Assimilation of Zenith Wet Delay observations using the ensemble Kalman Filter in a Poly-ZWD empirical model over the USA

Modeling the spatial and temporal variability of water vapor in the lower atmosphere is crucial for meteorological and geodetic applications, as it directly influences weather prediction and satellite-based positioning. However, traditional empirical models often struggle to capture rapid water vapor fluctuations, limiting their accuracy and practical utility. These models are also typically grid-based and involve numerous parameters, making real-time calibration against current observations challenging. To address these limitations, this study applies an ensemble-based Calibration and Data Assimilation (C/DA) approach using the Ensemble Kalman Filter (EnKF), which sequentially adjusts model parameters based on observational data, thereby improving short-term prediction accuracy. Specifically, we enhance the estimation of Zenith Wet Delay (ZWD) through the development of a regional empirical model, Poly-ZWD. This model employs third-order polynomials for horizontal variations due to their flexibility in capturing spatial trends with fewer coefficients, and B-spline functions for temporal variations because of their compact support and strong local control, which enable smooth and efficient time-dependent modeling. The model was built using ERA5 reanalysis data from 2016 to 2020. Poly-ZWD spans the contiguous United States (27°–49°N, 94°–68°W) and incorporates 680 parameters, which collectively capture the spatial and temporal behavior of ZWD across the domain. These parameters were recalibrated using GNSS-derived ZWD observations from 460 stations across the U.S. for the year 2021, improving alignment with real-world atmospheric conditions and enhancing model performance compared to the original PCA-ZWD derived coefficients. The recalibrated model, referred to as C/DA Poly-ZWD, was evaluated against ZWD estimates from 15 independent GNSS test stations and 7 radiosonde sites. Results show that the proposed model achieves a root mean square error (RMSE) of approximately 1.1 cm, outperforming both ERA5 and GTrop models. While RMSE increases gradually from 1.1 cm to around 6 cm over a 24-h forecast horizon, the calibrated model consistently maintains superior accuracy compared to the considered empirical models. Notably, the C/DA approach provides more accurate short-term ZWD predictions than ERA5 within a 3-h forecast window. These findings highlight the effectiveness of ensemble-based C/DA techniques in enhancing real-time ZWD modeling capabilities, with promising implications for improving GNSS-based positioning accuracy and short-term weather forecasting.