Title: Graph Neural Network Reconstruction of Urban Temperature Fields with Uncertainty Awareness Under Sensor Deployment Limits

Abstract:

Accurately reconstructing spatially continuous daily temperature maps from limited observational data is critical for monitoring urban climates and assessing heat risks. However, real-world implementation is often hindered by constraints on sensor budgets and the physical spacing required between devices. To address these challenges, this study introduces an uncertainty-aware graph neural network (GNN) framework designed to reconstruct daily maximum temperature fields from sparse sensor data. The system facilitates distance-constrained sensor placement and generates probabilistic exceedance maps. By employing a graph-attention-based mean-residual architecture trained via Gaussian negative log-likelihood, the model simultaneously forecasts the temperature field and a spatially varying predictive uncertainty map.

To optimize sensor placement, we utilize a Proper Orthogonal Decomposition with QR factorization (POD-QR) strategy, enforcing a minimum inter-sensor distance of 4 km. This approach is benchmarked against random feasible placement and farthest-point sampling methods. The framework’s performance was assessed within a Montreal-area polygon using Daymet v4.1 daily temperature data at 1 km resolution. A rigorous temporal hold-out protocol was applied, with training data spanning 2020–2023 and testing data from 2024.

Results across sensor budgets ranging from 10 to 40 sensors indicate that the proposed GNN consistently surpasses both inverse distance weighting and ordinary kriging in terms of Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) on unobserved nodes. The impact of sensor placement is most significant at lower budget levels, with its influence diminishing as the number of sensors increases. A practical saturation point emerges around 30 sensors under the specified spacing constraint. Furthermore, probabilistic evaluations demonstrate that uncertainty calibration improves with higher sensor density, offering a superior balance between sharpness and calibration compared to kriging. These findings validate the proposed framework as a robust solution for uncertainty-aware temperature reconstruction and decision-making in heat-risk mapping.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC