

ORIGINAL ARTICLE 

Year : 2016  Volume
: 39
 Issue : 2  Page : 107112 


Extreme value statistical analysis of meteorological parameters observed at Kudankulam site during 2004–2014
Jayasudha Prabhu^{1}, Thomas George^{1}, B Vijayakumar^{1}, PM Ravi^{2}
^{1} Environmental Survey Laboratory, KKNPP, Tirunelveli, Tamil Nadu, India ^{2} Health Physics Division, BARC, Mumbai, Maharashtra, India
Date of Web Publication  13Sep2016 
Correspondence Address: B Vijayakumar Environmental Survey Laboratory, Anuvijay Township,Tirunelveli  627 120, TamilNadu India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09720464.190388
For any civil engineering work, knowledge of extreme weather conditions at the site of interest is essentially required to design engineering structure that can withstand such extreme weather stresses. This paper presents an analysis of extreme values of meteorological parameters like temperature, estimated wind gust at 10 m height, wind speed, daily, monthly, and annual rainfall for 2004–2014. The yearly variations of these meteorological parameters were subjected to distribution analysis. Various distribution function parameters for each variable are determined. Extreme values corresponding to return periods of 50 and 100 years are worked out. These studies carried out in Kudankulam provide an insight into the extreme values of the considered variables over a period, generally during the expected lifetime of the reactor units and help the designer to arrive at the design basis values of different parameters as regards the safety of the units. Keywords: Design basis, extreme value analysis, meteorological
How to cite this article: Prabhu J, George T, Vijayakumar B, Ravi P M. Extreme value statistical analysis of meteorological parameters observed at Kudankulam site during 2004–2014. Radiat Prot Environ 2016;39:10712 
How to cite this URL: Prabhu J, George T, Vijayakumar B, Ravi P M. Extreme value statistical analysis of meteorological parameters observed at Kudankulam site during 2004–2014. Radiat Prot Environ [serial online] 2016 [cited 2022 Aug 13];39:10712. Available from: https://www.rpe.org.in/text.asp?2016/39/2/107/190388 
Introduction   
Knowledge of meteorological parameters of a site plays a vital role in designing of engineering structures. The design of engineering structures requires an understanding of extreme weather conditions that may occur at the site of interest, which is very essential so that the structures can be designed to withstand weather stresses. Such a study apart from common weather variables such as temperature, wind speed, and rainfall may include aspects such as flood, earthquake, and lightning in the locality before actually designing the structures. These weather condition parameters are characterized after subjecting the relevant data to statistical treatment. Depending on different meteorological parameters, these conditions will vary. In Kudankulam site, 2 units of 1000 MWe each of pressurized water reactor type (VVER) have been constructed, and the first unit attained criticality in July 2013. These studies provide an insight into the extreme values of the considered variable over a period, generally during the expected lifetime of the reactor units and help the designer to arrive at the design basis values of different parameters as regards the safety of the units. In view of the long life of nuclear reactors, civil structures should be designed to withstand extreme weather conditions likely to occur in another 50–70 years. The longterm analysis of rainfall at any place finds use in many applications such as irrigation engineering, water harvesting, public health engineering, drainage system design, and construction of dams.^{[1]}
Description of site
Kudankulam site (latitude 8° 9' 52” N and longitude 77° 42' 41” E) is located along the coast of Gulf of Manner, 25 km North East of Kanyakumari. Two units of VVER type reactors of 1000 MWe each have been constructed at Kudankualm and the first unit attained criticality on July 2013. A wellequipped micrometeorological laboratory is located at 0.7 km downwind distance from the site with a 60 m tower.
Materials and Methods   
Database and analysis
Primary meteorological variables such as wind speed, wind direction, atmospheric temperature, relative humidity, atmospheric pressure, and precipitation are measured using the sensors such as cup anemometer, wind vane, RTD (PT1000) sensor, solid state capacitance, metal wafer pressure sensor and tipping bucket rain gauge, respectively. These sensors are installed on 60 m tower and connected to a data acquisition system. The acquisition is done by the online MetDas Software which is Meteorological Data Acquistion System developed by Environmental Survey laboratory, BARC, Kudankulam. Hourly averaged and minute averaged data are recorded for all the above parameters. These data are the basic raw data used for extreme value analysis. The instruments used for various parameters with details are shown in [Table 1].
Longterm statistical analysis
From continuous data acquisition software, the raw data of the daily maximum and minimum of the atmospheric air temperature, relative humidity, atmospheric air pressure, hourly averaged wind speed, hourly rainfall in a day, a month and annual rainfall, yearly extreme values are obtained and used for extreme value analysis. The basic meteorological parameters data set used for extreme value analysis is given in [Table 2]. Rainfall data are given in [Table 3]. Wind data are required during the design stage for assessing the stability structures. Dynamic loading is especially needed in the design of tall structures such as cooling towers, transmission towers, communication towers, stack, etc., For dynamic calculations by wind gust effectiveness factor method, 5 min averaging period wind data is essential. Wind gust is estimated from standard 10 m height hourly averaged wind speed. Conversion of hourly averaged wind speed data into 5 min average wind gust using modification factor of,  Table 2: Yearwise extreme meteorological parameters at Kudankulam (20042014)
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V_{t}/V_{1h} = 1.15ss
where V_{t} is velocity for averaging time, t s and V_{1h} is velocity with averaging time 1 h.^{[2]}
Extreme value analysis
The data analysis was carried out as per the procedure described by Daoo et al.^{[3]} The meteorological variables chosen for this analysis are maximum and minimum air temperature, air pressure, maximum wind speed, minimum relative humidity, maximum rainfall in a day, a month, and annual rainfall. The values are arranged in ascending order for maximum and descending order for minimum and each data point is assigned a rank “m.” For data with the same value, although the rank is same, it is suitably designed so as not to leave gaps in the ordered data array. The probability of nonexcedence of a particular magnitude “X” of the data point of the rank “m” was obtained as,
P (X) = m/(M + 1)
Where “M” is the total number of data points.
The data were plotted for a linear fit between the data variables and reduced variate is a function of the probability of nonexcedence. Correlation coefficient between Y versus X_{p} and LN (Y) versus X_{p} for all the variables were found out to choose the best fit. It was found that the (R 1) correlation coefficient between Y versus X_{p} and (R 2) correlation coefficient between LN (Y) versus X_{p} range from 0.950 to 0.996. The (R 1) and (R 2) for all the variables are given in [Table 4]. The (R 1) coefficient of correlation is greater for Y versus X_{p} in the case of the maximum annual air temperature, hourly averaged wind speed at 60 m height, daily and monthly maximum rainfall. These variables obey Fisher–Tippet Type I distribution. The (R 2) coefficient of correlation between LN (Y) versus X_{p} is greater for minimum annual air temperature, minimum relative humidity, estimated 5 min wind gust, hourly averaged wind speed at 10 m height, annual rainfall and hence these variables obey Fisher–Tippet Type II distribution. [Figure 1],[Figure 2],[Figure 3],[Figure 4],[Figure 5],[Figure 6],[Figure 7],[Figure 8],[Figure 9] show the plots of extreme value distribution of different meteorological parameters.  Table 4: Summary of correlation analysis of extreme value of meteorological parameters
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 Figure 4: Extreme value analysis of maximum hourly wind speed 10 m height
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 Figure 5: Extreme value analysis of maximum hourly wind speed 60 m height
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Equation for a straight line in the plot of Y versus X_{p} can be written as:
Y = α + β1*(X_{p})(1)
Where X_{p} is the reduced variant corresponding to P (X), defined as,
X_{p}= −Ln (−Ln [P (X_{p})])(2)
−Ln (P[X_{p}]) = exp (X_{p}) or
P (X_{p}) = exp (−exp [X_{p}])
Similarly the equation for the straight line plot of Ln (Y) verses X_{p} is,
Ln (Y) = Ln β_{2}+ (1/ϒ) X_{p}(3)
With the help of Equation 2, it is possible to transform Equation 1 and 3 to obtain the expressions for the two widely used extreme values distribution functions ^{[4]} as follows:
P (X) = exp (−exp [−(Y − α)/β1])(4)
Fisher–Tippet TypeI
P (X) = exp (−[Y/β_{2}]^{−ϒ}](5)
Fisher–Tippet TypeII
Where P (X) is the probability that value of the variable does not equal or exceed Y, also called Probability of nonexcedence.
In Equations 4 and 5, α, β1 can be identified as location and scale parameters of the TypeI distribution function and β2, ϒ as the scale and shape parameters of the TypeII distribution function. TypeI distribution can be obtained from TypeII by a logarithmic transformation of the variables.
Thus from the slope and intercept of the straight lines obtained as shown in plots in [Figure 1],[Figure 2],[Figure 3],[Figure 4],[Figure 5],[Figure 6],[Figure 7], the distribution parameters α, β1, β2, and ϒ can be determined. Using these parameters in Equation 4 and 5, the probability of nonexcedence P(X) was calculated. These parameters then define P (X) completely and enable one to obtain the probability that a given value is exceeded irrespective of whether the value lies within the observed range or not.
The parameter needed for actual application is a design value of the parameter with defined probability. Contrarily, when the design value is selected the probability of excedence of this value over a given period (say expected lifetime of structure or reactor units) can be worked out. Extreme meteorological phenomena which are very complex are usually scaled in terms of their intensity. These intensity values may be expressed in terms of either a qualitative characteristics such as damage or quantitative physical parameter such as wind speed. In the case of the tornado, the physical parameter is the estimated maximum gust wind speed. The evaluation should be based in this case on the implication for safety and impact of wind may be analyzed using FUJITA scales for the maximum possible damage to structures. For this purpose, a mean recurrence interval (MRI) or return period is defined as
MRI = 1/(1 – P[X])(6)
Using the value of the distribution parameters in [Table 5], MRI for any value of the parameter or conversely the value of the parameter for any return period can be arrived. [Table 6] gives the MRI or return period values for all the meteorological parameters studied for 50 and 100 years of return period.  Table 5: Distribution parameters for extreme value probability functions
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 Table 6: Estimates of extreme meteorological parameters at Kudankulam for mean recurrence interval of 50 and 100 years
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Results and Discussion   
Based on the degree of correlation between X_{p} and Y, it is seen that the meteorological variables maximum annual air temperature, maximum hourly averaged wind speed at 60 m height, daily and monthly maximum rainfall obey Fisher–Tippet TypeI distribution whereas 5 min wind gust, maximum hourly averaged wind speed at 10 m height, annual (maximum) rainfall, minimum temperature, minimum relative humidity obey Fisher–Tippet TypeII distribution functions. The values are summarized in [Table 5][Table 6]. Kudankulam coastal site is characterized by high wind speed. MRI values for wind speed at 10 m height for 100 years is 21.3 m/s and estimated 5 min gust wind speed is 24.5 m/s. These values are useful in arriving at the design basis values to ensure the safety of civil structures, reduce the risk to life and property caused by unsafe structures. From gust wind value, it is observed that Kudankulam falls in “F0” FUJITA scale which is associated with the least damaging gale tornado. The MRI values of 100 years of other parameters such as maximum, minimum temperature along with minimum humidity are 43.6°C, 16.3°C, and 12.09%, respectively. These values derived for the site provide possibilities of generation of cracks with time in civil structures due to thermal variation and humidity values will be useful in the design of cooling towers.^{[5]} The results of the maximum daily rainfall analysis may be used for drainage height estimation and annual rainfall data for water harvesting, irrigation and design areas, water budgeting, etc.^{[6]}
Conclusions   
The distribution parameters of the extreme value distribution functions and return period values for all the meteorological parameters have been analyzed by the correlation coefficient method. The parameters obey either Fisher–Tippet TypeI or Fisher–Tippet Type II distribution. Extreme value distribution function parameters have been established for all the meteorological parameters recorded at Kudankulam site for the return period of 50 and 100 years. Wind speed and 5 min gust wind shows that Kudankulam falls in “F0” FUJITA scale which is associated with the least damaging gale tornado. These values are also used for the expected lifetime of the reactor units and help the designer to arrive at the design basis values of different parameters as regards the safety of the units with respect to stresses due to weather conditions.
Acknowledgments
The authors are thankful to Dr. K. S. Pradeepkumar, Associate Director, HSEG, BARC and Dr. R.M. Tripathy, Head, HPD, BARC for their kind inspiration and constant motivation during the study. The authors express their sincere thanks to Site Director, Kudankulam for extending excellent infrastructural facility to MMLab. Help and cooperation received from all ESL colleagues in this work is thankfully acknowledged.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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4.  Fisher RA, Tippette LH. Limiting forms of the frequency distribution of the largest and the smallest number of a sample. Proc Camb Philos Soc 1928;24:18090. 
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6]
