travel time (75-term equation)



travel_time = travel_time(SA,CT,p,lat)


Calculates the round-trip acoustic travel time for a path from the
bottle concerned up the vertical water column to the sea surface and
back to the bottle.
This function evaluates the pressure integral of specific volume divided
by the product of sound speed and the gravitational acceleration, grav,
(which is a function of latitude and pressure).
In order to avoid nonlinear equation of state effects due to the
nonlinear dependence of sound speed and specific volume on their input
parameters, the vertical data is interpolated so that the data is no
more than max_dp_i apart (this is a presure interval). 
This function evaluates the pressure integral of specific volume using 
SA and CT interpolated with respect to the intergral of bouyancy 
frequency N2 using the method of Barker et al. (2017).  This "curve 
fitting" method uses a Piecewise Cubic Hermite Interpolating Polynomial 
to produce a smooth curve with minimal artificial watermasses  between
the observed data points.
The sound speed and specific volume calculations are based on the
75-term equations for specific volume (Roquet et al., 2015), as opposed
to being based on the Gibbs equations for specific volume and sound 
Note that this 75-term equation has been fitted in a restricted range of 
parameter space, and is most accurate inside the "oceanographic funnel" 
described in McDougall et al. (2003).  The GSW library function 
"gsw_infunnel(SA,CT,p)" is avaialble to be used if one wants to test if 
some of one's data lies outside this "funnel".  


SA   =  Absolute Salinity                                       [ g/kg ]
CT   =  Conservative Temperature                               [ deg C ]
p    =  sea pressure                                            [ dbar ]
        ( i.e. absolute pressure - 10.1325 dbar )
lat  =  latitude in decimal degress north                [ -90 ... +90 ]
SA & CT need to have the same dimensions.
p and lat may have dimensions Mx1 or 1xN or MxN, where SA & CT 
are MxN.


travel_time = travel_time                             [ s ]


SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
CT = [28.8099; 28.4392; 22.7862; 10.2262;  6.8272;  4.3236;]
p =  [     10;      50;     125;     250;     600;    1000;]
lat = 4;
travel_time = gsw_travel_time(SA,CT,p,lat)
travel_time =


Paul Barker, Trevor McDougall and Randy Watts  [ ]


3.06.12 (15th June, 2020)


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.  Available from the TEOS-10 web site.
McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: 
 Accurate and computationally efficient algorithms for potential 
 temperature and density of seawater.  J. Atmosph. Ocean. Tech., 20,
 pp. 730-741.
Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate
 polynomial expressions for the density and specifc volume of seawater
 using the TEOS-10 standard. Ocean Modelling.
The software is available from