Abstract. A neural-network-based method, quantile regression neural networks (QRNNs), is
proposed as a novel approach to estimating the a posteriori distribution of
Bayesian remote sensing retrievals. The advantage of QRNNs over conventional
neural network retrievals is that they learn to predict not only 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 to 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.
A neural network approach to estimating a posteriori distributions of Bayesian retrieval problems
