مدل‌سازی آماری میانگین سالا‌نه دما در ایستگاه مهرآباد تهران

با توجه به اهمیت پدیده تغییرات آب‌وهوایی و گرمایش جهانی، آگاهی از رفتار گذشته، حال و آینده عناصر آب‌وهوایی از اهمیت شایان توجهی برخوردار است. در همین راستا، در پژوهش حاضر تلاش می‌شود داده‌های میانگین سالانه دما در ایستگاه مهرآباد تهران از سال 1330 تا 1394 بررسی شود. بدین‌منظور و برای شناسای تغییرات زمانی میانگین دمای سالانه، مدل‌سازی آماری–خانواده مدل‌های آریما (arima) به‌کار گرفته شد. برای نیل به این هدف، معنی‌داری آماری مراتب و اجزای مختلف مدل، برای پیش‌بینی وارسی شد. در نهایت دو مدل arima(0,1,1)con و arima(2,1,0)con به‌عنوان مدل‌های رقیب انتخاب شدند. معیارهای نهایی نشان دادند که مدل arima(0,1,1)con به‌عنوان مناسب‌ترین مدل برازنده بر دمای سالانه ایستگاه مهرآباد تهران است. همچنین، آزمون‌های آماری خودهمبستگی، ضریب همبستگی پیرسون، همگنی نرمال استاندارد، وانیومن، انحرافات تجمعی، نقاط عطف، علامت و پورت مانتئو برای وارسی رفتار باقی‌مانده‌های مدل پیش‌بین استفاده شد. علاوه‌بر این، شیوه‌های ترسیمی برای نرمال‌بودن باقی‌مانده‌ها، استقلال، ثابت‌بودن واریانس بر روی باقی‌مانده‌های مدل arima(0,1,1)con، در راستای بالا بردن اطمینان آماری عدم‌قطعیت مدل پیش‌بین انجام شد. یافته‌های حاصل از مدل نشان می‌دهد که به‌طور میانگین هر سال نسبت به سال قبل از خود حدود میزان 0.038 درجه سلسیوس افزایش دما را تجربه می‌کند. میانگین دمای 16 ساله پیش‌بینی به‌طور میانگین برابر 17.742 درجه سلسیوس خواهد بود. نتایج آزمون‌ها نیز نشان دادند باقی‌مانده‌های مدل arima(0,1,1)con رفتار تصادفی دارند، که نشان می‌دهد مدل حاصل، برازنده پیش‌بینی برای سری زمانی میانگین سالانه دما در ایستگاه مهرآباد تهران است.

Statistical modeling of the mean annual temperature at Mehrabad station, Tehran

Regarding climate changes and global warming, it seems that the behavior of climate elements in the future should be predicted and known. Therefore, in this study, using modeling by a set of ARIMA statistical models, models on the time series of the mean annual temperature at Mehrabad station in Tehran during 19512015 were fitted to investigate a significant model by trial and error in order to identify the most appropriate model. Since the time series of the observations had a normal distribution, modeling was performed on the time series without applying Box Cox transformation. First, for static and nonstatic investigations, the time series of annual mean temperature observations was plotted simply in diagrams. In addition, the first and second order regression line equations were used to further ensure the type of time series behavior of the mean annual temperature. The results showed that the time series behavior of temperature at this station is linear. Since the time series behavior was linear, the order d = 1 was determined. Second, the firstorder differentiation was performed on the time series. In the third step, the order p and q were determined using autocorrelation and partial autocorrelation of the differentiated values ( ). After investigating the significance of the order of the components of each of the models, the following models were selected as significant models, respectively:1) ARIMA(0,1,12) ARIMA(2,1,0Since the first significant model was observed with suspicion, as a result each of the components (p, d, q) of the above two models were tested up to the 3th order. Finally, these two models were selected as significant models. Also, Akaike information criterion (AIC) was considered to determine the most appropriate model among the above two models. ARIMA model (0,1,1  had the minimum value of AIC compared to the other model. As a result, using this model, the temperature time series at this station was predicted from the end of the period to ¼ of the first time series. Given the concept of uncertainty, which underlies descriptive and inferential statistics, as a result, it seems that uncertainties should be expressed with high statistical certainty. In this regard, we used statistical tests of autocorrelation, Pearson correlation coefficient, standard normal homogeneity, cumulative deviations, milestones, sign on the time series of ARIMA model residues (0,1,1 , and drawing methods for residual normality, residual independence, constant residual variance and portmanteau test to consider further criteria to increase the statistical reliability of the applied model. The results of all statistical tests showed the random residual time series of the model.  These tests showed that the best model for modeling the time series of the mean annual temperature at Mehrabad station, Tehran is ARIMA model (0,1,1 . Since the upper and lower limits of the predicted series as well as the predicted observations show the same behavior of the temperature time series at Mehrabad station, it can be said that the estimation of the predicted numerical values is still appropriate for this model to predict the temperature variable at this station. Finally, the results showed that the mean temperature of the predicted series is likely to be 17.742 ͦ C, and the mean annual temperature will increase by 0.038 ͦ C compared to the previous year.