In situ and real-time observation of the solid-liquid interface during upward Bridgman growth of succinonitrile-0.5 wt% acetone in a cylinder was carried out. This first article concentrates on the study of the emergence and building of nonplanar patterns. By observation under white light in the solidification direction, bright field images and video records of the interface microstructure were obtained, which allowed dynamical phenomena such as the ripening and arrangement of cellular arrays with time. All results show a significant influence of natural convection in the melt. In particular, a microstructure gradient was observed at the interface. From a phenomenological model based on a boundary layer approach, its origin can be attributed to a ramp in solute concentration along the growth front created by tangential fluid flow. Statistical analyses of the evolution of primary spacing and array disorder show that the stable arrangement can still be described as a honeycomb disturbed by Gaussian noise. Convection was also found to be responsible for primary spacings smaller than that given by theoretical diffusive models and experiments on thin samples.