Spatial classification with limited feature observations has been a challenging problem in machine learning. The problem exists in applications where only a subset of sensors are deployed at certain regions or partial responses are collected in field surveys. Existing research mostly focuses on addressing incomplete or missing data, e.g., data cleaning and imputation, classification models that allow for missing feature values, or modeling missing features as hidden variables and applying the EM algorithm. These methods, however, assume that incomplete feature observations only happen on a small subset of samples, and thus cannot solve problems where the vast majority of samples have missing feature observations. To address this issue, we propose a new approach that incorporates physics-aware structural constraints into the model representation. Our approach assumes that a spatial contextual feature is observed for all sample locations and establishes spatial structural constraint from the spatial contextual feature map. We design efficient algorithms for model parameter learning and class inference. Evaluations on real-world hydrological applications show that our approach significantly outperforms several baseline methods in classification accuracy, and the proposed solution is computationally efficient on a large data volume.