in these fields include weak equatorial trade winds
(Milliff et al., 1999), which we ignore, and too
much low level moisture (relative humidity always
above 80%), which is corrected by reducing q air
by a factor f q :0.94. We then compute 6-hourly
values of:
E: air C E q sat ͗SST͘ m, y 9f q q air
Q lat :LE
Q sen : air C air C H U air ͗SST͘ m, y 9T air
(5.1.13)
Q lw : T
4
air[ 0.3990.05ea
1/2
air ] F ͗C͘m, y
;4T
3
air ͗SST͘ m, y 9T air
Here is the Stefan–Boltzman constant and an
emissivity :1 is used to account for some reflection of downwelling long-wave radiation; e air is
the vapour pressure (a function of the corrected
humidity, f q q air ) and q sat gives the saturation
humidity above sea water as a function of SST.
This Q lw formula (Berliand and Berliand, 1952)
with latitudinally varying cloud correction factor,
F(͗C͘ m, y ) (Bunker, 1976a), has been evaluated by
Fung et al. (1984).
The bulk transfer coefficients for evaporation,
C E , and sensible heat, C H , are found by adjusting
specified neutral, 10-m values for the heights and
stability of the atmospheric state data. These neutral, 10-m values are given by:
1000C D :2.70(m s
91 )/U N10
;0.142;0.0764(m
91
s)U N10
1000C E :32.7C
1/2
D
(5.1.14)
1000C H :
Ά
18.0C
1/2
D , stable
34.6C
1/2
D , unstable
These are plotted as a function of neutral 10-m
wind speed, U N10 , in Fig. 5.1.8, so they can be
compared to the many variations shown and discussed by WGASF (2000). The C D formulation is
within 10% of at least one of the five examples
shown in WGASF (2000) for all winds between
3 and 25 m s
91
. It is a fit to a compilation of
observations from 1 m s
91 to more than 25 m s
91
,
and its infinite value at zero wind is consistent
with the theoretical behaviour of wind over a
smooth plate. The dependence of C E and C H on
the square root of C D is also theoretical, while the
stability dependence of C H is observed (WGASF,
2000). The complete set of transfer coefficients
(5.1.14) has been used to produce flux climatologies that are consistent with alternatives (Doney
et al., 1998b).
Note that because ISCCP provides both ͗C͘ m,y
used in the Q lw formula (5.1.13) and ͗I͘ m,y , there
can be considerable cancellation of error; a satellite retrieval that gives too much cloud underestimates ͗I͘ m,y but makes Q lw less negative, often
by about the same amount. This benefit would not
be expected if solar radiation and cloud were
derived from independent data sources. Although
the NCEP/NCAR re-analysis covers the years
1958 to the present, we restrict the computation of monthly means ͗H in ͘ m, y , ͗F in ͘ m, y and
͗D in ͘ m, y to the first three WOCE years, y:1991 to
1993. Extension to the end of WOCE awaits the
acquisition of ISCCP data for later years.
5.1.4.1 The surface heat flux
Levitus et al. (2000) show that the temperature of
the world ocean increased from the 1950s to the
1990s at a rate equivalent to a surface heat imbalance of only 0.3 W m
92
. They also find that the
upper 300 m cooled between 1990 and 1995. It
is, therefore, inconsistent that even with the
ϳ17 W m
92 more cooling due to the drying factor,
SECTION 5 FORMATION AND TRANSPORT OF WATER MASSES
328
U
(m s
–1 )
N10
2.5
2
1.5
1
0.5
5
1 0
1 5
2 0
2 5
3 0
1000 C
C
C
C
C
Hu
Hs
D
E
x
Fig. 5.1.8 Neutral 10-m transfer coefficients as a
function of the neutral 10-m wind speed, U N10 . The drag
coefficient is C D , C E is the Dalton number, and C Hu and
C Hs are the neutral Stanton numbers in unstable and
stable atmospheric conditions, respectively.
(Milliff et al., 1999), which we ignore, and too
much low level moisture (relative humidity always
above 80%), which is corrected by reducing q air
by a factor f q :0.94. We then compute 6-hourly
values of:
E: air C E q sat ͗SST͘ m, y 9f q q air
Q lat :LE
Q sen : air C air C H U air ͗SST͘ m, y 9T air
(5.1.13)
Q lw : T
4
air[ 0.3990.05ea
1/2
air ] F ͗C͘m, y
;4T
3
air ͗SST͘ m, y 9T air
Here is the Stefan–Boltzman constant and an
emissivity :1 is used to account for some reflection of downwelling long-wave radiation; e air is
the vapour pressure (a function of the corrected
humidity, f q q air ) and q sat gives the saturation
humidity above sea water as a function of SST.
This Q lw formula (Berliand and Berliand, 1952)
with latitudinally varying cloud correction factor,
F(͗C͘ m, y ) (Bunker, 1976a), has been evaluated by
Fung et al. (1984).
The bulk transfer coefficients for evaporation,
C E , and sensible heat, C H , are found by adjusting
specified neutral, 10-m values for the heights and
stability of the atmospheric state data. These neutral, 10-m values are given by:
1000C D :2.70(m s
91 )/U N10
;0.142;0.0764(m
91
s)U N10
1000C E :32.7C
1/2
D
(5.1.14)
1000C H :
Ά
18.0C
1/2
D , stable
34.6C
1/2
D , unstable
These are plotted as a function of neutral 10-m
wind speed, U N10 , in Fig. 5.1.8, so they can be
compared to the many variations shown and discussed by WGASF (2000). The C D formulation is
within 10% of at least one of the five examples
shown in WGASF (2000) for all winds between
3 and 25 m s
91
. It is a fit to a compilation of
observations from 1 m s
91 to more than 25 m s
91
,
and its infinite value at zero wind is consistent
with the theoretical behaviour of wind over a
smooth plate. The dependence of C E and C H on
the square root of C D is also theoretical, while the
stability dependence of C H is observed (WGASF,
2000). The complete set of transfer coefficients
(5.1.14) has been used to produce flux climatologies that are consistent with alternatives (Doney
et al., 1998b).
Note that because ISCCP provides both ͗C͘ m,y
used in the Q lw formula (5.1.13) and ͗I͘ m,y , there
can be considerable cancellation of error; a satellite retrieval that gives too much cloud underestimates ͗I͘ m,y but makes Q lw less negative, often
by about the same amount. This benefit would not
be expected if solar radiation and cloud were
derived from independent data sources. Although
the NCEP/NCAR re-analysis covers the years
1958 to the present, we restrict the computation of monthly means ͗H in ͘ m, y , ͗F in ͘ m, y and
͗D in ͘ m, y to the first three WOCE years, y:1991 to
1993. Extension to the end of WOCE awaits the
acquisition of ISCCP data for later years.
5.1.4.1 The surface heat flux
Levitus et al. (2000) show that the temperature of
the world ocean increased from the 1950s to the
1990s at a rate equivalent to a surface heat imbalance of only 0.3 W m
92
. They also find that the
upper 300 m cooled between 1990 and 1995. It
is, therefore, inconsistent that even with the
ϳ17 W m
92 more cooling due to the drying factor,
SECTION 5 FORMATION AND TRANSPORT OF WATER MASSES
328
U
(m s
–1 )
N10
2.5
2
1.5
1
0.5
5
1 0
1 5
2 0
2 5
3 0
1000 C
C
C
C
C
Hu
Hs
D
E
x
Fig. 5.1.8 Neutral 10-m transfer coefficients as a
function of the neutral 10-m wind speed, U N10 . The drag
coefficient is C D , C E is the Dalton number, and C Hu and
C Hs are the neutral Stanton numbers in unstable and
stable atmospheric conditions, respectively.