Ocean temperature anomalies persist far longer than atmospheric temperature anomalies because water has a much higher specific heat capacity than air. This large thermal inertia means the ocean absorbs and releases heat slowly, buffering and delaying temperature change, whereas the atmosphere, with low heat capacity, responds and equilibrates quickly.
Water's specific heat (~4184 J/kg·K) is roughly four times that of air (~1005 J/kg·K) on a per-unit-mass basis, and given the ocean's far greater mass...
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