Integral descriptors of the vertical structure of the ocean

We propose a simple polynomial expression for neutral density and nutrients as a function of potential temperature, pressure and salinity. The expression is applied to the 1988 North Atlantic A16N WOCE meridional section and the polynomial coefficients are calculated using an inverse technique. The resulting polynomials show good skill in reproducing the nutrients and density structure, as verified through an analysis of variance (ANOVA) test. The large-scale changes in the polynomial coefficients occur between equatorial (E), tropical (T), subtropical (ST), and subpolar (SP) waters. The temperature and pressure coefficients experience substantial changes at all transitions (E-T, T-ST, and ST-SP), while the salinity ones only have major variations at the T-ST transition. Mesoscale-like oscillations occur all along the section but are relatively small, except between about 40 and 50°N, in a region of rough bottom topography. The density field is reconstructed using individual and group coefficients, and the contribution of each coefficient is identified. The method is also applied to analyze the neutral density distribution in a nearly identical 2003 section, removing near-surface density values that may be related to different warming/cooling of the surface layer. The results show close resemblances but also some significant variations, which are discussed in terms of interdecadal variability. Hence, we argue that the set of calculated coefficients provides good integral descriptors for the vertical structure of the ocean.