<p>Estimating when anthropogenically-forced signals emerge from ambient natural climate variability is crucial for climate-change detection. Here we propose a new method for estimating the emergence time of climate signals based on a significance test on the nonlinear trend rather than the commonly-used method based on a signal-to-noise ratio. This method is less sensitive to the choice of a confidence level (0.1, 0.05 or 0.01) than the previous method to commonly-used signal to noise ratios (0.5, 1 or 2). For signals that tend to emerge in the late 21<sup>st</sup> century, our method tends to yield earlier detection dates, by taking the large number of degrees of freedom into account. Here, we apply this method to relative SST (RSST, SST minus its tropical mean) changes, which tend to emerge much later than SST change signals. RSST is an indicator of changes in the atmosphere vertical stability and thus of changes in tropical cyclones intensity and precipitation. By 2100, CMIP5/6 projections indicate greater than tropical average warming (positive RSST signal) in the central and eastern equatorial Pacific, equatorial Atlantic, and Arabian Sea, and reduced warming (negative RSST signal) in the three southern hemisphere subtropical gyres. In general agreement with observations, relative warming in the Arabian Sea and relative cooling in the South-Eastern Pacific are already detectable in a majority of models (median emergence time < 2020), making these regions suitable for testing a model's ability to predict a regional SST trend. In contrast, RSST signals in other regions do not become detectable until after 2050. Tropical precipitation projections indicate more (less) rainfall in regions of positive (negative) RSST change that typically emerge one or two decades later than RSST signals. This lack of currently-detectable regional rainfall trends in CMIP models makes it difficult to evaluate their ability to predict tropical regional rainfall trends. In general, signals tend to emerge later in CMIP6 than in CMIP5 due to both weaker signals and larger climate noise. The only exception is Sahel, where CMIP6 models already display a detectable rainfall increase, that is not yet detectable in CMIP5.</p>