4.1 Precipitation diversity in macro-scale
The precipitation time series introduced in section 2.2 were subjected to CA, and the results are presented in Fig. 2. Based on Ward’s method and Pearson correlation, the precipitation regimes in Iran are spatially classified into six distinct regions, which we call the macro-precipitation regions (MPR) of Iran. The mean annual hyetographs of the six regions illustrated in Fig. 2 show that precipitation in each region has a unique temporal distribution, sharply different from that of the others. The long-term mean annual precipitation depth in the six regions is plotted in Fig. 3. The MPR1 along the Caspian Sea with a mean annual precipitation of 885 mm and the southeastern desert provinces (MPR6) with 158 mm are the wettest and driest regions, respectively. Considering the moisture air masses entering the country, it seems that the spatial diversity of precipitation is greatly controlled by these air masses. Siberian cold continental air mass (known as (cP) air mass) enters from the north and is blocked by the Alborz Mountain ranges carries moisture from the Caspian Sea provides heavy precipitation in MPR1. The Sudan air mass enters from the south and southwest of the country carrying moisture from the Arabian Sea, the Red Sea, the Persian Gulf, and the Oman Sea (Alijani, 2000; Heydarizad et al. 2018) influences the precipitation regime in MPR2. The Mediterranean air mass affects the precipitation regime in MPR3. North Atlantic and Black Sea cyclones (Sabziparvar et al., 2015) being rich in humidity and entering from the northwest direction provide precipitation in MPR4.
The precipitation regime of MPR6 is controlled by the Maritime Polar air mass (mT) entering the country from the southeast direction (Indian ocean and Oman Sea). While the Mediterranean air moisture influences the precipitation regime of MPR5 but due to the desert nature of this region, the precipitation amount is considerably less than that of MPR3.
Table 1 presents the similarity between our classification and the previous ones. For example, MPR4 corresponds to zone 1, G3, and D of Domroes et al. (1998), Modarres (2006), and Samani and Karimi (2009), respectively.
Table 1
The Similarity between our classification and the previous ones in macro and meso scale.
Scale
|
This research
|
Domroes et al. (1998)
|
Modarres (2006)
|
Samani and Karimi (2009)
|
MPR
|
MPR1
|
2 and East part of 1
|
G6, G8
|
C
|
MPR2
|
-
|
G4, G7
|
H, I
|
MPR3
|
3
|
G2, G5
|
A
|
MPR4
|
1
|
G3
|
D
|
MPR5
|
-
|
G1
|
B, E
|
MPR6
|
-
|
F, G
|
Meso-precipitation zone
|
A
|
2
|
G8
|
C
|
B
|
East part of 1
|
G6
|
C
|
-
|
-
|
H
|
D
|
3
|
West part of G2, G5
|
A
|
E
|
-
|
-
|
I
|
F
|
West part of 1
|
G3
|
D
|
G
|
-
|
-
|
B
|
H
|
-
|
-
|
G
|
I
|
-
|
-
|
E
|
J
|
-
|
-
|
F
|
4.2 Precipitation diversity in mesoscale
In the previous section, we demonstrated that Iran's precipitation regime is dividable into six regions, mainly as the result of the moist air masses entering the country. However, due to vast area, complex topography, large latitude variations, and extensive nearby water bodies, its variabilities are more complex, so we examined the six regions to see if we can cluster them into more sub-regions. For this, the Hopkins statistic (Lawson and Jurs, 1990) was used. The Hopkins value for the 461 rain gauge stations is determined in the range of 0.65-0.80, indicating that the data are further groupable. The Gap Statistic method was also used to determine the optimal number of clusters for both hierarchical and K-Means Clustering. As presented in Fig. S1 (S stands for Supplementary Materials), the optimum number of groups is 10.
Also, we used the Sdbw index from the NbClust package (Charrad et al., 2012) for determining the optimal number of clusters for hierarchical and K-Means Clustering. All tests demonstrated that the optimal number of groups is ten. Figure S2 depicts the cluster dendrogram of 461 stations. Meso-precipitation zones of Iran based on Ward’s method-Euclidean distance and K-Means Clustering are shown in Fig. 4. The ten clusters (A to J) resulted from Ward’s method-Pearson correlation mapped on Fig. 5 present Iran's precipitation diversity in a mesoscale. We chose the meso-precipitation zones according to Ward’s method-Pearson correlation since it gives the best distinct classification (Fig. 5 compared to Fig. 4). Also, the long-term (1983-2016) mean annual hyetograph in zones A to J are plotted in Fig. 5. The mean annual precipitation in each zone is shown in Fig. 6. Zone A and J have the maximum (1293 mm) and minimum (123 mm) mean annual precipitation, respectively. Comparing Fig. 4 with Fig. 5, it is observed that zone MPR3 (Southwestern region) is divided into zones C and E. It is most probably due to the collision of the Mediterranean and the Sudan air masses. Similarly, MPR6 (Southeastern region) is divided into Zones H and J as the result of the occasional merging of the Sudan air mass with the Maritime air mass entering the country from the southeast direction (Indian ocean and Oman Sea). The similarity between our mesoscale precipitation zoning and the previous ones is tabulated in Table 1.
4.3 Precipitation diversity in Micro-scale
In the next step, we examined the possibility of division of each of the ten mesoscale zones (i.e., A to J) into smaller, rigorous homogeneous sub-zones. For this, several statistical indices from the NbClust package (Charrad et al. 2012) are tested to define the optimum number of sub-zones (micro-zones) in each of the ten mesoscale zones for K-Means Clustering and HCA and the Kaiser-Meyer-Olkin (KMO) criteria and Bartlett’s test, the total variance, eigenvalue, and score plot for PCA. Table S1 presents the statistical tests that indicated the same optimal number of micro-zones in each zone. The result of all tests was significant at a p-value= 0.05. As can be observed in the last column of Table S1, except for zone A, zones B, F, H, and J are dividable into two sub-zones, zones C, D, and E to three sub-zones, and zone G to four subzones. In other words, the spatiotemporal regime of Iran’s precipitation is classified into 24 micro-zones. Therefore, K-Means Clustering and HCA resulted in the 24 micro-zones that are shown in Figs. 7a, 7b and 7c and their dendrograms are plotted in Fig. S3.
The Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy is a standard test procedure to determine the suitability of using factor analysis (Kaiser, 1970). The KMO measure of sampling adequacy of nine meso-zones (B to J) was found greater than 0.95 (Table S2), above the generally recommended value of 0.60.
Bartlett’s test of sphericity (Bartlett, 1950) is applied for testing the null hypothesis that the variables of the correlation matrix are uncorrelated. The results of Bartlett's test of Sphericity for the nine meso-zones (B to J) were found significant (p<0.0001), Table S2.
Table S3 reveals the Eigenvalues, % of the variance and cumulative % of different factors in the non-rotational and rotational states. The number of components was extracted from the eigenvalue and the total variance of the components. Only those PCs with an eigenvalue greater than 1.0 that together explain more than 65 % of the total variances of the data was selected. In zones, B, F, H, I, and J the first two PCs together accounted for 65, 73, 78, 80, and 67 percent of the total variance, respectively. In zones, C, D, and E the first three PCs together accounted for 85, 79, and 92 % of the total variance, respectively. In zone G, the first 4 PCs explain 80% of the total variance. Although in zone B and J the total variance is less than 70 %, however, their eigenvalues are greater than 1.0. Therefore, PCA distinguishes 24 precipitation micro-zones the same as K-Means Clustering and HCA.
Score plots of PC1 vs PC2 for zones B to J are presented in Fig. S4, also shows the division of zones B to J into the same number of sub-zones.
The 24 micro-zones are mapped in Fig. 7a, Fig. 7b, Fig. 7c, and Fig. 7d based on K-Means Clustering, HCA (Ward’s method-Euclidean Distance), HCA (Ward’s method-Pearson correlation), and PCA method, respectively. The results of the four methods are closely similar. However, PCA gives more distinct zoning (Fig. 7d). The formation of 24 micro-zones is due to the vast area, complex topography, large latitude variations of the country, and also extensive nearby water bodies. The mean annual hyetographs of the 24 zones are plotted in Fig. 8 elucidating that while the pattern of the lon-term mean annual hyetograph of micro-zones in each zone (meso-zone) is the same, however, their monthly precipitation magnitude varies. The mean annual precipitation in each micro-zones is shown in Fig. 9. Micro-zone A and J2 have the maximum (1293 mm) and minimum (99 mm) mean annual precipitation, respectively. To better differentiate the 24 micro-zones visually, and to calculate the precipitation volume, Fig. 7d is plotted on a 0.25⸰grided map of Iran (Fig. 10). The limiting border of each micro-zone was approximately drawn with the help of the mean annual hyetograph of rainfall stations with a lower number of rainfall records (i.e., less than 33 years) and their similarity with the hyetographs of Fig. 8.