Comparing standard and Van't Hoff-based polynomial bases for the pure water sound speed equation

Two sets of basis functions have been used to represent the sound speed equation. One was the empirical polynomial expansion in temperature, and another was a polynomial expansion motivated by physical chemistry (the Van't Hoff equation), which expands the logarithm of the sound speed in polynomial terms of the inverse absolute temperature. We compare the performance of these two basis sets on the dataset published by Del Grosso and Mader [J. Acoust. Soc. Am. 52(5B), 1442-1446 (1972)] for pure water at temperatures ranging from 0.001 °C to 95.1264 °C and at atmospheric pressure. Both of these expansions fit the data within a standard deviation of ∼ 0.0029 m/s. The Akaike Information Criteria (AIC) ranked the Van't Hoff-based polynomials as better than standard polynomials at third and fourth orders, but slightly worse at fifth order. The fitting process employed contemporary Bayesian approaches that account for representational and observation uncertainties propagated throughout the fitting process to estimate parameter uncertainty. The posterior parameter uncertainty covariance matrix is provided so that the equation can be updated when new sound speed observations are available. The revised fit differs by less than 0.0045 m/s from the previous equation, but it is slightly smoother.