Introduction
With the onset of fall season, the air temperature on the Caspian Sea is diminished, but due to the difference in the specific heat capacity of air and water, the reduction rate of temperature is far greater than that of the sea. Therefore, the surface of Caspian Sea remains warmer than air. Establishment of dynamic high-pressure centers or diffusion of Siberian high pressure system over Caspian Sea especially during fall results in development of southward air stream over the sea. Caspian Sea as the first supplier of moisture resources for heavy precipitation and especially ultra-heavy precipitation of its southern coasts plays a principal role in explanation of the occurrence of precipitations in these coasts. The changes in Caspian Sea water temperature can result in variations in the precipitation in southern coasts of Caspian Sea. However, the seawater temperature is not sufficient for the precipitations of the southern coasts of Caspian Sea and the air temperature over the sea should also be taken into consideration. The sea-air temperature difference (ΔT), as humidity intake index, has attracted the attention of researchers to such an extent that it has become the most important thermodynamic factor in development of abundant and heavy precipitations in the southern coasts of Caspian Sea. Gradual increase of the sea surface temperature in its proper arrangement from the north to the south and intake of humidity from the sea (ΔT index) have been considered necessary for development of heavy and ultra-heavy precipitations in the southern coasts of Caspian Sea.
 
Materials and methods
In this research, the daily precipitation data of seven synoptic stations of Northern provinces of Iran have been collected from 1968 to 2013. The threshold of heavy precipitations was defined as the day in which its precipitation level is greater than the percentile 95 of that year. Then, all of the days in which at least five stations have recorded heavy precipitation were simultaneously extracted and considered as regional heavy precipitation days. By extracting the air temperature at 2 meter above the sea level (Air2m) and the sea surface temperature (SST), the ΔT value was calculated as follows:
 
Using Ward linkage method and correlation between the data, ΔT values were clustered in the days in which regional heavy precipitation had occurred in the northern stations of Iran. In each of the clusters, the day that had the greatest correlation with other days was selected as the sample. For the sample days, SLP, VWnd, Uwnd, and HGT data in 1000 HPa for analysis of synoptic conditions leading to regional heavy precipitation were extracted from http://www.esrl.noaa.gov. The relationship between regional heavy precipitation in the stations and ΔT was analyzed to interpret the extracted clusters.
 
Results and discussion
With the onset of fall season, the air temperature experiences more rapid decline than seawater temperature. Therefore, in this season, the sea will be warmer than air. The long-term mean (1986-2013) of SST and Air2m and ΔT during fall has been shown in Fig. 1.
 




 
 
 




Fig.1: Long-term mean (1986-2013) of SST and Air2m and ΔT during fall.
 
The relationship between regional heavy precipitation and ΔT was investigated in the studied stations. Unexpectedly, direct relationship between ΔT in the south Caspian Sea and regional heavy precipitation does not exist in all of the stations. This relationship only applies to the stations located in the East, whereas in the stations situated in the West, this was inverse relation. 
Using Ward linkage method and calculation of the correlation between the data, three clusters were recognized. In each of the clusters, the day that had the greatest correlation with other days was selected as the representative of the cluster (Fig. 2). The first cluster is representative of the days with regional heavy precipitation in conditions where ΔT gradient reaches its maximum from Northwest to the southeast. The second cluster represents incidence of regional heavy precipitation in conditions where the maximum ΔT gradient is from the north to the south. Eventually, the third cluster can be considered as the greatest ΔT gradient observed from the West to the East (also Southwest to Northeast).




 
 
 




 
Fig.2: ΔT in 13 Sep 1977 (lesf cluster), 22 Oct 1988 (middle cluster) and 29 Sep 1986 (right cluster)
 
Investigation of synopsis maps of regional heavy precipitation in the selected days suggests their similar synoptic conditions such that establishment of high-pressure center in the northwest Caspian Sea leads to influx of cold-air from more northern latitudes and over Caspian Sea towards southern latitudes. The stations located in the east part of the study area will receive greater precipitation when ΔT reaches its maximum level in the southern coasts of Caspian Sea (the second cluster). In contrast, the stations located in the West will receive greater precipitation when ΔT gradient increases from the east to the west (the third cluster).
 
Conclusion
With the increase in ΔT in the southern parts of Caspian Sea, regional heavy precipitation grows significantly only in the eastern part of the study area. The results obtained from ΔT clustering unveiled three clusters, where the first, second, and third clusters represented the maximum ΔT gradient from the Northwest to the southeast, north to the south, and west to the east, respectively. The stations located in the east part of the studied region will have greater precipitation when ΔT reaches its maximum in the southern coasts of Caspian Sea (the second cluster). In contrast, the stations located in the West will receive the maximum precipitation when ΔT gradient increases from the east to the west (the third cluster). These results were in line with those obtained from investigation of the correlation between ΔT and regional heavy precipitation. The analysis of synoptic maps indicated that in all of the three clusters, establishment of high-pressure center in the northwest part of Caspian Sea results in infusion of cold air from more northern latitudes over Caspian Sea and towards southern latitudes.