  Spatio-temporal forecasting is challenging attributing to the high
nonlinearity in temporal dynamics as well as complex location-characterized
patterns in spatial domains, especially in fields like weather forecasting.
Graph convolutions are usually used for modeling the spatial dependency in
meteorology to handle the irregular distribution of sensors' spatial location.
In this work, a novel graph-based convolution for imitating the meteorological
flows is proposed to capture the local spatial patterns. Based on the
assumption of smoothness of location-characterized patterns, we propose
conditional local convolution whose shared kernel on nodes' local space is
approximated by feedforward networks, with local representations of coordinate
obtained by horizon maps into cylindrical-tangent space as its input. The
established united standard of local coordinate system preserves the
orientation on geography. We further propose the distance and orientation
scaling terms to reduce the impacts of irregular spatial distribution. The
convolution is embedded in a Recurrent Neural Network architecture to model the
temporal dynamics, leading to the Conditional Local Convolution Recurrent
Network (CLCRN). Our model is evaluated on real-world weather benchmark
datasets, achieving state-of-the-art performance with obvious improvements. We
conduct further analysis on local pattern visualization, model's framework
choice, advantages of horizon maps and etc.
