The solute distribution in front of directionally growing ice crystals in a water-KCl solution was observed in situ as well as the three-dimensional interfacial patterns, using a Mach-Zehnder interferometer. We give a direct evidence for the constitutional supercooling and discuss the wavelength selection of perturbation. The morphological instability occurred much earlier than the establishment of the steady-state condition of diffusion field. The steady-state analysis using Mullins-Sekerka theory could not predict the wavelength of perturbation. However, when the measured values of solute distribution and growth I ate at the time of instability are substituted for the parameters assuming the quasi-steady state, it is found that the analysis precisely predicts the experiments.