[論文レビュー] Probabilistic Weather Forecasting with Hierarchical Graph Neural Networks

Joel Oskarsson, Tomas Landelius+2 more|arXiv (Cornell University)|Jun 7, 2024

Hydrological Forecasting Using AI被引用数 5

ひとこと要約

Graph-EFMを導入。階層グラフニューラルネットワークを用いた確率的天気予報モデルで、各時刻につき1回の前方伝播のみで空間的に一貫したエンサンブル予報を生成。

ABSTRACT

In recent years, machine learning has established itself as a powerful tool for high-resolution weather forecasting. While most current machine learning models focus on deterministic forecasts, accurately capturing the uncertainty in the chaotic weather system calls for probabilistic modeling. We propose a probabilistic weather forecasting model called Graph-EFM, combining a flexible latent-variable formulation with the successful graph-based forecasting framework. The use of a hierarchical graph construction allows for efficient sampling of spatially coherent forecasts. Requiring only a single forward pass per time step, Graph-EFM allows for fast generation of arbitrarily large ensembles. We experiment with the model on both global and limited area forecasting. Ensemble forecasts from Graph-EFM achieve equivalent or lower errors than comparable deterministic models, with the added benefit of accurately capturing forecast uncertainty.

研究の動機と目的

• Motivate the need for probabilistic forecasting to capture uncertainty in chaotic weather systems.
• Develop a hierarchical graph neural network framework to enable spatially coherent forecasts.
• Introduce Graph-EFM, a latent-variable probabilistic model enabling efficient ensemble sampling.
• Demonstrate Graph-EFM on global (1.5°) and limited-area (10 km) forecasting and assess calibration.
• Provide training objectives and improved GNN layers tailored for probabilistic MLWP.

提案手法

• Propose a hierarchical mesh graph with multiple spatial scales to propagate information and impose spatial coherence.
• Formulate Graph-EFM as a latent-variable model where Zt is top-level latent representing uncertainty, with Xt conditioned on Zt and past states.
• Define a two-part single-step model: a latent map p(Zt|Xt−2:t−1, Ft) and a predictor p(Xt|Zt, Xt−2:t−1, Ft) realized as a deterministic mapping with skip connections.
• Train with a variational objective (ELBO) using a learned q(Zt|Xt−2:t−1, Xt, Ft) and include a CRPS term for ensemble calibration.
• Use Propagation Networks (a variant of Interaction Networks) to improve information flow from grid to latent top-level and back.
• Optionally evaluate deterministic Graph-FM as a baseline and GraphCast/GraphCast+SWAG as additional baselines.

実験結果

リサーチクエスチョン

• RQ1 Can a hierarchical GNN with latent variables accurately model the distribution of future weather states?
• RQ2 Does Graph-EFM produce calibrated ensemble forecasts with spatially coherent fields at global and regional scales?
• RQ3 How does the probabilistic Graph-EFM compare to deterministic Graph-FM and existing baselines in RMSE, CRPS, and SpSkR across lead times?
• RQ4 What is the impact of the hierarchical graph design on sampling efficiency and ensemble diversity?
• RQ5 How well can the model handle limited-area modeling with boundary conditions (LAM) using the same framework?

主な発見

Lead time	Variable	Model	RMSE	CRPS	SpSkR	RMSE	CRPS	SpSkR
5 days	z500	GraphCast*	387	236	-	808	498	-
5 days	z500	Graph-FM	363	223	-	825	510	-
5 days	z500	GraphCast*+SWAG	437	269	0.07	960	590	0.12
5 days	z500	Graph-EFM (ms)	472	211	0.77	756	333	0.83
5 days	z500	Graph-EFM	399	169	1.18	695	299	1.15
5 days	2t	GraphCast*	1.65	1.00	-	2.82	1.69	-
5 days	2t	Graph-FM	1.57	0.94	-	2.82	1.66	-
5 days	2t	GraphCast*+SWAG	2.03	1.20	0.06	3.58	2.04	0.13
5 days	2t	Graph-EFM (ms)	1.76	0.77	0.75	2.55	1.09	0.82
5 days	2t	Graph-EFM	1.64	0.71	0.98	2.32	1.00	0.99
10 days	z500	GraphCast*	808	498	-	-	-	-
10 days	z500	Graph-FM	825	510	-	-	-	-
10 days	z500	GraphCast*+SWAG	960	590	0.12	-	-	-
10 days	z500	Graph-EFM (ms)	756	333	0.83	-	-	-
10 days	z500	Graph-EFM	695	299	1.15	-	-	-
10 days	2t	GraphCast*	2.82	1.69	-	-	-	-
10 days	2t	Graph-FM	2.82	1.66	-	-	-	-
10 days	2t	GraphCast*+SWAG	3.58	2.04	0.13	-	-	-
10 days	2t	Graph-EFM (ms)	2.55	1.09	0.82	-	-	-
10 days	2t	Graph-EFM	2.32	1.00	0.99	-	-	-
24 h	z500	GraphCast*	153	108	-	201	138	-
24 h	z500	Graph-FM	230	162	-	354	238	-
24 h	z500	GraphCast*+SWAG	219	136	0.08	376	206	0.10
24 h	z500	Graph-EFM (ms)	400	261	0.22	711	470	0.23
24 h	z500	Graph-EFM	172	91	0.84	219	115	0.75
24 h	wvint	GraphCast*	1.51	1.01	-	2.06	1.32	-
24 h	wvint	Graph-FM	1.64	1.08	-	2.48	1.58	-
24 h	wvint	GraphCast*+SWAG	1.78	1.17	0.05	2.34	1.50	0.05
24 h	wvint	Graph-EFM (ms)	2.39	1.43	0.16	3.51	2.12	0.13
24 h	wvint	Graph-EFM	1.61	0.79	0.57	2.08	1.00	0.53
57 h	z500	GraphCast*	201	138	-	-	-	-
57 h	z500	Graph-FM	354	238	-	-	-	-
57 h	z500	GraphCast*+SWAG	376	206	0.10	-	-	-
57 h	z500	Graph-EFM (ms)	711	470	0.23	-	-	-
57 h	z500	Graph-EFM	219	115	0.75	-	-	-
57 h	wvint	GraphCast*	2.06	1.32	-	-	-	-
57 h	wvint	Graph-FM	2.48	1.58	-	-	-	-
57 h	wvint	GraphCast*+SWAG	2.34	1.50	0.05	-	-	-
57 h	wvint	Graph-EFM (ms)	3.51	2.12	0.13	-	-	-
57 h	wvint	Graph-EFM	2.08	1.00	0.53	-	-	-

• Graph-EFM achieves lower CRPS than baselines across several variables and lead times, indicating better distributional accuracy.
• Ensemble mean from Graph-EFM often improves RMSE over deterministic models, especially at longer lead times.
• Without perturbing initial states, Graph-EFM attains SpSkR near 1, indicating well-calibrated uncertainty; SWAG-based ensembles can be poorly calibrated.
• For LAM (Nordic MEPS data), Graph-EFM provides spatially coherent ensembles, though short-lead RMSE gains are modest.
• The hierarchical graph structure enables efficient sampling of large ensembles (e.g., 80 members in global forecasting in ~200 seconds on a single GPU).
• Extreme weather case studies (e.g., hurricane Laura) illustrate the model’s ability to capture location and wind uncertainty in ensemble forecasts.