Ocean chemistry and the speed of sound in seawater

• We show that ocean sound speed profiles can be accurately and efficiently represented by a form of the classic van ‘t Hoff equation.

For over 50 years scientists have represented the speed of sound in sea water (V) 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. 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. The van 't Hoff slope is indicative of 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 appears to offer a potentially powerful proxy for separating the typically comingled properties of temperature and depth in describing ocean chemical profiles and rates.