4)s
I.. ti. WIt’I’1;HMANh’
( 5 c )
(5d)
f(2) = I , , - ( L , - K L l ) ) CAP( -K(% - %,,),L, ]
L = L , - ( L , - K % ( ) ) 7 P
In all of thcse four hypotheses appears the parameter L , . which stands for
the asymptotic mixing length to he approached for Z --* XI, except for ( 5 4
wherc f,, is only a parameter since L -+ 0 for Z --* z... The parameter L ,
controls the thermal stratification of the PBL which is described by the
internal stratification parameter p,
(6 1
11 = WL*
where tl = KuJis the internal scale height of the PRL and L , the Monin
Obukhov stability length. A n empirical relationship between L , and i i has
been given by Wippermann (1972):
(7)
}l = -53.4 - 28.8 log,&,)
The hypothesis (Sa) has been given for the neutral case ( p = 0, i.e.,
L , = 0.014) by Lettau (1962) where K ~ L , , .
was chosen to be 33.62 (or
L , = 0.012). ’The hypothesis (5b) is that one by Blackadar (1962) in a somewhat modified form: in the original one Blackadar has the factor 6.75 x
10 .JICg instead of L , showing that his asymptotic mixing-length depends
on external parameters and does not satisfy the requirements of Rossbynumber similarity. The hypothesis (5c) is that one by R u i n tit ctl. (1963) and
later on used by Appleby and Ohmstede (1964); it is nondimensionalized
and slightly modified. Equation (Sd) is a hypothesis by Wippermann (1971a)
which relates L with the (not yet known) dependent variable T instead o f
with the independent variable Z as do hypotheses (Sa), (Sb). and (5c); thercfore a model using the hypothesis (5d) is less a priori. However this hypothesis has a defect too: L(Z .+ w ) # L,, in a baroclinic PBL.
The set of equations (1)-(4) is a closed system for the four variables A‘(%).
Y(Z). k ’ , ( Z ) , and L(Z). The boundary conditions are
z = z, :
(Ha)
x = I
(8b)
Y E 0
(Hc)
K, = %(j
(8d)
L - hZ0
I.. ti. WIt’I’1;HMANh’
( 5 c )
(5d)
f(2) = I , , - ( L , - K L l ) ) CAP( -K(% - %,,),L, ]
L = L , - ( L , - K % ( ) ) 7 P
In all of thcse four hypotheses appears the parameter L , . which stands for
the asymptotic mixing length to he approached for Z --* XI, except for ( 5 4
wherc f,, is only a parameter since L -+ 0 for Z --* z... The parameter L ,
controls the thermal stratification of the PBL which is described by the
internal stratification parameter p,
(6 1
11 = WL*
where tl = KuJis the internal scale height of the PRL and L , the Monin
Obukhov stability length. A n empirical relationship between L , and i i has
been given by Wippermann (1972):
(7)
}l = -53.4 - 28.8 log,&,)
The hypothesis (Sa) has been given for the neutral case ( p = 0, i.e.,
L , = 0.014) by Lettau (1962) where K ~ L , , .
was chosen to be 33.62 (or
L , = 0.012). ’The hypothesis (5b) is that one by Blackadar (1962) in a somewhat modified form: in the original one Blackadar has the factor 6.75 x
10 .JICg instead of L , showing that his asymptotic mixing-length depends
on external parameters and does not satisfy the requirements of Rossbynumber similarity. The hypothesis (5c) is that one by R u i n tit ctl. (1963) and
later on used by Appleby and Ohmstede (1964); it is nondimensionalized
and slightly modified. Equation (Sd) is a hypothesis by Wippermann (1971a)
which relates L with the (not yet known) dependent variable T instead o f
with the independent variable Z as do hypotheses (Sa), (Sb). and (5c); thercfore a model using the hypothesis (5d) is less a priori. However this hypothesis has a defect too: L(Z .+ w ) # L,, in a baroclinic PBL.
The set of equations (1)-(4) is a closed system for the four variables A‘(%).
Y(Z). k ’ , ( Z ) , and L(Z). The boundary conditions are
z = z, :
(Ha)
x = I
(8b)
Y E 0
(Hc)
K, = %(j
(8d)
L - hZ0