A neural network approach to estimating a posteriori distributions of Bayesian retrieval problems

Abstract

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.

Towards an operational Ice Cloud Imager (ICI) retrieval product

“…Zhang et al, 2010), frequently as part of "mixed-phase" clouds. Results in Pfreundschuh et al (2019) indicate that ICI has some sen-sitivity to such super-cooled liquid water and it should thus be considered in future work. Also the super-cooled liquid water in updraft regions of convective cells should be taken into account, especially as the drops here can be of millimetre size and the liquid water content can reach several grams per cubic metre (Lawson et al, 2015).…”

Synergistic radar and radiometer retrievals of ice hydrometeors

“…As has been shown also by other studies, the passive observations do provide information on the vertical distribution of ice in the atmospheric column (Wang et al, 2017;Grützun et al, 2018), but the information content is limited to a few degrees of freedom. It is therefore unlikely that the vertical resolution of the passive-only retrieval can be improved drastically without further constraining it a priori, as it is typically done in retrievals that use Monte Carlo integration or neural networks (Pfreundschuh et al, 2018).…”

Towards an operational Ice Cloud Imager (ICI) retrieval product

“…There are close connections between BMCI and the standard use of neural nets (Pfreundschuh et al, 2018). Such neural nets (NN), a form of machine learning, have been applied on both simulated ICI data (Jimenez et al, 2007;Wang et al, 2017) and ISMAR field data (Brath et al, 2018).…”

“…For a description of BMCI and its relationship to Bayesian estimation, see e.g. Kummerow et al (1996) or Pfreundschuh et al (2018). In short, BMCI is based on a "retrieval database" consisting of n pairs of atmospheric state, x i , and corresponding observation, y i , with the constraint that x i is approximately distributed according to reality, i.e.…”