**Authors**

**Abstract**

Introduction

The relationship between topography and precipitation in order to estimate the type and amount of precipitation in mountainous areas has always been of great importance for climatologists. In most of researches done based on regression model, the independent parameters such as elevation, slope, aspect, longitude and latitude have been used and the rule of distance to describe the spatial variability has been neglected while the mentioned parameter has a determining rule in spatial variability of precipitation; as an example, Marquinez et al (2003; 2) used the distance from coast line of Cantabrian in northern Spain as an independent variable to describe the spatial variability of precipitation in mountainous areas.

Materials and Methods

In the present work, the significant relation between precipitation and parameters of elevation, slope, aspect, longitude, latitude, distance from west baseline and distance from ridge axe has been considered using the multivariate regression model. In fact, the west baseline is the furthest west line of the case-study (located on the borders of Iran and Iraq) where the air masses arrive and the distance from their is a criterion for keeping away from humidity sources and the distance from ridge axe is considered as a distance from the high part of the mountain axis as a function of raising of air masses. The area under study is divided by homogenous areas via precipitation variability. The area under study in this research is the mountainous area of western Iran located in the central Zagros. 269 precipitation recording stations, including the meteorology organization (synoptic, climatology and rain gauge stations) and rain gauge stations related to the Ministry of Power have been used and after converting the data of Power Ministry to A.D dates( because the mentioned organization has not used A.D dates) all of the stations that have a complete data between 1995 -2004 were selected (in the present work a complete statistical period of ten years has been used to prevent the errors of the stations with no data).

Results and Discussion

There are some assumptions in each multivariate regression model where assuming them being correct, the regression results are valid; otherwise the model should be substituted by another one. The assumptions are (Esmailian 2006; 230):

• The errors mean is zero e.g.

• Although the variance of errors is passive, it is constant e.g.

• The co-variances of errors of i and j are zero e.g.

• The three mentioned assumptions are equivalent with

Considering the accuracy of the mentioned assumptions in a linear regression model, we should pay attention to the assumptions of normality of residuals and consider the constancy of variance.

To investigate normality of the residual, Kolmogorov-Smirnov(K-S) Test histogram P-P and Q-Q can be used. The invariability of the variance of residual can be investigated using the scatter plot. In addition there are two or more independent variables in multiple regressions; therefore, two tests are needed to identify their significance; namely, a regression equation significance test at the first stage and a test for the significance of each of the partial coefficients at the next stage. In this study, in order to test the significance of the regression, T statistic was used and the autocorrelation in noise was tested using Durbin-Watson (D-W) -the test is based on first order autocorrelation error (cited in Khezri; 2009, 100). The normality of dependent variables was investigated using K-S test and in order to explore the significant relationship between the independent variables (slope angle, aspect, elevation, longitude, latitude, distance from west baseline and distance from ridge axe) and dependent variables, the Pierson correlation was used. Adjusted coefficient of determination (R2) in this model indicates that about 0.57 of precipitation variability in mountainous central Zagros can be explained using the independent variables in this model. Meanwhile taking into account the significance level of each variable and with regard to comparing them with error level of 0.1, it was confirmed that the coefficients of longitude, latitude, elevation, distance from ridge and slop angle are significant at 0.99.

Equation precipitation after assessing the validation of the regression model for the studied area was calculated as follows:

Where X is the longitude, Y is the latitude, Dr is the distance from ridge axe, S is the slop angle, H is the elevation and P is the logarithm of the precipitation.

Conclusion

The results of this study showed that topographies have a mechanical effect on the entered air masses and strengthen them when they are rising. The amount of precipitation increases as the elevation increases, but it should be considered that the maximum precipitation is not coinciding upon the ridge axe. Based on average of profiles, windward in both western and eastern regions is wetter than in the upwind section.

In order to model spatial variability, the recent study used the distance from ridge axe and the distance from west baseline for the first time in Iran. Due to having no statistical significance for the distance from west baseline variable, it is not suggested to be used for the next researches that are aimed to model spatial variability of precipitation. With regard to the significance of distance from the ridges variable (99 %), it is suggested that researchers utilize the variable in future studies for modeling the spatial variability of precipitation in Zagros and especially central Zagros.

The relationship between topography and precipitation in order to estimate the type and amount of precipitation in mountainous areas has always been of great importance for climatologists. In most of researches done based on regression model, the independent parameters such as elevation, slope, aspect, longitude and latitude have been used and the rule of distance to describe the spatial variability has been neglected while the mentioned parameter has a determining rule in spatial variability of precipitation; as an example, Marquinez et al (2003; 2) used the distance from coast line of Cantabrian in northern Spain as an independent variable to describe the spatial variability of precipitation in mountainous areas.

Materials and Methods

In the present work, the significant relation between precipitation and parameters of elevation, slope, aspect, longitude, latitude, distance from west baseline and distance from ridge axe has been considered using the multivariate regression model. In fact, the west baseline is the furthest west line of the case-study (located on the borders of Iran and Iraq) where the air masses arrive and the distance from their is a criterion for keeping away from humidity sources and the distance from ridge axe is considered as a distance from the high part of the mountain axis as a function of raising of air masses. The area under study is divided by homogenous areas via precipitation variability. The area under study in this research is the mountainous area of western Iran located in the central Zagros. 269 precipitation recording stations, including the meteorology organization (synoptic, climatology and rain gauge stations) and rain gauge stations related to the Ministry of Power have been used and after converting the data of Power Ministry to A.D dates( because the mentioned organization has not used A.D dates) all of the stations that have a complete data between 1995 -2004 were selected (in the present work a complete statistical period of ten years has been used to prevent the errors of the stations with no data).

Results and Discussion

There are some assumptions in each multivariate regression model where assuming them being correct, the regression results are valid; otherwise the model should be substituted by another one. The assumptions are (Esmailian 2006; 230):

• The errors mean is zero e.g.

• Although the variance of errors is passive, it is constant e.g.

• The co-variances of errors of i and j are zero e.g.

• The three mentioned assumptions are equivalent with

Considering the accuracy of the mentioned assumptions in a linear regression model, we should pay attention to the assumptions of normality of residuals and consider the constancy of variance.

To investigate normality of the residual, Kolmogorov-Smirnov(K-S) Test histogram P-P and Q-Q can be used. The invariability of the variance of residual can be investigated using the scatter plot. In addition there are two or more independent variables in multiple regressions; therefore, two tests are needed to identify their significance; namely, a regression equation significance test at the first stage and a test for the significance of each of the partial coefficients at the next stage. In this study, in order to test the significance of the regression, T statistic was used and the autocorrelation in noise was tested using Durbin-Watson (D-W) -the test is based on first order autocorrelation error (cited in Khezri; 2009, 100). The normality of dependent variables was investigated using K-S test and in order to explore the significant relationship between the independent variables (slope angle, aspect, elevation, longitude, latitude, distance from west baseline and distance from ridge axe) and dependent variables, the Pierson correlation was used. Adjusted coefficient of determination (R2) in this model indicates that about 0.57 of precipitation variability in mountainous central Zagros can be explained using the independent variables in this model. Meanwhile taking into account the significance level of each variable and with regard to comparing them with error level of 0.1, it was confirmed that the coefficients of longitude, latitude, elevation, distance from ridge and slop angle are significant at 0.99.

Equation precipitation after assessing the validation of the regression model for the studied area was calculated as follows:

Where X is the longitude, Y is the latitude, Dr is the distance from ridge axe, S is the slop angle, H is the elevation and P is the logarithm of the precipitation.

Conclusion

The results of this study showed that topographies have a mechanical effect on the entered air masses and strengthen them when they are rising. The amount of precipitation increases as the elevation increases, but it should be considered that the maximum precipitation is not coinciding upon the ridge axe. Based on average of profiles, windward in both western and eastern regions is wetter than in the upwind section.

In order to model spatial variability, the recent study used the distance from ridge axe and the distance from west baseline for the first time in Iran. Due to having no statistical significance for the distance from west baseline variable, it is not suggested to be used for the next researches that are aimed to model spatial variability of precipitation. With regard to the significance of distance from the ridges variable (99 %), it is suggested that researchers utilize the variable in future studies for modeling the spatial variability of precipitation in Zagros and especially central Zagros.

**Keywords**