Volumetric Radar Echo Motion Estimation Using Physics-Informed Deep Learning: A Case Study Over Slovakia

Abstract

In precipitation nowcasting, most extrapolation-based methods rely on two-dimensional radar composites to estimate the horizontal motion of precipitation systems. However, in some cases, precipitation systems can exhibit varying motion at different heights. We propose a physics-informed convolutional neural network that estimates independent horizontal motion fields for multiple altitude layers directly from volumetric radar reflectivity data and investigate the practical benefits of altitude-wise motion field estimation for precipitation nowcasting. The model is trained end-to-end on volumetric observations from the Slovak radar network and its extrapolation nowcasting performance is evaluated. We compare the proposed model against an architecturally identical baseline operating on vertically pooled two-dimensional radar composites. Our results show that, although the model successfully learns altitude-wise motion fields, the estimated displacement is highly correlated across vertical levels for the vast majority of precipitation events. Consequently, the volumetric approach does not yield systematic improvements in nowcasting accuracy. While categorical metrics indicate increased precipitation detection at longer lead times, this gain is largely attributable to non-physical artifacts and is accompanied by a growing positive bias. A comprehensive inter-altitude motion field correlation analysis further confirms that events exhibiting meaningful vertical variability in horizontal motion are rare in the studied region. We conclude that, for the Slovak radar dataset, the additional complexity of three-dimensional motion field estimation is not justified by questionable gains in predictive skill. Nonetheless, the proposed framework remains applicable in climates where precipitation systems exhibit stronger vertical variability in horizontal motion.

Figures (16)

• Figure 1: The figure shows the locations of the four ground radar stations comprising the Slovak radar network. The overlapping lightly shaded circular areas show the maximum extent of the radar coverage.
• Figure 2: Example of the radar reflectivity denoising process: (a) raw reflectivity field containing non-meteorological echoes and small-scale noise, and (b) corresponding reflectivity field after polarimetric filtering and morphological denoising. Both of the images are created by displaying the vertical column maximum from the 3D volume for each pixel (CMAX).
• Figure 3: Bar chart showing the mean fraction of grid points with reflectivity exceeding 0 and 20 Z at each altitude level. A rapid decrease in rainy pixel occurrence with height is observed, reflecting the limited vertical extent of many precipitation events in the dataset.
• Figure 4: Month-wise distribution of rainy pixel ratios in the dataset. For each radar volume, the ratio of light precipitation was computed as the percentage of pixels exceeding 20 Z at the lowest altitude slice (500 m above ground level). Boxes span the interquartile range (Q1–Q3), with the median indicated by a horizontal line. Whiskers extend to the most extreme values within 1.5 times the interquartile range, while points beyond the whiskers denote outliers.
• Figure 5: Correlation matrix showing the mean pixel-wise Pearson correlation coefficients between horizontally co-located radar reflectivity slices at different altitude levels from 500 to 8000 m above ground level. Only samples where non-zero reflectivity was observed at each altitude were included in the calculation.