Extended Data Fig. 5: Thermal displacement methodology.

Steps for calculating thermal displacement are illustrated for a sample location in the Gulf of Alaska (145° W, 50° N). For each ice-free grid cell in the global ocean (n ≈ 500,000), the following steps are taken. a, The 1982–2011 monthly climatological temperature (grey) is calculated from the OISSTv2 data (magenta). b, The monthly climatology is subtracted to obtain monthly anomalies (magenta), which are then linearly detrended (black). c, MHWs (red) are identified as months in which the detrended SST anomaly (black) exceeds a seasonally varying 90th-percentile threshold (dotted black line). For each month with an MHW occurring (August 2019 is highlighted here for example), the detrended SST anomaly (1.3 °C in this case; d) is subtracted from the observed SST (10.3 °C; e) to obtain the ‘normal’ temperature for that month of the year corrected for the warming trend (9.0 °C). e, Thermal displacement is the shortest distance (521 km; white arrow) to SST at or below the ‘normal’ temperature (cyan contour). For the future projections, the same methodology is used after adding the mean projected SST change to the time series in a.