TEOS-10 Excel: Implementation of the Thermodynamic Equation Of Seawater – 2010 in Excel

Excel implementation of the Thermodynamic Equation Of Seawater - 2010 (TEOS-10) (www.teos-10.org). The spreadsheet templates and associated VBA functions compute Absolute Salinity (S_A), Conservative Temperature (Θ) and derived thermodynamic properties of seawater – conservative density (σ_Θ), in situ density (ρ_{SA, Θ, p}) and sound speed (c). Vertical profile template plots for these parameters are included, as well as a S_A - Θ diagram template, which includes plotting of the density field (computation of user selected σ_Θ lines is included). Estimation of Absolute Salinity relies on the interpolation of data from casts of seawater from the world ocean (IOC, SCOR and IAPSO, 2010), and this Excel workbook includes a subset of the TEOS-10 look-up tables necessary for this estimation, namely the Absolute Salinity Anomaly (deltaSA_ref) and the Absolute Salinity Anomaly Ratio (SAAR_ref) look-up tables.

The user simply needs to paste new data into the spreadsheet to automatically compute the oceanographic parameters referred above.

This tool may prove to be extremely useful among all who are not comfortable of using the full-featured TEOS-10 programming language environments (e.g., MATLAB, FORTRAN), but rather need a simpler way of computing fundamental properties of seawater (density, sound speed), while adhering to current standards.

Returned values are exactly the same, up to 15 decimal places (i.e., difference = 0.000000000000000), as the ones obtained with the MATLAB version of the GSW (Gibbs Sea Water) toolbox (McDougall and Barker, 2011).

During quality control, a few issues were detected with the interpolated values returned by the GSW toolbox when there is missing data in the reference anomaly look-up table. It was though decided, for these situations, to move from a level pressure horizontal interpolation (as performed by the GSW toolbox) to a vertical interpolation, method that has proven to return more robust results.

Data sets

The three green data tab’s structure is identical, the only thing different being the data sets included in each. The ‘TEOS-10 Test Data’ spreadsheet includes a testing data set from the GSW Toolbox, located in the NW Pacific at 162.5º E 33º N. ‘TS-55’ data is a 1º longitude x 1º latitude historical average vertical profile in the NE Atlantic, off the Iberian Peninsula, centred at 10.5º W 40.5º N and ‘CTD-020’ is a CTD cast in the same grid bin, at 10º 01º W 40º 05’ N (Martins, 1998).  Seawater properties in coloured columns are computed on the fly from user data input in white cells. The data included (in white cells) can be replaced by user data. Spreadsheet lines can be added (or deleted) and, if additional lines are required, it would only be necessary to copy down the coloured cells for the formulae to propagate over the extra lines, without any other adjustments being needed. The only caution users should have, is to not move the data (white cells) to other location, as the spreadsheet formulae will ‘follow’ this operation disrupting the original cell referencing. Users can also opt to add new data spreadsheets to the Excel workbook, where they can then simply paste the whole content of one of the original data tabs for the new spreadsheet to become fully functional.

The yellow ‘Surface data’ tab content differs from the other data spreadsheets on what refers to the input of the location coordinates. In this spreadsheet, longitude and latitude are input in the first two columns, allowing in this way the assignment of distinct coordinates for each line. This is useful if the data set is not a vertical cast at a given location but a set of measurements on different locations, typical at the same pressure level (e.g., surface measurements). The data included are ‘fictitious’ and used here to demonstrate the use of the template. The location of the first four data lines is in the Baltic sea. Conditions in the Baltic are different from the open ocean (McDougall, 2010) and TEOS-10 treats this adjacent sea as a special case where Absolute Salinity is computed algebraically from Practical Salinity.

Version 2.1 upgrades

The salinity input radio buttons now read Practical Salinity, Conductivity (mS/cm), and Salinometer Ratio (Rt).

The conductivity ratio function added in v.2.0 calculates Practical Salinity from the conductivity ratio (R), of a sample at temperature (t), and pressure (p) relative to SSW at t=15 °C and p=0, which is not the conductivity ratio measured by a laboratory salinometer, where both the sample and the reference SSW are at the same temperature. The input for the salinometer ratio input for computing Practical Salinity has been now added [function SP_salinometer(Rt, t)], where 't' is the temperature of the salinometer thermostable bath.

Version 2.0 upgrades

Support for calculation of Practical Salinity from the Conductivity Ratio was added. This led to a substantial upgrade of the input template with the addition of a group of radio buttons for selecting the input salinity (Practical Salinity, Conductivity or Conductivity Ratio) and another group of radio buttons for temperature selection between ITS-90 or IPTS-68.

Version 1.2 upgrades

Leaving the Longitude or Latitude cells empty, sets up Absolute Salinity Anomaly to zero. This is useful for inland and coastal waters where it could be better to ignore anomaly calculations.

For inland locations, Absolute Salinity Anomaly is zero and SA is set equal to SR. Thermodynamic properties are calculated accordingly, considering in this way valid inland measures (e.g., rivers, lakes); previous versions displayed 'NOT in OCEAN' for Absolute Salinity Anomaly and no further calculations were performed.

Function Hill_ratio_at_SP2(t) was added (translated from GSW MATLAB). This function corrects the value of SP for SP < 2 based on the Hill et al. (1986) algorithm. This algorithm is adjusted so that it is exactly equal to the PSS-78 algorithm at SP = 2.

References

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater – 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides, No. 56, UNESCO (English), 196 pp. www.teos-10.org/pubs/TEOS-10_Manual.pdf

Martins, C.G., 1998. “OCEANUS: um Atlas Digital Oceanográfico aplicado ao estudo da Estrutura, Variabilidade e Climatologia do Atlântico ao largo de Portugal Continental”. PhD Thesis. Universidade de Lisboa, 348 pg. + 2 floppy disks.

McDougall, T.J. and Barker, P.M., 2011: Getting started with TEOS-10 and the Gibbs Seawater (GSW) Oceanographic Toolbox, 28pp., SCOR/IAPSO WG127, ISBN 978-0-646-55621-5. Available at www.TEOS-10.org

McDougall, T.J., Jackett, D.R., Millero, F.J., Pawlowicz, R. and Barker, P.M., 2012. A global algorithm for estimating Absolute Salinity. Ocean Science, 8(6), pp.1123-1134. doi.org/10.5194/os-8-1123-2012