Accurately measuring the aerosol optical depth (AOD) is essential for our understanding of the climate. Currently, AOD can be measured by (i) satellite instruments, which operate on a global scale but have limited accuracies; and (ii) ground-based instruments, which are more accurate but not widely available. Recent approaches focus on integrating measurements from these two sources to complement each other. In this paper, we further improve the prediction accuracy by using the observation that the AOD varies slowly in the spatial domain. Using a probabilistic approach, we impose this smoothness constraint by a Gaussian random field on the Earth's surface, which can be considered as a two-dimensional manifold. The proposed integration approach is computationally simple, and experimental results on both synthetic and real-world data sets show that it significantly outperforms the state-of-the-art.

Aerosol Optical Depth (AOD), recognized as one of the most important quantities in understanding and predicting the Earth's climate, is estimated daily on a global scale by several Earth-observing satellite instruments. Each instrument has different coverage and sensitivity to atmospheric and surface conditions, and, as a result, the quality of AOD estimated by different instruments varies across the globe. We present a method for learning how to aggregate AOD estimations from multiple satellite instruments into a more accurate estimation. The proposed method is semi-supervised, as it is able to learn from a small number of labeled data, where labels come from a few accurate and expensive ground-based instruments, and a large number of unlabeled data. The method uses a latent variable to partition the data, so that in each partition the expert AOD estimations are aggregated in a different, optimal way. We applied the method to combine AOD estimations from 5 instruments aboard 4 satellites, and the results indicate that it can successfully exploit labeled and unlabeled data to produce accurate aggregated AOD estimations.