161

A New Approach to the Specification of the Design Wind Speed
Considering Long-term Trends in the Wind Climate
Michael KASPERSKI
Ruhr-University Bochum
Department of Civil and Environmental Engineering Sciences
44780 Bochum, Germany
e-mail: michael.kasperski@rub.de

Abstract
Any analysis of extreme values of wind climates with the aim of estimating design wind speeds suffersfrom statistical uncertainties induced by short observation periods. As can be shown by simulations, theidentification of the ‘true’ parameters of a wind climate is virtually impossible. The situation is even worse
if trends have to be evaluated in regard to their statistical significance. These trends may result from a global
climate change which can also affect the wind climate. Particularly, trends in the number and intensity ofstorms seem to be of basic interest. The corresponding probability distributions are the Poisson distribution
with describing parameter λ (average number of storms per year) and the Generalized Pareto distribution
with describing parameters s and k (scale parameter and shape factor). The new approach is based on theidea that the observed parameters λobs, sobs, kobs and the corresponding linear trends aλ, obs and as, obs may beobtained from a large range of combinations of λ, s, k, aλ and as. In a first step, the probabilities are calculated that the observed parameters will be obtained for each combination λ, s, k, aλ and as. Then, for eachcombination, the design wind speed is calculated (for different target probabilities and different design
working lives). Sorting the obtained design wind speeds and integrating their corresponding probabilities
gives the non-exceedance probability curve of the probable design wind speed. The ‘best estimate’ isobtained by applying a target confidence interval of 75% which has previously been introduced as a basis
for estimating design values for the resistance side when dealing with statistical uncertainties from confinedensembles. Based on the findings for the wind climate at Düsseldorf, it is strongly recommended to consider
non-stationary features when specifying design wind speeds. The assumption of a stationary wind climate
may lead to considerable underestimations of design wind speeds.
Key words: extreme wind climate, design wind speed, statistical uncertainties, long-term trends,
climate change

1. Introduction
Although the appropriate specification of the design
wind speed is of vital importance to the wind resistanceof a structure, experts have failed to agree on a uniform
method for estimating this value based on meteorological observations of wind speeds. The discussions deal
with almost any aspect of the problem, starting with thequestion on the basic ensemble (extremes over a certain
threshold or yearly extremes), the appropriate extreme
value distribution (Gumbel or Reverse Weibull), therepresentative variable (v or v² or even v³), the fitting
method (BLUE or least-square fit), the sampling period(calendar year or meteorological year) and so on(Kasperski, 2009). Furthermore, many codes hide theactual design value by specifying a partial factor and acharacteristic value which refers to a specific return
Global Environmental Research
13/2009: 161-168
printed in Japan

period. The large variety of code-concepts – with return
periods from 5 to 1000 years and recommended partial
factors from (at first sight confusing) 0.93 to 1.6 –reflects the basic uncertainty of the experts rather thanthe different demands in regard to the reliability of thestructures.
The basic cause of the never-ending discussions liesin the low statistical stability of the extreme-value
analysis which usually is based on only a few decades of
meteorological observations. This can be shown by
simulations which are based on a probabilistic modelwith two key variables for the extreme wind climate:
the number of storms per year N and the intensity perstorm v. The corresponding model is shortly describedin section 2. Specifying the design target values forwind speed in terms of an appropriate exceedance
probability then allows identifying the large un©2009 AIRIES162

M. KASPERSKI

certainties (section 3).
The ongoing discussions on global climate change
and its possible impacts on the extreme wind climate
form a further challenge when specifying the design
value of the wind load. For an appropriate wind resistantdesign of future buildings and structures, long-term
trends in the wind climate have to be considered. However, the available observation periods are usually too
short to identify the shape and the intensity of nonrandom long-term trends with sufficient statisticalstability.
Accepting that the ‘true’ parameters of the extreme
wind climate, including long-term trends, cannot be
identified leads to the understanding that virtually any
wind climate may hide behind the observed parameters,
though with different probabilities. Based on simulations, these probabilities can be identified. They provide
the probabilistic basis for a new concept of getting thebest estimate of the design wind speed. The basic idea of
this new approach is described in section 4 and one firstexample of its application is provided in section 5.

2. Basic Variables of the Extreme Wind
Climate and Target Design Values
A general approach to the analysis of the extreme
wind climate considers at least the following two basic
variables: the number of events, N, per year and theintensity, v, of an individual event. For this approach, anappropriate threshold value has to be chosen. As sufficient condition for independent events, often the time
between two exceedances of the threshold value can beused, e.g. 12 to 24 hours for strong frontal depressions.
Sampling the events for an appropriate aeolian year(continuous twelve-month period in which a complete
annual climatic cycle occurs) prevents that a single
storm may be discontinued by the sampling unit ‘year.’
The non-exceedance probability of a reference value
vref per year is obtained as follows:∞p( v ≤ v ref | year) =∑ p(N) ⋅ p(v ≤ v )
ref

N

(1)

N =0

It is important to note, that in the presence oflong-term trends the parameter ys plays a significant
role.
For a stationary wind climate, i.e. for the nonexceedance probability of vref being the same in eachyear, equation (2) becomes:p(v ≤ v ref | lifetime) = p(v ≤ v ref | year) L

A reasonable model for the number of events per
year is obtained with the Poisson distribution:p( N ) =The non-exceedance probability of a reference value
vref for the whole design working life of the structure isaccumulated over a set of single years as follows:

ys : starting year of exposure
L : design working life in years
pi : non-exceedance probability of vref in year i(4)

λ : average number of events per year
For the intensity of the single events, the Generalised
Pareto distribution may be used (Holmes & Moriarty,1999):⎡⎣p(v ≤ v ref ) = 1 –- ⎢1+

v ref − vs ⎤
⋅ k⎥
s
⎦

−1/ k

(5)

vs : threshold values : scale parameterk : shape factor
In case of a negative shape factor, the distribution
has a finite upper tail which can not be exceeded. The
corresponding largest value is given as:v max = vs − s / k(6)

For k = 0, the exponential distribution is obtained:⎛ ( v − vs ) ⎞p(v ≤ v ref ) = 1 –- exp ⎜ − ref
⎟
s
⎝
⎠

s =

(7)

(2)

1
2
⋅ m ⋅ ⎡1+ ( m/σ ) ⎤
⎣
⎦
2
(8)

ys +L
i=ys

λN − λ⋅eN!

The two parameters s and k can easily be obtained
from the mean value m and the standard deviation σ ofthe exceedances of the threshold value, i.e. from the newvariable (v–vs):N : number of storms per yearp(N) : probability of N storms per yearp(v≤vref) : non-exceedance probability per event.

p(v ≤ v ref | lifetime) = ∏ pi (v ≤ v ref )

(3)

k=

1 ⎡
2
⋅ 1–
1- ( m/σ ) ⎤⎦2 ⎣For the specification of the appropriate design target
values it is reasonable to distinguish structural classes inregard to their importance level. The recently publishedA New Approach to the Specification of the Design Wind Speed

structural classptarget / year
(ISO 4354, 2009)
ptarget /working life
(Kasperski, 2009)

A

B

C

D

1/20001/1000

1/500

1/200

0.025

0.05

0.10

0.20

(a)
2.6

identified number of storms per year

Table 1 Target values of the exceedance probability of thedesign value wdes of the wind load or wind load effectfor the ultimate limit state.

ISO 4354 (ISO 2009) distinguishes four classes:

2.0

1.8

1.6

30

40

50

60

70

80

90

100

80

90

100

80

90

100

years of observation

(b)
3.0

2.5

2.0

1.5

1.0
20

30

40

50

60

70

years of observation

(c)
0.1

0.0

identified shape parameter

The statistical stability of the estimated parameters λ,s and k can be studied based on simulations. In thefollowing, a wind climate is assumed with vs = 14.1 m/s,
λ = 2, s = 2.0 m/s and k = – 0.1. A single simulation run
leads to a random number of M storms in K years
observation period and a corresponding ensemble of M
random wind speeds. From these data, a random value λof the average number of storms per year is obtainedplus random values of the shape parameter s and thescale factor k. Based on 106 independent simulation runs,
90% confidence intervals are estimated for the threedescribing parameters for different observation periods.
Based on these simulations, Fig. 1 shows the change inthe confidence interval for observations periods of 20 to
100 years. Even an observation period of 100 years is
not long enough to suppress the random scatter in theidentified parameters.
The statistical uncertainties in the estimated valuesof λ, s and k lead to uncertain estimates for the design
wind speed. Basically, the effect of the uncertainties will
increase with decreasing target exceedance probability,
i.e. with longer design working life and higher importance of the structure.

2.2

20

The corresponding target values for the ultimate
limit state are specified in ISO 4354 with reference to asingle year and are summarized in Table 1. In a moregeneral approach the target probabilities refer to thedesign working life of the structure. The respective values are also given in Table 1. Both demands are approximately the same for a 50-year design working life.
Strictly speaking, the target values refer to the design
wind load. For a general solution it is reasonable todemand the same target exceedance probabilities for thedesign wind speed.

3. Statistical Uncertainties in the Describing
Parameters of the Extreme Wind Climate

2.4

1.4

identified scale parameterA : structures with a special post-disaster function (hospitals, schools, transmission lines, bridges)
B : buildings which as a whole contain people in crowds(high-rise buildings, stadia, concert halls)
C : normal structures (office buildings, commercial
buildings, factories, residential buildings)
D : structures presenting a low degree of hazard to life
and other properties (farm buildings, house chimneys,
roofing tiles)

163

-0.1

-0.2

-0.3

-0.4

-0.5
20

30

40

50

60

70

years of observation

Fig. 1 Influence of the observation period on the 90%-confidence
interval of the statistical parameters of extreme windclimate.
(a) number of events per year λ, (b) scale parameter s,(c) shape factor k

The basic influences of uncertain scale parametersand shape factors on the trace of the non-exceedance
probabilities of the wind speed are shown in Fig. 2
considering a range from 1.5 to 3 for the scale parameterand a range from – 0.45 to 0.1 for the shape factor. The

164

M. KASPERSKI

(a)

(b)
1.75
s = 1.5

2.25
2
2.5 2.75 m/s

k = -0.35 -0.25 -0.15 -0.05

non-exceedance probabilty

non-exceedance probabilty

0.99

0.9

0.5
0.1
0.01
0.001
10

15

20

25

+0.05

0.999

0.999

0.99

0.9

0.5
0.1
0.01
0.001
10

30

15

20

25

30

wind speed [m/s]wind speed [m/s]Fig. 2 Influence of s and k on the trace of the non-exceedance probability of the wind speeds.
(a) λ = 2, k = – 0.1 , (b) λ = 2, s = 2 m/s

average number of storms per year is assumed to be 2.
Assuming a design working life of 50 years, the design
wind speeds for class B and class C buildings are
obtained approximately as the 99.8% and 99.9% fractile.
Depending on the actual combination of s and k,considerably different design wind speeds are obtained.

4. Best Estimate of the Design Wind Speed
The simulations suggest that the ‘true’ parameters of
the extreme wind climate cannot be identified. It has tobe concluded that virtually every wind climate may hidebehind the observed parameters, though, with different
probabilities. The probability p, that a specific triple (λ,s, k) randomly leads to the observed triple (λobs, sobs,kobs), can be obtained from simulations. In the next step,for each triple (λ, s, k), a design wind speed can be estimated. Sorting the design wind speeds in ascendingorder with their corresponding probabilities allows constructing a probability distribution of the uncertain
design wind speed:i(p ( v des ≤ v des, i ) = ∑ p j vdes ( λ j , s j , k j )
j=1

)

(9)

This new approach can easily be extended tolong-term trends. Assuming only linear trends in thefirst approach leads to two further variables, the slope
for the number of storms per year aλ and the slope forthe intensity of individual events av. Equation (9) thenbecomes:i(p ( v des ≤ v des, i ) = ∑ p j v des ( λ j , s j , k j , a λ , j , a v, j )
j=1

)

(10)
The final design wind speed can be obtained basedon a chosen confidence level. Basic demand of any

estimation of a design value of actions or action effects
is to avoid an underestimation of the design value by
applying an appropriate one-sided confidence. The probability of underestimation can be understood as the error
probability; the complementary probability is the confidence. The question arises, how small the error
probability should be. An intuitive choice would lead tosmall values, say in the range of 1% to 5%. It is however important to note that the probability of overestimation increases with decreasing error probability. In
civil engineering, the question on the appropriate error
probability has already been answered in the context of
estimating the design value for the resistance based on
experiments. The Eurocode (CEN, 2002) for instancerecommends 75% as an appropriate confidence interval,
i.e. the corresponding error probability would be 25%.
Consequently, the best estimate of the design windspeed is obtained as the 75% fractile value of the probable design wind speeds.

5. Example of Application
The new method is applied to the extreme wind climate at Düsseldorf, Germany. The governing storms arestrong frontal depressions which mainly occur during
the period from October to March. As representativevalue, the largest hourly mean wind speed of independent events is used. Figure 3 shows the identified probability density for the average number of storms per
year and the identified probability distribution for thestrongest hourly mean value of individual storms. It is
worth mentioning that the respective ensembles are
obtained applying the German aeolian year which extends from the 1st of May of one year to the 30th ofApril of the consecutive year (Kasperski, 2007).
Although the observation period at Düsseldorf consistsof 55 years, there is a considerable uncertainty in theidentified parameters of the extreme wind climate.
Based on simulations, in Fig. 4 the probability densitiesof the triples (λ, s, k) are shown which randomly lead toA New Approach to the Specification of the Design Wind Speed
(a)

165

(b)

Fig. 3 Observed parameters of the extreme wind climate at Düsseldorf airport (1952-2007).

(b)(a)
0.00100.00080.03

0.0006freque0.02

0.0004ncy

0.00020.2

0.0000
1.0
0.01

0.0

1.5

-0.2

2.0

60

70

80

90

100

110

120

130

true number of events in 55 years

3.0

-0.6
3.5

sh
a

sc
ale

0.00

-0.4

2.5

pe

e
relativ

rel. frequency of getting 92 events

0.04

-0.8
4.0

Fig. 4 Randomness in identified parameters.
(a) probability density for observing 92 events in 55 years for different λ-values(b) joint-probability density for getting the observed parameters sobs and kobs from an ensemble with 92 events

the observed values, assuming that the number of storms
per year and the intensity of the storms are statisticallyindependent. The full simulation involves 106 independent runs each corresponding to the sub-period of
55 years. The resulting possible range for λ is from 1.18
to 2.27. For the scale parameter, the simulation
identifies a range from about 1.0 to 3.5 m/s, while theshape factor probably lies between – 0.5 and +0.25.
A more refined analysis of the wind climate at
Düsseldorf suggests that there might be long-term trends
in the number of storms per year and in the intensity ofthe storms. Applying a linear shape for the trends leads
to the identified increases shown in Fig. 5. The observed
trends are not negligibly small. Over the observation
period of 55 years, the study suggests that the number ofstorms has increased by about 60% from 1.3 to 2.1
storms per year. Similarly, the average intensity of astorm has increased by about 5% from 15.4 to 16.1 m/s.
In terms of wind loads this increase corresponds to 10%.
A step of 10% wind load approximately corresponds toa doubling of the exceedance probability over a lifetimeof 50 years, i.e. the observed increase in wind speeds

166

M. KASPERSKI

corresponds to a difference of one structural class.
It is important to note, that a confined ensemble may
contain a random trend although the ‘true’ process isstationary. However, without knowing the ‘true’ parameters of the underlying process, there is no way to study
the randomness of trends in confined ensembles. Only
the new concept provides the basic possibility ofconsidering long-term trends in the scope of a consistentprobabilistic approach.
The new approach therefore introduces the linear
trends in the number of storms per year and the intensityof the individual storms as further uncertain variables.
Simulations then lead to the joint probabilities of λ and s
and their corresponding trends which randomly lead tothe observed parameters. Sufficiently stable estimates ofthese joint-probabilities, however, require an enormous
number of independent simulations. For the joint
probabilities in Fig. 6, approximately 55.4 and 77.5
billion simulations have been performed. Both joint(a)probabilities suggest only a small probability that there
is no increasing trend in the number of storms per year
and/or the intensity of the individual storms with valuesof about 10%.
The last step in the analysis is to combine the joint
probabilities of all the parameters to obtain a cumulative
probability distribution of the uncertain design windspeeds. As input parameters, the design working life andthe structural class may be varied. Figure 7 shows thecorresponding traces for stationary and non-stationary
wind climate assuming a class B building. For the
non-stationary wind climate, two different years havebeen chosen for the actual start of the exposure.
The corresponding final design wind speeds are
summarized in Table 2. Additionally, design windspeeds are given which are obtained by directly using
the observed parameters. The new concept reveals thebasic danger of underestimating the design wind speed
when using the observed parameters without any further
(b)

8

22

max. hourly mean wind speed [m/s]number of storms per year

7
6
5
4
3
2
1
0
1950

1960

1970

1980

1990

2000

20

18

16

14

0

2010

20

40

60

80

100

no. of storm

year

Fig. 5 Identified linear trends in the number of storms per year and the intensity of the individual storms.
(a) slope aN = 0.01472 / year, (b) slope av = 0.00749 per storm

(a)

(b)

0.016
0.008

0.014
0.012

0.006

0.008

f (av, s)

0.006
0.004

0.002

2.50
2.25
2.00
1.75
1.50
1.25

0.00

0.01

0.02

a

N

0.03

4.0
3.5
3.0
2.5
2.0

0.000
-0.01
0.00

λ

0.002
0.000
-0.02
-0.01

0.004

0.04

0.05

1.00
0.06

Fig. 6 Joint probabilities of parameters leading to the observed trends.
(a) aN and λ, (b) av and s

0.01

a

v

1.5
0.02
0.03

1.0

s

f (aN, λ)0.010

A New Approach to the Specification of the Design Wind Speed(a)

Table 2 Best estimate of the design wind speeds for different
values of the design working life, class B.

1.0
0.9

non-exceedance probability

167

10

0.8
0.7

L [years]
observed
parameters
new concept
non-stationary new concept,
wind climate ys = 2009
new concept,
ys = 2029
stationary
wind climate

20 50
80

0.6
0.5
0.4
0.3

10

20

50

80

21.90

22.55

23.34

23.71

23.74

24.71

25.98

26.62

25.05

26.39

28.97

31.19

26.23

27.65

30.31

32.57

(all design wind speeds in m/s)

0.2
0.1
0.0
20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

design wind speed [m/s]

(b)
1.0

non-exceedance probability

0.9
0.8

10
20

0.7

6. Conclusions

50
0.6

80

0.5
0.4
0.3
0.2
0.1
0.0
20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

31

32

33

34

35

design wind speed [m/s]

(c)
1.0
0.9

non-exceedance probability

trends in the wind climate leads to further increases ofthe design wind speeds. The further into the future theexposure starts, the larger the design wind speeds willbe. For an exposure starting in 2009, there is an additional increase of about 11% to 37% for wind loads. If
the exposure starts in 2029, a further 10% increase in
the wind load will be required to counterbalance theeffects of the probable long-term trends.

0.8

10

0.7

20
50

0.6

80
0.5
0.4
0.3
0.2
0.1
0.0
20

21

22

23

24

25

26

27

28

29

30

design wind speed [m/s]Fig. 7 Cumulative probability distributions for design windspeed.
(a) stationary wind climate, (b) non-stationary windclimate beginning of exposure in 2009, (c) nonstationary wind climate beginning of exposure in 2029.

considerations. Even for the assumption of a stationary
wind climate, the best estimates for the design windspeeds are 8.4% to 12.3 % larger than the design windspeeds directly based on the observed data. In terms ofwind loads, the differences are 17.5% to 26.1% for lifetimes from 10 to 80 years. Consideration of long-term

The low statistical stability of extreme-value analysis
of wind speeds has led in recent decades to completely
diverging concepts for wind resistant design. As can beshown by simulations, the identification of the ‘true’
statistical parameters of a wind climate is virtually
impossible. It has to be concluded that a set of observed
parameters can be obtained for a large variety of ‘true’
parameters. However, the probability of getting theobserved parameters differs for different sets of ‘true’
parameters. This has led to the basic idea of developing
a probabilistic approach to the most probable design
wind speed, considering the statistical uncertainties in
the observed parameters for the extreme wind climate,including the presence of long-term trends. Based on
simulations, the non-exceedance probability of anuncertain design wind speed can be obtained. The best
estimate of the design wind speed is given with a
75%-confidence level. The new method allows overcoming the discrepancies between the actually used concepts for the specification of the design wind speed.
Based on the findings for the wind climate at Düsseldorf,
it is strongly recommended to consider non-stationary
features when specifying design wind speeds. The assumption of a stationary wind climate may lead toconsiderable underestimations of design wind speeds.

Acknowledgment
Part of this work was sponsored by the Federal
Ministry of Research and Education as part of thejoint-research project RegioExAKT. This support is
gratefully acknowledged.

168

M. KASPERSKI

References
C.E.N. (2002) EN 1990 – Basis of Structural Design.
Holmes, J.D. and W.W. Moriarty (1999) Application of the generalised Pareto distribution to wind engineering, Journal of Wind
Engineering and Industrial Aerodynamics, 83: 1-10
ISO (2009) ISO 4354 – Wind Actions on Structures
Kasperski, M (2007) Design wind loads for a low-rise building
taking into account directional effects, Journal of Wind
Engineering and Industrial Aerodynamics, 2007: 1125-1144
Kasperski, M. (2009) Specification of the design wind load – acritical review of code concepts, Journal of Wind Engineering
and Industrial Aerodynamics, 2009: 335-357

Michael KASPERSKI
Born in Herne, Germany on 25
September 1958, Michael Kasperski
graduated with a degree in Civil Engineering in 1983 at Ruhr University
Bochum. He obtained his doctorate inengineering in 1988 at the same
University for his work on cooling
towers under wind load. Finally, in 1998
the Department of Civil and Environmental Engineering Sciences of Ruhr University Bochum awarded him ahabilitation doctorate in engineering for his research work in the field“Bases of Design in Structural Engineering.” This research fieldcomprises the theory and application of development of probabilistic
models of actions and action effects, of structural resistance and of staticand dynamic behaviour of structures. Beside theoretical approaches,
further design tools include field and laboratory tests and simulations.
Finally, the field involves study of problems dealing with the specificationof basic design targets in terms of limit states for structural safety andserviceability.
Since 2002 Michael Kasperski has headed the Research Team EKIB
at Ruhr University Bochum. Additionally he serves as BIT Part Time
Professor at the Beijing Institute of Technology in Beijing, China. One ofhis major research interests lies in the field of wind engineering. He iscurrently member of the editorial board of the International Journal ofWind and Structures. His other major research topics are structuraldynamics, especially under human-induced actions, serviceability ofstructures in regard to vibration and reliability of structures.
The research results of the Research Team EKIB form the basis forhis consultancy and codification work. Currently, Michael Kasperski is acommittee member of the ISO TC 98 – Bases of Design of Structures andsome of the related working groups. In the national codification field he ismember of the German Committee NABau 00.02.00 Actions on
Structures.

(Received 18 September 2009, Accepted 22 November 2009)