A recursive Newton method for interpolating seawater density tables

Abstract

Density is among the most significant aspects of seawater's physical characteristics, which is altered as a result of the elements' makeup, water content, and temperature. In order to contribute to the calculation of saltwater density, we have developed a new mathematical formula, simple and easy to be used, Based on Newton's method for salinity ranging from S = 0 to 40. Then, we developed a computational program with the Fortran language, which was effectively validated using reference values of the most accurate densities presented in the form of a table, more structured reference by a step (degree) Δs = 0.2. The outcomes were made available at temperature T = 20 °C and a pressure p = 5 107 pa. The findings demonstrate a good degree of value agreement of the calculated density compared to reference readings which exist in several previous studies. To take into account the significant seawater density gradient brought on primarily by the salinity rising with depth, a more practical density model is developed. The numerical analysis's findings show that, despite its slightness, the proposed functional model based on depth and latitudinal density variations approaches continuous evolution. The real seawater density distribution was depicted in this study with remarkable precision, with an error rate that was judged to be no greater than 1.52 10−4%.