vanilla Vision Transformer and Unified Variable Transformer) with more sophisticated 3D and 4D techniques (Spatio-Temporal Transformer, Spatio-Variable Transformer, and Physics-Informed Transformer). FogNet-v2.0, a PIT model, emerges as the front-runner, outperforming other models and benchmarks, including the 3D CNN-based FogNet. FogNet-v2.0 improves prediction accuracy across most metrics except for the Critical Success Index (CSI). Key innovations of this research include correctly forecasting fog events, improved skill scores, reduced miss cases, and the development of an explainable, physics-informed vision transformer. This paper highlights the integration of physical principles with machine learning for precise, interpretable weather prediction models, showcasing the efficacy of advanced tokenization and physics-informed methodologies in addressing the complexities of atmospheric phenomena.

Geoscience applications have been using sophisticated machine learning methods to model complex phenomena. These models are described as black boxes since it is unclear what relationships are learned. Models may exploit spurious associations that exist in the data. The lack of transparency may limit user’s trust, causing them to avoid high performance models since they cannot verify that it has learned realistic strategies. EXplainable Artificial Intelligence (XAI) is a developing research area for investigating how models make their decisions. However, XAI methods are sensitive to feature correlations. This makes XAI challenging for high-dimensional models whose input rasters may have extensive spatial-temporal autocorrelation. Since many geospatial applications rely on complex models for target performance, a recommendation is to combine raster elements into semantically meaningful feature groups. However, it is challenging to determine how best to combine raster elements. Here, we explore the explanation sensitivity to grouping scheme. Experiments are performed on FogNet, a complex deep learning model that uses 3D Convolutional Neural Networks (CNN) for coastal fog prediction. We demonstrate that explanations can be combined with domain knowledge to generate hypotheses about the model. Meteorological analysis of the XAI output reveal FogNet’s use of channels that capture relationships related to fog development, contributing to good overall model performance. However, analyses also reveal several deficiencies, including the reliance on channels and channel spatial patterns that correlate to the predominate fog type in the dataset, to make predictions of all fog types. Strategies to improve FogNet performance and trustworthiness are presented.

Atmospheric AI modeling is increasingly reliant on complex machine learning (ML) techniques and high-dimensional gridded inputs to develop models that achieve high predictive skill. Complex deep learning architectures such as convolutional neural networks and transformers are trained to model highly non-linear atmospheric phenomena such as coastal fog [1], tornadoes [2], and severe hail [3]. The input data is typically in the form of gridded spatial data composed of multiple channels of satellite imagery, numerical weather prediction output, reanalysis products, etc. In many studies, the use of complex architectures and high-dimensional inputs were shown to substantially outperform simpler alternatives. A major challenge when using complex ML techniques is that it is very difficult to understand how the trained model works. The complexity of the model obfuscates the relationship between the input and prediction. It is often of interest to understand a model’s decision-making process. By exposing the model’s behavior, users could verify that the model has learned physically realistic predictive patterns. This information can be used to calibrate trust in the model. The model may have also learned novel patterns within the data that could be used to gain new insights into the atmospheric process. Extracting learned patterns could be used to generate hypotheses for scientific discovery. The rapid adoption of complex ML models and the need to understand how they work has led to the development of a broad class of techniques called eXplainable Artificial Intelligence (XAI). These methods probe the models in various ways to reveal insights into how they work. Correlations among input features can make it challenging to produce meaningful explanations. The gridded spatial data common in atmospheric modeling applications typically have extensive correlation. Spatial autocorrelation is present among the cells of each spatial grid, but autocorrelation may exist across the gridded data volume due to spatial or temporal relationships between adjacent channels. In addition, there may be correlations between distant locations due to teleconnections between them. Correlated input features may cause high variance among the trained models. If grid cells are highly correlated, then the target function that the network is attempting to learn is ill-defined and an infinite number of models can be generated that achieve approximately equal performance. Even assuming a perfect XAI method exists, the attribution reflects only the patterns learned for a given model. It is arbitrary which of the correlated features are used by a given model. This can lead to a misleading understanding of the actual relationship between the input features and target. A potential solution is to group the correlated features before applying XAI. Attribution can be assigned to each group rather than to individual cells. In this case, all the correlated cells will be permuted at the same time to analyze their collective impact on the output. The purpose is to reveal the contribution of each group of related cells toward the model output. Ideally, the explanations are insensitive to the random choice among correlated features learned by the model. Without grouping, the user can be misled to consider a feature as not being related to the target because of the presence of correlated features. With grouping, the explanations should better reveal the learned patterns. Grouping features based on correlation can be challenging. The correlation rarely equals one and the strength of the correlation influences the variance among trained models. Calculating the correlation can be difficult because of partial correlations and fuzzy, continuous boundaries. The choice of groups can greatly influence the explanations. Another challenge is that it is not straight-forward to assess the quantitative accuracy of an XAI technique. This is because there is rarely a ground truth explanation to compare to. If we knew the attribution, we would not need XAI methods. Synthetic benchmarks for analyzing XAI have been proposed as a solution [4]. It is possible to define a non-linear function such that the contribution of each grid cell’s value to the function output can be derived. This attribution map represents the ground truth for comparison the the output of XAI methods that are applied to a model that very closely approximates the hand-crafted function. In this research, we develop a set of benchmarks to investigate the influence of correlated features on the variation in XAI outputs for a set of trained models. We then explore how features can be grouped to reduce the explanation variance so that users have improved insight into the learned patterns.  First, we create a set of very simple mathematical demonstrations that precisely demonstrate the influence of correlated features and how grouping features provides a solution. Using insights from these experiments, we develop a tool for detecting when correlated features are likely to cause misleading explanations. We then create a set of more realistic benchmarks that are based on atmospheric modeling problems such as sea surface temperature and coastal fog prediction. By defining benchmarks with known ground truth explanations, we can analyze various techniques for grouping the grid cells based on their correlations. Based on our findings, we offer recommendations for strategies to group correlated data so that users can better leverage XAI results toward model development and scientific insights. [1] Kamangir, H., Collins, W., Tissot, P., King, S. A., Dinh, H. T. H., Durham, N., & Rizzo, J. (2021). FogNet: A multiscale 3D CNN with double-branch dense block and attention mechanism for fog prediction. Machine Learning with Applications, 5, 100038.[2] Lagerquist, R. (2020). Using Deep Learning to Improve Prediction and Understanding of High-impact Weather.[3] Gagne II, D. J., Haupt, S. E., Nychka, D. W., & Thompson, G. (2019). Interpretable deep learning for spatial analysis of severe hailstorms. Monthly Weather Review, 147(8), 2827-2845.[4] Mamalakis, A., Ebert-Uphoff, I., & Barnes, E. A. (2022). Neural network attribution methods for problems in geoscience: A novel synthetic benchmark dataset. Environmental Data Science, 1, e8.