ON SPATIAL SCALES AND LIFETIMES OF SST ANOMALIES BENEATH A DIFFUSIVE ATMOSPHERE

The authors identify spatial and temporal scales in a one-dimensional linear, diffusive atmospheric energy balance model coupled everywhere to a slab mixed layer of fixed depth. Mathematically, the model is ide ntical to a heat conducting rod, which over its entire length both rad iates and is in contact with a large but finite ''reservoir.'' Three c haracteristic timescales mark, respectively, the atmosphere's adjustme nt to a sea surface temperature (SST) anomaly, the decay of a pointwis e SST anomaly, and the radiative decay of a large-scale SST anomaly. T he first and the third of these timescales are associated with diffusi ve length scales characterizing, respectively: the distance over which heat is diffused in the atmosphere before being lost to the ocean ben eath, and the distance over which heat is diffused in the coupled syst em before being radiated to space. For spatial scales between the two diffusive lengths, the SST anomaly does not decay exponentially but wi th the square root of time; this regime has not previously been identi fied. Apparent discrepancies between published discussions of diffusiv e length scales are reconciled.