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Persistence of wind direction
Atmospheric Environment
Pergamon Press 1972.Vol. 6, pp. 889-898.Printed in Great Britain.
PERSISTENCE
OF WIND
DIRECTION
V. V. SHIRVAIKAR Health Physics Division, Bhabha Atomic Research Centre, Bombay-85, India (First received 3 January 1972 and in finaI form 12 June 1972) Abstract-Persistence of wind direction is a neglected subject. However, it is one of the significant parameters in dosage evaluation from short term releases of pollutants to the atmosphere. In this paper this topic is studied in detail using the continuous wind data from three nuclear power station sites in India. It is found from the analysis that longer persistence periods are less frequent. The frequency of occurrence of different persistence periods obeyed a log-normal distribution at two sites whereas at the third site, though the behaviour was qualitatively similar, no known analytic function could be fitted. The extrema and the averages of the wind speeds averaged over individual persistence periods, showed a dependence upon the persistence period as follows: (1) the average maximum wind speed decreased with persistence; (2) the average minimum wind speed increased with persistence; (3) the average of the average wind speed first increased with increasing persistence and then tended to a stable value. Such analysis is useful in defining the worst meteorological conditions at nuclear station sites for applications in hazard evaluation. Some of the applications of the persistence analysis are discussed, and it is shown that dosage at any site from short term (h) continuous release of fission products has a maximum and that this maximum, which is different for different sites, can be used to grade the sites. An expression for return periods of persistences has been derived. This expression gives the return period in actual time units.
INTRODUCTION IN THIS paper, certain features of wind direction persistence are presented, based on the continuous wind records obtained at three nuclear power station sites in India. Wind direction persistence as defined here is the period over which the direction remains constant (i.e. within a given sector width defining the direction) irrespective of the wind speed. Under calm conditions, direction is not defined and persistence may be considered as broken. Wind direction persistence is always finite extending at the most over a few tens of hours. It was shown in an earlier paper (SHIRVAIKAR et al., 1969) that for correct evaluation of dosages from continuous sources of pollution it is necessary to introduce the finiteness of the wind direction persistence into the dosage expression. It was also shown in the same paper that the minimum wind speed associated with a given period of wind direction persistence (henceforth called simply persistence or persistence period) increases with increasing persistence period at any site. Wind direction persistence has not been studied extensively. In fact, the only other works, in addition to the above, concerning the topic were a paper by SINGER (1967) expressing persistence in terms of a parameter S which he called steadiness of wind and a report by VAN DERHOVEN(1970) giving certain climatological aspects of persistence. The steadiness of wind defined by Singer is 1.
S = 2 arc sin 0 ?7 lOI where v is the vector wind, Iv j is the scalar wind speed, and the bar indicates averaging. 889
890
V. V. SHIRVAIKAR
S is therefore an indirect way of expressing the probability of occurrence of persistence and has been utilised by SINGER and NACLE (1970) for comparison of nuclear reactor sites. However, the index cannot be used directly in dosage evaluation. 4 unified study of, (i) persistence in the context of the association of wind speed and persistence period and (ii) frequency of occurrence of various persistence periods would therefore make the comparison of the hazards at a site more realistic and absolute. 2. DESCRIPTION OF DATA AND METHOD OF ANALYSIS Continuously recorded data of wind speed and direction are available from two coastal and one inland stations at the three nuclear power station sites in India. These are: Tarapur (19”N, 71”E) on the west coast, Kalpakkam (12”N, 80”E) on the east coast and Kota (25”N, 76”E), in inland site. Wind direction is recorded using low-torque potentiometer type wind vanes at about 8@1OOft height coupled to O-l ma Esterline Angus recorders (3 in. h-l chart speed). Averages of wind direction and speed are taken over 60 min periods. The persistence period in this study is therefore in whole hours. Data for I yr at Tarapur and Kalpakkam and data for three years at Kota were analysed for persistence to give the frequency of occurrence of various persistence periods. The average wind speeds for individual persistence periods were found and from these the minimum average Urnin,average U,, and maximum average wind speed U,,, associated with each period. The extremum averages therefore averages over the period of persistence and do not refer to any single hour. The wind directions are classified into 16 points of the compass i.e. N, NNE, NE, ENE etc. The analysis assumed that calms and missing data broke the persistence. The periods of the analysed data presented here were as follows: Tarapur : 1 yr 1968 Kalpakkam : 1 yr April 1969-March 1970 Kota : 3 yr 1967-1969 3. PROBABILITY CONSIDERATIONS The analysis of persistence shows that the frequency of occurrence of longer persistence periods decreases progressively. Data available at many sites where persistence statistics are required are usually collected over short periods of about 1 yr. A knowledge of the frequency distribution of persistence periods should be useful in determining the probability of occurrence of long persistence periods, and their return periods. Various distributions were tried for the three sites. Tarapur and Kota sites gave a linear plot (FIG. 1) on a log-probability paper indicating a log normal distribution. (1) where f is the probability density for persistence period T in hours and log r is the standard deviation of log T.Equation (1) which is normalised to give unity when integrated from T = 1 to a, can be used as an extrapolation function. In FIG. I the graphs are normalised such that total cummulative probability from T = 1 to ZJ is 0.5. The actual cumulative probability is therefore double that read from the graphs in FIG. 1. The values of 7 were 2.97 h at Tarapur and 2.28 h at Kota.
891
Persistence. of Wind Direction
FIG. 1. Log-probability plot of persistence frequency at three nuclear power station sites in India. The cumulative probability of periods equal to a greater than the given period is shown by the ordinate, The maximum probability is set at 50 per cent since only right wing of the distribution is significant.
At Kalpakkam, no analytic function could be fitted, but the trend was such that the frequency of occurrence of long periods decreases sharply. Equation (1) is a continuous probability distribution fitted to discrete points. Cumulative probability tables should therefore be used to calculate the probabilities of individual persistence periods from equation (1) as shown in the following example: Suppose probabilities for T = 2 h is required for Kota. The value of variate is x = log T/log T = 0*844. From statistical tables, for the normal distribution, the cumulative probability from x = 0 to 0.844 is 0.3004. The probability from x = 0 to + 03 is 05. Hence the probability for If = 2 h and more is 2 (0.5~*30~) = 0.3992 compared with the observed 0.364 (see FIG. 1). Similarly, the probability for T = 3 h and more is 0.1819. Thus, the probability for 2 h persistence is the difference of the two, i.e. 0.2173 (observed: 0.1975). 4. RELATION
OF
WIND
SPEED
AND
PERSISTENCE
The maximum average, the average and the minimum average wind speeds are plotted against the persistence period at Kota and Kalpakkam in FIGS. 2 and 3. In the case of Urnin,the curve represents a lower envelope of the points. The general behaviour of the speed with respect to persistence is: (1) the maximum wind speed U,,, decreases with increasing persistence; (2) average wind speed U,, increases initially but stabilises to a constant value; (3) the minimum wind speed Unrn increases with increasing persistence. The behaviour at Tarapur was also similar and therefore not shown here. These plots are useful in defining the extreme meteorological conditions (from diffusion considerations) at a site. In FIG. 2 the envelope for a 1-yr analysis, namely 1968, is also shown by the dotted curve. As would be expected, this is to the left of the envelope for a 3 yr analysis.
892
V.
V. .~-~
SHIKV.~IKAR
-...-.-____.__._ U,&ota
1967-69
loam-_-U ,o,Koto
EJ67- 69
0
Oi i 18,
4
26.7
‘km h-’ lJ,,Kota
l99’-
FIG. 2. Dependence of the maximum, average and minimum wind speeds on persistence period. The wind speeds are the average wind speeds over each period and do not refer to basic 1 h values. The curve in the lowest graph is the lower envelope. The dotted line is the envelope for 1 yr data; the pointshowever arenot shown. Station: Kota(inland SiteinRajasthan).
In FIGURES2 and 3, the statistical weight of the points for large Tis poor. In many instances, there was only one occasion of a long persistence period, giving the same value for Urnin,U,, and U,,,. It may therefore appear from the curves in these figures that Urninis greater than the corresponding U,, or U,,, but this is not the case.
5. DEPENDENCE OF PERSISTENCE ON TIME AND SECTOR WIDTH
AVERAGING
The analysis presented here uses an averaging time of 1 h and 22.5” direction sectors. That persistence depends upon these two parameters will be obvious from the following example. Consider a 2-h wind direction record which oscillates with an amplitude of 90” and a period of 30 min. Such records are not unusual at night. Analysis during 1 h or 30 min averaging period with 22.5” sector will show a persistent mean wind direction. However, if the averaging period used is 10 min the analysis would show a complete break in persistence. Similarly it is obvious that with increasing sector width, the persistence will increase. This is best seen from the TABLE 1 constructed from the figures presented by VAN DER HOVEN (LX. cit.) for Daytona Beach.
893
Persistence of Wind Direction
50
f
E Y
40
P 3o 20
0
““““‘1””
IO
Per&once,
h ”
FIG. 3. Same as FIG. 2, but at Kalpakkam on east coast, south of Madras. All data is for 1 yr period only. TABLE 1. MAXIMUMOBSERVED PERSISTENCE PERIODSAT DAYTONABEACH Maximum observed persistence period in hours Sector width
22.5” 67.5” 112.5”
Spring
Summer
13 68 90
20 74 160
6. RETURN
Fall 19 50
150
Winter 25 42 90
PERIODS
If F (T) is the probability of occurrence of periods of less than T, the quantity R(T) =
1 1 - F(T)
is defined as the return period of persistences equal to or greater than T (GIJMBEL, 1952). Actually the return period defined above is dimensionally not a time period, but is a pure number defining the mean number of persistence events after which a persistence period equal to or greater than T may be observed. To obtain the return A.E.6/12--B
V. V. SH~RVAI~~IR
893
periods in time units (hours in the present case) which we shall call here ‘return interval’ and denote by R*(T) we proceed as follows: To avoid confusion we shall consider an analogous case of a series of rods of different lengths arranged end to end in a straight line. The rods are to have lengths such that the length of the line, measured in centimeters, corresponds to the peristence period in hours, and the sequence of arrangement corresponds to the sequence of observation of the persistence periods. The return period R (T) then corresponds to the number of rods whereas the return interval R*(T) corresponds to the total length that one has to traverse between two rods A and B of length greater than or equal to T cm. We are interested in finding the distance between the end of A to beginning of 5. The number of rods in this distance is R (T) - 1. If n,, n2 . , . . . . nT_ 1 are the number of rods of length, 1,2, . . T -- 1 cm respectively, andfiJi etc. are the corresponding frequencies then ni
f’.
2
[R(T) -- I] L-!-
F(T)
and T-l
R*(T)
:E
2i
ci T-l
x
I=;
n,
I
R(T)- ’
i=l
F(T)
x.fi
i=l
T-l
i.e.
R*(T) = R(T)
c
i X ,fi.
(3)
i=l
For large T, R*(T)
= constant
x R(T)
since F(T) w 1 and R(T) 9 1. This return period is still an underestimate since the occurrence of calms has been ignored. With the rod-analogy, the occurrence of calms corresponds to a gap caused by two rods not being kept contiguous, but separated by a vacant space. A correction on the lines similar to above may be made if persistence analysis of calms is available. An approximate correction can, however, be made if R*(T) is simply multiplied by a factor (1 + C/100) where C is the percentage of calms occurring at the site. The value of C was 0.73 per cent at Tarapur, 12.8 per cent at Kota and 3.4 per cent at Kalpakkam. Values of R (T), R*(T) and Uminfor typical persistence periods are shown in TABLE 2 for Kota. Such tables are useful in assessing the hazards as well as their probability of occurrence at a site, from accidental release of pollutants. It is to be borne in mind in such analysis that they are based on data for limited period of time, usually 1 yr. Experience as well as statistical considerations show that the values of 7 in equation (1) can change from year to year and the minimum wind speed for a given persistence period will decrease with increased period of sampling.
895
Persistence of Wind Direction 2. RETURN
TABLE
PERIODS, RETURN INTERVALS SPEEDS AT KOTA
ANI) MINIMUM
WIND
Persistence &
R U-1
R*VYt (h)
2 6 8 12 16 24
2.5 34.2 86.5 397 1300 8300
I.68 60.7 169 796 2630 16800
3 3 3.5 5.3 7.7 16
t Corrected for calms. Probability values were calculated using the distribution function and not from the observed values. 7. CERTAIN In this section
APPLICATIONS
OF THE
PERSISTENCE
ANALYSIS
we shall discuss some applications of the analysis of wind direction
persistence. 7.1. Dosage e~al~atjun An important application of the persistence analysis is in assessing the environmental consequences of accidental release of pollutants from a single source; specifically, it is customary to carry out analysis of the radiological hazards following a maximum credible accident to a nuclear reactor. Such analysis is then used to prescribe a population exclusion distance from the reactor and for estimating the degree of containment required for the radioactive fission products (SHIRVAIKAR and GANGULY, 1969). An accidental release of fission products may occur at any time. Hence, to ensure safety, the assessment of radiological doses should be made under “worst meteorolo~cal conditions” obtainable at the site, so that under all other conditions the doses are less than the above. The reactor safety features and exclusion distance are to be such that the doses do not exceed some accepted limits. 7.2.
Worst meteorological conditions
The term “worst meteorolo~~l condition” above refers to the conditions of atmospheric diffusion and other parameters leading to high doses and does not include other hazards, e.g. hurricanes affecting structural integrity. From the theory of atmospheric diffusion the doses depend upon: (1) atmospheric stability (PASQUILL, 1962); (2) wind speed ; (3) wind direction persistence (SHIRVAIKAR et al., lot. cit.). “Worst meteorological conditions” therefore imply a combination of these three parameters giving highest doses at the exclusion distance. Often, the conditions specified are those of strong stability, and wind speed of l-2 m s-l and imply that the wind direction persistence is infinite. It is, however, seen from FIGS. 2 and 3 that the lowest wind speed of say 1 m s-l has a maximum persistence associated with it. An appropriate value at Kota would be 8 h. Alternately, if we take 12 h persistence to define worst conditions, in order
896
V. V. SHIRVAXAR
to cover the estimated release period of fission products following a maximum credible accident to a reactor, then the wind speed should be 1.5 m s- I. 7.3. An ~s~lute index for ~o~parjso~ of nuclear power station sites A more important aspect of persistence in the evaluation of dosage and setting of worst meteorological conditions is the associated stability class. The Pasquill diffusion categories A-F (PASQUILL, 1962) are associated with wind speed, stability increasing with decreasing wind speed at night. For example, the most stable category F usually used as the worst meteorological condition defines wind speed of 2 m s-l (7.2 km h-l), This corresponds to a 10 h persistence both at Kota nad Kalpakkam, using 1 yr data. Longer persistences will have wind speeds corresponding to less stable conditions and the situation will not be the worst. Thus nature seems to impose an upper limit to the dosage, which could be used as an absolute indicator for comparison of sites for nuclear installation. This perhaps is one of the most important aspects of the persistence analysis. This point may be illustrated with the help of FG 4 in which the dosages thus computed at 1 km distance from source are plotted against persistence period for the three nuclear power station sites. The source strength is assumed to be 1 Ci s-t at ground level. In caiculating the dosages, the wind speed used was U,,, obtained from the envelopes in FIGS. 2 and 3, and a similar graph for Tarapur. Since Kalpakkam and Tarapur data were analysed for 1 yr, the dotted curve in FIG. 2, which is also for 1 yr, was used. Also, points up to 24 h persistence only were used to draw the envelope for the Tarapur data. Pasquill’s catagories of stability were obtained from the values of Urninfor night time clear sky conditions, so that the dosages obtained are the maximum possible. A difficulty arises when Uminis less than 2 m s-l. Since under these conditions Pasquill categories for night time are not defined, probabIy because of uncertainties introduced by meandering of the wind. Category F, i.e. the most stable category, was used in this case because this would give higher dosage than if the corrections due to meandering are introduced. The dosages given in FE. 4 are therefore an upper limit to those expected at the site, using 1-yr data. The dosage first increases due to increasing exposure period, but falls when the effect of increasing wind speed becomes overriding. The sharp drop is due to transition from Category F (Urnin ,< 3 m s- ‘) to the less stable category E (Umlnbetween 3 and 5 m s-l). However, the main points in this figure are: [l) each site has a maximum possible dosage Dmax (2) sites can be graded with respect to Drnax. Since the main issue in comparison of the sites is the dosage, D,,, is an absolute index. Using this index, we find that Tarapur is the best site with Kalpakkam and Kota following in that order. The values of D,,, are, however, very close to each other, which indicates that sites may not differ appreciably from one another in the radiological consequences of the maximum credible accidents to reactors, providing non-meteorological parameters are the same. Other considerations therefore enter in the grading of the site, one of them, which is of meteorological significance, is the calculated annual dosage to the public from normal operations. The above dose analysis has been based on 1 yr data. As the data extends over Larger periods of say 3 or 10 yr it is natural to expect, that lower values of Urn*,,would
897
Persistence of Wind Direction
*t
2
4
6
8
Persistonce,
IO
7
12
14
I6
h
FIG. 4. Variation of dosage with persistence period. Source: 1 Ci s-r at ground level. Pasquill model is used to calculate the dosage. Wind speeds used are the Urn,,, values for various persistenccs obtained from the envelopes such as in FIGS.2 and 3. Lower three curves are for 1 yr data. Upper curve is for 3 yc data. Pasquill stability categories used correspond to the night time conditions and U,,,,, values.
be found for a given T. This is also seen from the 3y curve for U& envelope in FIG. 2, &,, will consequently change. As would be expected, it will increase as seen from the uppermost graph in FIG. 4 which is calculated from 3 yr data. D=, here has increased about 1.5 times, Statistically, this higher D,,, is a better estimate. This has to be weighed against the fact that the probability of obtaining this higher D,,,,x in a given time of say 1 yr is much smaller than the lower value of D,,, as obtained from 1 yr data. 7.4. Cooland warer e~~e~t trajectory in takes A third application with engineering significance is the following?. Large lakes often form a source of cooling water supply to large nuclear or thermal power stations. Here, the cold water intake and the hot water effluent points are separated by distance so that the hot water does not reach the cold water intake to cause a “short circuit”. Such a short circuit decreases station efficiency. In a large lake, however, the water currents are primarily wind driven and the trajectory of the hot plume in the water depends upon the wind direction persistence. An optimum location can therefore be made of the intake and discharge points using the persistence data (analysed for each direction) so that the short circuitry periods are minimised. t The author is grateful to Dr. J. S. tion.
SASTRY
of Health Physics Divn. for pointing out this applica-
898
V. V. SHIRVAIKAR 8. CONCLUDING
REMARKS
Wind direction persistence, hitherto ignored, does seem to have applications which, no doubt, will increase in future. It is therefore recommended that this analysis form part of the routine climatological analysis wherever possible. Acknowledgements-The author thanks Dr. A. K. GANGULY, Head, Health Physics Division and Dr. K. G. VOHRA for their encouragement in the work. The help given by Ss. L. N. SHARMAand N. S. PANCHALin the analysis is gratefully acknowledged. REFERENCES GUMBELE. J. (1954) Statistical theory of extreme values and some practical applications. NBS. Appl. Math. Ser. 33, 51. PASQUILLF. (1962) Atmospheric Diffusion, p. 297. Van Nostrand. SHIRVAIKARV. V. and GANGULYA. K. (1969) Systematics of reactor siting. Progress in Nuclear Energy. Series XII, Health Physics, Vol. 2, part I, pp. 393-430. Pergamon Press, Oxford. SHIRVAIKARV. V., KAP~~R RAME~HK. and SHARMAL. N. (1969) A finite plume model based on wind persistence for use in environmental dose evaluation. Atmospheric Environment 3, 135-144. SINGERI. A. (1967) Steadiness of the wind. J. Appl. Meteor. 6, 1033-1038. SINGERI. A. and NAGLEC. M. (1970) Variability of wind direction within the United States. Nuclear Safety 11, 34-39. . ’ VAN DER HOVEN I. (1969) Wind persistence probability. ESSA Tech. Memo. EARLTM-ARL 10,
Pergamon Press 1972.Vol. 6, pp. 889-898.Printed in Great Britain.
PERSISTENCE
OF WIND
DIRECTION
V. V. SHIRVAIKAR Health Physics Division, Bhabha Atomic Research Centre, Bombay-85, India (First received 3 January 1972 and in finaI form 12 June 1972) Abstract-Persistence of wind direction is a neglected subject. However, it is one of the significant parameters in dosage evaluation from short term releases of pollutants to the atmosphere. In this paper this topic is studied in detail using the continuous wind data from three nuclear power station sites in India. It is found from the analysis that longer persistence periods are less frequent. The frequency of occurrence of different persistence periods obeyed a log-normal distribution at two sites whereas at the third site, though the behaviour was qualitatively similar, no known analytic function could be fitted. The extrema and the averages of the wind speeds averaged over individual persistence periods, showed a dependence upon the persistence period as follows: (1) the average maximum wind speed decreased with persistence; (2) the average minimum wind speed increased with persistence; (3) the average of the average wind speed first increased with increasing persistence and then tended to a stable value. Such analysis is useful in defining the worst meteorological conditions at nuclear station sites for applications in hazard evaluation. Some of the applications of the persistence analysis are discussed, and it is shown that dosage at any site from short term (h) continuous release of fission products has a maximum and that this maximum, which is different for different sites, can be used to grade the sites. An expression for return periods of persistences has been derived. This expression gives the return period in actual time units.
INTRODUCTION IN THIS paper, certain features of wind direction persistence are presented, based on the continuous wind records obtained at three nuclear power station sites in India. Wind direction persistence as defined here is the period over which the direction remains constant (i.e. within a given sector width defining the direction) irrespective of the wind speed. Under calm conditions, direction is not defined and persistence may be considered as broken. Wind direction persistence is always finite extending at the most over a few tens of hours. It was shown in an earlier paper (SHIRVAIKAR et al., 1969) that for correct evaluation of dosages from continuous sources of pollution it is necessary to introduce the finiteness of the wind direction persistence into the dosage expression. It was also shown in the same paper that the minimum wind speed associated with a given period of wind direction persistence (henceforth called simply persistence or persistence period) increases with increasing persistence period at any site. Wind direction persistence has not been studied extensively. In fact, the only other works, in addition to the above, concerning the topic were a paper by SINGER (1967) expressing persistence in terms of a parameter S which he called steadiness of wind and a report by VAN DERHOVEN(1970) giving certain climatological aspects of persistence. The steadiness of wind defined by Singer is 1.
S = 2 arc sin 0 ?7 lOI where v is the vector wind, Iv j is the scalar wind speed, and the bar indicates averaging. 889
890
V. V. SHIRVAIKAR
S is therefore an indirect way of expressing the probability of occurrence of persistence and has been utilised by SINGER and NACLE (1970) for comparison of nuclear reactor sites. However, the index cannot be used directly in dosage evaluation. 4 unified study of, (i) persistence in the context of the association of wind speed and persistence period and (ii) frequency of occurrence of various persistence periods would therefore make the comparison of the hazards at a site more realistic and absolute. 2. DESCRIPTION OF DATA AND METHOD OF ANALYSIS Continuously recorded data of wind speed and direction are available from two coastal and one inland stations at the three nuclear power station sites in India. These are: Tarapur (19”N, 71”E) on the west coast, Kalpakkam (12”N, 80”E) on the east coast and Kota (25”N, 76”E), in inland site. Wind direction is recorded using low-torque potentiometer type wind vanes at about 8@1OOft height coupled to O-l ma Esterline Angus recorders (3 in. h-l chart speed). Averages of wind direction and speed are taken over 60 min periods. The persistence period in this study is therefore in whole hours. Data for I yr at Tarapur and Kalpakkam and data for three years at Kota were analysed for persistence to give the frequency of occurrence of various persistence periods. The average wind speeds for individual persistence periods were found and from these the minimum average Urnin,average U,, and maximum average wind speed U,,, associated with each period. The extremum averages therefore averages over the period of persistence and do not refer to any single hour. The wind directions are classified into 16 points of the compass i.e. N, NNE, NE, ENE etc. The analysis assumed that calms and missing data broke the persistence. The periods of the analysed data presented here were as follows: Tarapur : 1 yr 1968 Kalpakkam : 1 yr April 1969-March 1970 Kota : 3 yr 1967-1969 3. PROBABILITY CONSIDERATIONS The analysis of persistence shows that the frequency of occurrence of longer persistence periods decreases progressively. Data available at many sites where persistence statistics are required are usually collected over short periods of about 1 yr. A knowledge of the frequency distribution of persistence periods should be useful in determining the probability of occurrence of long persistence periods, and their return periods. Various distributions were tried for the three sites. Tarapur and Kota sites gave a linear plot (FIG. 1) on a log-probability paper indicating a log normal distribution. (1) where f is the probability density for persistence period T in hours and log r is the standard deviation of log T.Equation (1) which is normalised to give unity when integrated from T = 1 to a, can be used as an extrapolation function. In FIG. I the graphs are normalised such that total cummulative probability from T = 1 to ZJ is 0.5. The actual cumulative probability is therefore double that read from the graphs in FIG. 1. The values of 7 were 2.97 h at Tarapur and 2.28 h at Kota.
891
Persistence. of Wind Direction
FIG. 1. Log-probability plot of persistence frequency at three nuclear power station sites in India. The cumulative probability of periods equal to a greater than the given period is shown by the ordinate, The maximum probability is set at 50 per cent since only right wing of the distribution is significant.
At Kalpakkam, no analytic function could be fitted, but the trend was such that the frequency of occurrence of long periods decreases sharply. Equation (1) is a continuous probability distribution fitted to discrete points. Cumulative probability tables should therefore be used to calculate the probabilities of individual persistence periods from equation (1) as shown in the following example: Suppose probabilities for T = 2 h is required for Kota. The value of variate is x = log T/log T = 0*844. From statistical tables, for the normal distribution, the cumulative probability from x = 0 to 0.844 is 0.3004. The probability from x = 0 to + 03 is 05. Hence the probability for If = 2 h and more is 2 (0.5~*30~) = 0.3992 compared with the observed 0.364 (see FIG. 1). Similarly, the probability for T = 3 h and more is 0.1819. Thus, the probability for 2 h persistence is the difference of the two, i.e. 0.2173 (observed: 0.1975). 4. RELATION
OF
WIND
SPEED
AND
PERSISTENCE
The maximum average, the average and the minimum average wind speeds are plotted against the persistence period at Kota and Kalpakkam in FIGS. 2 and 3. In the case of Urnin,the curve represents a lower envelope of the points. The general behaviour of the speed with respect to persistence is: (1) the maximum wind speed U,,, decreases with increasing persistence; (2) average wind speed U,, increases initially but stabilises to a constant value; (3) the minimum wind speed Unrn increases with increasing persistence. The behaviour at Tarapur was also similar and therefore not shown here. These plots are useful in defining the extreme meteorological conditions (from diffusion considerations) at a site. In FIG. 2 the envelope for a 1-yr analysis, namely 1968, is also shown by the dotted curve. As would be expected, this is to the left of the envelope for a 3 yr analysis.
892
V.
V. .~-~
SHIKV.~IKAR
-...-.-____.__._ U,&ota
1967-69
loam-_-U ,o,Koto
EJ67- 69
0
Oi i 18,
4
26.7
‘km h-’ lJ,,Kota
l99’-
FIG. 2. Dependence of the maximum, average and minimum wind speeds on persistence period. The wind speeds are the average wind speeds over each period and do not refer to basic 1 h values. The curve in the lowest graph is the lower envelope. The dotted line is the envelope for 1 yr data; the pointshowever arenot shown. Station: Kota(inland SiteinRajasthan).
In FIGURES2 and 3, the statistical weight of the points for large Tis poor. In many instances, there was only one occasion of a long persistence period, giving the same value for Urnin,U,, and U,,,. It may therefore appear from the curves in these figures that Urninis greater than the corresponding U,, or U,,, but this is not the case.
5. DEPENDENCE OF PERSISTENCE ON TIME AND SECTOR WIDTH
AVERAGING
The analysis presented here uses an averaging time of 1 h and 22.5” direction sectors. That persistence depends upon these two parameters will be obvious from the following example. Consider a 2-h wind direction record which oscillates with an amplitude of 90” and a period of 30 min. Such records are not unusual at night. Analysis during 1 h or 30 min averaging period with 22.5” sector will show a persistent mean wind direction. However, if the averaging period used is 10 min the analysis would show a complete break in persistence. Similarly it is obvious that with increasing sector width, the persistence will increase. This is best seen from the TABLE 1 constructed from the figures presented by VAN DER HOVEN (LX. cit.) for Daytona Beach.
893
Persistence of Wind Direction
50
f
E Y
40
P 3o 20
0
““““‘1””
IO
Per&once,
h ”
FIG. 3. Same as FIG. 2, but at Kalpakkam on east coast, south of Madras. All data is for 1 yr period only. TABLE 1. MAXIMUMOBSERVED PERSISTENCE PERIODSAT DAYTONABEACH Maximum observed persistence period in hours Sector width
22.5” 67.5” 112.5”
Spring
Summer
13 68 90
20 74 160
6. RETURN
Fall 19 50
150
Winter 25 42 90
PERIODS
If F (T) is the probability of occurrence of periods of less than T, the quantity R(T) =
1 1 - F(T)
is defined as the return period of persistences equal to or greater than T (GIJMBEL, 1952). Actually the return period defined above is dimensionally not a time period, but is a pure number defining the mean number of persistence events after which a persistence period equal to or greater than T may be observed. To obtain the return A.E.6/12--B
V. V. SH~RVAI~~IR
893
periods in time units (hours in the present case) which we shall call here ‘return interval’ and denote by R*(T) we proceed as follows: To avoid confusion we shall consider an analogous case of a series of rods of different lengths arranged end to end in a straight line. The rods are to have lengths such that the length of the line, measured in centimeters, corresponds to the peristence period in hours, and the sequence of arrangement corresponds to the sequence of observation of the persistence periods. The return period R (T) then corresponds to the number of rods whereas the return interval R*(T) corresponds to the total length that one has to traverse between two rods A and B of length greater than or equal to T cm. We are interested in finding the distance between the end of A to beginning of 5. The number of rods in this distance is R (T) - 1. If n,, n2 . , . . . . nT_ 1 are the number of rods of length, 1,2, . . T -- 1 cm respectively, andfiJi etc. are the corresponding frequencies then ni
f’.
2
[R(T) -- I] L-!-
F(T)
and T-l
R*(T)
:E
2i
ci T-l
x
I=;
n,
I
R(T)- ’
i=l
F(T)
x.fi
i=l
T-l
i.e.
R*(T) = R(T)
c
i X ,fi.
(3)
i=l
For large T, R*(T)
= constant
x R(T)
since F(T) w 1 and R(T) 9 1. This return period is still an underestimate since the occurrence of calms has been ignored. With the rod-analogy, the occurrence of calms corresponds to a gap caused by two rods not being kept contiguous, but separated by a vacant space. A correction on the lines similar to above may be made if persistence analysis of calms is available. An approximate correction can, however, be made if R*(T) is simply multiplied by a factor (1 + C/100) where C is the percentage of calms occurring at the site. The value of C was 0.73 per cent at Tarapur, 12.8 per cent at Kota and 3.4 per cent at Kalpakkam. Values of R (T), R*(T) and Uminfor typical persistence periods are shown in TABLE 2 for Kota. Such tables are useful in assessing the hazards as well as their probability of occurrence at a site, from accidental release of pollutants. It is to be borne in mind in such analysis that they are based on data for limited period of time, usually 1 yr. Experience as well as statistical considerations show that the values of 7 in equation (1) can change from year to year and the minimum wind speed for a given persistence period will decrease with increased period of sampling.
895
Persistence of Wind Direction 2. RETURN
TABLE
PERIODS, RETURN INTERVALS SPEEDS AT KOTA
ANI) MINIMUM
WIND
Persistence &
R U-1
R*VYt (h)
2 6 8 12 16 24
2.5 34.2 86.5 397 1300 8300
I.68 60.7 169 796 2630 16800
3 3 3.5 5.3 7.7 16
t Corrected for calms. Probability values were calculated using the distribution function and not from the observed values. 7. CERTAIN In this section
APPLICATIONS
OF THE
PERSISTENCE
ANALYSIS
we shall discuss some applications of the analysis of wind direction
persistence. 7.1. Dosage e~al~atjun An important application of the persistence analysis is in assessing the environmental consequences of accidental release of pollutants from a single source; specifically, it is customary to carry out analysis of the radiological hazards following a maximum credible accident to a nuclear reactor. Such analysis is then used to prescribe a population exclusion distance from the reactor and for estimating the degree of containment required for the radioactive fission products (SHIRVAIKAR and GANGULY, 1969). An accidental release of fission products may occur at any time. Hence, to ensure safety, the assessment of radiological doses should be made under “worst meteorolo~cal conditions” obtainable at the site, so that under all other conditions the doses are less than the above. The reactor safety features and exclusion distance are to be such that the doses do not exceed some accepted limits. 7.2.
Worst meteorological conditions
The term “worst meteorolo~~l condition” above refers to the conditions of atmospheric diffusion and other parameters leading to high doses and does not include other hazards, e.g. hurricanes affecting structural integrity. From the theory of atmospheric diffusion the doses depend upon: (1) atmospheric stability (PASQUILL, 1962); (2) wind speed ; (3) wind direction persistence (SHIRVAIKAR et al., lot. cit.). “Worst meteorological conditions” therefore imply a combination of these three parameters giving highest doses at the exclusion distance. Often, the conditions specified are those of strong stability, and wind speed of l-2 m s-l and imply that the wind direction persistence is infinite. It is, however, seen from FIGS. 2 and 3 that the lowest wind speed of say 1 m s-l has a maximum persistence associated with it. An appropriate value at Kota would be 8 h. Alternately, if we take 12 h persistence to define worst conditions, in order
896
V. V. SHIRVAXAR
to cover the estimated release period of fission products following a maximum credible accident to a reactor, then the wind speed should be 1.5 m s- I. 7.3. An ~s~lute index for ~o~parjso~ of nuclear power station sites A more important aspect of persistence in the evaluation of dosage and setting of worst meteorological conditions is the associated stability class. The Pasquill diffusion categories A-F (PASQUILL, 1962) are associated with wind speed, stability increasing with decreasing wind speed at night. For example, the most stable category F usually used as the worst meteorological condition defines wind speed of 2 m s-l (7.2 km h-l), This corresponds to a 10 h persistence both at Kota nad Kalpakkam, using 1 yr data. Longer persistences will have wind speeds corresponding to less stable conditions and the situation will not be the worst. Thus nature seems to impose an upper limit to the dosage, which could be used as an absolute indicator for comparison of sites for nuclear installation. This perhaps is one of the most important aspects of the persistence analysis. This point may be illustrated with the help of FG 4 in which the dosages thus computed at 1 km distance from source are plotted against persistence period for the three nuclear power station sites. The source strength is assumed to be 1 Ci s-t at ground level. In caiculating the dosages, the wind speed used was U,,, obtained from the envelopes in FIGS. 2 and 3, and a similar graph for Tarapur. Since Kalpakkam and Tarapur data were analysed for 1 yr, the dotted curve in FIG. 2, which is also for 1 yr, was used. Also, points up to 24 h persistence only were used to draw the envelope for the Tarapur data. Pasquill’s catagories of stability were obtained from the values of Urninfor night time clear sky conditions, so that the dosages obtained are the maximum possible. A difficulty arises when Uminis less than 2 m s-l. Since under these conditions Pasquill categories for night time are not defined, probabIy because of uncertainties introduced by meandering of the wind. Category F, i.e. the most stable category, was used in this case because this would give higher dosage than if the corrections due to meandering are introduced. The dosages given in FE. 4 are therefore an upper limit to those expected at the site, using 1-yr data. The dosage first increases due to increasing exposure period, but falls when the effect of increasing wind speed becomes overriding. The sharp drop is due to transition from Category F (Urnin ,< 3 m s- ‘) to the less stable category E (Umlnbetween 3 and 5 m s-l). However, the main points in this figure are: [l) each site has a maximum possible dosage Dmax (2) sites can be graded with respect to Drnax. Since the main issue in comparison of the sites is the dosage, D,,, is an absolute index. Using this index, we find that Tarapur is the best site with Kalpakkam and Kota following in that order. The values of D,,, are, however, very close to each other, which indicates that sites may not differ appreciably from one another in the radiological consequences of the maximum credible accidents to reactors, providing non-meteorological parameters are the same. Other considerations therefore enter in the grading of the site, one of them, which is of meteorological significance, is the calculated annual dosage to the public from normal operations. The above dose analysis has been based on 1 yr data. As the data extends over Larger periods of say 3 or 10 yr it is natural to expect, that lower values of Urn*,,would
897
Persistence of Wind Direction
*t
2
4
6
8
Persistonce,
IO
7
12
14
I6
h
FIG. 4. Variation of dosage with persistence period. Source: 1 Ci s-r at ground level. Pasquill model is used to calculate the dosage. Wind speeds used are the Urn,,, values for various persistenccs obtained from the envelopes such as in FIGS.2 and 3. Lower three curves are for 1 yr data. Upper curve is for 3 yc data. Pasquill stability categories used correspond to the night time conditions and U,,,,, values.
be found for a given T. This is also seen from the 3y curve for U& envelope in FIG. 2, &,, will consequently change. As would be expected, it will increase as seen from the uppermost graph in FIG. 4 which is calculated from 3 yr data. D=, here has increased about 1.5 times, Statistically, this higher D,,, is a better estimate. This has to be weighed against the fact that the probability of obtaining this higher D,,,,x in a given time of say 1 yr is much smaller than the lower value of D,,, as obtained from 1 yr data. 7.4. Cooland warer e~~e~t trajectory in takes A third application with engineering significance is the following?. Large lakes often form a source of cooling water supply to large nuclear or thermal power stations. Here, the cold water intake and the hot water effluent points are separated by distance so that the hot water does not reach the cold water intake to cause a “short circuit”. Such a short circuit decreases station efficiency. In a large lake, however, the water currents are primarily wind driven and the trajectory of the hot plume in the water depends upon the wind direction persistence. An optimum location can therefore be made of the intake and discharge points using the persistence data (analysed for each direction) so that the short circuitry periods are minimised. t The author is grateful to Dr. J. S. tion.
SASTRY
of Health Physics Divn. for pointing out this applica-
898
V. V. SHIRVAIKAR 8. CONCLUDING
REMARKS
Wind direction persistence, hitherto ignored, does seem to have applications which, no doubt, will increase in future. It is therefore recommended that this analysis form part of the routine climatological analysis wherever possible. Acknowledgements-The author thanks Dr. A. K. GANGULY, Head, Health Physics Division and Dr. K. G. VOHRA for their encouragement in the work. The help given by Ss. L. N. SHARMAand N. S. PANCHALin the analysis is gratefully acknowledged. REFERENCES GUMBELE. J. (1954) Statistical theory of extreme values and some practical applications. NBS. Appl. Math. Ser. 33, 51. PASQUILLF. (1962) Atmospheric Diffusion, p. 297. Van Nostrand. SHIRVAIKARV. V. and GANGULYA. K. (1969) Systematics of reactor siting. Progress in Nuclear Energy. Series XII, Health Physics, Vol. 2, part I, pp. 393-430. Pergamon Press, Oxford. SHIRVAIKARV. V., KAP~~R RAME~HK. and SHARMAL. N. (1969) A finite plume model based on wind persistence for use in environmental dose evaluation. Atmospheric Environment 3, 135-144. SINGERI. A. (1967) Steadiness of the wind. J. Appl. Meteor. 6, 1033-1038. SINGERI. A. and NAGLEC. M. (1970) Variability of wind direction within the United States. Nuclear Safety 11, 34-39. . ’ VAN DER HOVEN I. (1969) Wind persistence probability. ESSA Tech. Memo. EARLTM-ARL 10,