

ORIGINAL ARTICLE 

Year : 2021  Volume
: 44
 Issue : 3  Page : 123130 


Statistical analysis of extreme value of meteorological elements observed for the last 31 years (1989–2019) at Narora site
Deepak Kumar^{1}, YP Gautam^{1}, Vimal Kumar^{1}, S Kumar^{1}, IV Saradhi^{2}, A Vinod Kumar^{2}
^{1} Environmental Survey Laboratory, Narora Atomic Power Station, Narora, Uttar Pradesh, India ^{2} Environmental Monitoring and Assessment Division, Bhabha Atomic Research Centre, Mumbai, Maharashtra, India
Date of Submission  29Jun2021 
Date of Decision  14Aug2021 
Date of Acceptance  15Aug2021 
Date of Web Publication  04Jan2022 
Correspondence Address: Deepak Kumar Environmental Survey Laboratory, Narora Atomic Power Station, Narora, Bulandshahr  202 389, Uttar Pradesh India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/rpe.rpe_27_21
Understanding of extreme weather conditions at the site of interest is essentially required in the design of engineering structures so that the structures can withstand weather stresses. This paper presents an analysis of extreme values of meteorological elements observed at Narora site for the last three decades (1989–2019). The elements considered are extreme air temperature (°C), minimum relative humidity (%), extreme wind gust (km/h), maximum rainfall (mm) in a day and a month, and annual rainfall. The extreme value analysis reveals that the maximum air temperature, maximum wind gust at 30 m, maximum monthly rainfall, and maximum annual rainfall obey FisherTippett Type1/Gumbel extreme value distribution, whereas minimum air temperature, minimum relative humidity (%), annual daily maximum rainfall (mm), and annual minimum rainfall (mm) obey FisherTippett Type2/Frechet extreme value distribution function. Distribution function parameters, i.e., location, scale, and shape parameter for each variable, have been determined. Extreme values corresponding to return periods of 50, 100, and 1000 years are worked out using best fit linear regression curve as a compliance of the Atomic Energy Regulatory Board Safety Guide Recommendations. The derived extreme values are particularly useful to designer for arriving at suitable design basis values of different elements to ensure the safety of the reactors and other civil structures in Narora region, with respect to stresses due to weather conditions. Extreme values corresponding to return periods of 50 and 100 years at Narora are compared with corresponding values at other three nuclear reactor sites in India, namely, Tarapur, Kalpakkam, and Trombay. In addition, the time series pattern analysis of rainfall for 31 years at the Narora site closely following the 2year moving average rainfall data pattern. These results can be used for water harvesting, irrigation, and floods management plans in the future.
Keywords: Design values, distribution parameters, extreme values, mean recurrence interval, reactor
How to cite this article: Kumar D, Gautam Y P, Kumar V, Kumar S, Saradhi I V, Kumar A V. Statistical analysis of extreme value of meteorological elements observed for the last 31 years (1989–2019) at Narora site. Radiat Prot Environ 2021;44:12330 
How to cite this URL: Kumar D, Gautam Y P, Kumar V, Kumar S, Saradhi I V, Kumar A V. Statistical analysis of extreme value of meteorological elements observed for the last 31 years (1989–2019) at Narora site. Radiat Prot Environ [serial online] 2021 [cited 2022 May 24];44:12330. Available from: https://www.rpe.org.in/text.asp?2021/44/3/123/334779 
Introduction   
Meteorological elements such as wind speed, rainfall intensity as well as total rainfall, storms, cyclones, and maximum and minimum temperature play a major role in the design of the nuclear facilities (NFs) from the safety view point. Rainfall forms an important input to other processes such as estimation of maximum water level at the proposed site, whereas wind speed is necessary to study structural safety, particularly of tall structures such as cooling towers, stacks, and transmission line towers. These meteorological parameters are beyond human control. Structural safety requirements for the important structures shall be designed such that they can withstand the parameters of the extreme value likely to occur during the lifetime of the facility. Parameters to be used as design basis should have a very low exceedance probability of occurrence during the lifetime of the facility. This is achieved by using the extreme value analysis technique. NFs design requires generation of such design basis values of the above parameters. Lifetime of the NFs is normally about several tens of years. The NFs are to be designed in such a way that they can withstand the occurrence of extreme values of the above parameters during their lifetime. The design value of a parameter considered in design should have a mean recurrence interval (MRI) much larger than the life time of the facility. In view of that Atomic Energy Regulatory Board, has recommended in its siting code^{[1]} for nuclear power plants, minimum values of MRI for severe wind speed, rainfall in a day, and cyclone pressure as 1000 years. These studies provide an insight into the extreme values of the variables considered over a period, generally during the expected lifetime of the structure, and help the designer to arrive at the design basis values of different parameters as regards the safety of the concern structure. In addition, longterm analysis of rainfall at any place is useful in many applications such as irrigation engineering, water harvesting, public health engineering, drainage system design, and construction of dams.^{[2]} This also helps in planning the pre and postflood operations.
Site description
Narora site lies in IndoGangetic alluvium, bordered on the north by the Shivalic foothills. The terrain is fairly flat and even and the land around the site is predominantly agricultural. The main crop is wheat followed by other cereals. There are guava and mango groves and vegetable farms around the site. Narora Atomic Power Station (NAPS) has twin units of pressurized heavy water reactor with an electrical generating capacity of 220 MWe each are operational since 1990. It is situated on the right bank of Lower Ganga Canal (LGC) and Parallel Lower Ganga Canal (PLGC) at a distance of 3.5 km toward downstream of Narora Barrage.
Materials and Methods   
Environment Survey Laboratory of BARC is operational at Narora since 1987 to carryout environmental surveillance and micrometeorological studies at NAPS site. Meteorological variables such as ambient air temperature, relative humidity, wind speed, wind direction, and rainfall are measured using the sensors such as RTD (PT1000) temperature sensor, solidstate capacitancebased relative humidity sensor, 3cup anemometer, wind vane, and tipping bucket rain gauge, respectively; these sensors are placed at surface as well as at 30 m tall meteorological tower, during the period from 1989 to 2019 obtained from the continuously acquisition of data through 24 Channel Data Logger. Before 2005, these variables were obtained from the continuously recorded charts on an hourly basis. After that, the data acquisition is done by the online MetDas Software which is Meteorological Data Acquisition System. Hourlyaveraged and minuteaveraged data are recorded for all the above parameters. These data are the basic raw data used for extreme value analysis.
Continuous data acquisition system stores the raw data in the database. Using hourly data, daily maximum, minimum, monthly, annual values of ambient air temperature, relative humidity, atmospheric air pressure, wind speed, rainfall, etc., and used for extreme value analysis. The statistical summary of basic meteorological parameters data set used for extreme value analysis is given in [Table 1]. Wind data are required during the design stage for assessing the stability of structures. Dynamic loading is especially needed in the design of tall structures such as cooling towers, transmission towers, communication towers, and stack. Requirement of the averaging period of the wind data for both dynamic and static loading aspects is different as per IS: 875.^{[3]}  Table 1: Statistical summary of meteorological elements at Environment Survey Laboratory, Narora Atomic Power Station, Narora for the period of 31 years (19892019)
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Extreme value data analysis procedure
The meteorological elements pass through a defined cycle; one can expect an absolute extreme value per year for each element. The annual extreme value of given element varies from year to year. To arrive at proper design basis value, the set of extreme data is to be subjected to statistical analysis so that the probability distribution of extreme values can be obtained. The probability of exceedance of any given design value in a given time, say, the expected lifetime of the structure, can be worked out from this distribution. The statistical summary of meteorological elements for a period of 31 years (1989–2019) used for extreme value analysis is given in [Table 1].
The data analysis was carried out as per the procedure described by Daoo et al.^{[4]} The meteorological elements chosen for this analysis are maximum and minimum air temperature, maximum wind speed, minimum relative humidity, maximum rainfall in a day, a month, and maximum and minimum annual rainfall collected at NAPS Narora site since 1989. The basic data set is arranged in ascending order for maximum and descending order for minimum, and each data point is assigned a rank “m.” Data with the same value, although the rank is same, these are assigned rank as m, m + 1, m + 2, etc., so as not to leave gaps in the ordered data array. P(x) is the probability of nonexceedance for maximum extreme data and the probability of exceedance for minimum extreme data of a particular magnitude “x” of the data point of the rank “m” was obtained as
Where “M” is the total number of data points.
The data were examined and plotted for a linear fit between the data values (Y axis) and reduced variate or function of probability of nonexceedance (X axis). Correlation coefficients 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 correlation coefficient between Y versus X_{p} and ln(Y) versus X_{p} ranged from 0.898 to 0.991. The correlation coefficients between Y versus X_{p} and ln(Y) versus X_{p} for all the variables are given in [Table 2]. The coefficient of correlation is greater for Y versus Xp in the case of maximum air temperature (°C), maximum wind speed (km/h) at 30 m, maximum monthly rainfall (mm), and maximum annual rainfall (mm); these variables obey FisherTippett TypeI distribution. Coefficient ln(Y) versus Xp is greater for minimum annual air temperature, minimum relative humidity (%), daily maximum rainfall (mm), and minimum annual rainfall (mm); these variables were found to obey Frechet distribution or TypeII distribution. [Figure 1],[Figure 2],[Figure 3],[Figure 4],[Figure 5],[Figure 6],[Figure 7],[Figure 8] shows the plots of typical values of extreme value distribution of different meteorological elements, namely maximum and minimum air temperature and annual rainfall, minimum relative humidity, maximum hourly wind speed wind speed, and maximum daily and monthly rainfall studied.  Table 2: Distribution parameters for extreme value probability functions for different meteorological parameters at Narora for the period of 31 years (1989–2019)
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 Figure 5: Extreme value analysis of daily maximum rainfall (mm) at Narora site
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Equation for the straight line in the plot of Y versus Xp was:
Where Xp is the reduced variate corresponding to P(x), defined as:
Where P(x) is the probability that the value of the variable does not equal or exceed Y (also called probability of non exceedance).
Similarly, the equation for the straight line graph of ln(Y) versus Xp is:
Equations (1) and (3) can be easily transformed into the expressions for the two widely used extreme value distribution functions (Fisher and Tippett, 1928), viz.,
FisherTippett TypeI
FisherTippett Type II
In Equation (5), α and β1 can be identified as location and scale parameters of the TypeI distribution function, and in Equation (6), β2 and γ can be identified as the scale and shape parameters of the TypeII distribution function. TypeI distribution can be obtained from TypeII by logarithmic transformation of the variable.
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],[Figure 8], the distribution parameters α, β1, β2, and γ can be determined. These parameters then define probability of nonexceedance P(x) completely and enable one to obtain the probability that a given value is exceeded.
[Table 2] gives variation of extreme meteorological parameters, type function, distribution parameters and coefficient of correlation (r).
The parameter needed for actual application is a design value of the element with defined probability. Contrarily, when the design value is selected, the probability of exceedance of this value over a given period (say, expected life time of the structure or nuclear reactors) can be worked out. For this, an MRI^{[5]} or return period is defined as
Using the values of the distribution parameters, MRI for any value of the parameter or, conversely, the value of the parameter for any return period can be obtained. For estimation of MRI lying between any ranges, Lieblein order statistics technique^{[6]} has to be used.
[Table 3] gives the MRI or return period values for all the meteorological parameters studied for 50, 100, and 1000 years of return period.  Table 3: Estimates of extreme meteorological parameters at Narora Atomic Power Station, Narora, for mean recurrence interval for 50, 100, and 1000 years
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Results and Discussion   
From 31year (1989–2019) annual rainfall data, it observed that annual rainfall fluctuates widely at Narora site. The lowest rainfall was 429.0 mm during 2002 and the highest rainfall was 1499.7 mm during 1998. The mean rainfall over the period of this study works out to be 795.0 mm, with standard deviation of 210.4 mm. The rainfall has been more than 1000 mm on only five occasions out of 31year period, and on 15 occasions, it was less than the mean value of 795.00 mm. Time series pattern analysis of rainfall is seen in [Figure 9] closely following the 2year moving average rainfall. Percentage cumulative frequency distribution curves were drawn for annual and monthly maximum rainfall with class width of 200 and 100 mm, respectively. All distributions were found unimodal. [Figure 10] plots of the distribution following Gaussian. 31year average monthwise rainfall is depicted in [Figure 11] along with the monthwise excessive year (1998) and monthwise deficit year (2002) rainfall. The maximum and minimum of average monthly rainfall over the period were 247.5 mm during July and 6.0 mm during December, respectively.  Figure 10: Cumulative frequency distribution of annual, monthly maximum rainfall
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 Figure 11: Monthly rainfall: 31 years average, excessive year (1998) and deficit year (2002)
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It is often required to know the balance rainfall, for season or month for planning purpose. A cumulative rainfall chart for sufficient number of years may prove useful in this regard. [Figure 12] shows the plot of 31year cumulative average monthly rainfall with balance rainfall, obtained by subtracting the cumulative value up to any chosen period from total cumulative. Resulting overall pattern after plotting the latter is symmetrical about a line passing the point of intersection of two curves and parallel to Xaxis. The plot also shows the cumulative rainfall for excessive year (1998) and deficit year (2002) as a sample for comparison. Trend shows that till June, both excess (1998) and deficit (2002) year have been reasonably following the 31year cumulative graph; after June, there was pickup in excess year rainfall. However, in deficit year (2002), rainfall has not quite caught up even after July resulting deficit rainfall at the end of years.  Figure 12: Cumulative 31year average monthwise rainfall, balance rainfall with excessive year (1998) and deficit year (2002) comparison
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Based on rainy days in the month and total rainfall in the month, the average daily rainfall is calculated. For this purpose, a rainy day is defined as a day having rainfall greater than or equal to 0.5 mm. The average daily rainfall at Narora site on an annual basis varies between 10.0 mm and 25.0 mm with mean of 15.8 mm; the corresponding number of rainy days in a year ranges between 24 and 71 with mean of 53 days.
The maximum and minimum air temperature recorded at Narora site during 31year period are 47.3°C and 0.3°C, respectively. Similarly, the minimum humidity (%) and maximum wind speed at 30 m height (km/h) are 6 and 60.1, respectively. [Table 1] summarizes the data.
The distribution parameters of the extreme value distribution functions obtained from the slope and intercept of straight line fit of each of the elements are summarized in [Table 2]. [Table 3] gives the extreme values of various meteorological parameters, for the return period 50, 100, and 1000 years. These values are confirming the studies carried earlier for the site for the period 1989–2001.^{[7]} Derived values are particularly useful for arriving at suitable design basis values to make sure the safety of the civil structures in and around the NAPS Narora site with respect to stress due to weather conditions. It is observed that maximum air temperature, maximum wind speed (km/h), maximum monthly rainfall (mm), and maximum annual rainfall (mm) obey FisherTippett TypeI, while other parameters obey FisherTippett TypeII distribution function. Such feature was also observed in the previous study at three other nuclear sites in India, viz., Tarapur,^{[8]} Kalpakkam, and Trombay, using data pertaining to different periods. The study also reported different return period values of various meteorological parameters derived from longterm meteorological data collected at respective sites. It will be interesting to compare the extreme values at the other nuclear reactor sites with corresponding parameters at Narora site obtained during the study. [Table 4] shows such comparison. It is observed that MRI values of maximum wind speed at coastal site are higher and MRI values of maximum temperature are lower, mainly due to land/sea breeze conditions. Daily rainfall is also higher for coastal site compare to inland site, which increases the possibility of flooding situation when high tide condition arises with the rainfall. The extreme parameters at particular site depend on climatological as well as topographical features of the site. Tarapur and Trombay,^{[4]} both being the coastal sites on the western coast separated by about 100 km only, are expected to be similar. For Kalpakkam^{[9]} and Narora sites, the former being coastal and situated on the eastern coast and later one is an inland site in the northern region.  Table 4: Comparison of estimates of extreme meteorological parameters at different nuclear power plant sites for mean recurrence interval for 50 and 100 years
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For CategoryI facilities including nuclear power plant, hazards associated with all relevant meteorological phenomena shall be identified and evaluated to arrive at the corresponding design basis parameter to ensure safety of the facilities to be located at the site. Mean annual frequency of exceedance for wind is 10^{−4}, as per IS: 875 (Part 3)^{[3]} code for wind load, design wind speed evaluated based on basic wind speed for Narora region is 50 m/s. Whereas based on extreme value analysis for the 31 years, the maximum wind speed for the MRI of 1000 years works out as 25.3 m/s, well below the design wind speed values. This implies that civil structure of NAPS is very safe for the wind load.
Design basis flooding event shall be selected by deterministic or probabilistic method. While using probabilistic method, the values corresponding to mean annual frequency of exceedance 10^{−4} shall be used for CategoryI facilities. For the inland site NAPS Narora[10], flooding can occur due to heavy incessant rain at the site/region and/or flood in the river/water body. Probable maximum precipitation for given duration, drainage area, and time of year design flood level at site is worked out to be 180.8 m (from sea level) at NAPS site. On the basis of that, emergency power diesel generator was located at the elevation of 187.3 m, resulting the margin of 6.5 m. This was again reviewed by the task force constituted after Fukushima accident and found safe against the 1000 years MRI of maximum precipitation in a day value 0.74 m considering the drainage area.
Based on the degree of correlation between Xp and Y{(or ln (Y)}, it is seen that the meteorological variables maximum air temperature (°C), maximum wind speed (km/h), maximum monthly rainfall (mm), and maximum annual rainfall (mm) obey FisherTippett Type1 distribution and other parameters obey FisherTippett TypeII distribution which has been ascribed to its observed bimodal frequency distribution function. The extreme value distribution function parameters established for all the meteorological variables recorded at Narora site for the return period of 50, 100, and 1000 years are useful in arriving reliability or risk estimation. It ensures the robustness of return period values with reliable uncertainty limits. Considering the design life of structures of CategoryI facilities including nuclear power plants, the 1000year return period is suitable and suggested for design value of severe wind speed, rainfall in a day, and cyclone pressure. These studies are in compliance with AERB recommendation in its siting code for nuclear power plants. Extreme values corresponding to return periods of 50 and 100 years return period at Narora are compared with corresponding values at other three nuclear reactor sites in India, namely, Tarapur, Kalpakkam, and Trombay. In addition to time series pattern analysis of rainfall for 31 years at Narora site closely following the 2year moving average rainfall data pattern, these results may be used for future plans in the water harvesting, irrigation, and floods management plans.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
References   
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12]
[Table 1], [Table 2], [Table 3], [Table 4]
