Environmental Engineering Reference
In-Depth Information
P
=
B
00
+
B
01
u
+
B
02
u
2
+
B
03
u
2
+
B
10
NRI +
B
20
NRI
2
+
B
30
NRI
3
+
B
11
NRI
u
+
B
12
NRI
u
2
+
B
21
NRI
2
u
(4)
Values −3, −2, −1, 0, 1, 2 of
P
correspond respectively to discrete classes A, B, C,
D, E and F;
P
= −2.5 corresponds to transition between classes A and B
etc
.
Regression coefficients in Eq. 4 are given in
Table 1.
Table 1.
Regression coefficients in Eq. 4
B
00
0.444109
B
20
0.095300
B
01
B
30
−0.177258
−0.008333
B
02
0.019689
B
11
0.266387
B
03
−0.000486
B
12
−0.011147
B
10
−1.343386
B
21
−0.014444
To avoid inconsistent and too extreme unstability, the stability function
P
is set
zero, if u > 7 m/s and values higher than 2.5 (appearing at low wind and negative
NRI) are set to 2.5. From graphical representation by Myrup and Ranzieri (1976)
we derive the polynomial fit for Monin-Obukhov length
L
:
L
-1
= A
00
+ A
01
Z + A
02
Z
2
+ A
10
Z + A
11
PZ+A
12
PZ
2
+ +A
20
Z
2
+ A
21
P
2
Z + A
22
P
2
Z
2
,
(5)
where
Z
= -log
z
o
(m). Regression coefficients are given separately for unstable
(
P
<0,
L
<0) and stable stratification (
P
> 0,
L
> 0) in
Table 2
.
Table 2.
Regression coefficients in Eq. 5
Coefficient
Unstable
Stable
Coefficient
Unstable
Stable
A
00
-0.002107
0.002309
A
12
0.004600
0.009098
A
01
0.001128
-0.001385
A
20
-0.015660
0.023065
A
02
-0.000379
0.000166
A
21
-0.001540
0.004786
A
10
-0.014491
-0.022966
A
22
0.002279
-0.004117
A
11
0.011234
0.006258
Polynomial fit (5) produces a non-physical maximum of
L
-1
in unstable
stratification and minimum in stable stratification for
z
o
> 0.5 m and Pasquill
stability close to neutral. These false extremums are removed, using linear inter-
polation for
L
-1
between values 0 and −0.0015 for unstable stratification and
between values 0 and 0.001 for stable stratification.
Comparison of monthly average frequencies of night-time stable conditions for
Tallinn by three different methods is given i
n Fig. 1.
The frequencies agree well with
sounding- and mast-based estimations, except the lower mast level, which obviously
includes all shallow inversions entirely in suburban canopy layer. A sharp maximum
at this graph most probably corresponds to snowmelt inversions. In general, surface
inversions are more frequent in summertime, when diurnal temperature variations
are larger.
