Two empirical seawater density models estimated based on the

analysis of WOA09 and WOCE-04 oceanographic data

Methodology

• The thermodynamic equation of seawater TEOS‐10 (Millero et al. 2008) was used to calculate the seawater density values from the experimental data of pressure, salinity, and temperature. The dependence of the seawater density on pressure p, salinity S, and temperature t is demonstrated in Figs. 1 and 2.

• The formulation of the empirical model for approximating the actual seawater density distribution by the global seawater density model

(1)

• The formulation of the empirical model for approximating the actual seawater density distribution by the pycnocline corrected global seawater density model (to account for density variations within the pycnocline due to temperature and salinity)

(2)

• The accuracy analysis of the global seawater density models in terms of the average and maximum errors computed from the experimental and theoretical density values ex and theor using the following expressions

(3)

• The estimation of the mean ocean saltwater density from the experimental density samples (collected at different depths D) using the weighted mean

(4)

Reference

Millero FJ, Feistel R, Wright DG, McDougall TJ (2008) Deep Sea Research Part I, Oceanographic Research Papers 55(1): 50-72

Motivation

In context of an inverse modelling of the Moho density interface from gravimetric data, the bathymetric stripping corrections are computed and applied to gravity field quantities adopting a constant value of the ocean density contrast. The ocean density contrast is defined as the difference between the mean density values of the Earth’s crust and seawater. This approximation yields relative errors up to 2% in computed values of the bathymetric stripping corrections.

Objective

A formulation of the functional model which closely approximates the global variations within the actual seawater density distribution. This density model is mathematically defined as a function of the ocean depth D (to account for density variations due to pressure) and the geographical latitude (to account for density variations due to salinity and temperature).

Input data

The global data of pressure/depth, salinity, and temperature from the World Ocean Atlas 2009 (provided by NOAA's National Oceanographic Data Center) and the World Ocean Circulation Experiment 2004 (provided by the German Federal Maritime and Hydrographic Agency).

Results

• The seawater densities of experimental data vary between 1020 and 1055 kg/m3 within the depth range of 6 km, and the mean value is 1038.5±2.4 kg/m3.

• The empirical model defined by means of the depth and latitudinal seawater density variations (eqn. 1) approximates the experimental data with a relative accuracy better than 0.45%. When incorporating the pycnocline density gradient correction to the global seawater density model (eqn. 2), the relative accuracy further improves to about 0.25% except for the shelf seas.

• The experimental density values at the ocean surface vary from 1022.0 to 1027.3 kg/m3 with the mean of 1024.83.0 kg/m3. This value is similar with the corresponding value of 1025.3 kg/m3 computed according to eqn. (4).

Fig. 4 The fit of latitude-averaged seawater density data (at depths down to 2.5 km) by the global seawater density distribution model (dashed line) given in eqn. (1), and by the pycnocline corrected global seawater density distribution model (solid line) introduced in eqn. (2).

Fig. 8 The maximum errors of fitting the experimental data by: (a) the global seawater density distribution model, and (b) the pycnocline corrected global seawater density distribution model. The limit of exactness of theoretical models (solid line).

D1000

a b

Fig. 7 The average errors of fitting the experimental data by: (a) the global seawater density distribution model, and (b) the pycnocline corrected global seawater density distribution model. The limit of exactness of theoretical models (solid line).

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Numerical analysis

• The latitudinal dependence of the global seawater density coefficients , , (in eqn. 1) and the pycnocline correction coefficient (in eqn. 2) is shown in Fig. 3.

• The comparison of the experimental and theoretical density values and the accuracy analysis are shown in Figs. 4-8.

Robert Tenzer, Gladkikh VladislavNational School of Surveying, Division of Sciences, University of Otago, Dunedin, New

Zealand

Pavel Novák Department of Mathematics, University of West Bohemia, Plzeň, Czech Republic

a b

Fig. 6 The fit of the surface seawater density data by the pycnocline corrected (solid line) and uncorrected (dashed line) global surface seawater density distribution models in eqns.(1) and (2), respectively.

Fig. 3 The latitudinal dependence of the parameters , , , and in eqns. (1) and (2).

Fig. 5 The fit of latitude-averaged seawater density data at depths down to 400 m by the global seawater density distribution model (dashed line), and by the pycnocline corrected global seawater density distribution model (solid line). The 5th and 95th percentiles and the depth-averaged values of the seawater density samples are shown by the dot-lines.

Fig. 1 The dependence of the seawater density on temperature (-2C t 40C) and salinity (0 S 42).

Fig. 2 The dependence of the seawater density on pressure (0 bars p 1000 bars) for t=10C, and S= 35.

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