Appendix A Derivation of Physical Quantities

A.1 Depth Using Cosine of Wire Angle

Depths in this database, which have been ascertained using cosine of wire angle (CWA), are determined by multiplying the length of cable payed out by the cosine of the wire angle, and adding 0.5. If the wire angle is less than 5o the depth can be taken as the length of wire payed out. Where therometric measurements were made on the same cast the depth can be determined more accurately by finding the ratio of the depth found by reversing thermometers to the depth found by cosine of wire angle, and multiplying by the latter depth. This method has not been used to find depth data for the database.

A.2 Depth and Temperature Using Reversing Thermometers

A.2.1 Temperature

For both protected and unprotected thermometers corrections must be applied to the reading of the main thermometer to allow for index error, which results from any incorrect etchings on the scale and any variations in capillary width.

Corrections are then applied for to allow for thermal expansion of the thermometers after they have been reversed. The corrections for protected thermometers are given by:

and for unprotected thermometers:

Vo = volume of mercury (in below 0o C) when thermometer is reversed

K = reciprocal of coefficient of thermal expansion of the thermometer glass

T" = main thermometer reading after index correction has been applied

t = auxiliary thermometer reading after index correction has been applied

Tw = corrected protected thermometer reading; i.e. Water temperature at depth of reversal (Stanton and Singleton 1980).

A.2.2 Depth

The protected thermometer reads the actual temperature of the water whereas the hydrostatic pressure of the water affects the reading of the unprotected thermometer. Once the corrected protected thermometer reading Tp and the unprotected thermometer reading Tu are known, the depth of reversal (D) can be calculated from:

where:

= mean density of water column above depth of reversal.

Q = pressure coefficient of individual unprotected thermometer, i.e. The rate of increase in apparent temperature with pressure.

However m varies with depth and location. Using a constant value for m r at 1000 m of 1.0294 kg.m-3 a more accurate value of D can be found using the formula:

D=D¹+ΔD

where:

and ΔD = correction due to change in with depth from its value at 1000 m.

According to Stanton and Singleton (1980), ΔD can be approximated by the quadratic expression:

A.3 Depth and Temperature Data from Bathythermographs

A mechanical bathythermograph has pressure and temperature sensors that activate a pen that makes a trace on a gold or smoked glass slide. Depth and pressure can be read off the slide with the aid of a scale produced for the specific instrument being used.

The temperatures from an expendable bathythermograph are obtained by reading from a chart or from digital data depending on the system used. Depth is obtained by taking an assumed rate of descent.

A.4 Physical Quantities Derived from the CTD Probe

A.4.1 Initial Processing of Data

Pressure, temperature and conductivity ratio data are sampled by the CTD control unit every 40 milliseconds. Data in a slice of about 1 dbar are averaged. Any data value that deviates from the preceding and succeeding data values by a given amount is not included in the average. The deviations allowed for each quantity are:

pressure ± 0.2 dbar
temperature ± 0.005 oC
conductivity ratio ± 0.004

The formulae below can also be used for calculating salinity and t s for bottle samples whose conductivity has been measured by a laboratory salinometer where the temperature is usually 15 ^oC.

A.4.2 Depth

Depth (D) is calculated from pressure (P) and latitude expressed in radians (radlat) using Saunders"

Method (Saunders 1981)

where:

c1=(5.92+5.25 (sin²(radlat))1000
c2=2.21E-6
dh=dynamic height anomaly (at present set to 0).

(From source code written by Michael Moore, NZOI, 20 August 1986.) This method differs from the standard UNESCO formula by less than 1 m over 7000 m.

A.4.3 Calculation of the Conductivity Ratio

Historically, CTD probes have reported conductivity as a ratio to a standard seawater sample and this is reflected in the database schema. Later CTD probes, such as the Sea Bird S-37, report the conductivity in units of either mmho/cm or (S/m). In order to load these later readings into the database, the conductivity readings must be converted to the conductivity ratio. The value for conductivity for standard seawater at 35 ppt, 15 degrees C, and 0 pressure [C(35,15,0)] was not agreed upon in the IEEE reports--Culkin & Smith used 42.914 mmho/cm (p 23), while Poisson used 42.933 mmho/cm (p 47). It really does not matter which value is used, provided that the same value is used during data reduction that was used to compute instrument calibration coefficients.

The CTD database ratios are computed using C(35,15,0) = 4.2914 S/m. If you are working in conductivity units of Siemens/meter (S/m), multiply your conductivity values by 10 before using the PSS 1978 equations.

Salinity (S) is calculated from pressure (P), temperature (T) and conductivity (R) using the following method.

Let C=conductivity and

Now:

where:

And:

where:

so given R, T and P, R_t can now be calculated using:

Salinity can then be calculated using the formula:

The coefficients A, B, C and D are polynomials in temperature (T) and are listed in Table 1:

Table 2: Temperature Coefficient s for the calculation of t s