Land motion in Europe imaged by GNSS

The densification of high-quality, permanent GNSS stations in Europe enables a large-scale investigation of deformation processes on the Earth’s surface. This work aims to interpolate the horizontal and vertical GNSS station velocities and thus produce velocity fields showing the land motion for Switzerland, the Alps and Europe. The GNSS station velocities are provided by the EUREF Working Group on European Dense Velocities. The data set contains horizontal (east, north) and vertical velocities for around 8000 stations in Europe. Five interpolation methods are implemented and compared, namely, Inverse Distance Weighting (IDW), Ordinary Kriging, K - Nearest Neighbors (KNN), Random Forest and Multilayer Perceptron (MLP). Latitude and longitude of the station locations are used as input features for the interpolation. Additional input features will be engineered for Random Forest and MLP. Generally, the performance of all five interpolation methods with latitude and longitude as features evaluated on the test data by Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Bias Error (MBE) is comparable for all velocity components in Switzerland, the Alps and Europe. RMSE and MAE vary among the methods by hundredths of a mm/year. The only exceptions are the horizontal velocity components for the extent of Europe, where MLP and Ordinary Kriging perform slightly worse than the other methods. The key findings of the qualitative analysis are that MLP and Ordinary Kriging produce the smoothest velocity fields, while IDW, KNN and Random Forest produce artifacts due to their mode of operation. All methods interpolate similar velocity fields where the station data is dense and greater differences when it is sparse. Especially for extrapolation areas where no data is available their performance is not verified. The interpolation of the GNSS station velocities in Switzerland, the Alps and Europe for this work shows that it is possible to produce velocity fields with accuracy level below 1 mm/year and the different phenomena of land motion can be clearly identified.