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corresponding closely but not exactly to the older expression ppt , parts per thou-
sand), and pressure. Common oceanographic usage is to express pressure in terms
ofthedeparturefromatmosphericpressureatthesurface,withunitsofbars
10 5 Pa
)
ordbar(whichcorrespondsreasonablycloselywithdepthinm).Thepracticalsalin-
ity scale relatesthe measuredconductivityof seawater to an internationalstandard,
and thus provides a unique salinity for given conductivity, temperature, and pres-
sure, all of which can be measured to high accuracy with modern oceanographic
instrumentation.TheUNESCOformulasfordensityas a functionofthe threestate
variablesaregiven,e.g.,byGill(1982,Appendix3)andareusedinthiswork.
At low temperatures, the impact of changes in salinity on density is amplified
relativeto temperaturechangesbecausethethermalexpansionfactor,
(
∂ρ
1
ρ
β T =
T ,
∂ρ
S )
1
ρ
is small. The haline contraction factor
is relatively insensitive to tem-
perature, as illustrated in Fig. 2.9a, where variation of
( β S =
β S with respect to
their values at the freezing point are shown as functions of temperature. Over the
rangeshown,
β T and
β S remainswithin2%ofitsfreezing
value.Atconstantpressure,the changeindensitymaybeexpressedas
β T increasesbyover400%while
δρ
ρ = β S δ
β
S
δ
T
T
Fig. 2.9 a Ratio of expansion and contraction factors to their values for water at freezing temper-
ature
86 C
(
1
.
)
as a function of water temperature. At freezing the ratio
β
/ β
T is about 33. At
S
4 C, it is about 8. b As in a, except ratios relative to the value at surface pressure
T
as
a function of pressure. At 400m, the thermal expansion factor for water at freezing is about 1.5
timesas large as at the surface. For water at T = 4 C, it is only about 1.1times as large
=
(
p
=
0
)
 
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