Abstract The sunspot penumbra is usually observed in the photosphere and it is of particular interest for its magnetoconvection, which seems to transport the heat from the top of the convection zone into the solar atmosphere. It is well known that the penumbra magnetic field extends into the upper layers of the solar atmosphere forming the so-called superpenumbra. Thanks to the application of the Self-organizing Map technique to a spectral data set containing monochromatic images acquired along the Ca ii 854.2 nm and Hα 656.28 nm lines, we were able to segment the penumbra and to measure the plasma velocity along the chromospheric portions of penumbral filaments. We found that the head, body, and tail of penumbral filaments show vertical flows compatible with the persistence of the Evershed flow. Instead, the inverse Evershed flow has been observed only in the outer portion of the superpenumbra. We found that two opposite Evershed regimes work next to each other, without overlapping, and both contribute to the downflow around sunspots. These results confirm the uncombed model of the sunspot penumbra and provide some hints that the downflow around sunspots may be ascribed to the magnetic field dragging the plasma down.