Basic wind speed map of India with long-term hourly wind data
N. Lakshmanan, S. Gomathinayagam*, P. Harikrishna, A. Abraham and
S. Chitra Ganapathi
Structural Engineering Rearch Centre, CSIR, Taramani, Chennai 600 113, India
Long-term data on hourly wind speed from 70 meteoro-logical centres of India Meteorological Department have been collected. The daily gust wind data have been procesd for annual maximum wind speed (in kmph) for each site. Using the Gumbel probability paper ap-proach the extreme value quantiles have been derived.
A design basis wind speed for each site for a return period of 50 years has also been evaluated. The site-specific changes in the design wind speeds in the con-temporary wind zone map for the design of buildings/ structures are highlighted and revision to the map is suggested.
Keywords:Anemograph stations, buildings and struc-tures, return period, wind speed map.
T HE wind speed map included in the IS:875 (Part-3)1, rves the primary purpo of choosing the ap
propriate basic wind velocity for the design of buildings and struc-tures. The recommended basic wind speed in the map refers to peak gust velocity averaged over 3 s duration, at a height of 10 m above ground level in a Category-2 terrain (open terrain with average obstructions on the surface being small and scattered), with a mean return period of 50 years. It is bad1 on the then available up-to-date wind data till 1982 from 43 anemograph (DPT, Dines Pressure Tube) stations spread over the country, obtained from India Meteorological Department (IMD). The cur-rently ud design wind speeds are bad on their return period at different locations. At the IMD meteorological stations, wind velocity is in general measured using the DPT installations at varying heights of 10–30 m. The records have been ud to carry out an extreme value analy-sis by veral meteorologists2–5 and by committee mem-bers responsible for the formulation of wind speed maps. In an attempt to re-examine the validity of the available basic wind speeds for different regions, the Structural Engineering Rearch Centre (SERC), Chennai, has under-taken reviewing of the basic wind speeds bad on the updated IMD data. However, only 70 out of the total 500 ground obrvatories of IMD spread out in India have the hourly wind data, including daily gust winds. SERC pro-cured all the available wind data from the 70 stations6. Most of the stations are either airports, aports or regional meteorological obrvatories. Isotachs (lines of equal velocity) in the wind speed map em impossible even now with the updated wind data, which are scanty and not available for longer
term at a clo enough grid of the meteorological stations. The number of stations where updated data are available from IMD is 3, 25, 9, 15, 17 and 0 respectively, for zones 1 to 6 of IS:875 (Part 3)1. The National Data Centre at IMD, Pune, which is the authorized clearing agency for the meteorological data, has supplied all the available data on wind speeds from 1966 to 2005, with a few gaps. The hourly data consist of eight ASCII decodable data files, with details of contents explained. In this article, a relook at the available wind data, analysis of gust wind speeds recorded at various sta-tions and probability of occurrence of wind speeds with a specific return period with proven methods of extreme value analysis techniques, are covered with a suggested revision for basic wind speed map.
Hourly wind data
As it is well known, wind speed in any region is highly variable naturally as well as owing to man-made indus-trial developments. For structural designs, even short-duration gusts are quite important becau any structure has to withstand the short-duration extreme wind loads with a safe level of member stress. The hourly wind speed records of 70 stations over different years in certain stations have a few gaps due to unavoidable stoppages in continuous operation of nsors and the recording instrumentation, power cuts and so on. Accord-ing to the contemporary version of IS:875 c
odal provi-sions, strong winds with speeds over 80 kmph are generally associated with cyclonic storms. In the hourly wind data-ba available with IMD, the daily gust wind peaks are assumed to include the cyclonic wind speeds as well, excepting regional tornado effects. It can be obrved that a good number of meteorological obrvations are available in zones 2, 4 and 5. There ems to be no long-term measurements in zone 6, which is the highest wind speed zone. In most of the hourly wind-data stations, the peak gust wind is picked up from the daily trace of anemo-
*For correspondence. (e-mail: s.in)
Figure 1. Distribution of daily gust wind speeds with some gap.
graph records. It is also to be noted that the continuity of data is limited in certain stations and missing gust wind data are also obrved in some stations. The databa of wind speeds from 43 stations up to the year 1982 has been ud in the formulation of the prent design wind speed map; this has not been significantly incread over the years. Out of the 70 IMD stations, about 56–58 stations have gust wind data at least for a few years up to 2005, with the newer stations having only less number of annual extreme wind-speed records. A typical extreme value analysis of the wind data of a lected station is discusd in the following ction.
Review of extreme value analysis
In general, extreme value distribution of load and strength
parameters of structural members and systems is important
for reliable analysis of design of components and struc-tures. For extreme wind speeds ud in the design of
structures, gust wind speed data should be available for
many years for every possible geographic location to be
specific. For the evaluation of wind loads on wind-nsitive structures, a regional design basis wind speed with a given return period is needed. The design wind speeds are derived from long-term record of wind gusts of specific region. Figures 1 and 2 show typical variation of daily gust wind speeds of Madras-Minambakkam station. The peaks are mathematically proved to be Raleigh-distri-buted for a parent with Gaussian process. Hourly gust wind data collected over every hour of a day for many years were obrved to be neither stationary nor follow a Gaussian distribution in most of the stations. The zero wind speeds in Figures 1 and 2 pertain to data which are not available for that hour or manifestation of a period of lull or ‘NO-WIND’. Extreme values are in general obrved to fit
into one of the exponential/logarithmic asymptotic forms commonly recognized as Type-I, Type-II and Type-III. All the three forms can be reprented by a single expression 3 given by a generalized extreme value (GEV):
1/()()exp 1,X x G x ξξμσ−⎧⎫−⎪⎪
⎡⎤=−+⎨⎬⎢⎣⎦⎪⎪⎩⎭ (1)
where μ, σ and ξ are the location, scale and shape
parameters respectively, which define the characteristicsclip是什么意思
of the extreme value distribution. The parameters have to be then evaluated from a valid databa of fairly long-term annual wind-speed records. If ξ > 0, GEV is known
as Type-II (Frechet) distribution with an unbounded upper
tail (μ – σ /ξ < x < ∞). The ca of ξ < 0 is called the
Type-III (rever Weibull) distribution, with a finite upper
limit (–∞ < x < (μ – σ /ξ)). As ξ → 0, the Type-I Gumbel 7
distribution is obtained which is given by
遒劲
G X
(x ) = exp{–exp[–(x – μ) /σ]}. (2)燕麦的功效
This distribution has been widely ud for modelling extreme wave heights, annual maximum flood levels and annual maximum wind speeds to arrive at characteristic values with specific return periods, for engineering design of buildings and structures. With the shape parame-ter approaching zero, the distribution is defined with location and scale parameters which are to be estimated from long-term data pertaining to any geographic loca-tion/site. The usual methods of extreme value analysis are
Figure 2. Peak distribution of daily gust wind speeds for one typical year.
Figure 3. Issues in the evaluation of basic design wind speeds for a
given return period.
tho of moments, maximum likelihood method, order-statistics approach and Gumbel’s probability paper approach. For the analysis of design wind speed estimates, the National Building Code of Canada (NBCC) has adopted 3 the peaks-over threshold (POT), r largest order
statistics approach (r -LOS) and Annual Maximum Gumbel (AMG) methods. The authors concluded that the (r -LOS)
is preferable over the other two methods and is more ver-satile since it has lower sampling variability associated with its extreme quantile (parameter) estimation. In this study a proven method of order statistics 8,9 is utilized, ensuring an unbiad and minimum variance estimator for a given sample size and exceedance probability, in Gumbel’s probability paper format. The various issues of evaluating a design basis wind speed from hourly wind data are given in Figure 3.
Method of moments
choo的用法In this method, the sample mean and sample variance are mathematically related to the location, scale and shape parameters of the GEV distributions. This method is an approximation of the probabilistic integral-bad appro-aches. Using the statistical relations of sample moments to the distribution parameters, the distribution can be realized. In the ca of inadequate number of samples, it is possible to simulate additional samples using Monte Carlo techniques, according to the fitted probability dis-tribution. However, the simulated data will be biad on the sample moments and the statistics. Thus the occur-rence of high wind speeds, their arrival quence or the return period will not be realistic. When the sample data are long enough, this method of simulation may result in the right characteristic values. Bad on this method an interactive computer program in VC ++, for site-specific cyclonic wind data processing has been developed at SERC
10,11
. Method of order statistics When the sample size is considerably small, such as the annual measured maxima of wind speeds at any given location, the method of moments approach may predict
the characteristic wind speeds of a given return period bad on poorly fitted extreme value distribution. This results in large variance in the simulated occurrence of wind speeds. A method bad on the theory of order sta-tistics was developed by Lieblein 12, which is bad on a linear function of a t of ordered values such as random wind speeds (U 1, U 2, . . . , U r ), that is,
1
,r i i i L w U ==∑ (3)
where U 1 ≤ U 2 ≤ ⋅ ⋅ ⋅ ≤ U r , and w i are weights that may be
decompod into
w i = a i + b i s p , (4)
where s p is the value of the standardized variate S at an exceedance probability p ; that is,
exp(–e –s ) = 1 – p or s p = – ln[– ln(1 – p )]. (5)
Then the estimator given in eq. (3) becomes
1
[()]r
i i i i p i L a U bU s ==+∑, (6)
textpatternwhere the weights a i and b i are functions of ‘r ’ and ‘p ’, and the following conditions are impod: The expectation of L , 1(),r p r
E L u s α=+ (7)
and the variance of L ,
Var(L ) = minimum. (8)
In view of eqs (6) and (7), the unbiad minimum vari-ance estimators for u r and αr are given as 8:
ˆr u = 1,r
ctm是什么意思
i i i a U =∑ (9)
11,ˆr
i i r i bU α==∑ (10)
Lieblein 12
obtained the relevant t of weights to be ud for values of r = 2–6 for the exceedance probability of over 90% (i.e. P ≥ 0.90) and also concluded that the rela-tive efficiency of the estimator is over 80% only when r = 5 or 6. He recommended that for sample sizes greater than 6, the entire t of sample space should be divided into subgroups of five or six, and the remainder in another subgroup. This is bad on the assumption that the t of extreme values constitutes a statistically independent ries of obrvations, which must be prerved while imple-menting this method. Usually the original data quence of the gust wind ries would satisfy this requirement. The method given by Ang and Tang 8 was coded in MATLAB 13 script language and a program developed for the extreme wind data analysis. The number of years of hourly wind data availability varied from site to site.
词组英语Hence the program takes interactively an option from the
ur, to enable the choice of the subgroup size (five or six)
so that the remainder subgroup size is non-zero. Within
the subgroup of extreme wind speeds, the data are
arranged in increasing order according to Lieblein’s
grace李秀英
requirement. In order to avoid repeating annual maximum
wind speed data, a random number generating scheme一年级语文拼音补习
was ud to marginally adjust the repeating data, from being not exactly equal. While assuming Gumbel prob-ability distribution, the ratio of sample rank to sample size fixes the probability of occurrence of any wind speed. Hence repeating data need to be fitted for predic-tion, with marginally differing probabilities. Some of the results of this analysis are discusd here. Results of extreme wind data analysis The hourly wind databa has been scanned for individual
stations bad on their specific identification number and the gust wind data pertaining to every available wind monitoring station have been parated into unique named files for statistical analysis. A typical plot of the
long-term daily gust wind is shown in Figure 1. It may be
obrved that there are veral days with either null or zero gust wind (no data available) recorded at the Madras-Minambakkam station. This is evident in the histogram given in Figure 4 a . To be realistic for design purpos (peaks over the mean are
important), the up-crossing peaks shown in the zoomed view of one-year daily gusts with peaks over the mean
given in Figure 2 were considered and their distribution is shown in Figure 4 b . The zero values and down-crossing valley points were eliminated in the count and only posi-tive up-crossing peaks were gathered during the period of
data collection. A high-resolution time history (say, 10–
20 samples/s) of wind data at any given site is not avail-able for long periods (in years), which is a li
操场的英文mitation un-avoidable even in developed countries. In general, if the
synoptic wind speed has been a stationary and Gaussian process, only then the extreme peaks could follow a
Raleigh distribution. It could have been stationary for a short duration, i.e. 10 min to 1 h, but is unlikely to be sta-tionary for the entire day or, for days, or for years. Hence, the daily gust wind data available at every station are with some limitations of sophistication in the instrumen-tation, data-collection reduction and recording. For com-pleteness, simple statistical details of the available daily
Figure 4. Histogram of daily gust/peak wind speeds of IMD databa.
gust wind speed records for all the IMD stations are given in Table 1. The peaks are not likely to have uniform spac-ing becau of synoptic as well as monsoon wind cli-mates. The arithmetic mean of the gust hourly wind speed data of IMD and of the peaks is given in Table 1. Their standard deviations and probable peak values are given in the columns marked as ‘Extreme’, with the assumption of the threshold peaks being the sum of the mean plus three times the standard deviations. There is always an ambigu-ity in this statistical analysis as the predicted extreme wind speeds include both data from synoptic as well as monsoon winds, since they span veral days of many years of data. It has been obrved in most of the IMD stations that the difference of extremes predicted using all the gust wind statistics as well as up-crossing peak order statistics is marginal. The total counts of the daily records in individual sta-tions indicate the number of years of data available in the site. More than ten stations have maximum gust speed (MGS) data less than 4–5 years, which are not uful for design wind prediction. Most of the gust wind speed records being from synop-tic/monsoon winds, it is likely to be highly variable from site to site. Bad on statistical scatter of gust wind statis-tics and up-crossing peak wind characteristics, Figure 5 provides part of the scatter of ‘mean gust wind speed’ (G -mean of 14,098 samples for Madras Minambakkam, from
July 1983 to 2005 shown in Figure 1) vs gust peak (which is the mean gust plus three times its standard deviation), peak–peak (which is the mean of 7374 peaks (indicated typically in Figure 2) plus its standard devia-tion). There is clo to 80% coefficient of determination of mean of peaks (EP-mean) and peak of peaks in the measured met-sites in India with the respective G -mean. Ca study of site-specific design wind speed To arrive at the method of evaluation of site-specific design basis wind speed using the limited long term annual (MGS) wind data available, the method of order statistics described earlier with 5 or 6 in each sub-group, and with a remainder sub-group having less than 5 or 6, has been implemented using MATLAB script program. The Madras-Minambakkam datat having 41 years of data has been illustrated as a typical ca study. The data span from the year 1969 to 2005; part of the data from July 1983 is shown in Figure 1 and is distributed as shown in Figure 4. There have been few years of repetition using probably additional instruments in the gust wind data. If the additional data belonged to the same station number, they were merged in one datat for analysis.
Gumbel’s probability paper approach was adopted and the arrival quences of extreme wind data according to the available records were prerved. The MATLAB script file developed for the analysis has the options to choo any one station data or to process all the station data. It also facili
tates the probability plots with predicted char-acteristic wind speeds for 50-year return period. The Gumbel’s probability paper approach resulted in the esti-mation of the scale and location parameters by graphical evaluation of the intercept and the slope of the fitted straight line on the probability paper. The Gumbel fitted annual extreme wind speed from the annual hourly data as given in the IMD databa is shown in Figure 6. The predicted value was around 126 kmph for a mean return period of 50 years, which is about 35 m/s. The dotted line above the mean line in Figure 6 gives the upper confi-dence limit of 84.13%, corresponding to 1σ variation of the predicted maximum wind speeds, which in this ca is about 37 m/s. The zonal classification in IS:875 is zone 5, which corresponds to 50 m/s. U of all the annual hourly data gives a lower design basis wind speed. Figure 6 shows horizontal scatter in the plots owing to repetition
of data in the measured period of 41 years. To get a linear fit in the probability plot minor adjustments to the repeat-ing data have been carried out manually avoiding exact
repetition. The resulting plot is shown in Figure 7, which
gives a prediction of slightly higher wind speed than the unadjusted values. Further improvements in the straight-
