2.3. Methods
The methodology used in this paper is divided into four main steps. First of all, we zoning precipitation in Iran using correlation. Then to determine the physical boundaries of precipitation regions, we used the kriging method. In third steps Pearson correlation was used to specified the places with high correlation with winter precipitation of Iran. Finally, multiple linear regression applied to find the best regression equation. To determine the effective areas in this study, the following conditions are considered: the correlation is more than 0.3, R2 more than 0.55, the low difference between the R2 and the R2-adj, the P-value is less than 0.05, and the correlation between the calculated anomaly of precipitation and the observed data is greater than 0.7.
Pearson Correlation
Correlation in the vast meaning is a measure of an association between variables. In correlated data, a variable is correlated with another variable, either in the positive correlation or in the opposite (negative correlation) direction. correlation coefficients are scaled a range from − 1 to + 1, where 0 indicates that there is no linear or monotonic association (Schober etal.,2018). Pearson’s coefficient of correlation was found by Bravais in 1846, but Karl Pearson was the first to explain, in 1896, the standard technique of its calculation. Pearson’s correlation coefficient is a measure of the strength of the linear relevance between two variables (Hauke etal.,2011). Pearson correlation equation can be written as below
$$r=\frac{{N\sum {xy - (\sum {x)(\sum {y)} } } }}{{\sqrt {\{ N} \sum {{x^2} - (\sum {x)2\} \{ N\sum {{y^2} - (\sum {y)2\} } } } } }}$$
1
Where N = Number of pairs of values, \(\sum x\)= Sum of the x values, \(\sum y\)=Sum of the y values (Obilor etal., 2018).
Kriging Method
In geo-statistics, kriging or Gaussian process regression is a method of interpolation for which the interpolated values are modeled by a Gaussian process governed by prior covariance. Under suitable molds on the priors, kriging gives the best linear unbiased forecast of the intermediate values (Lichtenstern, 2013). Kriging Function is (Equ.2)
$$\mathop Z\nolimits^{ * } =\mathop \sum \nolimits_{{i=1}}^{n} \mathop W\nolimits_{i} Z(\mathop x\nolimits_{i} )$$
2
Where: Z* is Estimated spatial variable, z (xi) is observed spatial variable wi is the weight of the variable statistic is the amount of observation.
Multiple Linear Regression
Regression analysis is a statistical method for estimating the relationship between a dependent and independent variable. The regression model with a dependent variable and a more independent variable is called multilinear regression. In multivariate regression analysis is formulated as
$$y=\mathop \beta \nolimits_{0} +\mathop \beta \nolimits_{1} \mathop x\nolimits_{1} +...+\mathop \beta \nolimits_{n} \mathop x\nolimits_{n} +\varepsilon$$
3
Where y is dependent variable, \(\mathop x\nolimits_{i}\) is independent variable, \(\mathop \beta \nolimits_{i}\) as parameter and \(\varepsilon\)is error (Uyanik and Güler,2013).
According to the topography and changes in spatial precipitation, the kriging method was divided into eleven precipitation zones in the cell size of 2.5°*2.5° (Map No. 1 and Table No. 1). The correlation between precipitation at each grid point (26 green point in Fig. 1) and all adjacent grid points is calculated. The pixels correlated with a coefficient higher than 0.7 were merged in one precipitation area. Finally, the following 11 regions were detected for Iran (White frame in Fig. 1). Then used kriging to determine the physical boundaries of precipitation zones. zones 1,2,5, and 9 containing one grid point, zones number 4,8, and 11 containing two grid points, zone 7 covering three grid points, zones 3 and 6 containing four grid points, and lastly the largest zone, number 10 being combining five grid points.
Zone 1 corresponds to the valley of the Aras River, it is characterized by annual rainfall of 250 mm up 500 mm. Zone 2 is located in the northwest of Iran, it is characterized by relatively high precipitation amount (about 400 mm yearly). Zone number 3 is the most extensive, this area starts from northwest with annual rainfall of 950 mm and extends to the south of Iran with annual rainfall of 250 mm. There are, of course, some regions in the area with a rainfall of more than 1000 mm yearly. Fourth zone is located in the western Alborz and south of coast Caspian Sea. Annual rainfall is between 650mm up to 2200 mm. Precipitation of next zone is between 400 to 200 mm yearly. The region 6 corresponds to South Zagros mountains. Its annual precipitation is between 260 to 150mm. Zone 7 is located in the northern margins of the desert (Dasht-e-Kavir). Zone 8 occupies the North-East of Iran, that is the zone with annual rainfall of 200 to 300 mm. The coastal region of Oman sea forms the zone 9. The zone number 10 comprises the Lut desert with very scarce precipitation over the whole year. The eleventh zone is located in the South-East of Iran and strongly influenced by monsoon (Table 1).
Table.1 Overall summary of geographical characters of precipitation zones of Iran
Precipitation Zones
|
Annual Precipitation(mm)
|
Geography Location
|
1
|
250–600
|
Aras Basin (NW of Iran)
|
2
|
280–850
|
Urmia Basin
|
3
|
250–1400
|
Zagros Mountain
|
4
|
650–2200
|
Caspian Sea coast
|
5
|
250–500
|
South slop Alborz mountain
|
6
|
150–300
|
Khuzestan plain-Bandar-Abaas
|
7
|
100–300
|
Central mountain and desert
|
8
|
100–250
|
North east (Khorasan)
|
9
|
100–200
|
North Oman Sea
|
10
|
30–100
|
Lut and Dasht Kavir
|
11
|
80–200
|
East of Iran
|
[3] - National Center for Environmental Prediction-National Center for Atmospheric Research NCEP/NCAR Reanalysis