Deep Ocean Oxygen Consumption Rates: Ocean Chemistry Clues from a van `t Hoff Based Formulation of the Speed of Sound in Seawater

Ocean water masses are undergoing change from warming climate. Dissolved oxygen is widely used as a water mass signature, and dissolved oxygen concentrations are declining. The rate of oxygen consumption is typically represented as a function of depth, yet while temperature is the dominant control the properties of temperature and depth are unfortunately comingled. We show that it is possible to more clearly separate the combined temperature and depth controls on ocean biogeochemical cycles via the sound speed proxy. For over 50 years scientists have represented the speed of sound in sea water as an ad hoc high order polynomial with up to 42 coefficients linking temperature, pressure, and salinity, or via an equation of state with 104 coefficients. (A "computationally efficient" version of the latter uses just 75 coefficients.) While this has allowed accurate calculation of sound speed profiles, these are formulations with no underlying molecular basis. We show that a simple van 't Hoff formulation with a plot of lnV versus 1/T, where T is the absolute temperature, as a basis leads to a simpler formulation with minimal error with at most only 28 coefficients required. This finding suggests that the dominant control on the speed of sound within the oceanic range appears to have the form of simple reversible equilibria within the water structure system and that V mimics, or may be treated as resulting from, a simple pressure perturbation between apparent equilibria within the water structures. Further, the van 't Hoff slope correctly indicates an endothermic reaction in which the sound wave loses energy into the ocean. Since sound speed profiles are fundamentally separable into their temperature and depth (pressure) dependencies their partial correlation with some chemical profiles may offer a potentially powerful proxy for separating the typically comingled properties of temperature and depth in describing ocean chemical profiles and rates.