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Data on ozone concentrations at four monitoring sites in central Canada are examined. Univariate extreme value methods do not allow for the required inference, and multivariate methods exploiting the joint dependence of the data are necessary. Families of multivariate extreme-value copulas with a flexible dependence structure and closed-form cumulative distribution functions have recently been derived. This article shows that maximum likelihood estimates of these parametric models may be obtained numerically and that their use can lead to increased efficiency in the estimation of margins. We do not, however, have any assurance that all data are well modeled by these distributions, because the space of multivariate extreme-value copulas is infinite-dimensional, and data on ozone levels are prone to outliers. This article addresses the robust methods required for proper analysis. [ABSTRACT FROM AUTHOR]