NOTES AND CORRESPONDENCE Temperature Advection: Internal versus External Processes

Local advection of temperature is the inner product of vector velocity and spatial gradient of temperature. This product is often integrated spatially to infer temperature advection over a region. However, the contribution along an individual direction can be dominated by internal processes that redistribute heat within the domain but do not control the heat content of the domain. A new formulation of temperature advection is introduced to elucidate external heat source and sink that control the spatially averaged temperature. It is expressed as the advection of interfacial temperature relative to the spatially averaged temperature of the domain by inflow normal to the interface. It gives a total advection of temperature that is identical to the spatial integration of local temperature advection, yet the contributions along individual directions depict external processes. The differences between the two formulations are illustrated by analyzing zonal advection of near-surface temperature in the eastern equatorial Pacific during the 1997–98 El Niño and the subsequent La Niña by an ocean general circulation model. The new formulation highlights the advection of warmer water at the western side of the Niño-3 region into (out of) the region to create part of the warming (cooling) tendency during El Niño (La Niña). In contrast, the traditional formulation is dominated by the effect of tropical instability waves within the region that redis-tribute heat internally. The difference between the two formulations suggests a need for caution in discerning mechanisms controlling heat content of a region. Spatial integration of local temperature advection does not explain external processes that control a domain’s heat content. The conclusion applies not only to the advection of oceanic temperature, but also to that of any property in any medium. 1.