Obtaining high-resolution, autonomous and continuous measurements of internal and interfacial convection at the ice–ocean interface is important to understand sea-ice desalination, compare the effects of gravity drainage and salt segregation, and give insight into the behaviour of the sublayer beneath the ice. We present the first digital image processing method that can be applied to Schlieren images from a quasi-2D Hele-Shaw cell to provide continuous high-frequency measurements of fingers and streamers, which are linked to interfacial and internal convection, respectively. Previous studies lack the ability to provide a temporal evolution of this dynamic system at a high enough resolution to investigate these interactions. The improved algorithm confirms previous results, while providing a more detailed and statistically acceptable description of the processes during artificial sea-ice growth. We demonstrate that internal convection exhibits a highly variable behaviour that changes in time. As the ice growth rate decreases to its minimum value, internal convection becomes periodically inactive while interfacial convection remains active throughout the experiments. This temporal change suggests a dominant, shorter time-period for gravity drainage to occur and a longer time-period over which salt segregation occurs, while the oscillation in expulsion behaviour suggests that the sublayer is more turbulent than diffusive.