The application of variations Random models in Province Precipitation forecasting and analysis

Majid Javari Assistant prof . of PayameNoor University Ilam , [email protected] Saied Alireza Alavi M.Sc.in Climatology, Isfahan Education , Iran Forough Tansaz M.Sc. in Isfahan Education , Iran

Abstract : The classical time series models have four components trend (T), seasonal variations (S) , cyclical changes (C) and irregular changes (I) . These components are used as single or combined in the climatic changes. In order to study these components , first these components should be measured in one of the additive and multiplicative models and then analyze them forecast them . To analysis climatic temporal variations, calculating different components of the time series accomplishes by different ways , least squares is the most important of these ways . For accomplishing this process paying attention to these case is important : selecting a suitable model before the final selecting by the use of accuracy indexes , determining the changing limits of the time series component as random , and studying the condition and quality of the variations (determining the maximum and minimum of the variation limit of the series). The present research is compiled in direction of the rainfall random changes rate in . Isfahan province with 107027 km2 includes % 6 /5 of area of the Iran . This province lies between 30 degrees and 42 minutes till 34 degrees and 30 minutes north lattude and between 49 degrees and 40 minutes till 55 degrees and 30 minutes east longituede .To achieve the above goal , the average of monthly rainfall per thirty years ( 1971 _ 2000 ) eighteen stations of synoptic and climatology are chosen and they have studied . and the normal amount of any station is compared by Anderson _ Darling method and other tests. And in the next period the several methods as Thumb method are used to ascertain the amount of seasonal changes in any station . To appoint the rain fall chronological changes , the multiple method in the form of moving average is used . The results of this resarch show that the most amount of random changes in rainfall are in the beginning of fall and then winter . The spring and the summer are in the next array . It is determined that in the winter season of Isfahan with decrease of rain average from west to east , the amount of variations of random rain is increased .In the autumn and spring seasons of Isfahan with decreasing the amount of rain from west to east the amount of variations in random rain is decreased and in summer the irrigular of random rain variations from west to east are increased. Keywords : Irregular changes , Additive and Multiplicative Models, Thumb Method , Anderson_Darling Method.

Introduction : The change of climate is the important subjects in this century . In these subjects changes of rainfall are more important for the changes of rainfall effect in all phenomena of environment . Studying and knowing this changes in projecting of regional and zonal are important . In the east and central region of Iran the rain is low and tried to random rainfall .The amount of percipitation in Isfahan province is measured minimum amount is 72mm in khor station and maximum amount is 570 mm in Imamghace station border of Chaharmohal Bakhtiyari province . So the amount of changes of annual percipitation reaches above 500 mm . Isfahan province lies in center of Iran .The more parts of Isfahan province have rainfall less than 200 mm that accures in rather region low percipitation of Iran. The amount of the rainfall changeable coefficient in stations of south and southwestern with the parts of Isfahan province are placed in forty percent till fifty percent and from east of to Khoor changeable coefficient highly incrase and reach to %60 in estern of Isfahan province . Isfahan province has rainfall changes from west to east and also in each station during the time their percipitaion are changed . Study and forecasting of the rainfall random changes are more important and it is provied such studies are necessary . The acquaintance of the research : One of the most important subjects in climatology is studying the rainning behavior in local surface ,region , zonal and worldwild . A lot of studies have done in above scales for determining 1 the changes of the rainfall . These changes show the importance of amount of rainning and regim of the rainfall in some different places in the world . A lot of foregin scientist have worked on analaysis of the climate changes .Anydike (1992 ) has worked on the changes of monthly and annual rainfall in centeral areas and south Nigeriyeh in period of 72 years . He has found that rainning is not random in these areas and he has studied the trend and the changes of rainfall period . Grosiman (1999) has analyzed the rainfall changes in Russia and Europe with series of one hundred years of rainning . He has pointed to the increase of the rainfall about 6 percent in northern latitude 30_70 degree in 100 years . He is belived that rainfall increased in orbit 55 degrees northern . In Iran some scientists have analyzed the climate changes by the methods of explainning .Some of them have studied climate changes by the methods of insufficiency .In Iran Kaviani(1992 ) tried the precipitation changes regime changes in Iran by the use of statistics method. Javari(2002) studied the precipitation and temperature variations of Iran by the use of time series models. Methodes of analysis data: After recived the data at first series examination and then normal distribution of any station is compared by Anderson _ Darling method . for example normal distribution data of Isfahan station is shown in figure1 . All data of eighteen stations of Isfahan province had normal distribution

Measurment of seasonality of the Isfahan Stations : The after measurment is the normal distribution of data must be analyzed and then forecasting the seasonal changes . To select analysis models different statistic tests (nonparametric and parametric tests) can be used. There is various tests to measure the series seasonality . In this paper Thumb rule was used .The Thumb rule a parametric test for seasonality is to compute tge lag L sample autocorrelation coefficient(Farnum 1989):

H0 ==PoL HPo=> a L (1)

Reject HO if rl > zα / n r l is sample autocorrelation of lag K . Conclusion of rule : If is rejected , we conclude with approximately 95% confidence that series have seasonal variations .These method which mentioned was used for Isfahan stations . For example the figure 2 was shown Feridoonshahr precipitation.

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Use from moving average method by multiplicative model: The moving average method used for series that have oscillations . Time spaces that use in moving average are difference .These spaces can be 3 _4 and 5 years and others scales of time . Time space depends on series . Time space are choosen for lowness and highness of curve change to levelness . Additive model is the result of time series ingredients addative and multiplicative model is result of time series ingredients multiplicative (Javari,2002, 69): YTSCI=××× (2) YTSCI=+++ (3) Y=real amount T=secular trend C= cyclical flactuations I = random variations

TSCI... TCI..=× 100 (4) S Result of data analysis is determined in table 1 .

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Table 1: Series (T.C) and (S.I) station of Isfahan The The add of the two by moveable TCSI... The moving average two of the moving average of SI.100=× of the concentrated average the 12 TC. T. c AVER1 AVER1 months T.C.S. I * * * * * * 12.6 * * * * * * 22.7 * * * * * * 8 * * * * * * 38.6 * * * * * * 1.7 * * * * * * 0 0 11.7208 23.4417 * * * 0 0 12.1583 24.3167 * * * 0 0 12.6792 25.3583 * * * 0 0 13.25 26.5 * * * 0 220.081 13.4042 26.8083 * 10.6 * 29.5 99.354 14.1917 28.3833 10.6 12.8417 10.6 14.1 278.332 14.1917 28.3833 12.8417 11.475 12.8417 39.5 43.966 14.3292 28.6583 11.475 13.8833 11.475 6.3 255.069 14.4667 28.9333 13.8833 12.6167 13.8833 36.9 161.751 14.4667 28.9333 12.6167 14.1917 12.6167 23.4 152.217 13.5333 27.0667 14.1917 14.1917 14.1917 20.6 0 12.4917 24.9833 14.1917 14.1917 14.1917 0 0 10.75 21.5 14.1917 14.4667 14.1917 0 33.774 9.7708 19.5417 14.4667 14.4667 14.4667 3.3 0 9.1417 18.2833 14.4667 14.4667 14.4667 0 0 7.425 14.85 14.4667 12.6 14.4667 0 115.761 6.1333 12.2667 12.6 12.3833 12.6 7.1 218.009 5.275 10.55 12.3833 9.1167 12.3833 11.5 5.581 5.375 10.75 9.1167 10.425 9.1167 0.3 412.178 5.3375 10.675 10.425 7.8583 10.425 22 117.308 5.2 10.4 7.8583 6.9917 7.8583 6.1 250 5.2 10.4 6.9917 5.275 6.9917 13 0 4.9042 9.8083 5.275 5.275 5.275 0 0 4.3458 8.6917 5.275 5.475 5.275 0 42.322 5.6708 11.3417 5.475 5.2 5.475 2.4 0 8.1042 16.2083 5.2 5.2 5.2 0 0 9.3583 18.7167 5.2 5.2 5.2 0 0 9.9333 19.8667 5.2 4.6083 5.2 0 0 10.1125 20.225 4.6083 4.0833 4.6083 0

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Table 2 :Determine the seasonal indicator of Isfahan station DEC NOV OCT SEP AUG JULY JUNE MAY APR MAR FEB JAN YEAR 99.354 220 0 0 0 0 * * * * * * 1971 218.01 116 0 0 33.77 0 0 152.2 161.8 255.07 43.966 278 1972 51.358 0 0 0 0 42.32 0 0 250 117.31 412.18 5.58 1973 393.87 0 47.84 0 0 29.58 0 2.815 162.6 155 412.35 377 1974 343.35 45.3 0 0 0 0 0 115.7 325.6 82.581 36.129 198 1975 165.65 18.1 253.7 0 0 8.264 33.74 111.8 200.1 197.88 176.41 61.2 1976 409.49 350 38.84 0 0.823 1.662 0 171 332.4 55.838 0 212 1977 351.56 157 0 0 0 0 0 13.31 3.363 88.93 116.32 145 1978 317.11 0.51 0.465 0.491 0.571 0 36.26 382.8 0 129.71 57.237 142 1979 191.24 90.8 136.4 0 0 0 0 0.57 124 176.91 433.9 138 1980 50.704 80.4 192.1 0 0 1.64 32.56 10.68 154.3 65.969 342.41 173 1981 155.37 269 135.6 0 5.109 0 0 61.15 6.685 390.34 66.714 324 1982 97.169 4.14 0 0 0 0 0 79.96 159 233.45 1.72 203 1983 216.27 279 3.81 0 0 0 0 157.1 178.4 456.62 67.939 230 1984 119.68 111 0 0 0 0 0 0 19.19 298.57 252.63 82.3 1985 315.45 391 0 0 2.352 0 0 92.37 417.2 325.22 55.739 77.6 1986 89.388 13.1 179.2 0 0 59.62 0 87.48 46.95 254.95 29.25 0 1987 16.713 45.7 12.35 0 0 8.038 0 0 140.4 444.84 249.06 54.9 1988 464.05 165 0 0 0 0 52.54 29.59 135.6 521.95 167.48 191 1989 156.3 0 0 0 0 80.38 0 5.732 48.04 80.949 189.47 215 1990 231.15 66.8 90.89 0 0 0 0 6.994 114 596.01 71.84 233 1991 76.888 0 0 0 31.57 12.82 76.89 189.3 72.1 193.85 127.02 194 1992 0 556 2.166 0 0.817 0 0 64.55 155.3 289.66 295.61 292 1993 50.872 405 261.4 0 0 0 0 0 23.52 340.59 217.7 25.1 1994 279.88 0 12.85 0 0 0 124 276.9 223.9 55.372 74.357 5.54 1995 151.65 60.2 0 0 0 11.25 1.482 132.3 73.45 389.34 146.7 147 1996 215.05 18 0.622 0 0 0 79.79 61.42 466.1 349.44 0 30.2 1997 13.581 0 161.3 0 8.316 9.108 0 46.6 6.743 389.36 344.28 159 1998 184.35 132 37.77 0 0 6.495 0 0 9.864 557.92 140.95 278 1999 * * * * * * 0 0 0 0 0 832 2000

100.484 187.1 124 54 0.017 2.87 9.35 15.08 77.7 138.3 258.4 156.2 183 MEAN Seasonal indicator 186.2 123 53.74 0.017 2.856 9.304 15.01 77.33 137.6 257.16 155.45 182

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Table 3: Getting trend cyclical fluctuation and random in Isfahan station

CI. TCI.. TCSI... I =×100 C CI.=× 100 T TCI. .=× 100 C T S * * 61.83 11.1956 6.922 * * 130.49 11.1913 14.603 37.9 73.38 27.81 11.1869 3.111 183.918 136.36 250.8 11.1826 28.046 19.782 99.42 19.67 11.1782 2.199 0 90.16 0 11.1738 0 0 6.56 0 11.1695 0 0 0 0 11.1651 0 0 0 0 11.1608 0 0 0 0 11.1564 0 300 71.51 214.53 11.152 23.925 72.147 94.15 67.93 11.1477 7.573 122.428 159.07 194.74 11.1433 21.701 36.499 99.69 36.38 11.139 4.053 107.393 120 128.87 11.1346 14.349 144.102 106 152.75 11.1302 17.002 137.859 173.69 239.45 11.1259 26.641 0 130.73 0 11.1215 0 0 79.82 0 11.1172 0 300 346.59 1039.76 11.1128 115.546 0 346.59 0 11.1084 0 0 346.59 0 11.1041 0 300 17.29 51.88 11.0997 5.758 155.284 35.85 55.66 11.0954 6.176 4.089 36.34 1.49 11.091 0.165 207.226 61.6 127.66 11.0866 14.153 42.654 50.18 21.4 11.0823 2.372 109.161 78.11 85.26 11.0779 9.445 0 35.56 0 11.0736 0 0 28.42 0 11.0692 0 300 77.71 233.13 11.0648 25.795 0 77.71 0 11.0605 0 0 77.71 0 11.0561 0 0 0 0 11.0518 0 0 0 0 11.0474 0 300 8.43 25.29 11.043 2.793

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The study of rainfall random changes average in Isfahan province: At first we need to study specification of stations base on longitude from west to east . The average of annuall rainfall of stations per thirty years (1971_ 2000) and eighteen stations of synoptic and climatology are choosen and they have studied . Table 4: specification of Isfahan province stations base on longitude from west to east row Name station Lattude Longitude Height Average of (degree_ (degree_ (meter) anuual minute) minute) Rainfall milimeter 1 Feridoonshahr 32 56 50 1 2490 515/33 2 Khansar 33 14 50 19 2300 353/28 3 Savaran 32 53 50 21 2150 398/54 4 Singerd 32 47 50 26 2100 360/48 5 Damaneh 33 1 50 29 2300 329/58 6 32 46 50 38 2100 327/76 7 Maymeh 33 26 51 1 1980 171/71 8 32 38 51 22 1350 154/86 9 33 59 51 27 982 132/59 10 32 34 51 3 1590 157/25 11 Kabootarabad 32 34 51 37 1580 124/68 12 31 59 51 5 1845 151/44 13 Isfahan 32 4 51 52 1550 124/89 14 33 32 51 56 1800 151/27 15 33 22 52 24 1381 116/3 16 32 24 52 37 1450 83/66 17 Naeen 32 52 53 5 1600 102/13 18 Khoor_Biyabanak 33 47 55 2 850 89/4

The survey of annual rainfall random changes average: In every station for getting the better showing of rainfall random amount we can get the average of thirty years of every month in percent for example : in Isfahan station the random changes average of the rainning have been showed by the Figure 3 . This figure shows that in every station the rainfall random changes reduced from winter to summer seasons . It means by reducing rainning , the rate is reduced too . But it shows these changes of autumn season among of seasons are very high . and it shows that in east stations of Isfahan these changes of rainning rate, its percent is very high in winter season.

The trend of rainfall random changes average in spring season : There are many irregulars in random changes average of raining in spring season . But these random changes are reduced from western to eastern stations of Isfahan province . It means that when the amount of rainning is reduced the random changes is reduced from west to east of Isfahan too. The 7 value of rainfall random changes average in spring season is reduced from west to east of Isfahan province. For example in Isfahan station the random changes average of the raining have been showed by the Figure 4:

Y t =−77.9042 0.5817t (5)

The average of rainfall random changes in spring season to percent The rainfall average in spring season to millimetre Linear (The average of rainfall random changes in spring season to percent )

100 90 80 70 60 50 40 30 20 10 0

r r n d n z h n r h a ad a e e s neh ba oo ha ah an h s an fab z K K ja Isf Natan Nae savaraSingerd adeganMaymeh Kashan ar oon Dama h a Shahreza ArdestanV id C N Falavarjanootara ab Fer K

Figure 4 :The value of the rainfall random changes average in spring season The value of rainfall random changes average in summer season : In summer season trend of rainfall random changes average decreases highly because in the first month of summer cyclons arrive in Isfahan province and in western stations cause the rainfall but in centeral and east stations amount of rainfall reaches to zero . In summer season the maximum random changes amount is 58 percent in Damaneh station and the minimum is 17 percent in Varzaneh station . In summer season as usuall we have lest rainfall in Isfahan and amount of random changes in most station is low . For example in Isfahan station the random changes average of the raining have been showed by the Figure 5: Y t = 44.6546− 1.199t (6)

The average of rainfall random changes in summer season to percent

The rainfall average in summer season to millimetre

Linear (The average of rainfall random changes in summer season to percent )

70 60 50 40 30 20 10 0

F K s S D C M N K F K S I N A V N K

s

a

e a a i a a h r a h a h a a a f a n

d v a

rid la n s b a rz o m a ja t e

y g

a a e h

h s o h o d e m v e f a ra a n s a

o a a a o re r e n a

rd t n n z e n

o r n b t a g n r

a e e z h ja n a n a

ra a h h

s d n n

h

b

a

a

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Figure 5: The value of the rainfall random changes average in summer season The value of rainfall random changes average in autumn season : In autumn season in all stations the percent the amount of rainfall random changes increases and also the range of diffrence between the stations is low . In this season the trend of rainfall random changes average decreasesed. or in other hand the rainfall from west to east decreases highly but rainfall random 8 changes average shows low decrease . For example in Isfahan station the random changes average of the raining have been showed by the Figure 6: Y t =−156.793 1.58t (7) The average of rainfall random changes in autumn season to percent

the rainfall average in autumn season to millimetre

Linear (The average of rainfall random changes in autumn season to percent )

200 180 160 140 120 100 80 60 40 20 0 N Kashan Falavarjan Kabootarabad Shahreza Esfahan N Ardestan Varzaneh N Khoor C M eidoonshahr Feri Kansar savaran ngerd Si D ajafabad atanz aeen hadegan am aym aneh eh

Figure 6: The value of the rainfall random changes average in autumn season The value of rainfall random changes average in winter season : In winter we have the most raining in Isfahan province . The maximum of rainfall is 253/22mm in ferydoonshahr station and the minimum of rainfall is 51/12 mm in khor_ Biyabanak . In this season as determined by figure 7 value of rainfall random changes average increases but rainfall from west to east decreases : Y t =−101.419 0.3346t (8)

The average of rainfall random changes in winter season to percent The rainfall average in winter season to millimetre Linear (The average of rainfall random changes in winter season to percent )

300 250 200 150 100 50 0

F K s S D C M N K F K S I N A V N K

s

a e a i h a a a h a a a a r a h

a f

n

v d r l a r n m j s b a t e a o y a

i g a a z a h e

d h h e s d o m o v

f a e a n r s a n o a a a r e o a r a n r n z e e t n

r b n o g d r t n a

e e h z a j

a n a n a h h a

r

d n s n a

h

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Figure 7 : The value of the rainfall random changes averag in winter season Time survey of rainfall random changes average in Isfahan province: When we look at the table 3 we understand that the most rainfall random changes are in autumn season and next seasons are winter, spring and summer . For each station one chart is established for example you see a sample of them in figures 4-7.

9 Table 3: rainfall random changes average (1971 _2000 ) row Name station Spring summer Autumn Winter 1 Feridoonshahr 77 18/16 172/08 101/81 2 Khansar 75/97 49/6 152/28 103/11 3 Savaran 73 43/54 144/28 101/57 4 Singerd 74/31 30/63 153/41 103/14 5 Damaneh 78/26 57/81 148//93 101/47 6 Chadegan 75/73 44/52 146 102/77 7 Maymeh 79/8 47/75 137/11 107/38 8 Najafabad 61/02 29/22 133/4 104/6 9 Kashan 78/95 44/95 134/7 104/74 10 Falavarjan 74/19 17/32 128/37 103/23 11 Kabootarabad 71/59 29/4 149/29 104/49 12 Shahreza 65/62 30/61 149/5 104/85 13 Isfahan 73/32 48/08 153/04 102/96 14 Natanz 72/63 25/97 132/18 107/12 15 Ardestan 74/17 16/6 125/38 110 16 Varzaneh 74 17/01 141/34 10/18 17 Naeen 55/1 17/01 141/34 101/18 18 Khoor_Biyabanak 68/14 25/33 132/23 109/33

The average of the rainfall random changes

200 150 100 50 0 winter autumn spring summer The average of the 102.96 153.29 73.32 48.04 rainfall random changes

Figure 8: The rainfall random changes in Isfahan station

The position of the average of rainfall random changes is showed in each stations . The most rainfall random changes amount are showed in autumn season and another seasons are in the next rows . Therefore in all stations the average of rainfall random changes is increased from winter to autumn seasons and it is reduced from spring to summer seasons . Conclusions : The factor of changes of the rainning is very important which influenced on dividng of the climates . These changes are acceptable in Isfahan province . The less amount of ranning is72mm in Khoor and Biabanak station of Isfahan province and the most amount of ranning is 576 mm in Imamghace station of Isfahan province . It is very changeable . The average of annuall rainfall is very changeable too. For example : in Isfahan station the rate of rainning was only 323mm in1954 and it was 31mm in1937 . It means extremly between the most rainning and the least rainning years is ten… In winter of Isfahan province with reducing of average of rainning from west to east the amount of rainfall random changes is increased . In spring and autumn seasons with reducing of rainning average from west to east , the amount of rainfall random changes is reduced . In summer the irregulars of the rainfall random changes are increased from west to east .With reducing of average of season rainfall in summer , spring and autumn ,from west to east of Isfahan the average of rainfall random changes is reduced . Only in winter with reducing of average of rainning from west to east of Isfahan province , the average of rainfall random changes is 10 increased . In Isfahan province , s stations the average of rainfall random changes is increased from winter to autumn , while the average of rainfall random changes is reduced from spring to summer . References: 1- Alizadeh , A.(1987): Principles of Applied Hydrology, Astaheh Ghodseh Razavi, Mashhad , Iran. 2- Cilchrist . W (1976): Statistical Forecasting, Nowyork , John Wiley,USA. 3- Groisman .P. YA (1999) : Data on Present- Day Precipitation Change in the Extratropical Part of the Northern Hemisphere , State . Hydrological Institute USSR . 4- Grotch .S. L (1999) : A statistical - Intercomparison Predictied by Four General Circulation Models in the Historical Data , Elsevier ,Newyork . 5- Javari . M (2002) : Temperature and precipitation changes of the Iran , PHD thesis , Tehran university . 6- Kaviani .M.R and Asakareh.H(2003) : The statistical study of long period trend of the Isfahan yearly precipitation , proceeding of third regional and first national conference on climate changes , Isfahan . 7- Loukas . A. & Quick .M ( 1996): Spatial & Tempral Distribution of Storm Precipitation in South Western British Columbia , Journal Hydrology ,Vol 174, January 1996 . 8- Nyroumand .H and Bozorghnia .A(1993) : Introduction to analysis of time series , pub Mashhad university. 9- Rind . D (1999) : Climate Variability & Climate Change ,Elsevier Newyork . 10- Winkler .J.A & Palutikof .J.P (1997) : The Simulation of Daily Temperature Time Series From GCM Output … , Journal ofClimate , Vol 10 , October 1997.

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