Supporting Online Material for: Penetration of Human-Induced Warming into the World’s Oceans

We start with the yearly averaged temperature anomaly, volume averaged (over a basin) at observed locations only using the “dd ” mask from the observations (S1). This is done independently for each of 16 vertical levels, from the surface to 700 m (we checked all the way to 3000 m, but the results showed little statistically significant signal below 700 m for most basins). The anomaly is with respect to the simultaneous value of the long control run fitted with a second order polynomial, to remove model drift. We then form decadal averages (the 1960s through the 1990s) to reduce the effects of annual and decadal climate variability not of interest here, and form anomalies over this period to match the treatment of the observations. Let the result be called Tv. The decadal averaging also helps eliminates the large scale spatial noise (S2), which the model will not reproduce since it did not see the exact forcing the real ocean did. For each of the five anthropogenically forced ensemble members (started from different times in the long control run) we form a so-called “concatenated ” signal (S3). This is a vector with 24 entries: one set of 4 decadal entries for each of the 6 basins (North and South Atlantic, Pacific, and Indian). It is laid out so that the first four entrie