J. Wind Eng. Ind. Aerodyn. 104–106 (2012) 558–564

Contents lists available at SciVerse ScienceDirect

Journal of Wind Engineeringand Industrial Aerodynamics

0167-61

http://d

n Corr

E-m

ishihara

journal homepage: www.elsevier.com/locate/jweia

A study of topographic multiplier considering the effect ofcomplex terrains and tropical cyclones

Yuka Kikuchi n, Takeshi Ishihara

Department of Civil Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan

a r t i c l e i n f o

Available online 26 May 2012

Keywords:

Topographic multiplier

Monte Carlo simulation of tropical cyclones

Reduction factors

Terrain complexity

05/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.jweia.2012.04.008

esponding author. Tel.: þ81 3 5841 1145; fa

ail addresses: kikuchi@bridge.t.u-tokyo.ac.jp (

@bridge.t.u-tokyo.ac.jp (T. Ishihara).

a b s t r a c t

A topographic multiplier is widely used to evaluate the effect of topography on the design wind speed.

The maximum value of directional topographic multipliers has been used as the topographic multiplier

in many design codes. However, this simplified method is conservative and overestimates the speedup

effect in some cases. In this paper a topographic multiplier considering wind directionality is proposed

by using Monte Carlo simulation, and investigated at two typical meteorological stations. Then a

reduction factor is proposed as the ratio of the topographic multiplier estimated by Monte Carlo

simulation to that obtained by the simplified method. A topographic variation coefficient is proposed as

the deviation of directional topographic multipliers and investigated systematically by using terrain

models. As a result, the reduction factor decreased as the topographic variation increased. An empirical

formula is proposed to improve the simplified method.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The prediction of extreme wind speeds is essential for structuraldesign. For practical purposes, basic wind speed maps are proposedin many countries. The map shows certain-year-recurrence windspeeds on flat terrains. For example, in the Architecture Institute ofJapan (AIJ, 2004), the map illustrates 100-year-recurrence windspeeds on subcategory II at 10 m height above the ground.Designers use this map to determine the design wind speed atthe construction site.

In complex terrains like escarpments and small hills, the speedupeffect by topography has to be considered. Conventionally, a topo-graphic multiplier is defined as the maximum value of directionaltopographic multipliers. It is widely used in design codes, althoughit sometimes overestimates the speedup effect since it does notconsider the wind directionality of tropical cyclones. On the otherhand, Monte Carlo simulation has been widely used to evaluateextreme wind speeds over complex terrains for tropical andsubtropical regions, where the design wind speed is mainly deter-mined by tropical cyclones. In this method, directional topographicmultipliers are multiplied to individual storms considering theirwind directions. The method was first suggested by Russell (1971)and developed by Tryggvason et al. (1976), Batts et al. (1980),Georgiou et al. (1983), Vickery and Twisdale (1995), Yasui et al.(2002), and Ishihara et al. (2005).

ll rights reserved.

x: þ81 3 5841 1147.

Y. Kikuchi),

This paper aims to propose a topographic multiplier consider-ing wind directionality by using Monte Carlo simulation fortropical cyclones and to evaluate the effect of terrain complexityand wind directions on topographic multipliers. In the followingsection, surface wind field models of tropical cyclones aredescribed and a numerical simulation is verified with observa-tions at a wind tunnel test. Monte Carlo simulation of tropicalcyclones is stated and its accuracy is verified with measurementsat two meteorological stations in Section 3. In the final section, atopographic multiplier considering the effect of complex terrainsand tropical cyclones is defined and compared to the conventionalone. A reduction factor is proposed as the ratio of the newtopographic multiplier to the conventional one and investigatedby using typical terrain models.

2. Wind field model of tropical cyclones

In this section, wind field models of tropical cyclones areexplained. First, a gradient wind speed is estimated from apressure field of tropical cyclones. Then, the surface wind speedis obtained with directional topographic multipliers and devia-tions of wind directions.

2.1. Wind field of tropical cyclones

The gradient wind field model expresses the balance thatexists between the forces by horizontal pressure gradient, Coriolisacceleration and centrifugal acceleration, in the presence ofgeneral storm translations. The gradient wind speed ugð x

!Þ at

Y. Kikuchi, T. Ishihara / J. Wind Eng. Ind. Aerodyn. 104–106 (2012) 558–564 559

the site x!

is evaluated by

ugð x!Þ¼�C sin ðf�yÞ�f r

2þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�C sinðf�yÞ�f r

2

� �2

þr

r@p

@r

sð1Þ

where C is the translation velocity; y and f are the approachangle and gradient wind direction measured counterclockwisepositive from East, respectively; f is the Coriolis parameter; r isthe distance from the tropical cyclone center; r is the air density;and p is the tropical cyclone pressure. The wind directionyg corresponding to this gradient velocity is given by

ygð x!Þ¼ p�f ð2Þ

The tropical cyclone pressure model used here was proposedby Schloemer (1954), which was expressed as a function of r:

pðrÞ�pc

p1�pc¼ exp �

Rm

r

� �ð3Þ

where pc is the center pressure, pN is the surrounding pressureand Rm is the radius at maximum wind speed, which can beidentified by the least squares method using the measured seasurface pressure at the meteorological stations; pN can be assumedto be 1013 hPa or identified simultaneously.

The effect of topography can be separated from that of tropicalcyclones0 pressure fields since the scale of topography is smaller(Ishihara et al., 2005). Surface wind speeds uT and directions yT onreal terrains of tropical cyclones are obtained as follows:

uTð x!

,yf Þ ¼ uf ð x!ÞStð x!

,yf Þ, ð4Þ

yTð x!

,yf Þ ¼ yf ð x!ÞþDtð x

!,yf Þ ð5Þ

where uf, and yf are wind speeds and directions on flat terrains,respectively, calculated using the following surface wind fieldmodels:

uf ð x!Þ¼ ugð x

!Þðz=zgÞ

au , ð6Þ

yf ð x!Þ¼ ygð x

!Þþysð1:0�0:4ðz=zgÞÞ

1:1ð7Þ

where the exponent index au and the gradient height zg areexpressed as functions of the absolute vorticity and the surfaceRosby number. Inflow angle ys is a function of the homogeneity ofvorticity and the surface Rosby number (Ishihara et al., 1997).St and Dt are the directional topographic multiplier and deviationof wind direction, respectively, which are calculated by Computa-tional Fluid Dynamics (CFD).

2.2. Evaluation of directional topographic multipliers and deviation

of wind directions

A CFD program, MASCOT (Microclimate Analysis System forComplex Terrain) is employed to evaluate the directional topo-graphic multiplier St and the deviation of wind direction Dt.

MASCOT is a nonlinear flow simulation model for the predic-tion of microscale wind climates on complex and steep terrains(Ishihara and Hibi, 2002). The Reynolds averaged Navier–Stokesequations and turbulence models expressed by the followingEquations are used, providing information on the mean velocitycomponents along the directions, the static pressure, turbulencekinetic energy and its dissipation:

@ruj

@xj¼ 0, ð8Þ

@rujui

@xj¼�

@p

@xiþ

@

@xjm @ui

@xj�ru0iu

0j

� �, ð9Þ

@rk

@tþ@rujk

@xj¼

@

@xjmþ mt

sk

� �@k

@xj

� ��ru0iu

0j

@ui

@xj�re, ð10Þ

@re@tþ@ruje@xj¼

@

@xjmþ mt

se

� �@e@xj

� ��Ce1

ekru0iu

0j

@ui

@xj�Ce2

re2

k: ð11Þ

In these equations, r is the fluid density and m is the laminarviscosity. The constants (Cm, Ce1, Ce2, and sk) are assigned tostandard values (1.44, 1.92, 1.0, and 1.3; Jones and Lauder, 1972).The turbulent viscosity mt is defined as a function of turbulencekinetic energy and dissipation:

mt ¼ Cmrk2

eThe fluctuating velocity components are identified by the

turbulent Reynolds stress tensor. In this study, the standard k–emodel is used to approximate the Reynolds stress:

ru0iu0j ¼

2

3rkdij�mt

@ui

@xjþ@uj

@xi

� �ð12Þ

To suit the computation of complex flow, an arbitrary non-orthogonal collocated grid system is used. The governing equationsare rewritten in the curvilinear coordinate system and solved usinga common discrete method. In this program, the finite volumemethod and the SIMPLE algorithm are adopted. The QUICK schemeis employed for convection terms in the equation of k and e and thesecond order central difference for the order terms. Rhie and Chow’sPWIM (pressure weighted interpolation method) is used to avoidpressure–velocity decoupling. For detailed information, refer toIshihara and Hibi (2002).

Using this model, wind speeds and directions on flat and realterrains are calculated with regard to the wind sector i:

Stið x!Þ¼

utið x!Þ

uf ið x!Þ, ð13Þ

Dtið x!Þ¼ ytið x

!Þ�yf ið x

!Þ: ð14Þ

St and Dt are obtained by a linear interpolation. St valuescomputed by MASCOT are compared with wind tunnel test data(Ishihara et al., 1999). In the experiment, the turbulent flow over acircular hill, having a cosine-squared cross section, was investi-gated using split-fiber probes designed for measuring flows withhigh turbulence and separation. Profiles of the mean and variancefor the three velocity components were presented and comparedwith those in the undisturbed boundary layer. In this study, one-thousandth of a mountain model of the wind tunnel test isprepared for CFD. The analytical domain in horizontal and verticalplanes are set to 3500 m and 900 m, respectively, the minimumintervals of mesh in horizontal and vertical are fixed at 10 m and3 m, and the surface roughness is given as 0.3 m as the windtunnel test. The topographic multipliers predicted by CFD agreefavorably with observations at the top of the mountain (Fig. 1).

Directional topographic multipliers St and deviations of winddirections Dt are evaluated at two meteorological stations locatedwith typical complex terrains: Murotomisaki and Nagasaki. Fig. 2illustrates elevation maps around the stations. The Murotomisakistation is on a cliff at the tip of the peninsula, which leads toincreased wind speed. In contrast, the Nagasaki station is sur-rounded by mountains and forests, which leads to decrease in windspeeds. Fig. 3 shows St and Dt computed with meshes and boundaryconditions in Table 1. The number of wind direction sectors is set at16 and the terrain subcategory is fixed to II as specified in AIJ inwhich z0 is 0.01. Wind directions are expressed in degrees progres-sing clockwise from North. At the Murotomisaki station, directionaltopographic multipliers are almost constant, except those around01 corresponding to wind from the land. Meanwhile, at the Nagasaki

Y. Kikuchi, T. Ishihara / J. Wind Eng. Ind. Aerodyn. 104–106 (2012) 558–564560

station, directional topographic multipliers have a clear peak due towind from the bay. The result indicates that topographic effect onwind speed is significant on complex terrains.

3. Monte Carlo simulation of tropical cyclones

In Monte Carlo simulation of tropical cyclones, tropical cycloneparameters are evaluated from a historical track record of pasttropical cyclones. Then synthetic tropical cyclones are generatedfor a long period to satisfy probability distributions and their

0

100

200

1 1.2 1.4 1.6 1.8

Hig

ht fr

om th

e gr

ound

(m)

Topographic multiplier

ExperimentCFD

Fig. 1. Comparison of predicted and measured directional topographic multipliers.

Fig. 2. Elevation maps around two station

00.20.40.60.8

11.21.41.6

-30

-20

-10

0

10

20

30

0 90 180 270 360

S t

Wind direction (°)

D t (°

)

St Dt (°)

Fig. 3. Directional topographic multipliers Sti and deviations of wind dir

correlations using a modified orthogonal decomposition method.Finally, surface wind speeds are predicted and extreme winddistributions of tropical cyclones are estimated.

3.1. Evaluation of tropical cyclone parameters

Tropical cyclones can be generated by Monte Carlo simulation(MCS) based on six tropical cyclone parameters. For each tropicalcyclone, four parameters, namely the central pressure pc, thetranslation velocity C, the approach angle y taken counterclock-wise positive from East and the minimum approach distance dmin

when the cyclone approaches the site of interest most closely, areobtained from the historical track record of tropical cyclones.Another parameter is the radius at maximum wind speed Rm,which can be identified by the pressure field model in Eq. (3).

s: (a) Murotomisaki and (b) Nagasaki.

00.20.40.60.8

11.21.41.6

-30

-20

-10

0

10

20

30

0 90 180 270 360

Wind direction (°)

S t D t (°

)

ections Dti at the two stations: (a) Murotomisaki and (b) Nagasaki.

Table 1Mesh and boundary conditions.

Murotomisaki Nagasaki

Location N3311500600 N3214400000

E1291520

0000 E13411003600

Area 5 km�5 km�10 km 5 km�5 km�10 km

Minimum mesh size (m)

Horizontal 50 50

Vertical 5 5

Resolution terrain 50 50

Resolution roughness 100 100

Inflow z0¼0.01 z0¼0.01

Wind direction sector 16 16

Y. Kikuchi, T. Ishihara / J. Wind Eng. Ind. Aerodyn. 104–106 (2012) 558–564 561

The other parameter is an occurrence rate of the tropical cyclonesat the specific site, l, which can be defined as the number oftropical cyclones that pass, and is obtained from the track recordsof past tropical cyclones. These six parameters are approximatedby analytical functions. Table 2 shows an example of the prob-ability distribution for these parameters estimated at the Mur-otomisaki meteorological station. Here, m is the averaged value, sis the deviation of each parameter, k is the shape factor, c is thescale factor and a is the mixed paramater, z is the coefficient ofquadratic function, and lm is the averaged number of tropicalcyclones hit Japan per year.

3.2. Generation of synthetic tropical cyclones

Synthetic tropical cyclones are generated for N years to satisfy themodeled probability distributions and the correlations of tropicalcyclone parameters. The change in pressure field of tropical cyclonescan be neglected since wind speeds and directions are estimated onlywhen tropical cyclones are located inside a simulation cycle with adiameter of 500 km. A modified orthogonal decomposition (MOD)method should be used to satisfy the statistical distribution functionsof tropical cyclone parameters and the correlations between them atthe same time, as proposed by Ishihara et al. (2005). The detailedprocedure of the MOD method is described below.

Five parameters describing a tropical cyclone are normalizedand written in vector form as follows:

xT ¼ flnðDpÞ, lnðRmÞ, lnðCÞ,y,dming ð15Þ

The covariance matrix of x is defined as S. The eigenvalues l(k)

and the eigenvectors F(k) are calculated by solving the followingequation:

½S�lðkÞE�FðkÞ ¼ 0 ð16Þ

Table 2Examples of the probability distributions of tropical cyclones paramete

Parameter PDF

Central pressure depth

Radius of maximum wind speed

Translation speed

FMðxÞ ¼ a� 1ffiffiffiffiffi2pp

sln xexp � 1

2

��

þð1�aÞ �k

C

x

C

� �k�1

exp

Translation directionFSðxÞ ¼

1ffiffiffiffiffi2pp

sexp � 1

2ln x�m

s

� ��Minimum distance dminðxÞ ¼ zðx2�xÞþ1000x�5

Number of typhoons per year lðxÞ ¼ lxm expð�lm Þ

x!

010203040506070

-4 -2 0 2 4 6 8 10

Win

d sp

eed

(m/s

)

Reduced variate -LN(-LN(F))

5010 500Return period (years)

Flat.(z0=0.01)Real.Obs.

Fig. 4. Extreme wind distributions at the two st

The independent parameters zi with five components are thengenerated following the approximated distributions to the intendedones for specified years and the number of the generated vectorsfollowing the estimated annual occurrence rate. The correlatedparameters xi can be obtained by the following equation:

xi ¼ ½Fð1ÞFð2ÞUUUFð5Þ��1zi ð17Þ

These vectors xi should be considered as a set of parameters fortropical cyclones. Although the correlation between each compo-nent of xi satisfies the target correlations, their probability distri-butions do not follow the target ones. The xi should be rearrangedin ascending order and modified so that its probability distribu-tion follows the target probability distributions. This operationhardly affects the correlations because it does not change the setof parameters.

3.3. Evaluation of extreme wind distributions

Wind speeds on flat and real terrains are calculated with windfield models expressed by Eqs. (1)–(7). Annual maximum windspeed ui can be extracted and ranked in ascending order from u1

to uN (Gumbel, 1958; IEC61400-1, 2005):

FðuiÞ ¼ 1�i

Nþ1ði¼ 1,. . .,NÞ ð18Þ

ui is plotted against a reduced variate yi as follows:

yi ¼�lnð�lnðFðuiÞÞÞ ð19Þ

The extreme wind distributions predicted by MCS for 10,000years are compared to those by observations at Murotomisaki andNagasaki meteorological stations. 10 minutes mean wind speed datais acquired from Automated Meteorological Data Acquisition System(AMeDAS) developed by Japanese Meteorological Agency. The datais available from 1995 to 2009. With regard to the Murotomisaki

rs.

Model parameters

lnx�mln xsln x

�2�

�x

C

� �k� �

m¼1.64, s¼0.12, k¼4.01, c¼49.7, a¼0.99

m¼1.98, s¼0.22, k¼2.16, c¼122.7, a¼0.57

m¼1.54, s¼0.21, k¼2.43, c¼43.07, a¼0.40

2�

m¼161.02, s¼36.29

00 z¼�166.11

lm¼3.30

010203040506070

-4 -2 0 2 4 6 8 10

Win

d sp

eed

(m/s

)

Reduced variate -LN(-LN(F))

Return period (years)5010 500

ations: (a) Murotomisaki and (b) Nagasaki.

Y. Kikuchi, T. Ishihara / J. Wind Eng. Ind. Aerodyn. 104–106 (2012) 558–564562

station, data until 2005 are used since the station was relocated in2006. Tropical cyclone data is collected from cyclones passing within500 km from the site with the center pressure less than 985 hPa.

In Fig. 4, the predicted distributions considering topographicaleffect (lines) show a good agreement with those by observations(plots), whereas the distributions without consideration of topo-graphic effect (dot lines) underestimate wind speeds at Murotomi-saki and overestimate it at Nagasaki. This indicates the importanceof considering speedup effect by complex terrains to evaluateextreme wind speeds and proves the accuracy of MCS.

4. Study of topographic multiplier

In this section, a topographic multiplier considering winddirections with Monte Carlo simulation is proposed. A reductionfactor is proposed as the ratio of the new multiplier to theconventional one and investigated using typical terrain models.

4.1. Definition of topographic multiplier considering wind directions

of tropical cyclones

In a conventional way, a topographic multiplier (St,max)is defined as the maximum value of directional topographical

Input parameters

Estimation of tropical cyclones parameters

Generation of synthetic tropical cyclones

Years

Estimation of gradient winds

Estimation ofsurface winds

Extreme wind distributions

YESNO

Tropical cyclone data base

Directional topographic multipliersDeviation of wind directions

Topographic multiplier S

Input parameters

Estimation of tropical cyclones parameters

Generation of synthetic tropical cyclones

Years

Estimation of gradient winds

Estimation ofsurface winds

Extreme wind distributions

YESNO

Tropical cyclone data base

Directional topographic multipliersDeviation of wind directions

Topographic multiplier tR

Fig. 5. Flowchart for evaluation of topographic multiplier by MCS, StR.

StRSt,max

0

0.4

0.8

1.2

1.6

0 1 2 3 4 5Reduced variate -LN(-LN(F))

Return period

505 10 20 1002

Topo

grao

hic

mul

tiplie

r

Fig. 6. Topographic multipliers with return pe

multipliers:

St,max ¼maxðStÞ ð20Þ

This simplified method is practical, but has a possibility ofoverestimation since wind directions are out of consideration. Atopographic multiplier considering wind directions by MCS StR isproposed as

StR ¼UtR=UfR ð21Þ

where UtR is R-year-recurrence wind speed on real terrains andUfR is that on flat terrains evaluated by MCS. This index considersthe probability of occurrence of wind direction. Fig. 5 summarizesa flow for obtaining StR with wind field models and MCS oftropical cyclones.

To evaluate the new topographic multiplier, a reduction factorrR is proposed as the ratio of the topographic multiplier by MCS tothat by the simplified method:

rR ¼ StR=St,max ð22Þ

Here, the smaller value of rR means that the new topographicmultiplier shows a lower value against the conventional one. Itexpresses the effect of taking wind directions into account.

The topographic multipliers are investigated at Murotomisakiand Nagasaki meteorological stations to see the effect of returnperiod. Fig. 6 shows variations of topographic multipliers withreturn periods. For short return periods, StR shows a small valuebecause the occurrence rate of wind directions with a largedirectional topographic multiplier is relatively low. For longreturn periods, StR increases, but does not reach St,max, since theprobability of wind directions with St,max is lower than 100%. Inthis study, 50-year-recurrence period is considered following theinternational standard for the design of wind turbine (IEC61400-1, 2005).

4.2. Relationship between reduction factors and complex terrains

Topographic multipliers and reduction factors at the twostations are summarized in Table 3. The reduction factor is largerat Murotomisaki than that at Nagasaki. This difference in reduc-tion factor is probably related to the distribution of directionaltopographic multipliers (Fig. 3). If all directional topographicmultipliers are the same, the proposed topographic multiplier

0

0.4

0.8

1.2

1.6

0 1 2 3 4 5Reduced variate -LN(-LN(F))

Return period

2 5 10 20 50 100

Top

ogra

ohic

mul

tiplie

r

riod at (a) Murotomisak and (b) Nagasaki.

Table 3Topographic multipliers by the simplified method St,max and MCS St50, reduction

factors r50, and topographic variation coefficients st, at the two stations.

St,max St50 r50 st

Murotomisak 1.37 1.29 0.94 0.21

Nagasaki 0.87 0.70 0.80 0.50

Y. Kikuchi, T. Ishihara / J. Wind Eng. Ind. Aerodyn. 104–106 (2012) 558–564 563

coincides with the simplified one. When the difference betweendirectional topographic multipliers and their maximum value islarge, the reduction factor will decrease. To quantitatively evalu-ate this difference, a topographic variation coefficient st isintroduced as follows:

st ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXMi ¼ 1

ð1�St=St,maxÞ2

( )=M

vuut ð23Þ

where St/St,max is a normalized topographic multiplier and M isthe number of wind direction sectors. This factor should be0 when all topographic multipliers are the same as those of asymmetric hill, and become larger for complex terrains. st

becomes 0.21 in Murotomisaki and 0.50 in Nagasaki.In order to investigate the relationship between reduction

factors and topographic variation coefficients, topographic multi-pliers are systematically examined for terrains modeled usingsquare cosine on an x–y plane.

z¼Hcos2ðp=2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðx=LxÞ

2þðy=LyÞ

2q

Þ ð24Þ

where H is the hill height; Lx and Ly are the radius of short andlong axis of the hill, respectively. The y axis corresponds with thesoutherly wind. Fig. 7 illustrates a cross-section of the model aty¼0. The four models have aspect ratios varying from 1 to 8 asshown in Table 4s. Case 1 is an isolated hill and Case 4 expressesa ridge.

0

100

200

300

-500 -400 -300 -200 -100 100 200 300 400 500

z, w

y,vH

0

x,u

2Lx

�

Fig. 7. Cross-section of model at y¼0.

Table 4Size for each hill model.

y (1C) 2Lx (m) 2Ly (m) H (m) Ly/Lx

Case 1 21.8 1000 1000 200 1

Case 2 11.3 1000 2000 200 2

Case 3 5.7 1000 4000 200 4

Case 4 2.9 1000 8000 200 8

1.1

1.2

1.3

1.4

1.5

1.6

0 90 180 270 360

Topo

grap

hic

mul

tiplie

r

Wind direction (°)

Case 2Case 3Case 4

Fig. 8. Variation of (a) directional topographic multipli

Fig. 8(a) and (b) depicts directional topographic multipliersand normalized ones calculated by CFD. For larger aspect ratios,directional topographic multipliers vary significantly and speedupeffects become smaller at 01 and 1801 because model slopes getgradual.

In order to investigate the sensitivity of the effect of terrainorientations on reduction factors, the axes of models are rotatedclockwise from the north at 451, 901, and 1351 as shown in Fig. 9.

For 12 cases, the proposed topographic multipliers are com-puted by conducting MCS for 10,000 years. Terrain models areassumed to be located at the same longitude and latitude as thoseof the Murotomisaki station for MCS. Topographic variationcoefficients, topographic multipliers by the simplified methodand MCS and reduction factors for each model are summarized inTable 5. The reduction factor decreases as topographic variationcoefficient increases, and variations in reduction factors are slightcompared with the reduction effect by terrain complexity. Theresult indicates that the reduction effect by considering winddirectionality works in combination with terrain complexity. Forpractical purposes, it is found that when topographic variationcoefficient is large, the MCS method is recommended since theeffect of considering wind direction of tropical cyclones is greater.

Fig. 10 plots all data including models and real terrains. Therelationship between reduction factors and topographic variationcoefficients are expressed as follows:

r50 ¼ 2�expðst=3Þ ð25Þ

0.7

0.8

0.9

1

1.1

0 90 180 270 360

Nor

mal

ized

topo

grap

hic

mul

tiplie

r

Wind direction (°)

ers and (b) normalized ones with wind directions.

Fig. 9. Terrain model rotated by (a) 01, (b) 451, (c) 901 and (d) 1351.

Table 5Topographic variation coefficients st, topographic multipliers by the simplified

method St,max and MCS St50 and reduction factors r50 for each model.

st St,max St50 r50

Case 1 0 – – 1

Case 2-0 0.04 1.520 1.490 0.980

Case 2-45 1.494 0.983

Case 2-90 1.498 0.986

Case 2-135 1.490 0.980

Case 3-0 0.09 1.496 1.443 0.965

Case 3-45 1.454 0.972

Case 3-90 1.443 0.965

Case 3-135 1.447 0.967

Case 4-0 0.17 1.525 1.419 0.930

Case 4-45 1.432 0.939

Case 4-90 1.442 0.946

Case 4-135 1.417 0.929

0.75

0.8

0.85

0.9

0.95

1

0 0.1 0.2 0.3 0.4 0.5 0.6

Red

uctio

n fa

ctor

Topographic variation coefficient

45°90°135°MurotomisakiNagasaki

Fig. 10. Variation of reduction factors with topographic variation coefficients.

Y. Kikuchi, T. Ishihara / J. Wind Eng. Ind. Aerodyn. 104–106 (2012) 558–564564

In order to improve the accuracy of simplified method, Eq. (26) isproposed to predict the topographic multiplier of 50-year-recur-rence wind speed by the product of the maximum of directionaltopographic multipliers St,max and the reduction factor r50. The lowerlimit is set to 1.0 because the wind speed decrease should not beadopted in the design of wind turbines (Ishihara, 2010).

S50 ¼maxðSt,maxr50,1Þ ð26Þ

5. Conclusions

The topographic multiplier considering the effect of complexterrains and tropical cyclones is proposed and investigated. Thefollowing conclusions are obtained:

1)

The accuracies of the CFD simulation and Monte Carlo simulationare verified with the wind tunnel test data and the observations attwo typical meteorological stations. Considering a speedup effect

by complex terrains was important to evaluate extreme windspeeds.

2)

A topographic multiplier considering wind directionality isdefined as the ratio of certain-year-recurrence wind speed onreal terrains to that on flat terrains. A reduction factor isintroduced as the ratio of the topographic multiplier by MonteCarlo simulation to that by the simplified method. The reductionfactors are investigated at the two meteorological stations. Thereduction factor at the Murotomisaki station is less than that atthe Nagasaki station.

3)

A topographic variation coefficient is proposed as the deviationof directional topographic multipliers and is investigatedsystematically by using terrain models. The reduction factordecreases as the topographic variation coefficient increases.The speedup ratio of 50-year-recurrence wind speed is eval-uated as the product of the maximum of directional topo-graphic multipliers and the reduction factor to improve thesimplified method.

4)

The proposed topographic multiplier considering the winddirectionality for strong winds is the general framework andcan be used for strong winds induced by extratropical cyclones.

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