Estimation of Wind Speed in the Suburban Atmospheric Surface Layer

Tanja LiksoMeteorological and

Hydrological Service, Zagreb, Croatia

Outline

1. Introduction2. Data description3. Methodology 4. Results5. Conclusion

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).

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

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.

2. Data description

Fig. 2.2. Panoramic photo of the Zagreb-Maksimir Obesrvatory area. Geographical coordinates are:

= 45° 49´ 19˝ N,

= 16° 2´ 1˝ E

123 m above mean sea level

3. Methodology3.1 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

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).

Fig. 3.3 A typical wind speed profile for unstable, neutral and stable conditions (after Oke, 1987).

L

z

z

z

k

uzu m

m

0

ln)( (1)

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).

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)

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

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 * with the assumption about neutral atmospheric static stability (z/L 0)

1

2

12

ln

)()(

z

zzuzuk

u

1

2

12

ln

)()(

z

zzθzθk

θ

gkθ

uTL

2

M-O length

(6) (7)

(8)

2) Depending on the sign of M-O length, new values of u* and * enter the calculation where appropriate stability corrections are introduced

If L<0 (unstable conditions) stability functions for momentum and heat (Paulson, 1970; Dyer, 1974):

2)(tan2

2

1ln

2

1ln2 1

2

x

xx

L

zm

2

1ln2

2x

L

zh

4

1

161

L

zx

where

(9)

(10)

(11)

If L > 0 (stable conditions) → stability correction functions (Beljaars and Holtslag, 1991)

d

bc

L

dz

d

c

L

zb

L

azΨm

exp

1exp

3

21

2

3

d

bc

L

dz

d

c

L

zb

L

azΨ h

(12)

(13)

where a = 1, b = 0.667, c = 5 and d = 0.35.

Relations for u* and * taking into account stability corrections:

L

z

L

z

z

z

zuzuku

mm12

1

2

12

ln

)()(

L

z

L

z

z

z

zzk

hh12

1

2

12

ln

)()(

(14) (15)

- Taking into account these new, improved values of u* and *, 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:%1 1

n

nn

L

LLn = 1,2,... (16)

2) Empirical procedure is based on approximate solutions for the relationship between M-O stability parameter z/L and Richardson number

2121

2)/ln(

)( uzzz

zT

g

z

uz

g

Ri m

21zzzm zm – geometric mean height

T(z1) – air temperature at first level

(17)

Lee (1997)

Ri

Ri

z

z

zz

z

cL

z*

00 1ln

1

42

432

00 1.06.01

3.31513ln

RiRi

RiRiRiRi

z

z

zz

z

L

z

42

432

00 1.06.01

1.275ln

RiRi

RiRiRiRi

z

z

zz

z

L

z

Unstable conditions

100

z

zfor

for 4

0

10z

z

Stable conditions:

(18)

(19)

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):

L

zψ

z

z

L

zψ

z

z

zuzu2

m0

2

1m

0

1

21

ln

ln

)()(

z1 = 2 m, z2 = 10 m

(20)

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 .

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.

Verification parameters:

N

iii OF

NBIAS

1

)(1

N

iii OF

NMAE

1

1

N

iii OF

NRMSE

1

2)(1

(21)

(22)

(23)

Fi (i=1,2,...,N) – estimated values, Oi – observed values

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).

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

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)

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

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

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