Water Vapor Probabilistic Retrieval Using GNSS Signals

In this paper, we propose a novel Bayesian procedure to update the probability distribution for a set of possible atmospheric states, once ground measures of temperature, pressure, humidity, and tropospheric delay of Global Navigation Satellite System (GNSS) signals are made. It is based on a representative dataset of matching pairs of reanalysis atmospheric states and ground measures. By applying the basic rules of probability theory and logic inference, a computable expression for the conditional probability of the states given the measures is found. This allows us to select the most plausible atmospheric conditions, consistent with ground observations. Compared with more conventional techniques, the proposed approach has the advantage of always giving a result, even if not all the measures are available. Moreover, it provides the probability distributions of the retrieved quantities, which collapse to the corresponding prior distributions in the worst case of no significant measures. In any case, the final uncertainties are fully quantified, as needed for many meteorological applications, including data assimilation and ensemble forecasts for a numerical weather model. In addition to the theoretical details, a practical example of operational application, using a ten-year dataset on a Mediterranean test site, is also presented. The most probable retrieved atmospheric profiles of water vapor and temperature, as well as the corresponding values of precipitable water, are compared with balloon measurements on such a test site, showing good agreement and a significant improvement when the GNSS delay measure is added. In particular, the precipitable water retrieval turns out at least as accurate as that obtained with conventional approaches.