Inverse modeling of salinity–temperature–depth relationships: Application to the upper eastern North Atlantic subtropical gyre

Abstract

We test the skill of a polynomial fit to reproduce the upper ocean (down to 750 m) salinity in the eastern North Atlantic (from the Canary Islands to the Iberian Peninsula, approximately 12° × 12°) as a function of temperature and depth. A historical database, constructed by merging several regional datasets, is used. An ANOVA test is performed to determine the optimum degree of temperature and depth in the polynomial fit. The polynomial coefficients are estimated by solving an inverse model where we control the size of both coefficients and residuals. We divide the basin in 21 zones (2° × 2°) and four regions (each comprising several zones), and run the inversion for the whole basin, as well as for each individual region and zone. This allows us to assess the sensitivity of the model to changes in the spatial domain, and to investigate the spatial variability of the polynomial coefficients. Regions are defined by applying a cluster analysis to objectively group those zones with similar oceanographic properties. The seasonality of the coefficients is addressed with data from the whole basin and individual regions. We find that, for either the whole basin or individual regions, seasonal coefficients predict salinity more accurately than annual ones, but annual coefficients per zone yet provide the best results. The depth-averaged error estimating salinity is less than 0.086 psu.

Introduction

Temperature (T) and salinity (S) in the ocean are linked. This fact, which helps to define water masses, drove investigators to develop empirical relationships between both variables to take advantage of bathythermograph measurements, in order to finally infer the dynamics of the ocean (Stommel, 1947). This idea has largely been exploited in the past decades, improving the methodologies and applying it to different basins in the global ocean (Flierl, 1978, Emery and Dewar, 1982, Siedler and Stramma, 1983, Kessler and Taft, 1987, Hansen and Thacker, 1999, Marrero-Díaz et al., 2001, Marrero-Díaz et al., 2006).

Nowadays the necessity of developing robust methodologies is even more prominent, as the applicability of T/S empirical relationships has increased with new technologies, as it may be used to detect drifts in salinity sensors of profiling floats, as pointed out by Thacker (2007), or in operational oceanographic projects for developing rescue services protocols (Machín et al., 2008).

Our main goal here is to develop and test an inverse method between several thermodynamic variables, specifically a relationship for salinity (S) as a function of temperature (T) and depth (d), for the upper eastern North Atlantic Ocean (east of 19°W from 26°N to 38°N). Inverse methods have turned into very useful geophysical data-analysis techniques, that permit to estimate unknown variables in models by assimilating real observations. The main characteristics of this inverse methodology are applicability (just a few coefficients are necessary), robustness (the mean prediction error, or residual, is forced to remain below certain threshold value), and spatial and temporal coherence (the coefficients are also forced to remain within certain limits, so that they change smoothly between adjacent zones and seasons). The novel characteristic of the method, as compared with other work, is this coherence which relies on the fact that the coefficients have actual physical meaning (Machín and Pelegrí, 2009b).

The manuscript is organized as follows: Section 2 presents the historical dataset used while Section 3 describes the details of the inverse model approach. Results are shown in Section 4 and their validation in Section 5, to sum up in Section 6 with the main conclusions.