The effect of teleconnection patterns on monthly rainfall in Khorramabad and Kermanshah stations

Introduction
The climate of a region is influenced by many factors, some of which are planetary and some are regional and local. Teleconnection patterns are the origin of anomalies. Therefore, revealing the relationships between climatic parameters and teleconnection patterns is important for further understanding of climatic fluctuations and variability in each region. The purpose of this research is to investigate climate anomalies using Teleconnection patterns are the origin of anomalies that are seen Therefore, revealing the relationships between climatic parapatterns. For this purpose, the rainfall data of two observation stations (Khorram-Abad and Kermanshah) were collected during a period of 68 years (1951-2018). In this research, two types of data were used. 1- The monthly rainfall data of two synoptic stations of Khorramabad and Kermanshah were obtained from the National Meteorological Organization. 2- Data related to remote connection patterns including: Polar Oscillation (AO), North Atlantic Oscillation (NAO), Scandinavian Pattern (SCA), East Atlantic Pattern (EA), East Atlantic-West Russia Pattern (EA/WR) ), the North Tropical Atlas pattern (TNA), the Polar-Eurasia pattern (POL) and the Meridian Wind pattern (AMM), the Southern Oscillation (SOI), the combined pattern (Best) of the East Pacific-North Pacific Oscillation (EP/NP), Water surface temperature in Niño 1 and 2 (Niño 1+2) and water surface temperature in Niño 3 and 4 (Niño 3.4)) were obtained from the NOAA website.
 
Materials and Methods
Analytical statistics and inferential statistics methods were used to determine the effect of Teleconnection indicators on rainfall in the region. First, the rainfall time series of each station was tested for significance using the Anderson-Darling test at the 95% confidence level. Also, to evaluate the condition of independence of time series, the sequence test was used. Then, the Teleconnection indices were divided into two groups. Atlantic Ocean-based indices (AO, NAO, SCA, EA, EA/WR, TNA, POL, AMM) and Pacific Ocean-based indices (SOI, Best, EP/NP, Nino 1+2, Nino 3.4) And their interaction. In most statistical materials, parametric tests such as variance analysis, correlation analysis, regression analysis, etc., are based on the assumption that the measurements within each statistical population have a normal distribution and an equal variance-covariance structure.The hypothesis of establishing a normal distribution is related to the distribution of the studied population and not the samples.In order to be able to accept this hypothesis, that hypothesis must be substantiated in theoretical fields, that is, the values must be symmetrically centered around the average number. In this regard, data that have a skewness (lack of symmetry) or are strongly integrated in a part of the measurement scale, affect the variance-covariance between the variables. Analysis of variance is one of the parametric methods that evaluates the relationship between a dependent variable and an independent variable.In this approach, the independent variable is considered as the agent variable and the dependent variable as the response variable. In order for the results of the analysis of variance to be valid, several assumptions must be considered when applying its formulas. The first assumption is that the observations are independent. It means that each observation is uncorrelated with another observation. The second assumption is that the observations are normally distributed. That is, all observed measures of central tendency, including mean, mode, and median, should be the same. The third assumption is that the variance is homogeneous. That is, the sizes of the distribution of scores should be determined. This assumption is called homogeneity of variance. Therefore, before applying the statistical tests, first, the time series of monthly rainfall of Khorramabad and Kermanshah stations were tested for significance using the Anderson-Darling test at the 95% confidence level. If any of the precipitation time series is not normal, we tried to normalize that time series by using Johnson transformation functions. If these functions were not able to place the precipitation time series in the normal range. Kruskal-Wallis method, which is equivalent to non-parametric analysis of variance, was used to test the precipitation of these non-normal time series. In the following, in order to find out whether the average monthly rainfall of Khorramabad and Kermanshah synoptic stations has changed during the different phases of the teleconnection patterns, or in other words, whether the average monthly rainfall in the west has undergone changes due to the positive or negative phase of these patterns, first the values The standardized index of these patterns was divided into three levels: neutral, positive and negative. Then one-factor analysis of variance and Kruskal-Wallis test were implemented on these three levels as factors and the time series of monthly rainfall as the response variable.
 
Conclusion
The distribution values of Kruskal-Wallis statistics for the months of October and September and the values of the analysis of variance statistics for other months of the year revealed that the influence of the indices based on the Atlantic Ocean has less homogeneity and order than the indices based on the Pacific Ocean. In a way that the phase change of the Pacific Ocean indicators has caused a significant change in the rainfall of October and November in Khorramabad and October in Kermanshah. If the influence of the patterns based on the Atlantic Ocean does not have such an arrangement. In general, the patterns of the Atlantic Ocean have caused a significant change in precipitation mainly in the winter season, while the patterns based on the Pacific Ocean have had a significant effect on the precipitation in the autumn season. In this regard, the East Atlas-West Russia pattern had the most significant effect on the precipitation of these two stations, while the polar oscillation pattern, the Eurasia polar pattern, and the meridian temperature pattern caused a significant change in precipitation in only one month and one station. Also, the Scandinavian pattern has a significant effect on the October rainfall in Khorramabad, January, March and December in Kermanshah. On the other hand, the East Atlas pattern and the North Tropical Atlas pattern have had a significant effect on February rainfall in Kermanshah and October in Khorramabad. On the other hand, the East Atlas pattern and the North Tropical Atlas pattern have had a significant effect on February rainfall in Kermanshah and October in Khorramabad. The East Atlas and Scandinavian patterns have a significant effect on the October rainfall in Khorramabad and Kermanshah. In general, the patterns of the Atlantic Ocean have caused a significant change in precipitation mainly in the winter season, while the patterns based on the Pacific Ocean have had a significant effect on the precipitation in the autumn season.