Assessment of ZWD field predictions using the dynamic mode decomposition method

The existing water vapor present in the lower regions of the atmosphere plays a pivotal role in both weather forecasting and the propagation of signals in satellite-based observations. This parameter introduces a delay in GNSS observations, known as tropospheric wet delay. Accurately predicting the spatial distribution of this parameter can significantly enhance our ability to forecast rainfall and floods. It can also improve satellite-based positioning techniques. One mathematical technique that proves invaluable in modeling various temporal aspects of a signal is the Dynamic Mode Decomposition (DMD) method. To construct the necessary snapshot matrix in the DMD method, we have opted to employ B-spline coefficient time series, computed by assimilating GNSS-derived Zenith et Delay (ZWD) values into the GPT3w model as a reference, with the Ensemble Kalman Filter (EnKF) method serving as the core of the assimilation process. In the DMD procedure, we have utilized a dataset spanning approximately 30 consecutive days, with a temporal resolution of roughly 5 min, to predict B-spline coefficients representing the spatial distribution of ZWD values for a 24-h period ahead. This dataset comprises ZWD values collected from 241 GNSS stations located in Germany and nearby regions throughout the year 2018. Comparative analysis has been performed, including 10 excluded GNSS stations from the assimilation and DMD procedure and 10 existing radiosonde stations within the study region. The results of the analysis step demonstrate the superiority of the proposed method over the ERA5, GFS, and GPT3w models, showcasing the Root Mean Squared Error (RMSE) of approximately 0.8 cm. This performance marks a substantial improvement, being approximately 51%, 57%, and 74% lower than each respective
model. In the prediction phase, the proposed method outperforms the ERA5 and GFS models up to the 6-h and 24-h prediction windows in comparison with the GPT3w model.