Tracking the photospheric horizontal velocity field with shallow U-net models

Context. Understanding the horizontal velocity field of the highly magnetized plasma within the solar atmosphere is essential to understanding the complicated dynamics and energy evolution of solar phenomena at various scales, from small-scale swirls to coronal mass ejections. Most traditional methods estimate the photospheric horizontal velocity field by tracking bright features. These reconstructed velocity fields may differ from the ground truth because the photosphere is not a single layer but has a depth of ~500 km. The observed bright features are combined emissions from different heights in the photosphere. Aims. In this work, we aim to develop a series of models for tracking the photospheric horizontal velocity field with high accuracy from high-resolution observations using a modified shallow U-Net architecture and to evaluate the performance of different models. Methods. We used photospheric intensity, vertical magnetic field strength, and horizontal velocity fields from a realistic 3D radiative numerical simulation of a quiet-Sun region generated using the Bifrost code to train and validate the shallow U-Net models. We built three shallow U-Net models: an intensity model using photospheric intensity as the input, a magnetic model using vertical magnetic field strength as the input, and a hybrid model combining both. Results. All three models yield good performances, among which the hybrid model shows the best performance with a correlation coefficient of 0.85 with the ground-truth velocity field. Comparisons with the Fourier local correlation tracking (FLCT) and the DeepVel methods demonstrate the superiority of the shallow U-Net models. Based on the research of this work, we have released a software named SUVEL for public use to extract photospheric horizontal velocity fields from high-resolution observations. SUVEL is only designed to be used on photospheric observations in the quiet-Sun regions with high temporal (best at 10 s, preferably less than 50 s) and high spatial resolutions.