كاربرد مدل هاي فوريه در برآورد دماي ماهانه و آينده نگري آن مطالعه موردي : دماي مشهد

Application Fourier Models to estimate and predict climate elements "A case study: monthly mean temperature of Masshhad city modeling"

Due to important of climatic elements on environmental management, climate element modeling has more attention by scientific society. The monthly mean of climatic elements has up-down sinuous and regular behaviors. These behaviors have been estimated and predicted by sinuously function based on different frequency. One of the useful tools is the Fourier modeling. In this paper the authors defined Fourier models and base on this theory had been fitted a Fourier modeling on Mashhad monthly mean temperature by 106 year long data since 1891 Jan to Dec 1996. The data have collected from three references: since 1891 to 1950 it is recorded in World Weather Record that published by world meteorological organization. This report contains temperature in degree Fahrenheit. In this period there was tow epoch missing value. The missing values are given from Oil National Company in Ahwaz. Since 1950 to 1996 it recorded by meteorological organization of Islamic Republic of Iran by degree Celsius. We change the degree Fahrenheit of world meteorological organization to degree Celsius for orchestrates after and before 1951. The data during 1951-1996 collected from water ministry of Islamic Republic of Iran. Then the data tested for homogeneity and analyses after that. The Masshhad model contains an order and a sinuously - cosine descriptive variables. The sinuously - cosine components are known as harmonics that create series behaviors. The long of oscillatory components are same long as half series long. Determining of significant and important sinuously components are carry out by periodogram toll. Based on this tool we can look for significant latent cycle by try and fault. The periodogram shows variation of series base on frequency. This tool analyses all changes in differences frequency as universality. Up on above methods the best fitted model on monthly mean temperature of Mashhad defined by 106ʹʹʹ harmonic. Then the hypnosisʹs of model have been tested for normality and independent of error and stationary in variance. The model was significant in 0.01 levels and there is no harmonic to make it better. Due to kind of fitted model to masshhad temperature, the model contains an oscillatory (deterministic) and a stochastic component. In this case we can purpose the Fourier models as tow variable regressions model that contain a constant and multiple variables.The correlation and determine coefficient and standard error of residual obtained 0.976, 95.2% and 1.912 respectively. It is necessary to point out that before modeling we tested linear trend in data based on Pearson method. If there are trend or not a constant can be added to the model or not. It cleared that there are no trend based on 106 year long of Mashhad monthly temperature. The prediction of monthly mean temperature and its confidences interval was predicted since 1997 Jan to 2004 Dec base on estimated model. To make the 95% confidences interval we add and different 3.748 from the predicted value. This can calculate from standard error of residual and standard value of Z square (1.96) value in 95% confidence. The predicted value stands as an oscillatory around a horizontal axis and the interval line shown stationary in all vector. The defined methods in this paper may apply for all oscillatory equal intervals discontinued time series. But it may apply for continued time series too by dividing time axis as equal interval.