Environmental time series usually vary systematically in response to meteorological conditions and thus often are not stationary. In this article a class of additive models are introduced for environmental time series, in which both mean levels and variances of the series are nonlinear functions of relevant meteorological variables. Backfitting algorithms in nonlinear regression are adopted to estimate the unknown functions in the model, and the maximum likelihood method is used to estimate the parameters in the noise component. Asymptotic properties of the parameter estimates, including consistency and limiting distribution, are derived under mild conditions. The model is applied to daily maxima of ground-level ozone concentrations in the Chicago area for possible long-term trend assessment. Compared to alternative models, the proposed models gave more accurate estimations for the 95th and 99th percentiles of the ozone distribution.