Aims: The purpose of this paper is to characterize the statistical properties of solar granulation in the photosphere and low chromosphere up to 650 km. Methods: We use velocity and intensity variations obtained at different atmospheric heights from observations in Ba II 4554 Å. The observations were done during good seeing conditions at the VTT at the Observatorio del Teide on Tenerife. The line core forms rather high in the atmosphere and allows granulation properties to be studied at heights that have been not accessed before in similar studies. In addition, we analyze the synthetic profiles of the Ba II 4554 Å line by the same method computed taking NLTE effects into account in the 3D hydrodynamical model atmosphere. Results: We suggest a 16-column model of solar granulation depending on the direction of motion and on the intensity contrast measured in the continuum and in the uppermost layer. We calculate the heights of intensity contrast sign reversal and velocity sign reversal. We show that both parameters depend strongly on the granulation velocity and intensity at the bottom photosphere. The larger the two parameters, the higher the reversal takes place in the atmosphere. On average, this happens at about 200-300 km. We suggest that this number also depends on the line depth of the spectral line used in observations. Despite the intensity and velocity reversal, about 40% of the column structure of granulation is preserved up to heights around 650 km.