A Hierarchical Bayesian Approach for Aerosol Retrieval Using MISR Data

Abstract

Atmospheric aerosols can cause serious damage to human health and reduce life expectancy. Using the radiances observed by NASA's Multi-angle Imaging SpectroRadiometer (MISR), the current MISR operational algorithm retrieves aerosol optical depth (AOD) at 17.6 km resolution. A systematic study of aerosols and their impact on public health, especially in highly populated urban areas, requires finer-resolution estimates of AOD's spatial distribution. We embed MISR's operational weighted least squares criterion and its forward calculations for AOD retrievals in a likelihood framework and further expand into a hierarchical Bayesian model to adapt to finer spatial resolution of 4.4 km. To take advantage of AOD's spatial smoothness, our method borrows strength from data at neighboring areas by postulating a Gaussian Markov random field prior for AOD. Our model considers AOD and aerosol mixing vectors as continuous variables, whose inference is carried out using Metropolis-within-Gibbs sampling methods. Retrieval uncertainties are quantified by posterior variabilities. We also develop a parallel Markov chain Monte Carlo (MCMC) algorithm to improve computational efficiency. We assess our retrieval performance using ground-based measurements from the AErosol RObotic NETwork (AERONET) and satellite images from Google Earth. Based on case studies in the greater Beijing area, China, we show that 4.4 km resolution can improve both the accuracy and coverage of remotely sensed aerosol retrievals, as well as our understanding of the spatial and seasonal behaviors of aerosols. This is particularly important during high-AOD events, which often indicate severe air pollution.

KEY WORDS:

• Fine retrieval resolution
• Hierarchical Bayesian model
• MCMC
• Remote sensing
• Spatial dependence

Acknowledgments

The authors gratefully acknowledge support from the National Science Foundation grants DMS-0907632, DMS-1107000, SES-0835531 (CDI) and CCF-0939370; Army Research Office grant W911NF-11-1-0114; the National Science Foundation of China (60325101, 60872078); Key Laboratory of Machine Perception (Ministry of Education) of Peking University; and Microsoft Research of Asia. The authors thank Dr. Susan Paradise, Dr. Amy Braverman, and the MISR (Multi-angle Imaging SpectroRadiometer) team for their great support and Derek Bean for editing advice. We also thank the AERONET PIs, Hong-Bin Chen, Philippe Goloub, Pucai Wang, Zhanqing Li, Brent Holben, and Xiangao Xia for establishing and maintaining the Beijing and Xianghe AERONET stations, especially Pei Wang from Peking University for collecting Aerosol Optical Depth (AOD) data in Beijing. We thank Graham Shapiro for implementing the projection of AOD retrievals to Google Earth. We thank Dr. Chengcai Li from Peking University and Yang Liu from Emory University for discussions. Last but not least, we thank Hal Stern, Editor of JASA's Applications and Case Studies, the anonymous Associate Editor, and Referee for their thoughtful comments and suggestions that helped us improve our work and article.

Notes

For example, an AOD value of 2.5 corresponds to 92% of radiation scattered or absorbed.

SSA is defined as the ratio of scattered radiation to total extinct radiation (scattered and absorbed).

The number of nonzero elements of the MISR's 74 mixing vectors is no more than three.

MISR observes the Earth's surface in 233 swaths; each swath contains 180,560 × 140 km² MISR blocks.

The other parameters, such as the ambient pressure, take the default values unless otherwise specified. The MISR team has kindly given us access to the SMART dataset.

Such origins include MISR camera measurement errors, RT calculation noises, differences between the proposed and true values for AOD and mixing vectors, choices of component aerosols, and errors in estimating surface-leaving radiances.

We found close-to-0 correlations (−0.0445) between our retrievals’ residuals at different viewing angles, but nontrivial correlations (0.5714) between residuals at different spectral bands. In the current work, we are building this dependence structure among different bands in our model.

We attach in the Appendix two trace plots showing one example of each type, up to the first 1000 iterations.

The noise's standard deviation σ is set as 10% of the averaged radiance, while the MISR operational algorithm estimates σ as 5% of the same average.

Excluding cloudy pixels can sometimes reduce the total dimensions to around 5000 for one MISR block.

The Beijing station is visited by the Terra satellite every 5 to 9 days.

Latitude: 39.97689° North; longitude: 116.38137° East.

Latitude: 39.75360° North; longitude: 116.96150° East.

The capital and largest city of Liaoning Province in Northeast China.