Assessing the Utility of Volumetric Motion Fields for Radar-based Precipitation Nowcasting with Physics-informed Deep Learning

Peter Pavlík; Anna Bou Ezzeddine; Viera Rozinajová

cs.LGMar 13, 2026

Assessing the Utility of Volumetric Motion Fields for Radar-based Precipitation Nowcasting with Physics-informed Deep Learning

Authors: Peter Pavlík, Anna Bou Ezzeddine, Viera Rozinajová

Organizations: Kempelen Institute of Intelligent Technologies, Sky Park Offices, Bottova 7939/2A, Bratislava 811 09, Slovakia · Faculty of Information Technology, Brno University of Technology, Božetěchova 2, Brno 612 00, Czech Republic

Abstract

Estimating motion from spatiotemporal geoscientific data is a fundamental component of many environmental modeling and forecasting tasks. In this work, we propose a physics-informed deep learning framework for estimating altitude-wise motion fields directly from volumetric radar reflectivity data. The model utilizes a fully differentiable semi-Lagrangian extrapolation operator to process three-dimensional inputs as independent horizontal slice sequences, enabling efficient inference of horizontal motion across multiple altitude levels. Using a multi-year radar dataset from Central Europe, we evaluate the impact of altitude-wise motion estimation on extrapolation-based precipitation forecasting and conduct a systematic dataset-scale analysis of inter-altitude motion consistency. The results show that the estimated motion fields exhibit strong vertical coherence, with high correlation across altitude levels, which results in limited improvement over traditional two-dimensional approach in this setting. The proposed framework provides a general tool for efficiently analyzing motion structure in volumetric geospatial data. The findings indicate that, in regions dominated by vertically coherent precipitation systems, the added complexity of volumetric motion modeling may offer limited benefit, warranting careful consideration in the design of efficient spatiotemporal advection models.

Figures & tables

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.

Panel of Figure 2 — 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

\mathrm{dB}

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: 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.

Figure 5: The figure illustrates the 3D U-Net architecture used for horizontal motion field estimation. Feature map blocks indicate tensor dimensions, with the first dimension representing time and the remaining two corresponding to horizontal spatial coordinates. The encoder progressively reduces spatial resolution while increasing channel depth using 3D convolutions and spatial pooling, whereas the decoder restores resolution via upsampling and reduces the number of channels by convolutional processing. Skip connections link corresponding encoder and decoder stages to preserve fine-scale spatial information. The temporal dimension is gradually collapsed in the decoder, yielding a single motion field representing the dominant advection over the input (and near-future) radar sequence. The final layer outputs two channels corresponding to the horizontal motion components.

Figure 6: Mean absolute error of extrapolation-based nowcasts as a function of lead time. The blue dashed line corresponds to the 2D motion field model, while the solid green line represents the volumetric motion field model operating on altitude-wise radar slices.

Figure 7: Mean squared error of extrapolation-based nowcasts as a function of lead time. The blue dashed line corresponds to the 2D motion field model, while the solid green line represents the volumetric motion field model operating on altitude-wise radar slices.

Figure 8: Mean error (bias) of extrapolation-based nowcasts as a function of lead time. The blue dashed line corresponds to the 2D motion field model, while the solid green line represents the volumetric motion field model operating on altitude-wise radar slices. The black dotted line indicates zero bias.

Figure 9: The figure shows categorical verification metrics – Precision, Recall, and Equitable Threat Score (ETS) – as functions of forecast lead time for the baseline 2D motion-field extrapolation model and the proposed volumetric extrapolation model. Results are shown for precipitation intensity thresholds of 1, 5, and 10

\mathrm{mm}\text{\,}{\mathrm{h}}^{-1}

. Columns correspond to a fixed binarization threshold, while rows compare the two models using the same metric across the selected thresholds.

Figure 10: Mean error (bias) of extrapolation-based nowcasts as a function of lead time. In addition to the baseline 2D CMAX model and the 8-level volumetric model shown in Fig. 8 , we include intermediate configurations operating on data pooled to 2 and 4 vertical levels. The black dotted line indicates zero bias.

Panel of Figure 11 — Figure 11: Vertically pooled CMAX representations of a severe precipitation event over Slovakia on July 5th 2022. The top row shows three consecutive radar observations, with the first image (t+0 min) corresponding to 15:15 UTC and the following two images taken at 40-minute intervals. The bottom row shows the corresponding extrapolations obtained by advecting the final observation using the volumetric motion field estimated by the proposed 3D Motion Field U-Net. The vertically averaged 3D motion field is overlaid for reference. Zoomed regions highlight a non-physical cell-splitting artifact produced by the volumetric approach. The animated figure is available online at: https://pavlikp.github.io/3DMF/#figure-12

Figure 12: Mean Pearson correlation coefficients between horizontal motion fields estimated at different altitude levels. Correlations are computed only over precipitating regions and averaged over the full dataset. Note: Each horizontal layer consists of a max-pooled pair of neighboring radar volume slices (altitude 1000 $\mathrm{m}$ represents pooled layers at 500 and 1000 $\mathrm{m}$ and so on).

Figure 13: Two-dimensional histogram of dataset samples as a function of precipitation coverage and inter-altitude motion field correlation. The horizontal axis shows the ratio of CMAX-pooled pixels exceeding 20 $\mathrm{dB}$ , while the vertical axis shows the Pearson correlation between horizontal motion fields estimated at the lowest altitude layer (500–1000 $\mathrm{m}$ above ground level) and a mid-level layer (2500–3000 $\mathrm{m}$ above ground level). Red hues indicate the highest density of samples, dark blue no such samples. The three crosses denote events selected for qualitative evaluation.

Panel of Figure 14 — Figure 14: Estimated horizontal motion fields and corresponding precipitation fields at the lowest altitude layer (500–1000 $\mathrm{m}$ above ground level; left) and a mid-level layer (2500–3000 $\mathrm{m}$ above ground level; right) for three events selected for their low inter-altitude motion correlation and high precipitation coverage. The animated figures are available online at: https://pavlikp.github.io/3DMF/#figure-16

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Precipitation nowcasting over the immediate 10-90 min period is important for flood management and real-time decision-making in urban regions. Conventional short-range forecasting with high-resolution numerical weather prediction requires frequent data assimilation, model initialization, and spin-up, introducing computational latency. Machine learning provides an alternative by learning storm evolution directly from high-frequency observations and producing forecasts quickly after training. This is particularly relevant for Mumbai, India, where monsoon convection, land-sea interactions, and localized intense rainfall make short-term prediction difficult. Here, we develop a compact radar-only nowcasting framework that combines multi-elevation reflectivity, Doppler radial velocity, and radial-velocity-gradient proxy features within an encoder-decoder U-Net. Using the most recent radar volume scan, the model predicts 12 future composite reflectivity fields at 7.5-min intervals up to 90 min lead time. The derived velocity magnitude, divergence-like, directional-shear, and vorticity-like channels represent kinematic signatures associated with convergence and boundary interactions without requiring full wind-field retrieval. A high-reflectivity attention module improves sensitivity to convective cores, and physics-guided attribution examines whether the learned sensitivities are meteorologically meaningful. The model is trained using Mumbai Doppler radar observations from May to August 2023 and evaluated on temporally independent events. At 90 min lead time, Critical Success Index values are 0.437, 0.332, and 0.193 for

\geq

10,

\geq

20, and

\geq

30 dBZ thresholds, respectively. Compared with persistence, the model gives lower RMSE and higher spatial correlation at longer lead times. Once trained, it runs on a standard computer, generating nowcasts within seconds for real-time use.

Abstract

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