Geophysical studies are plagued by short and noisy time series. These time series are typically nonstationary, contain various long-period quasi-periodic components, and have rather low signal-to-noise ratios and/or poor spatial sampling. Classic examples of these time series are tide gauge records, which are influenced by ocean and atmospheric circulation patterns, twentieth-century warming, and other long-term variability. Remarkable progress recently has been made in the statistical analysis of time series. Ghil et al. <2002> presented a general review of several advanced statistical methods with a solid theoretical foundation. This present article highlights several new approaches that are easy to use and that may be of general interest. Extracting trends from data is a key element of many geophysical studies; however, when the best fit is clearly not linear, it can be difficult to evaluate appropriate errors for the trend. Here, a method is suggested of finding a data-adaptive nonlinear trend and its error at any point along the trend. The method has significant advantages over, e.g., low-pass filtering or fitting by polynomial functions in that as the fit is data adaptive, no preconceived functions are forced on the data; the errors associated with the trend are then usually much smaller than individual measurement errors.