This document presents a methodology for estimating wind speed in suburban areas. Wind speed data was collected at the Zagreb-Maksimir Observatory in Croatia. The study estimated wind speed at 2m using gradient methods and Monin-Obukhov similarity theory, taking into account stability corrections. Effective roughness length was estimated according to wind direction, with higher values for western winds. Estimated wind speeds matched observed values well, with closer matches when accounting for roughness length variations. The methodology allows extrapolating wind data to other heights for modeling and applications in the wider suburban area.

1. Estimation of Wind Speed in
the Suburban Atmospheric
Surface Layer
Tanja Likso
Meteorological and Hydrological
Service, Zagreb, Croatia

2. Outline
1. Introduction
2. Data description
3. Methodology
4. Results
5. Conclusion

3. 1. Introduction
Fig.1.1 Schematic of climatic
scales and vertical layers in
urban areas: planetary boundary
layer (PBL), urban boundary
layer (UBL) (modified from Oke,
1997).

4. 1.1 Main goal of this paper
- The wind speed estimation at 2 m above the ground
using the routine weather elements for the Zagreb-
Maksimir Observatory
- The estimation of the effective roughness length and
its dependance on wind direction
- The comparison between measured and estimated
wind speed at 2 m above the ground ignoring and
taking into account the dependence of effective
roughness length on wind direction was performed

5. 2. Data description
Fig. 2.1 A photo of the
instrumentation, including
anemometer musts for the wind
speed measurements at 2 m (1)
and 10 m (2) heights above the
ground, respectively and the
immediate surroundings for
special observations at the
Zagreb-Maksimir Observatory.

6. 2. Data description
Fig. 2.2. Panoramic
photo of the Zagreb-
Maksimir Obesrvatory
area. Geographical
coordinates are:
j= 45° 49´ 19˝ N,
l= 16° 2´ 1˝ E
123 m above mean
sea level

7. 3. Methodology
3.1 Atmospheric boundary-layer structure
Fig. 3.1 Schematic
atmospheric boundary-layer
structure for
aerodynamically rough
flow in neutrally-stratified
conditions (Garratt,
1994).
zg- boundary layer depth
z – height
z0m – aerodynamic
roughness length

8. Fig. 3.2 The wind speed
profile near the ground
including: a) the effect of
terrain roughness (after
Davenport, 1965), and b) to
e) the effect of stability on
the profile shape and eddy
structure (after Thom, 1975).

9. Fig. 3.3 A typical wind speed
profile for unstable, neutral and
stable conditions (after Oke,
1987).
þ ý ü
î í ì
z
ö çè
( ) ln (1)
÷ø
ö
u z u m
- æ ÷ ÷ø
æ
ç çè
ö çè
÷ø
= æ *
L
z
z
k
m
y
0

10. Fig 3.4 Examples of surface
layer wind profile curves over
various terrain situations with
roughness length z0 and
displacement height d, when
at a nearby meteorological
station the measured wind
corresponds to a potential
wind speed up = 10 m/s (with
mesowind um = 13.1 m/s).
Interrupted profile curves
indicate the height range
where mesoscale wind
variations make average wind
estimates highly unreliable
(after Wieringa, 1986).

11. Fig. 3.5 Generalized
mean (spatial and
temporal) wind speed
profile in a densely
developed urban area.
Dashed line represents
the profile extrapolated
from the inertial sublayer,
solid line represents
actual profile (after WMO-No.
8, chapter 11)

12. 3.2 Roughness length
- Aerodynamic roughness length – smaller than
physical height of the roughness elements; it
can change if the roughness elements on the
surface change (changes in the height and
coverage of vegetation, construction of
houses, deforestation, etc.)
- Effective roughness length - representative
for a larger area; it takes into account
inhomogeneities of the surface in the upwind
direction

13. 3. 3 Methodology adopted
- gradient method for estimation of the wind
speed at 2 m height
- based on the Monin-Obukhov (M-O) similarity
theory ® for estimation of the M-O length
iterative and empirical procedure were used
1) Iterative procedure
The computation starts with estimates for the
typical quantities of turbulence scales, i.e. u*
and q* with the assumption about neutral
atmospheric static stability (z/L ® 0)

14. [ ]
u = k u z - u z *
( ) ( )
2 1
ln
2
z
1
z
[ ]
θ = k θ z - θ z *
( ) ( )
2 1
ln
2
z
1
z
M-O length
= *
gkθ
*
L Tu
2
(6) (7)
(8)

15. 2) Depending on the sign of M-O length,
new values of u* and q* enter the
calculation where appropriate stability
corrections are introduced
If L<0 (unstable conditions) ® stability
functions for momentum and heat
(Paulson, 1970; Dyer, 1974):

16. æ + + ÷ø
æ æ 1 + x 1
x ÷ ÷ø
÷ø
2 y = 2ln ln - 2tan - 1
( x
)
+ p L
2
2
2
ö
ç çè
ö çè
z
ö çè
m
ö
÷ ÷ø
ç çè æ + = ÷ø
z
çè
æ
ö 2
2ln 1
x2
L
h y
1
4
x = æ -
z
1 16 ÷ø
ö L
çè
where
(9)
(10)
(11)

17. If L > 0 (stable conditions) → stability
correction functions (Beljaars and
Holtslag, 1991)
bc
d
Ψ az c
dz
m L
÷ø
+ - = + æ - exp
d
b z
L
L
æ- ÷ø
ö çè
ö çè
Ψ az h
1 2 2
bc
dz
c
b z
- = æ + exp 1
ö çè
÷ø
ö çè
æ - + ÷ø
ö çè
æ- ÷ø
ö çè
æ - + ÷ø
3
3
d
L
d
L
L
(12)
(13)

18. where a = 1, b = 0.667, c = 5 and d = 0.35.
Relations for u* and q* taking into account
stability corrections:
[ ]
z
ö çè
÷ø
u k u z u z
z
ö çè
æ + ÷ø
- æ
-
= *
2 1
L
L
z
z
m m
2
1
2 1
ln
( ) ( )
y y
[ ]
z
ö çè
÷ø
q q
z
ö çè
æ + ÷ø
- æ
-
= *
2 1
L
L
z
z
k z z
h h
2
1
2 1
ln
( ) ( )
y y
q
(14) (15)

19. - Taking into account these new,
improved values of u* and q*, the new
improved value of M-O length is
obtained, and so on. Usually not more
than 3 iteration steps are needed to
achieve a sufficient accuracy of 1% in
successive values of M-O length:
L L
- +
n n
L
1 £ 1%
n
n = 1,2,... (16)

20.  2) Empirical procedure ® is based on
approximate solutions for the relationship
between M-O stability parameter z/L and
Richardson number
g
q
= » D
q
2 ln( / )
2 1 ( )2
( ) u
1
z z z
T z
¶
u
¶
æ
ö z
çèz
g
Ri m D
÷ø
¶
¶
q
1 2 z z z m = zm – geometric mean height
T(z1) – air temperature at first level
(17)

21.  Lee (1997)
ö
÷ ÷ø
ö
ç çè æ
- ÷ ÷ø
æ
ç çè
ö
1 ln
÷ ÷ø
æ
-
ç çè
=
Ri
Ri
z
z
z
z z
z
L c
*
0 0 1
b
ö
÷ ÷ø
æ
2 3 4
Ri Ri Ri Ri
´ + - + ÷ ÷ø
z
ln 13 15 3.3
ç çè
Ri Ri
- +
ö
æ
ç çè
÷ ÷ø ö
æ
-
ç çè
z
= 2 4
z
0 0 1 0.6 0.1
z z
z
L
ö
÷ ÷ø
æ
2 3 4
Ri Ri Ri Ri
´ + - + ÷ ÷ø
z
ln 5 7 2.1
ç çè
Ri Ri
- +
ö
æ
ç çè
ö
÷ ÷ø
æ
-
ç çè
z
= 2 4
z
0 0 1 0.6 0.1
z z
z
L
Unstable conditions
10
z
=
z
0
for
z
for 4
= 10
z
0
Stable conditions:
(18)
(19)

22.  If wind speed is available at the height z2,
then, an estimation of wind speed at other
level in surface layer can be obtained using
(Holtslag and Van Ulden, 1983):
ù
ù
úû
é
é
êë
ψ z
ö çè
ψ z
ö çè
÷ø
ö
ö
- æ ÷ ÷ø
æ
ln
æ
ç çè
úû
êë
÷ø
- æ ÷ ÷ø
ç çè
=
L
z
z
z
L
z
u z u z
2
m
1
2
0
1
m
0
1 2
ln
( ) ( )
z1 = 2 m, z2 = 10 m
(20)

23. 4. Results
Fig. 4.1 Comparison
of effective roughness
length estimation
using three principles:
1) RMSE principle 2)
principle based on
standard deviation of
wind speed and 3)
principle based on
median wind gust
factor .

24. Fig. 4.2 The rose of the mean
effective roughness length
according to wind direction
sectors for the Zagreb-Maksimir
Observatory. z0 values are
obtained using the RMSE
principle.

25.  Verification parameters:
ù
úû
é - = å=
1 ( )
êë
N
i
i i F O
N
BIAS
1
ù
úû
é - = å=
êë
N
i
i i F O
N
MAE
1
1
ù
úû
é - = å=
1 ( )2
êë
N
i
i i F O
N
RMSE
1
(21)
(22)
(23)
Fi (i=1,2,...,N) – estimated values, Oi – observed values

26. Fig. 4.3 Comparison between
estimated (using gradient method)
and observed values of wind
speed at 2 m above the ground for
the Zagreb-Maksimir Observatory;
dependance of z0 on wind direction
is neglected (R2 = 0.76).

27. Fig. 4.4 The same as in
Fig. 4.3 but taking into
account the dependence of
z0 on wind direction (R2 =
0.85).

28. 5. Conclusion
 Results obtained using both procedures are
in excellent agreement except in case of very
stable conditions when Ri > 1.
 Limitation of presented method in
reproducing intermittent turbulence is directly
caused by the use of a stability functions
 The classification of z0 according to wind
direction (z0 values obtained are higher for
western than for eastern quadrants of wind
direction)

29.  The obtained results suggest that the wind
observation at the standard level (10 m) is
representative for the area of about one
kilometre in the upwind direction
 The wind data extrapolation at lower or higher
levels, based on standard measurements at
10 m, can provide values of the wind
representative for wider inhomogeneous
(regarding surface roughness) suburban area
of the city of Zagreb

30.  These data can be used for
atmospheric modeling, estimation of
turbulent fluxes, wind energy, civil
engineering and air pollution
applications, etc.

31. Thank you for
listening