The relationship between the large-scale relative vorticity fields and precipitation over Iran

Iran is located in the mid-latitude belt of arid and semi-arid regions of the Earth. Precipitation in Iran is characterized by high spatiotemporal variability and plays an essential role in hydrological processes and water resource management. More than half of Iran is covered by desert with semi-desert terrains in the centre and the east. In most areas of the country, the annual average precipitation is about or less than 250 mm. The Central Plateau has less than 100 mm per year. Shahdad station in Kerman province as one of the driest regions in Iran receives 40 mm of rainfall annually. Only a narrow range of the southwestern coast of the Caspian Sea and a few provinces in the west of Iran receive heavy rainfall that exceeds 1,000 mm annually. With regard to frequent droughts in Iran, it is crucial to identify the influence of the large-scale atmospheric circulation patterns on its precipitation. The atmospheric circulation is the principal forcing factor for the regional variability of precipitation and other climate variables (Dunkelon & Jacobeit 2003; Xoplaki et al. 2004; Flocas et al. 2010; Vicente-Serrano et al. 2011; Fekadu 2015; Ghassabi et al. 2022; Jamshidi & Samani 2022). Among the atmospheric components, there is a belief that relative vorticity is an important indicator of synoptic scale motions in mid-latitudes (as discussed in Flocas et al. 2001; Lolis et al. 2008; Ahrens 2011; Campins et al. 2011; Alijani 2012; Perron & Sura 2013; Lolis & Turkes 2016). Daily relative vorticity is an appropriate quantity, as it presents the main order of magnitude of daily cyclonicity or anti-cyclonicity (Bartzokas et al. 2003; Lolis et al. 2008). Vorticity is a fundamental measure of rotation in the flow around an axis (Perron & Sura 2013).

After digital computer systems became available, the statistical analyses of large datasets like canonical correlation analysis (CCA) improved empirical studies. Xoplaki et al. (2004), Fekadu (2015), Al-Khalidi et al. (2017), and Riaz et al. (2021) used CCA to investigate the connections between different climatic variables and large-scale atmospheric circulations. Though using the CCA statistical method is usual in climatological studies around the world, it has not yet entered into climatic studies in Iran. Various methods except CCA have been used to study the relationship between atmospheric circulation patterns and Iran's climatic phenomena. Alijani (2002) explored the spatiotemporal variations of the 500-hPa flow patterns and their relationship with the climate of Iran-applied S-mode PCA. Also, Raziei et al. (2012) examined the relationships between large-scale atmospheric circulation types and seasonal regimes of daily precipitation over Iran using PCA and a composite methodology that is a combination of several atmospheric fields such as the 500-hPa geopotential height and relative vorticity and the 850-hPa streamlines and so on. Using the PCA method and cluster analysis, Fatemi et al. (2015) and Omidvar et al. (2016) identified the relationship between atmospheric circulation patterns and humid periods in central Iran. Simultaneously, an analysis on the extreme rainfall events was carried out by Rousta et al. (2016). Darand et al. (2018) assessed synoptic conditions leading to extremely warm periods in Western Iran using cluster analysis.

Ghassabi et al. (2022) analyzed the influence of 18 different patterns of atmospheric circulation on dry and wet events in Iran using PCA and clustering method. Jamshidi & Samani (2022) analyzed spatiotemporal diversity of precipitation in Iran using some statistical methods like as PCA and CA. None of these studies used the CCA method.

Current study investigates the connection between the 500- and 850-hPa relative vorticity fields and precipitation in Iran during the rainy season using CCA to identify the main vorticity centres of action for precipitation in the various sub-regions of Iran. The remainder of this study is organized as follows: Section 2 describes the study area and utilized data and methodology. Section 3 provides the results and discussion in two subsections for relative vorticity distribution at the 500- and 850-hPa levels. Section 4 summarizes and concludes the study.

Relative vorticity data were calculated using the zonal component and the meridional component of wind speed values derived from NCEP-DOE (as shown in Figure 1(a)). NCEP-DOE Reanalysis II is an improved version of the NCEP-NCAR Reanalysis I that fixed errors and updated parameterizations of physical processes (Kistler et al. 2001; Kanamitsu et al. 2002). The monthly precipitation data were obtained from synoptic meteorological stations, which have continuous and complete data since 1981. According to the various homogeneity tests such as run test and cumulative deviation or Buishand range test, these data have a satisfactory quality and acceptable homogeneity at a significance level of 0.05 (mentioned tests are available in Ahmed & Deni 2013; Rahimzadeh & Nassaji Zavareh 2014).

The period of 1981–2020 was selected for this study since global analysis much improved after 1979 because of the major improvement of the overall observing system and the satellite data entry (Marosz 2009; Mooney et al. 2011). The spacing of the grid 2.5° × 2.5° can be considered satisfactory for climatological studies (Lolis et al. 2008; Flocas et al. 2010). In addition, Campins et al. (2011) and Hoskins & Hodges (2002) believed that when high-resolution datasets are used, the vorticity is a very noisy field. So, a smoothing or a reduction of resolution is necessary in these cases.

CCA is applied to identify statistical relationships between the two sets of variables mentioned above. This multivariate statistical method was initially developed from an interdependence model and first applied in climatology during the 1980s (Barnett & Preisendorfer 1987; Nicholls 1987).

CCA is often used in atmospheric sciences to identify predictors or forecasters within the datasets. CCA is a multivariate statistical technique that identifies coupled patterns in two sets, with associated time series being maximally correlated (Wilks 2011). Therefore, relationships between variables are highlighted through this method.

Pairs of spatial patterns (canonical loadings) are derived from two sets of variables to maximize the correlation of their time coefficients (canonical scores). Thus, each set of coupled patterns represents that part of the variance in both variable groups that are significantly correlated. Rao^,s F-test can determine the number of significant canonical correlations.

CCA investigates the relation between two sets of variables X₁, X₂, … , X_p and Y₁, Y₂, … , Y_q. First, the two linear combinations are formed: W₁ = a₁₁X₁ + a₁₂X₂ + …+ a_1pX_p and V₁ = bY₁ + b₁₂Y₂ + …+ b_1qY_q with the coefficients a₁₁, a₁₂, … , a_1p and b₁₁, b₁₂, … , b_1q calculated in such a way that their correlation coefficient, C₁ = cor (W₁, V₁), is maximized. W₁ and V₁ are called the canonical variates or the latent variables and C₁ is called the canonical correlation. In the next step, another set of canonical variates is identified W₂ = a₂₁X₁ + a X₂ + …+ a_2pX_p V₂ = b₂₁Y₁ + bY₂ + …+ b_2qY_q. Such that C₂ = cor (W₂, V₂) is maximized, by the condition that the two sets of canonical variates W₁, V₁, and W₂, V₂ are uncorrelated. This procedure is continued up to the mth set of canonical variates, where m = min (p, q). Thus, m pairs of canonical variates (W₁, V₁), (W₂, V₂), … , (W_m, V_m) are created in such a way that: the corresponding canonical correlations C₁, C₂, … , C_m are maximized and (ii) cor (V_j, V_k) = cor (W_j, W_k) = cor(W_j, V_k) = 0, j ≠ k. As with PCA, only the statistically significant pairs are used, as indicated by the χ² test (Von Storch & Zwiers 2004).

Prior to the CCA, the original fields of relative vorticity and Iran precipitation were submitted to two kinds of pre-processing. At first, each monthly time series was standardized by dividing by the standard deviation after subtracting the monthly mean (1981–2010) (Wilks 2011).

Then, the S-mode principal component analysis (PCA) with Varimax rotation was applied to the correlation matrices of the 850- and 500-hPa relative vorticity and precipitation data to reduce the dimensions of these transformed data and to obtain uncorrelated field variables. This kind of pre-processing removes noise from the original data and explained variances of the canonical patterns (DuNkelon & Jacobeit 2003; Von Storch & Zwiers 2004). Varimax rotation keeps the principal components (PCs) uncorrelated and succeeds in better interpretation of the results (Bartzokas et al. 2003; Jolliffe & Cadima 2016). Rotating the PCs tends to give more distinct areas with positive and negative loadings on the PC maps.

The application of PCA on Iran's monthly precipitation field led to six main PCs accounting for 72% of the total variance (as shown in Figure 1(b)). Also, the application of PCA on relative vorticity data led to 20 PCs for 850 hPa and 18 PCs for 500 hPa of relative vorticity, accounting for 70 and 80% of the total variance, respectively. (The relevant PC maps of relative vorticity are not shown.)

According to Figure 1(b), which agrees with the results of Raziei et al. (2013) and Raziei (2017), the first PC of Iran's precipitation is located in the northwest of Iran. The second PC is extended from the east to the south. The third PC is in the southwest, and the fourth PC is in the central dry regions. The fifth PC is on the Caspian Sea's southern coast, and the sixth PC is in the northeast of Iran. CCA was applied to the PCA factor scores of each set (first: precipitation and 500-hPa relative vorticity, second: precipitation and 850-hPa relative vorticity). An introductory period of 1981–2010 was used to apply CCA, and 10 years from 2011 to 2020 were used to test the CCA results.

CCA revealed three statistically significant canonical pairs (at 99% confidence level) at the 500 hPa, accounting for 82.4% of the common variance of both fields. Table 1 shows these three canonical pair characteristics.

The first canonical pair (W₁ for 500-hPa relative vorticity, V₁ for precipitation) accounts for 39.4% of the common variance (Table 1).

After calculation of canonical variates of relative vorticity and precipitation (W_s and V_s), the correlation of each canonical variate with relative vorticity and precipitation factor scores was determined under a structural correlation. Table 2 shows the structural correlation between canonical variates of the 500-hPa relative vorticity (W_s) and the significant PCs of relative vorticity. It is observed that the first canonical pair (W₁) is correlated with the first factor of relative vorticity resulting from PCA (r = −0.7).

Table 3 shows the correlation between V_s and PCs of Iran precipitation. The first, second, and fifth precipitation PCs of PCA are significant. The first canonical variate (V₁) highly correlates to the second precipitation factor over the east of Iran as −0.89. The second (V₂) is correlated with the fifth precipitation factor over the Caspian Sea's southern coast as −0.85, and the third canonical variate (V₃) is correlated with the first precipitation factor over the northwest of Iran as 0.77.

According to Figures 3(a) and 3(b), it was found that W₁ is highly negative correlated to relative vorticity over a wide area extending from the eastern Mediterranean to Iran and Afghanistan (first PC of 50- hPa relative vorticity). On the other hand, V₁ in an area from east to the south of Iran from Razavi Khorasan and South Khorasan to Kerman and Hormozgan provinces (second PC of precipitation), has an inverse correlation with the amount of monthly precipitation in that area. According to this pattern, precipitation in the provinces, as mentioned above, will be lower because the relative vorticity tends to negative values in the Eastern Mediterranean region, Iran and Afghanistan. The negative vorticity region as shown in Figure 3(a) indicates the location of the ridge. The east of Iran is in front of this ridge, which is the area of descending motions and causes weather stability in this part of Iran. Whenever the relative vorticity in this region tends to positive amounts, it leads to ascending motions in the east of Iran.

The Z scores of (W₁) and (V₁) values are compared with precipitation of 1981–2010. It shows that positive (W₁) and (V₁) values are simultaneous with the negative precipitation anomalies in the east and the south of Iran. Most of this pattern and lack of precipitation have occurred mainly in November (based on precipitation data). These areas mostly have winter precipitation and during November there is still a ridge in the middle levels of atmosphere.

Positive Z scores of canonical variates of W₃ and V₃ are simultaneous with positive precipitation Z scores in the northwest of Iran. In northwest Iran's precipitation in autumn is more than winter, because Mediterranean cyclonic tracks are extended to more southern areas in the winter, and so, the northwest Iran will be under the influence of cold and relatively dry air mass, leading to precipitation reduction in winter.

According to Table 5, the first canonical pair (W₁) is correlated with the eighth factor of relative vorticity as 0.7, W₂ with the sixth factor as 0.7 and W₃ with ninth factor as −0.6. Also, Table 6 shows that first, second, third, and fifth precipitation PCs are significant. At the 850-hPa level, the canonical variate V₁ is correlated to the second precipitation factor as 0.45, V₂ with the first precipitation factor as 0.7 and V₃ with the fifth precipitation factor as 0.6.

However, in November, when the Arabian anticyclone is not still located on the Arabian Sea, clockwise movements transfer the humidity sources of the south of Iran to the west. So, in November, precipitation increases in the west, while eastern Iran receives less rainfall than the long-term average. Most of the negative values of W₁ are observed in November. The study supports the analysis of Raziei et al. (2013). They found that the westward migration of the Arabian anticyclone from its climatological mean position provides more precipitation in western Iran, while its eastward displacement provides precipitation on the eastern side of Iran.

This area covers the domain of the first and third precipitation PCs (PC₁ and PC₃). Hence, precipitation in the west of Iran increases by increasing positive vorticity at the 850-hPa level on the Eastern Mediterranean. The synoptic reason is that the west of Iran is located before the Zagros mountain area and on the path of the Mediterranean and Cyprus cyclones that bring instability and humidity to the east. So this region can benefit from the entry of humid currents resulting from cyclogenesis of Cyprus and Eastern Mediterranean in the winter. These conditions at the 850-hPa level are enhanced with the 500-hPa trough over Eastern Mediterranean, as Raziei et al. (2013) showed that Iran precipitation is largely governed by the geographical location of both the 500-hPa trough over the Middle East and the 850-hPa Arabian Sea anticyclone. Based on Raziei (2017), the northwest and southwest Iran is characterized by the autumn and winter rainfall regime. Of course, the precipitation regime of southwest Iran is characterized by a winter rainy season that is confirmed with this work by a comparison of the 850 hPa (W₂) and (V₂) values with corresponding precipitation Z scores.

In the winter, the formation of the anticyclonic system over Eastern Europe and the extension of its clockwise currents could create a northerly and north-easterly wind over the Caspian Sea and increases the precipitation on its southwestern coast. This analysis agrees with the findings of Raziei et al. (2012).

Formerly, it had been observed at the 500-hPa level that there is a negative correlation between precipitation on the southwestern coast of the Caspian Sea and relative vorticity in Eastern Europe. The presence of a ridge and clockwise currents at the 500- and 850-hPa levels in Eastern Europe result in the formation of mid-level trough over the southern part of the Caspian Sea and simultaneously creation of northerly winds over the Caspian Sea near the surface that increase precipitation in southwestern coast of the Caspian Sea.

Iran has a high spatiotemporal variable precipitation and is facing a water crisis. Due to frequent droughts in Iran, knowing the influence of general atmospheric circulation components on the precipitation is crucial.

This study has sought to quantify relationships between the relative vorticity as a component of atmospheric circulation and precipitation as a hydrological variable over Iran. In order to identify the relationship between the 500- and the 850-hPa relative vorticity fields over a region affecting on Iran's climate and the precipitation over Iran during the rainy season, CCA was applied to these three fields extending over the introductory period of 1981–2010.

Three main 500-hPa relative vorticity action centres were found that connected to Iran's precipitation. The first is located over the Eastern Mediterranean, the Middle East and Iran, where changes in the relative vorticity are positively related to the precipitation of eastern and southeastern Iran. In contrast, relative vorticity in east Europe is proportional to the precipitation of the southwest coast of the Caspian Sea. The third is located in the cyclogenesis area of Cyprus, Turkey, and the Black Sea and affects northwest Iran's precipitation. As in the same way, we found that three relative vorticity centres of action at the 850-hPa level affect Iran's precipitation. The first is the 850-hPa relative vorticity on the Arabian Sea, which has an inverse relationship with precipitation in the east side of Iran due to its clockwise currents and humidity transfer. The second is located in eastern Mediterranean, mainly affecting the precipitation in the west of Iran, and the third is over Eastern Europe and the Black Sea, which has a high negative connection with precipitation in the southwestern coast of the Caspian Sea. The links are strong, and it can be asserted that changes in the precipitation conditions over the various regions of Iran are due to spatiotemporal variations of relative vorticity centres of action at the various pressure levels. This point gives rise to precipitation forecast skills. The above results are consistent with the results of the research by Raziei & colleagues (2012, 2013), which has already been fully explained.

As mentioned, 10 years from 2011 to 2020 were used to test the CCA results. So, the distributions of the 500- and the 850-hPa relative vorticity were analyzed in some wet and dry months in the domain of the main PCs of Iran precipitation in the rainy season in these years. Most of these observations such as relative vorticity distribution in February 2017 as a wet month in east Iran or November 2016 as a dry month in northwest Iran have confirmed the CCA results strongly.

It is worth to mention one of the weaknesses of this study. PCA method has determined six separate PCs for Iran precipitation. But during analyzing of the relationship between the PCs of 500-hPa relative vorticity and the PCs of Iran precipitation, precipitation of PC3 and PC6 in Iran have not determined and have been missed because it is not clear which atmospheric components influence on them. In the same way precipitation of PC4, PC6 and southern part of PC2 have not been determined during analyzing of the 850-hPa relative vorticity. To determine these PCs, some other methods or some other atmospheric circulation components are required.

This analysis gives insight into how the most important CCA pair is associated with the relative vorticity and the precipitation conditions over Iran. CCA is a suitable method in synoptic climatological studies, and it is suggested to use this method to investigate the relationship between other components of general atmospheric circulation and surface phenomena.

All relevant data are available from an online repository or repositories: https://psl.noaa.gov/data/gridded/data.ncep.reanalysis2.html and https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.html.

The authors declare there is no conflict.