Ensemble based estimation of wet refractivity indices using a functional model approach

The estimation of the wet refractivity indices is crucial for applications like weather predictions or improving the accuracy of real-time positioning techniques. Traditionally, solving the inverse tomography problem to estimate these atmospheric parameters has been challenging due to its ill-posed nature and high computational demands, necessitating additional constraints. To overcome these challenges, the data assimilation method is proposed here to integrate Global Navigation Satellite System (GNSS) observations into a background model. In this study, the Ensemble Kalman Filter (EnKF) was served as the assimilation core to reduce the computational load and to enable the epoch-wise estimation of wet refractivity indices. The Global Pressure and Temperature 3 (GPT3w) model was utilized as the background, and wet refractivity indices at each epoch were transformed into B-spline coefficients, representing state vector parameters. Subsequently, GNSS derived zenith wet delay (ZWD) values were integrated into the model using the EnKF method. The study's region encompassed the western parts of Europe and incorporated approximately 893 GNSS stations. Evaluation spanned from 1 January 2017 to 31 December 2017. The estimated wet refractivity indices from the proposed method were compared with observations from 16 existing radiosonde stations, radio occultation data, and ZWD values from the 47 selected GNSS test stations. Additionally, calculated ZWD values, resulting from the integration of wet refractivity indices, were compared to the ZWD values from 47 test stations in the study region. The numerical results demonstrated that the proposed method achieved a root mean square error value of approximately 2.6 ppm, which was nearly 49% and 18% lower than that of the considered empirical and numerical atmospheric models, respectively.