  We have constructed a Bayesian neural network able of retrieving tropospheric
temperature profiles from rotational Raman-scatter measurements of nitrogen and
oxygen and applied it to measurements taken by the RAman Lidar for
Meteorological Observations (RALMO) in Payerne, Switzerland. We give a detailed
description of using a Bayesian method to retrieve temperature profiles
including estimates of the uncertainty due to the network weights and the
statistical uncertainty of the measurements. We trained our model using lidar
measurements under different atmospheric conditions, and we tested our model
using measurements not used for training the network. The computed temperature
profiles extend over the altitude range of 0.7 km to 6 km. The mean bias
estimate of our temperatures relative to the MeteoSwiss standard processing
algorithm does not exceed 0.05 K at altitudes below 4.5 km, and does not exceed
0.08 K in an altitude range of 4.5 km to 6 km. This agreement shows that the
neural network estimated temperature profiles are in excellent agreement with
the standard algorithm. The method is robust and is able to estimate the
temperature profiles with high accuracy for both clear and cloudy conditions.
Moreover, the trained model can provide the statistical and model uncertainties
of the estimated temperature profiles. Thus, the present study is a proof of
concept that the trained NNs are able to generate temperature profiles along
with a full-budget uncertainty. We present case studies showcasing the Bayesian
neural network estimations for day and night measurements, as well as in clear
and cloudy conditions. We have concluded that the proposed Bayesian neural
network is an appropriate method for the statistical retrieval of temperature
profiles.
