An automatic parameter optimization system for a coupled ocean-sea ice model is applied to investigate uniqueness of parameter set obtained from data assimilation. We set up a parameter optimization experiment, in which 15 model parameters are optimized simultaneously using a 23-years optimization window. A series of 11 independent experiments are conducted to examine spread of objective functions, optimized sea ice fields and associated optimal parameters. The result shows sufficiently small spreads of objective functions and ice fields, whereas a significantly large spread of optimized parameters. This indicates the system gives an unique solution regarding the simulated ice fields, whereas multiple solutions regarding the associated model parameters. A correlation analysis shows the optimal parameters are inter-related and covariant. A principal component analysis (PCA) reveals that the first 3 principal components explain 70% of the variation of the optimal parameter sets, indicating a contraction of the model parameter space.