Quantifying the lead time required for a linear trend to emerge from natural

We introduce a simple analytic expression for calculating the lead time required for a linear trend to emerge in a Gaussian first order autoregressive process. The expression is derived from the standard error of the regression and is tested using the NCAR Community Earth System Model Large Ensemble of climate change simulations. It is shown to provide a robust estimate of the point in time when the forced signal of climate change has emerged from the natural variability of the climate system with a predetermined level of statistical confidence. The expression provides a novel analytic tool for estimating the time of emergence of anthropogenic climate change and its associated regional climate impacts from either observed or modeled estimates of natural variability and trends. 11