“Eyeballing” Trends in Climate Time Series: A Cautionary Note

In examining a plot of a time series of a scalar climate variable for indications of climate change, we might pick out what appears to be a linear trend commencing near the end of the record. We demonstrate that visual determination of the starting time of the trend can lead us to incorrectly declare a trend to be significant when we base our assessment on standard linear regression analysis; in fact a presumed level of significance of 5% can be smaller than the actual level by up to an order of magnitude. We suggest an alternative procedure that is more appropriate for assessing the significance of a trend whose starting point is identified visually.