The integration of Artificial Intelligence (AI) into Earth science, including areas such as geology, ecology, and hydrology, brings potential for significant advancements. Despite this potential, applying deep learning techniques to spatial data in this field is often hindered by the lack of domain knowledge. This paper studies the integration of spatial domain knowledge and deep learning for Earth science. The problem is challenging due to the sparse and noisy input labels, spatial uncertainty, and high computational costs associated with a large number of sample locations. Existing works on neuro-symbolic models focus on integrating symbolic logic into neural networks (e.g., loss function, model architecture, and training label augmentation), but these methods do not fully address the specific spatial data challenges. To bridge this gap, we propose a Spatial Knowledge-Infused Hierarchical Learning (SKI-HL) framework, which iteratively infers labels within a multi-resolution hierarchy, and trains the deep learning model with uncertainty-aware multi-instance learning. The evaluation of real-world hydrological datasets demonstrates the enhanced performance of the SKI-HL framework over several baseline methods.