A Mathematical Model of the Global Ocean Saltwater Density Distribution

Abstract

We formulate a functional model which closely approximates the actual seawater density distribution. The meth- odology of finding a theoretical density model is based on the analysis of the global data of pressure/depth, salinity, and tem- perature from the World Ocean Atlas 2009 (provided by NOAA's National Oceanographic Data Center) and the World Ocean Cir- culation Experiment 2004 (provided by the German Federal Maritime and Hydrographic Agency). The seawater density values are calculated according to the thermodynamic equation of sea- water TEOS-10. The global seawater density model is defined as a function of the ocean depth (to account for density variations due to pressure) and geographical latitude (to account for density varia- tions due to salinity and temperature). A more complex functional density model is formulated to account for a large seawater density gradient within the pycnocline caused mainly by a combination of decreasing water temperature and increasing salinity with depth. The results of numerical analysis reveal that the new functional model based on the depth and latitudinal density variations approximates the actual seawater density distribution with a rela- tive accuracy better than 0.45%. When incorporating the pycnocline density gradient correction, the accuracy further improves to about 0.25% (except for the shelf seas with the pres- ence of the continental hydrological signal and other oceanographic factors). The results also show that the average seawater density (estimated from the experimental data used in this study) is 1038.5 ± 2.4 kg/m 3 .