We compare global‐scale changes in satellite estimates of the temperature of the lower troposphere (TLT) with model simulations of forced and unforced TLT changes. While previous work has focused on a single period of record, we select analysis timescales ranging from 10 to 32 years, and then compare all possible observed TLT trends on each timescale with corresponding multi‐model distributions of forced and unforced trends. We use observed estimates of the signal component of TLT changes and model estimates of climate noise to calculate timescale‐dependent signal‐to‐noise ratios (S/N). These ratios are small (less than 1) on the 10‐year timescale, increasing to more than 3.9 for 32‐year trends. This large change in S/N is primarily due to a decrease in the amplitude of internally generated variability with increasing trend length. Because of the pronounced effect of interannual noise on decadal trends, a multi‐model ensemble of anthropogenically‐forced simulations displays many 10‐year periods with little warming. A single decade of observational TLT data is therefore inadequate for identifying a slowly evolving anthropogenic warming signal. Our results show that temperature records of at least 17 years in length are required for identifying human effects on global‐mean tropospheric temperature.