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The Application of Variations Random Models in Isfahan Province Precipitation Forecasting and Analysis

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The Application of Variations Random Models in Isfahan Province Precipitation Forecasting and Analysis The application of variations Random models in Isfahan Province Precipitation forecasting and analysis Majid Javari Assistant prof . of PayameNoor University Ilam , Iran [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 . 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 Anarak 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. 2 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 . 3 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 4 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
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