Assimilation of GNSS delays along slant paths into the WRF model: two experiments over Italy

Reliable Numerical Weather Prediction (NWP) are of utmost importance to our daily life. In addition, they are of fundamental to help mitigation of severe and catastrophic weather events.

Atmospheric water vapor is a fundamental element of weather forecasting, nevertheless its accurate observation is difficult, mainly because of its high spatiotemporal variability. 

A reliable way to estimate water vapor is through Global Navigation Satellite Systems (GNSS) satellites, whose signals are received from ground-based stations and permit to calculate Zenith Total Delay (ZTD). ZTD can be easily related to Precipitable Water Vapor (PWV). 

The GNSS observation at the zenith uses delays from different directions to improve the estimate of the delay in the vertical direction, thus strengthening the solution. This process, however, reduces the number of observations available for each GNSS receiver. Anyway, the high quality of GNSS observations in the zenit direction has become a reference for other instruments and has been widely assimilated in NWP models worldwide.

Estimating the delay in different directions poses challenges for the convergence of the solution and for errors in the retrieved slant total delay (STD). Similarly, while the assimilation of the zenith delay for GNSS receivers is well-established, the assimilation of the delay in the inclined directions remains largely unexplored.

In this work, GNSS information along slant paths is assimilated into the Weather Research and Forecasting (WRF) model. Two approaches are shown: the first considers the assimilation of the delay along slant paths, the second the assimilation of precipitable water vapor along slant paths.

In the first approach, the assimilation of STD is done through the use of tropospheric gradients in the East and North directions. Gradients assimilation has been recently added in a version of the WRFA Data Assimilation (WRFDA) and presented in the paper of Thundathil et al. (2024). The same method was applied in Torcasio et al. (2026). 

An application of GNSS gradients assimilation over Italy is presented. The impact on the precipitation prediction of GNSS gradients assimilation both alone or in combination with GNSS-ZTD data assimilation is shown for a case study, comparing the results with a model configuration not assimilating GNSS data. Results show an improvement when GNSS data assimilation is applied: event intensity and location are better represented and false alarms are reduced. The configuration assimilating both GNSS-ZTD and gradients has the best performance. 

A second experiment considers PWV data assimilation along slant paths (PWVS). In this case, the STD signal is converted in precipitable water vapor and assimilated in WRF, increasing the number of observations in comparison to the assimilation of precipitable water vapor in the vertical direction. We consider an experiment of one month showing the problems involved in the assimilation of PWVS, its results, and its comparison with corresponding forecast without the assimilation of GNSS observations and with the assimilation of GNSS delay in the zenith direction.

 

References

Torcasio R.C. et al. (2026) https://doi.org/10.1007/s12210-025-01399-1

Thundathil R. et al. (2024) https://doi.org/10.5194/gmd-17-3599-2024