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Atmospheric Measurement Techniques An interactive open-access journal of the European Geosciences Union

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© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
29 Mar 2018
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Atmospheric Measurement Techniques (AMT).
A neural network approach to estimate a posteriori distributions of Bayesian retrieval problems
Simon Pfreundschuh1, Patrick Eriksson1, David Duncan1, Bengt Rydberg2, Nina Håkansson3, and Anke Thoss3 1Department of Space, Earth and Environment, Chalmers University of Technology, Gothenburg, Sweden
2Möller Data Workflow Systems AB, Gothenburg, Sweden
3Swedish Meteorological and Hydrological Institute (SMHI), Norrköping, Sweden
Abstract. This work is concerned with the retrieval of physical quantities from remote sensing measurements. A neural network based method, Quantile Regression Neural Networks (QRNNs), is proposed as a novel approach to estimate the a posteriori distribution of Bayesian remote sensing retrievals. The advantage of QRNNs over conventional neural network retrievals is that they not only learn to predict a single retrieval value but also the associated, case specific uncertainties. In this study, the retrieval performance of QRNNs is characterized and compared to that of other state-of-the-art retrieval methods.

A synthetic retrieval scenario is presented and used as a validation case for the application of QRNNs to Bayesian retrieval problems. The QRNN retrieval performance is evaluated against Markov chain Monte Carlo simulation and another Bayesian method based on Monte Carlo integration over a retrieval database. The scenario is also used to investigate how different hyperparameter configurations and training set sizes affect the retrieval performance. In the second part of the study, QRNNs are applied to the retrieval of cloud top pressure from observations by the moderate resolution imaging spectroradiometer (MODIS). It is shown that QRNNs are not only capable of achieving similar accuracy as standard neural network retrievals, but also provide statistically consistent uncertainty estimates for non-Gaussian retrieval errors.

The results presented in this work show that QRNNs are able to combine the flexibility and computational efficiency of the machine learning approach with the theoretically sound handling of uncertainties of the Bayesian framework. Together with this article, a Python implementation of QRNNs is released through a public repository to make the method available to the scientific community.

Citation: Pfreundschuh, S., Eriksson, P., Duncan, D., Rydberg, B., Håkansson, N., and Thoss, A.: A neural network approach to estimate a posteriori distributions of Bayesian retrieval problems, Atmos. Meas. Tech. Discuss.,, in review, 2018.
Simon Pfreundschuh et al.
Simon Pfreundschuh et al.

Model code and software

A validation study for the application of quantile regression neural networks to Bayesian remote sensing retrievals S. Pfreundschuh A cloud top pressure retrieval using QRNNs S. Pfreundschuh
Simon Pfreundschuh et al.


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Short summary
A novel neural network based retrieval method is proposed that combines the flexibility and computational efficiency of machine learning retrievals with the consistent treatment of uncertainties of Bayesian methods. Numerical experiments are presented that show the consistency of the proposed method with the Bayesian formulation as well as its ability to represent non-Gaussian retrieval errors. With this, the proposed method overcomes important limitations of traditional methods.
A novel neural network based retrieval method is proposed that combines the flexibility and...