Modeling and assessing climatic trends

Climate studies often fit linear trends to data. In many cases simplifying assumptions such
as independent errors and constant variance are used. We review a variety of approaches to
estimating linear trends, and illustrate with US temperature data how oversimplified assumptions
may lead to false significance. We outline a variety of methods to fit nonlinear trend
models. Using the Berkeley Earth global data set we show that a bent cable fit is better than
a linear fit for this series. We also review spatial and spatiotemporal trend models in mean,
variance and extremes, as well as models with long term memory structure.