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R. Feistel et al.: Oceanographic application and numerical implementation of TEOS-IO: Part 1 
Ocean Sci., 6, 633-677, 2010 
www.ocean-sci.net/6/633/2010/ 
Additional library versions are available for specibc applica 
tion purposes such as the Gibbs SeaWater (GSW) Library for 
oceanographic models (IOC et al., 2010), consistent with the 
one described in this paper. This SIA library replaces (i.e., 
updates and extends) the code versions published previously 
(Feistel, 2005; Feistel et al., 2005). 
In this paper we provide formulas, derivations and expla 
nations for the quantities implemented in the library and their 
thermodynamic relations to the potential functions. The lat 
ter are basic relations which remain valid independent of any 
details of the fits used to approximate the potentials or the 
numerics used to evaluate the functional relations; they will 
not change when new approximations to the thermodynamic 
potentials are determined in the future. 
The oceanographic applications of the quantities discussed 
here are explained in detail in IOC et al. (2010). Formulas for 
seawater properties at the ocean-atmosphere interface such 
as the vapour pressure and the latent heat in equilibrium with 
humid air consistent with the library functions described here 
are developed in a separate article (Feistel et al., 2010a). Ad 
ditional details on the library structure and the numerical im 
plementation are available from a companion paper (Wright 
et al., 2010a). 
The code is organised in vertical columns representing the 
four constituents: fluid water, ice, seawater and air, and in 
horizontal levels with increasing complexity at higher lev 
els. The code is hierarchically organised; higher level rou 
tines make use of routines from lower levels but code at each 
level neither needs nor has access to procedures from higher 
levels. Level 0 provides fundamental constants, mathemat 
ical methods and formulae for conversions between Abso 
lute Salinity and Practical Salinity given the measurement 
location plus some general relations. Level 1 contains the 
Primary Standards, i.e. the thermodynamic potentials, their 
basic constants and coefficients, and further necessary em 
pirical or theoretical functions. Levels 2-4 contain proper 
ties derived directly or indirectly from level 1 by mathemat 
ical and numerical manipulations without additional empiri 
cal formulas or constants. Level 2 contains explicit relations. 
Levels 3 and 4 require iteration procedures to numerically 
solve implicit equations. Levels 1-3 describe only single 
phase properties, while level 4 procedures calculate phase 
equilibria and properties of composite, multi-phase systems. 
Level 5 is an additional application layer within which input 
and output units may be more convenient for the user than 
the basic SI units that are used rigorously at the lower lev 
els. Level 5 also contains additional empirical coefficients in 
speed-optimized code, derived as “approximate” correlation 
functions representing reduced data sets computed from the 
lower, “exact” levels. 
The following sections explain the thermodynamic rela 
tions and auxiliary equations implemented in the library level 
by level, with the exception of level 0, which provides gen 
eral information required by the library, and level 5, which is 
only numerically different from the lower ones. Within each 
level, the sections consider the four columns or their combi 
nations. In the appendix, the formulas are described which 
are implemented in the library to iteratively solve implicit 
equations. When appropriate, function names defined in the 
library are mentioned in the text of this paper along with the 
related equations; they are emphasized by means of a distinct 
font type. The complete list of modules and functions avail 
able from the library is described in the companion paper, 
Part 2 (Wright et al., 2010a). 
The core levels 1-4 of the SIA library take as input pa 
rameters absolute pressure in Pa, absolute ITS-90 tempera 
ture in K, and Absolute Salinity in kg/kg. Absolute Salin 
ity of Standard Seawater is most accurately estimated by 
Reference Salinity (Millero et al., 2008) which is propor 
tional to Practical Salinity in the valid range of the 1978 
Practical Salinity Scale (PSS-78). For seawater with com 
position anomalies, estimates for the difference between Ab 
solute and Reference Salinity are available for the global 
ocean and the Baltic Sea (McDougall et al., 2009; IOC et 
al., 2010; Feistel et al., 2010b). A routine for conversions 
between Practical Salinity and Absolute Salinity is included 
in the SIA library at level 0 (functions asal_f rom_psal 
and psal_from_asal) using an algorithm adapted from 
the GSW library (McDougall et al., 2009). A function 
that permits the computation of Density Salinity as an es 
timate of Absolute Salinity from measured in situ density, 
e.g., in the laboratory, is also available in the SIA library 
(function sea_sa_si). Further details are available from 
the companion paper, Part 2 (Wright et al., 2010a). De 
tails on the use and the uncertainties of the different salin 
ity scales are described by Wright et al. (2010b). Con 
version routines between different pressure units (function 
cnv.pressure), temperature scales and units (function 
cnv_temperature), as well as between various salinity 
measures (function cnv_salinity) are available at level 5 
of the library for convenience. 
In order to shorten the main article for technical reasons, 
29 tables with groups of thermodynamic properties and their 
equations were moved to the Digital Supplement of this pa 
per. They are referred to here as Table S1 to S29; their equa 
tions are numbered as Sl.l etc. Because of their key role 
in the SIA library, the various potential functions themselves 
are summarised in Table 1 rather than in the supplement. 
The information provided in this paper is a reference for 
mathematical and thermodynamic details of the algorithms 
implemented in the SIA library. It is intended to ease the 
readability of the open source code and its numerous com 
ment lines, and to encourage users to add new required 
properties, correlations or applications to the levels 2-5, 
guided by the examples and equations expained here. For 
high-speed requirements, tailored look-up tables for arbitrary 
property combinations can easily be compiled from the SIA 
code which is rather comprehensive but not speed-optimized. 
While this paper was under review, the authors of the 
dry-air formulation (Lemmon et al., 2000) used in the SIA