This paper and associated software implement the
Thermodynamic Equation Of Seawater – 2010 (TEOS-10) in Excel for an
efficient estimation of Absolute Salinity (

The development of software to facilitate the efficient calculation of the properties of seawater has allowed users to better understand the marine environment, assisting members of the student, research, and industrial communities alike. One such initiative, the Gibbs Sea Water (GSW) toolbox (McDougall and Barker, 2011), implements the Thermodynamic Equation of Seawater – 2010 (TEOS-10) into software that calculates required seawater properties through the utilisation of programming languages (e.g. MATLAB, FORTRAN, C) that require a working understanding and knowledge of computer programming. As such, the toolbox may not be as readily accessible to all practitioners within the field of marine data analysis (e.g. Buzzetto-More et al., 2010; Bosse and Gerosa, 2017). The aim of this paper is to present an implementation of TEOS-10, within Microsoft Excel, a popular and readily available application. This new implementation requires no specialist knowledge to operate; it is therefore hoped that all groups interested in analysing sea water properties may benefit from free and open access to this new tool.

Seawater can be defined as a thermodynamic system with one liquid phase and
two components: (i) pure water and (ii) dissolved salts. At the end of the 19th century, J. Willard Gibbs, established the Gibbs phase rule (Gibbs, 1874–1878), which states
that, for a multiphase system in thermodynamic equilibrium, such as
seawater, the degrees of freedom of the system, i.e. the number of
independent variables needed to define it, equal the number of components
subtracted by the number of phases plus two. For seawater this adds up to three (

As measurement technologies advance and our understanding of the oceanic
environment evolves, standards relating to physical parameters frequently
change in response. The definition of salinity has undergone several
variations during the last century (Millero, 2010) and the temperature
standard changed in 1989 from IPTS-68 to ITS-90 (Preston-Thomas, 1990). The
current TEOS-10 has introduced a
new salinity quantity, Absolute Salinity (

The polynomial nature of EOS-80 allowed the easy implementation of
algorithms for the computation of seawater properties, which led to the
proliferation of stand-alone applications, interactive websites, and Visual
Basic for Applications (VBA) modules. Direct measurement of Absolute
Salinity can be made with the aid of a densimeter (IOC, SCOR and IAPSO,
2010: p. 82), but in GSW it is estimated from interpolation of measured
Absolute Salinity Anomalies stored in a world atlas look-up table. This
difficulty might be a possible explanation for the absence of any previous
application of TEOS-10 in Excel, except for a tool (GSW_Sys_v1.0.xlsm)

Section 2 of this paper introduces the new TEOS-10 Excel workbook, explains its operation, and describes the world ocean look-up tables. Section 3 describes the translation of the original MATLAB code into VBA and discusses the interpolation method used for missing data in the reference look-up table, followed by the conclusion and summary in Sect. 4.

An Excel workbook file that implements a subset of the GSW toolbox accompanies this paper. The file includes sample data that can be easily
replaced by new user data to obtain ocean vertical profiles and

The workbook (Fig. 1) contains four data spreadsheets (three light green
tabs and one yellow), two plotting spreadsheets (blue tabs), six TEOS-10
look-up tables (purple tabs), and an info tab (green). Pressing Alt

The structure of the three light green data tabs is identical, the only
difference being the data sets incorporated in each. The “TEOS-10 Test Data”
spreadsheet includes a testing data set from the GSW toolbox, located in the
NW Pacific at 33

TEOS-10 Excel workbook (v.2.1) light green data tab. Seawater properties in coloured columns are computed on the fly from user data pasted into white cells.

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 for 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 at different locations, typically at the same pressure
level (e.g. surface measurements). Fictional data are included 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 being a
specific case. Whilst for the world ocean the estimation of

TEOS-10 Excel workbook (v.2.1) Surface Data tab. Surface data from different locations (location coordinates for each line). Four samples are from the Baltic Sea and one from the NW Pacific; the last sample (without long/lat coordinates) is from an estuary.

The Vertical Profiles tab includes five plots that use the TS-55 and CTD-020 data sets and one plot with the TEOS-10 Test Data data set. Two of these plots are reproduced in Figs. 3 and 4. Changing the data will update the plots accordingly, and the user can add extra profiles by right-clicking the plot area, clicking “Select Data”, and then editing the data sources.

Sound speed vertical profile of two data sets included in TEOS-10 Excel. This plot is one of six included in the Vertical Profiles tab.

This is a template for plotting Absolute Salinity–Conservative
Temperature diagrams. Since the introduction of TEOS-10,

Figure 6 shows the [ndepth_ref] look-up table which contains
the number of pressure levels in each of the seawater samples that
constitute the Atlas. On close inspection, it becomes apparent that the
empty cells represent land, and the “white” shapes approximate to a map of
the world land masses. The top of the spreadsheet is the South Pole, the bottom
is the North Pole, and the Greenwich Meridian (0

Comparison between in situ and Conservative Temperature of the TEOS-10 Test Data included in TEOS-10 Excel. This plot is one of six included in the Vertical Profiles tab.

This tab lists all released versions of TEOS-10 Excel, providing detailed information on the updates included in each version.

List of all VBA modules and formulas included in TEOS-10 Excel (v.2.1). Direct translations from GSW are marked with “YES”, and original or modified functions are marked with “NO”.

Absolute Salinity (

The [ndepth_ref] look-up table. The table has 45 rows
(latitude) by 91 columns (longitude). South is at the top (first row is
86

Table 1 lists all functions (VBA modules) and formulas included in TEOS-10
Excel (v.2.1). Most modules are a direct translation into VBA of the GSW
MATLAB counterpart (McDougall and Barker, 2011), and the original credit and
references were kept in the code comments; however, due to the different way
matrices are handled in MATLAB versus VBA, some functions needed to be
redesigned, namely how accessing the Atlas look-up tables is managed.
Returned values from TEOS-10 Excel are the same, for every parameter, as the
ones obtained with the GSW toolbox up to 15 decimal places, i.e.
difference

A VBA module to calculate Practical Salinity from the conductivity ratio
(

Reference Salinity (

The function {

The function {

3D interpolation cube. Points are defined by their grid position
(lon*, lat*,

The standard basic 3D interpolation model assumes that the cube dimensions
are

There are pressure levels in the Atlas reference casts where data are missing. Figure 8 illustrates this situation.

The [deltaSA_ref] table: reference data missing for pressure levels 33 and 34 of columns 8, 9, 10, and 11.

The GSW toolbox fills these gaps by averaging the neighbouring four points
in the grid at the same pressure level. As the ocean is horizontally
stratified, this is logical, but neighbour points themselves might also
lack data at the same level, which may compromise the result. A

The

The

The Atlas Absolute Salinity Anomaly Ratio (

The Absolute Salinity Anomaly (

Absolute Salinity (

If the location is in the Baltic Sea, the world atlas salinity anomalies do
not apply (McDougall, 2010) and Absolute Salinity is computed algebraically
from Practical Salinity with the function {

Limits for the Baltic were taken from Fig. 2 of Feistel et al. (2010).
The function {

The temperature standard used in TEOS-10 as argument to all functions is
ITS-90 (Preston-Thomas, 1990). If the ITS-90 radio button is selected
(column C of the spreadsheet), the temperature input values are copied; if
IPTS-68 is selected instead, the IPTS-68 temperature will be converted to
ITS-90 using Eq. (20).

Potential temperature (

Conservative Temperature (

Potential density (

In situ density (

Sound speed (

The Atlas Absolute Salinity Anomaly (column F of the data spreadsheets) is
not used for any calculation, as Absolute Salinity Anomaly (

To our knowledge, TEOS-10 Excel is the first implementation of the Thermodynamic Equation Of Seawater – 2010 outside the official GSW toolboxes. It does not aim to reproduce the full-featured GSW environment as it implements only a small subset of the TEOS-10 functions. Opening the possibility of estimating a relevant set of seawater parameters within a well-known and friendly environment (Excel), however, will hopefully democratise the compliance with current oceanographic standards among a large community of researchers and students who are not at ease with the use of high-level programming languages. As discussed in the paper, some issues were detected with the GSW interpolation when there are missing data in the Atlas reference tables. In these cases, TEOS-10 Excel adopts an alternative approach to the interpolation method, which has produced better results (Sect. 3.3.2). Nonetheless, this is perhaps a situation that deserves further research.

TEOS-10 Excel is available for download at

CGM developed the code, tested the data, and prepared the original draft. JC critically reviewed and edited the initial and final versions of the paper.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This paper was edited by Trevor McDougall and reviewed by Paul Barker and Trevor McDougall.