Ocean temperatures did not rise like water filling a bathtub; they rose like a person climbing stairs: two broad steps upward, with waves of natural variability lapping around them, advancing and retreating. The first step occurred in 1925/26, the second in 1987/88. Each added about 0.28°C to average temperatures in the tropics and 0.36°C in northern mid-latitudes.

These steps were uncovered when a simple model was applied to sea surface temperatures: two factors, the known oscillations (El Niño in the tropics, the Pacific Decadal Oscillation in northern mid-latitudes) and a step function that changes level from -1 to +1 at the times of the jumps. The model explained 86% of the variability in the tropics and 81% in northern mid-latitudes. In other words, most of the twentieth-century warming in these belts was not a smooth trend but two abrupt transitions.

The test was rigorous: coefficients obtained from only the 1910–1940 data reproduced the entire subsequent record up to 2012 with a correlation of 0.86. This means the relationships found are robust, not tailored to a specific segment.

Before this work, it was unclear why warming proceeded unevenly: rapid growth at the start of the century, a plateau in the middle, and growth again at the end. Some attributed this to external forcings, others to internal variability. Now it is clear that a significant portion can be described as two jumps against a background of ordinary oscillations. No smooth trend is required.

A staircase with two broad steps: that is what twentieth-century warming looks like. The waves of El Niño and the Pacific Decadal Oscillation continue to advance and retreat, but the average level after each step remains higher. The next step, if it occurs, the model will predict only after it happens, but now we know what to look for.