Environmental Engineering Reference
In-Depth Information
2. Methods
The calculation scheme is based on two classical relationships: (i) definition of
Pasquill stability classes through wind speed and net radiation index (Turner,
1964) and (ii) Pasquill classes as a discrete empirical function of surface rough-
ness
z
o
and Monin-Obukhov length
L
(Golder, 1972; Myrup and Ranzieri, 1976).
Both relations (i, ii) are made continuous through an interpolation procedure as
well as the discrete net radiation index (NRI) is replaced with a continuous function
of solar elevation, corrected with cloud cover. As the first step, NRI is expressed
as a continuous function of solar elevation and corrected with cloud amount. Then
the Pasquill class is expressed as a continuous “Pasquill function”
P
of NRI and
wind speed
u
. Then
L
is expressed as a function of
P
and
z
o
.
The friction velocity is expressed from modified-logarithmic wind profile law
through 10-m wind speed, surface roughness and
L
; then the surface heat flux
through
L
and friction velocity. Surface roughness
z
o
should be in such cases
typically estimated from information on landscape (classification provided, e.g. by
Stull, 1997).
As a validation case study, the frequency of night-time stable atmospheric
conditions was studied for Tallinn, Estonia for years 2005-2007:
1.
Based on the method developed here and two alternative criteria of stable
stratification: (a)
P
> 0.5, (b)
L
< 100 m
2.
Potential temperature inversions from radio sounding profile, 00 GMT
3.
From a meteorological mast located in outskirts of Tallinn - measured
potential temperatures Q at heights of 8 and 22 m
3. Results and Discussion
Clear-sky NRI, originally ranging from 0 to 4, is approximated as a function of
solar elevation
h
o
:
2
NRI
=
0
.
0914
h
−
0
.
0005
h
(1)
o
o
o
Corrected NRI for cloud amount
C
(tenths) is
(
)
NRI
=
NRI
1
+
0
01
C
2
(daytime)
(2)
o
(3)
NRI
=
0
02
C
2
−
2
(night-time)
Approximations (1) - (3) are based on the algorithm by Turner (1964).
We derived a continuous counterpart of Pasquill stability classes, here denounced
as
P
, depending on NRI and 10 m wind velocity
u
(m/s). A polynomial fit accord-
ing to discrete presentation by Turner (1964) is:
