Observation impact explanation in atmospheric state estimation using hierarchical message-passing graph neural networks**This paper is significantly revised from an earlier version [] presented at the Explainable Machine Learning for Sciences Workshop (XAI4Sci) in conjunction with the 38th AAAI Conference on Artificial Intelligence (AAAI 2024) held in Vancouver, Canada, in February 2024.

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Abstract The impact of meteorological observations on weather forecasting varies with the sensor type, location, time, and other environmental factors. Thus, the quantitative analysis of observation impacts is crucial for the effective and efficient development of weather forecasting systems. However, existing impact analysis methods are dependent on specific forecast systems, because system-specific adjoint models are used and the sensitivity of the observation to the forecast is measured. This study investigates the impact of observations on atmospheric state estimation in weather forecasting systems by developing a novel graph neural network (GNN) model specialized for analyzing the heterogeneous relations between observations and atmospheric states. The observation impact can then be assessed by applying explainable methods to the proposed GNN model, which is independent of forecasting systems. Further, we develop a novel application called ‘CloudNine,’ a system that provides impact analysis for individual observations with visualization. Our GNN model comprises hierarchical message-passing modules that separately analyze spatial correlations between observations at close locations and atmospheric states at close locations and then examine correlations between observations and atmospheric states. To consider the different factors influencing these correlations, we utilized geo-coordinates and types of observations in the attention mechanism of the modules with their feature vectors. We then applied gradient-based explainability methods to quantify the significance of the different observations in the estimation. Evaluated using data from 11 satellites and land-based observations, the results highlight the effectiveness of the proposed model and the visualization of observation impacts, enhancing the understanding and optimization of observational data in weather forecasting.