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A novel segmentation method is proposed for the analysis of bivariate time series of intensities and angles that often occur in environmental applications. The model is based on a mixture of copula-based cylindrical distributions, whose parameters evolve according to a latent Markov chain. The model parsimoniously accommodates typical features of cylindrical time series such as circular-linear correlation, multimodality, skewness and temporal auto-correlation. A computationally efficient Expectation-Maximization algorithm is described to estimate the parameters and a parametric bootstrap routine is exploited to compute confidence intervals. These methods are illustrated on cylindrical time series of wave heights and directions in the Adriatic sea.