Geoscience Reference
In-Depth Information
where T is temperature and p is pressure.
2
Salinity is usually ignored in the case of fresh-
water bodies, but even there it may be signi
cant under a complete ice cover when tur-
bulence is absent. Results from marine research are mainly used to obtain the properties of
water in brackish and saline lakes. Seawater is a chemically uniform solution, where only
the total concentration of dissolved salts varies, but lake waters are lake-speci
c, and
therefore each lake would need an own equation of state. However, the seawater case is
usually taken as the approximation. Standard seawater formulae are valid for the salinity
range from 0 to 40
‰
, and therefore another approach needs to be employed for hypersaline
lakes. The in
cant only in very deep lakes.
The equation of state of seawater is an empirical function with about 40 parameters
(UNESCO 1981, see Appendix 1). It can be formulated as:
fl
uence of pressure on density is signi
q
ð
T
;
0
;
0
ÞþDð
T
;
S
;
0
Þ
1
p
=
K
ð
T
;
S
;
p
Þ
qð
T
;
S
;
p
Þ
¼
ð
:
Þ
2
4
where
(T, S, 0) is salinity correction at zero
gauge pressure, and the secant bulk modulus K = K(T, S, p) gives the pressure effect.
The pressure distribution in a lake can be obtained from the hydrostatic law
ˁ
(T, 0, 0) is the density of pure water and
ʔ
dp
dz
¼
q
g
ð
2
:
5
Þ
where z is the vertical co-ordinate positive up, and g = 9.81 m s
−
2
is the acceleration due
to gravity. The surface (z =
ʶ
) boundary condition for the gauge pressure is p(
ʶ
) = 0; note
that
ʶ
-
z is the depth below the lake surface, and if the density is constant, we have
p =
z). In fresh water, p(10 m) = 0.98 bar, i.e. a 10-m water column corresponds
approximately to the pressure of one standard atmosphere
ˁ
g
·
(
ʶ
-
10
4
bar,
the density increase due to pressure is about 0.5 % per 10 kbar or about 1 km depth. The
pressure effect can be ignored in lakes less than 100 m deep (p < 10 bar).
In deep lakes also the adiabatic temperature change is an important factor in the vertical
strati
≈
≈
×
1 bar. Since K
2
cation. When a water parcel rises up, its temperature decreases due to decreasing
pressure, and in sinking down adiabatic warming takes place in a symmetric manner. The
adiabatic change of temperature can be expressed as
ʓ ≡
-
dT/dz
∣
ad
=
ʱ
gT/c
p
, where
ʱ
is the
coef
cient of thermal expansion, and c
p
is the speci
c heat at constant pressure (see Curry
Ckm
−
1
. The temperature corresponding to
the surface temperature after adiabatic cooling is called the potential temperature.Ina
neutrally strati
and Webster 1999); in fresh water,
ʓ
*
0.12
°
ed deep fresh water lake, the potential temperature is constant, and therefore
the in situ temperature increases by the adiabatic lapse rate with depth.
2
Pressure is taken as the
, which is the pressure above the sea level atmospheric
pressure. Usually pressure is given in bars; the SI unit is Pascal and 1 bar = 100 kPa. The pressure of
one standard atmosphere is 1013.25 mbars.
'
gauge pressure
'
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