  Due to insufficient local area information, numerical weather prediction
(NWP) may yield biases for specific areas. Previous studies correct biases
mainly by employing handcrafted features or applying data-driven methods
intuitively, overlooking the complicated dependencies between weather factors
and between areas. To address this issue, we propose WeatherGNN, a local NWP
bias-correction method that utilizes Graph Neural Networks (GNNs) to exploit
meteorological dependencies and spatial dependencies under the guidance of
domain knowledge. Specifically, we introduce a factor GNN to capture
area-specific meteorological dependencies adaptively based on spatial
heterogeneity and a fast hierarchical GNN to capture dynamic spatial
dependencies efficiently guided by Tobler's first and second laws of geography.
Our experimental results on two real-world datasets demonstrate that WeatherGNN
achieves the state-of-the-art performance, outperforming the best baseline with
an average of 4.75 \% on RMSE.
