Approximating the energy transport across oceanic sections

A straightforward thermodynamic integration shows that the transport of the product of density in situ, potential temperature, and specific heat at constant pressure (the last two evaluated at sea level atmospheric pressure) across oceanic sections at which both the mass and the salt transports are zero approximates the internal energy transport to an accuracy of a few percent and the total energy transport to order 0.1%. It is misleading to call this water‐property transport “heat flux.”