Understanding the development of trends and identifying trend reversals in decadal time series is becoming more and more important. Many climatological and atmospheric time series are characterized by autocorrelation, heteroskedasticity and seasonal effects. Additionally, missing observations due to instrument failure or unfavorable measurement conditions are common in such series. This is why it is crucial to apply methods which work reliably under these circumstances. The goal of this paper is to provide a toolbox which can be used to determine the presence and form of changes in trend functions using parametric as well as nonparametric techniques. We consider bootstrap inference on broken linear trends and smoothly varying nonlinear trends. In particular, for the broken trend model, we propose a bootstrap method for inference on the break location and the corresponding changes in slope. For the smooth trend model we construct simultaneous confidence bands around the nonparametrically estimated trend. Our autoregressive wild bootstrap approach combined with a seasonal filter, is able to handle all issues mentioned above. We apply our methods to a set of atmospheric ethane series with a focus on the measurements obtained above the Jungfraujoch in the Swiss Alps. Ethane is the most abundant non-methane hydrocarbon in the Earth's atmosphere, an important precursor of tropospheric ozone and a good indicator of oil and gas production as well as transport. Its monitoring is therefore crucial for the characterization of air quality and of the transport of tropospheric pollution.