Chapter 1: INTRODUCTION
which are in reasonably good agreement with data in the above wind speed
range.
Advanced bulk flux algorithms are based on the Monin-Oboukhov
similarity theory (see Section 1.7.2), representing the fluxes in terms of
mean quantities. While there are many algorithms available today, we will
restrict our discussion to the COARE 3.0 bulk flux algorithm (Fairall et al.,
2003).
The transfer coefficients depend on the Monin-Oboukhov stability
parameter
/ O
z L
]
:
1/ 2
1/ 2
1/ 2
1
0
0
/ 1
c
c
c
F
F
F
F
]
N \ ]
ª
º
¬
¼
(1.40)
where z is the height of measurements, O
L is the Oboukhov buoyancy
length scale,
1/ 2
0
0
/ ln /
c
z z
F
F
N
is the transfer coefficient under neutral
stratification (] = 0), F
\ is an universal function of stability parameter ] ,
N is the von Karman constant (commonly used value N = 0.4), and 0
z F is the
surface roughness length for property F under neutral stratification in the
atmospheric boundary layer. The stability parameter is given by the formula
of Zilitinkevich (1966):
3/ 2
' ' 0.61
w
Twq
g z
T
w u
N
9
c c
4
c c
,
(1.41)
where g is the acceleration of gravity, and T is the absolute temperature in K.
It is convenient to define a velocity scaling parameter
1/ 2
a
u
wu
c c
,
which is known as the friction velocity (in the atmosphere, in this case) and
respective scaling parameters for temperature
' '/
a
a
w
u
4
4
, and
humidity
/ a
q
wq u
c c
. Here w u
c c denotes the streamwise component of
the vertical momentum flux. The kinematic fluxes in (1.41) can then be
replaced with a
u , a
4 , q obtained by iteration within the bulk algorithm.
The bulk model formulated in (1.31), (1.40), and (1.41) has to be
completed with representations (parameterizations) of the roughness length
(or, equivalently, the transfer coefficients) and the profile stability functions
( F
\ ). The roughness length can be parameterized with Charnock’s (1955)
velocity roughness formula plus a smooth flow limit expression from Smith
(1988):
15
which are in reasonably good agreement with data in the above wind speed
range.
Advanced bulk flux algorithms are based on the Monin-Oboukhov
similarity theory (see Section 1.7.2), representing the fluxes in terms of
mean quantities. While there are many algorithms available today, we will
restrict our discussion to the COARE 3.0 bulk flux algorithm (Fairall et al.,
2003).
The transfer coefficients depend on the Monin-Oboukhov stability
parameter
/ O
z L
]
:
1/ 2
1/ 2
1/ 2
1
0
0
/ 1
c
c
c
F
F
F
F
]
N \ ]
ª
º
¬
¼
(1.40)
where z is the height of measurements, O
L is the Oboukhov buoyancy
length scale,
1/ 2
0
0
/ ln /
c
z z
F
F
N
is the transfer coefficient under neutral
stratification (] = 0), F
\ is an universal function of stability parameter ] ,
N is the von Karman constant (commonly used value N = 0.4), and 0
z F is the
surface roughness length for property F under neutral stratification in the
atmospheric boundary layer. The stability parameter is given by the formula
of Zilitinkevich (1966):
3/ 2
' ' 0.61
w
Twq
g z
T
w u
N
9
c c
4
c c
,
(1.41)
where g is the acceleration of gravity, and T is the absolute temperature in K.
It is convenient to define a velocity scaling parameter
1/ 2
a
u
wu
c c
,
which is known as the friction velocity (in the atmosphere, in this case) and
respective scaling parameters for temperature
' '/
a
a
w
u
4
4
, and
humidity
/ a
q
wq u
c c
. Here w u
c c denotes the streamwise component of
the vertical momentum flux. The kinematic fluxes in (1.41) can then be
replaced with a
u , a
4 , q obtained by iteration within the bulk algorithm.
The bulk model formulated in (1.31), (1.40), and (1.41) has to be
completed with representations (parameterizations) of the roughness length
(or, equivalently, the transfer coefficients) and the profile stability functions
( F
\ ). The roughness length can be parameterized with Charnock’s (1955)
velocity roughness formula plus a smooth flow limit expression from Smith
(1988):
15