Potential Enthalpy: A Conservative Oceanic Variable for Evaluating Heat Content and Heat Fluxes

Abstract

Potential temperature is used in oceanography as though it is a conservative variable like salinity; however, turbulent mixing processes conserve enthalpy and usually destroy potential temperature. This negative production of potential temperature is similar in magnitude to the well-known production of entropy that always occurs during mixing processes. Here it is shown that potential enthalpy?the enthalpy that a water parcel would have if raised adiabatically and without exchange of salt to the sea surface?is more conservative than potential temperature by two orders of magnitude. Furthermore, it is shown that a flux of potential enthalpy can be called ?the heat flux? even though potential enthalpy is undefined up to a linear function of salinity. The exchange of heat across the sea surface is identically the flux of potential enthalpy. This same flux is not proportional to the flux of potential temperature because of variations in heat capacity of up to 5%. The geothermal heat flux across the ocean floor is also approximately the flux of potential enthalpy with an error of no more that 0.15%. These results prove that potential enthalpy is the quantity whose advection and diffusion is equivalent to advection and diffusion of ?heat? in the ocean. That is, it is proven that to very high accuracy, the first law of thermodynamics in the ocean is the conservation equation of potential enthalpy. It is shown that potential enthalpy is to be preferred over the Bernoulli function. A new temperature variable called ?conservative temperature? is advanced that is simply proportional to potential enthalpy. It is shown that present ocean models contain typical errors of 0.1°C and maximum errors of 1.4°C in their temperature because of the neglect of the nonconservative production of potential temperature. The meridional flux of heat through oceanic sections found using this conservative approach is different by up to 0.4% from that calculated by the approach used in present ocean models in which the nonconservative nature of potential temperature is ignored and the specific heat at the sea surface is assumed to be constant. An alternative approach that has been recommended and is often used with observed section data, namely, calculating the meridional heat flux using the specific heat (at zero pressure) and potential temperature, rests on an incorrect theoretical foundation, and this estimate of heat flux is actually less accurate than simply using the flux of potential temperature with a constant heat capacity.