Modeling spatial dependencies in geographic data is of crucial importance for the modeling of our planet. Graph neural networks (GNNs) provide a powerful and scalable solution for modeling continuous spatial data. However, in the absence of further context on the geometric structure of the data, they often rely on Euclidean distances to construct the input graphs. This assumption can be improbable in many real-world settings, where the spatial structure is more complex and explicitly non-Euclidean (e.g., road networks). In this paper, we propose PE-GNN, a new framework that incorporates spatial context and correlation explicitly into the models. Building on recent advances in geospatial auxiliary task learning and semantic spatial embeddings, our proposed method (1) learns a context-aware vector encoding of the geographic coordinates and (2) predicts spatial autocorrelation in the data in parallel with the main task. We show the effectiveness of our approach on two climate-relevant regression tasks: 3d spatial interpolation and air temperature prediction. The code for this study can be accessed via: https://bit.ly/3xDpfyV.