Figure 3 shows long-term mean sinuosity for winter and fall during the 1979-2020 period. As can be observed, the value of sinuosity is maximized in winter over mid-latitudes, particularly over Iran. Thus, the conditions required for atmospheric turbulence and precipitation are met, and long-term mean sinuosity index for winter amounts to 1.35. Among the winter months, maximum sinuosity is observed in January and March (Fig. 4). As the subtropical high shifts back toward lower latitudes in fall, westerly flows tend to extend in the same direction and enforce the conditions required for meridian wind. The consequent formation of troughs in the middle layers of the atmosphere amplifies instability, and the mean rate of sinuosity amounts to 1.31 in fall. Among the fall months, maximum sinuosity is observed in December and November (Fig. 4). In this season, the location of the subtropical high and its orbital and meridional extension are of great significance in specification of sinuosity in the middle layers of the atmosphere. Thus, the value of sinuosity in the atmosphere increases in October as the high shifts southward to lower latitudes.
Mean monthly sinuosity for the winter and fall months in the 1979-1999 and 2000-2020 periods indicate the variation in sinuosity during these two sub periods. Similarly in annual scale, the value of sinuosity exhibits great variation within an interval of two years. These changes are made as a result of the nature of large-scale atmospheric patterns; thus, the variation is effective in the temporal and spatial distribution of climatic factors such as precipitation. The figure for mean sinuosity in January indicates that the parameter has decreased at the end of the first sub period with respect to the initial years, and has increased at the end of the second sub period. The variation in February is similar to that in January. The highest value of sinuosity in the first sub period has occurred in 1987, and that in the second sub period is observed as 1.46 in 2019. In March, there have been higher values of sinuosity in the second sub period than in the first in most of the years. Since 2012, mean sinuosity has increased in this month. Unlike for the other months, the rate of sinuosity in the 2000-2020 period exhibits a decrease for October with respect to that in 1979-1999. The highest value of sinuosity in this month is observed between 1979 and 1988. For November, sinuosity exhibits a decrease in the 1990s with respect to the mean value for the entire period, while an increase is observed for the 2010s. In December, the maximum value of sinuosity in the first sub period has occurred in 1987, while sinuosity rate has been higher in 2004, 2019, and 2018 than in the other years in the second sub period. Mean sinuosity is greater for December than for November and October. The values of mean monthly cumulative sinuosity indicate that higher rates of sinuosity are observed for January, March, and December than for the other months under examination. Mean sinuosity rate has been greater in the second sub period than in the first. Throughout the period of 42 years, sinuosity has been maximal in 2019 and minimal in 2010 (Fig. 4).
The values of mean monthly sinuosity for the period under investigation Figure 4 indicate that maximum sinuosity is observed for January, March, and December, while the minimum has occurred in October. Moreover, increase is observed in sinuosity for all the 500hPa contours, simultaneous with the increase in monthly sinuosity. Cases of increase in sinuosity by more than 1.3 exhibit increase in all the contours and decrease in their differences, while greater differences are observed in the rate of sinuosity for months with lower values of mean sinuosity (Fig. 5). In January, March, and December, where 500hPa sinuosity exhibits increase, the same trend is observed for all the contours. For October, with lower values of sinuosity, the highest values are observed in the 575 and 565 dam contours and the lowest in the 558dam contour, since westerly flows are weakened in October with respect to those in the other months. For this month, it is of great significance in specification of mid-layer sinuosity and atmospheric instability when the flows extend southward. Overall, mean sinuosity is greater in the 575 dam contour than in the 565 and 558 dam contours.
The values of mean monthly sinuosity in the 2000-2020 and 1979-1999 periods, in Table 1, indicate increasing significant trends in sinuosity in all the months except for October at 95% confidence level, with the greatest increase observed in January and March, by 0.002 and 0.003, respectively. Mean sinuosity during the second sub period, with a rate of 1.29 is greater than that in the first, with a rate of 1.28 representing an average growth rate of 0.014.
Table 1
The difference between the sinuosity values of the first period (1999 to 1979) and the second period (2000 to2000)
month
|
First Period (1979-1999)
|
Second Period (2000-2020)
|
Second Period- first Period
|
JAN
|
1.31
|
1.33
|
0.02
|
FEB
|
1.29
|
1.30
|
0.01
|
MAR
|
1.30
|
1.33
|
0.03
|
OCT
|
1.19
|
1.2
|
-0.01
|
NOV
|
1.29
|
1.29
|
0.01
|
DEC
|
1.31
|
1.33
|
0.02
|
Figure 6 shows mean seasonal 500hPa sinuosi. Clearly, mean seasonal sinuosity has reached to more than 1.3 in 1993 and 1997 but dropped to less than 1.3 in 1999 and 1981, where it exhibits the lowest values in the first sub period. By contrast, there is a considerable initial decrease in sinuosity in the second sub period, which has amounted to the highest values throughout the 42-year period in the final years, particularly in 2011, 2015, and 2019. Such an increase in sinuosity indicates intensified meridian 500hPa westerly flows, while a decrease in sinuosity raises the orbital flow and stability. An increase in sinuosity causes the flows to tend to extend toward lower latitudes, which can increase the probability of occurrence of the blocking phenomenon (Hojati and Masoodian 2021). Mean seasonal sinuosity during winter indicates an increasing trend in sinuosity. The parameter has assumed the lowest values throughout the period in 1989 and 2010 and the highest in 1993, 2011, 2015, and 2019. Thus, the values of mean seasonal sinuosity suggest that sinuosity has been greater in winter than in fall, although the monthly rate in December equals those observed for the winter months (Table 1).
The dynamic patterns effective on precipitation can vary greatly under the influence of NO oscillation (Dorn 2003). The relationships between AO and NAO and precipitation (Bannayan 2010; Yadav 2009; Gong et al. 2014) and anomaly in sinuosity and the above indices, shown in Fig. 7, indicate close correlations between sinuosity and AO and NAO in both sub periods, where positive anomaly in AO and NAO has relatively increased sinuosity (Fig. 7a). As the above indices have turned negative in 2010, sinuosity has decreased to a minimum. With an increase in sinuosity by 0.2, daily precipitation has increased by 3 mm, monthly precipitation by 10 mm, and annual precipitation by 38 mm. There has been a closer relationship between sinuosity and teleconnection indices in the second than in the first sub period. Overall, the relationship between sinuosity and the AO index has amounted to 0.65 and that for NAO to 0.52. Moreover, the statistical relationship between sinuosity in the middle layers of the atmosphere and annual precipitation has exceeded 0.74, indicating a close relationship between sinuosity and precipitation in the study area (Fig. 7b). The increase in the sinuosity index values of 500 hPa flows over Iran has been accompanied by positive anomaly in precipitation. It can be stated in general that precipitation over Iran increases/decreases as AO and NAO assume positive/negative phases, and sinuosity rises in the middle layers of the atmosphere, indicating that AO and NAO are effective in the atmospheric pattern variation in the middle layers (Fig. 7a).
3.1 The relationship between sinusoidal and extreme precipitation
As mentioned in the section on the data and methodology, the sinuosity values were calculated for two kernel ranges, including a large one, i.e. 10°S to 60°N 80°W to 70°E, and a small one, i.e. 10°S to 60°N 0 to70°E. Figure 8 shows mean daily sinuosity upon widespread and heavy precipitation over the country for the small range. In these conditions, sinuosity has been greater in all the months under examination in the 575 and 565dam contours than in the others. In other words, sinuosity exhibits the highest frequency over Iran in these contours. In an examination of the 575, 565, and 558dam contours, the greatest variation is observed in the 558dam contour. In October and November, the above contour accounts for the lowest sinuosity, while the 575dam contour exhibits the highest. In March and January, the same sinuosity is observed for the 558 and 575dam contours, and atmospheric sinuosity could be identified in these months in all the 500hPa contours due to the high intensity of atmospheric waves (Fig. 3). During the second sub period, sinuosity has been less in the 558dam contour than in the first sub period but greater in the other contours. The decrease in sinuosity in this contour may be accounted for by the enhanced high pattern in fall, functioning as a barrier against precipitation flows and systems, which would be consistent with the decreasing trend in sinuosity observed in this research for October (Table.1). However, the above claim requires further investigation. Overall, mean cumulative sinuosity during the study period has been 1.48 in the 575dam contour, 1.40 in the 565dam contour, and 1.30 in the 558dam contour. Over the entire period of investigation, the above contours exhibit increase in 500hPa sinuosity in the 2010s, maximized in 2019 (Fig. 8).
Figure 9 shows anomaly in the frequency of rainy days and sinuosity. The results of examination of sinuosity upon widespread precipitation indicate that the frequency of rainy days has varied consistently with the variation in sinuosity. For a change of 0.2 in sinuosity, the frequency of rainy days has changed to three days more/less than the mean value. Similarly in Figure 8, positive anomaly is shown to have occurred in the frequency of rainy days as sinuosity has increased in 1990, 1984, 2010, 2013, and 2019.
Mean daily sinuosity upon widespread and heavy precipitation over the country indicates annual and monthly variation. As 500hPa westerly flow sinuosity has increased/decreased, the frequency of days with heavy precipitation has increased/decreased. Mean sinuosity has been 1.55 during the 1979-1999 period and 1.59 in the following period of 21 years, i.e. 0.4 more in the second sub period than in the first (Fig. 10a).On the other hand, the frequency of widespread and heavy precipitation over the country has amounted from 6.95 in the former to 7.22 in the latter, indicating an increase by 0.277. In general, the increase in 500hPa sinuosity rate justifies the rise in heavy precipitation (Fig. 10b).
3.2 Case studies
For explanation of the variation in sinuosity in the middle layers of the atmosphere, four of the patterns leading to widespread and heavy precipitation over Iran were selected, for which the sinuosity index was calculated. Then, the 500hPa geopotential height pattern and 850hPa specific humidity were drawn. Widespread precipitation has occurred in most regions as heavy precipitation, as it has persisted with high intensity for several days. An examination of the geopotential height map indicates that westerlies have been split to two branches, northward and eastward, upon widespread precipitation following a formation of atmospheric blocking, when the 500hPa cut off low has caused the flows to shift eastward at a low rate, increasing the sinuosity index and precipitation in the study area. Mid-layer cut off lows have taken shape in all the examined patterns, increasing sinuosity due to the meridian extension of flows toward lower latitudes. An examination of sinuosity maps upon heavy precipitation indicates the formation of two blocking patterns with separate cores to the east and west of the Mediterranean. A similar examination for widespread precipitation demonstrates that it has occurred in more than 80% of cases under the influence of the bipolar pattern. Specifically, the Specifically, the initial blocking core has taken shape over Eastern Atlantic and Western Mediterranean following an amplification of the meridian index of high flows, and the second cutoff low core has taken shape over the Mediterranean within the next 24 hours, leading to widespread precipitation over Eastern Mediterranean, including Iran, following an amplification of vorticity and injection of moisture from humid regions. The initial core has extended westerlies toward lower latitudes, and increased high atmospheric wave amplitude, enabling atmospheric instability by amplifying flows and raising wind speed. Table 2 shows the times when widespread and heavy precipitation begins and ends and the atmospheric patterns causing them.
Table 2
Start/End Dates selected Case for inclusive comprehensive and heavy rainfall and Average rainfall of stations during the period, atmospheric pattern causer to precipitation and their spatial position (the first position is the North Atlantic blocking and the second position is the eastern Mediterranean blocking)
Start Time
|
End Time
|
Average precipitation(mm)
|
Atmospheric patterns
|
blocking core 1 location
|
blocking core 2 location
|
1Feb 1993
|
6 Meb1993
|
36
|
Blocking, Eastern Mediterranean Sea through, cut of low
|
20N 35 N
-15W 0
|
20N 35N
30E 50E
|
24Mar2003
|
30Mar2003
|
29
|
Blocking,
westerly bifurcation,
Cut of low
|
20N 35N
-30W 15E
|
15N 35N
15E 45E
|
23Dec2004
|
30Dec2004
|
30.03 m
|
Blocking(cut of low)
|
20N 40N
-15W 15E
|
20N 35N
30E 50E
|
19Mar2019
|
31Mar2019
|
42.1 m
|
Blocking(Cut of low),
westerly bifurcation
|
30N 45N
-30W 0
|
25N 40N
10E 48E
|
3.3 Case 1
Patterns adopted upon widespread precipitation over Iran, which have led to extreme or ultraheavy precipitation in some cases. In the first instance, concerning February 1993, a powerful cutoff low pattern has been established over Eastern Mediterranean, and an initial low core has taken shape at the same time over Eastern Mediterranean, at 30°N. These conditions have caused the extension of flows toward lower latitudes, trough deepening, and an increase in upward flow shift. The cores of the two deep troughs separated through northward stack extension at 15°E can be observed within 15N 40°N. The mid-layer inverse S blocking pattern causes cold weather to pour down from higher latitudes toward the Mediterranean, and then brings about widespread precipitation over Iran as the pattern cycles to inject moisture from the Mediterranean and Atlantic. A value of 1.48 is observed for the sinuosity index upon precipitation, and western flows have extended to 20°N following trough deepening (Fig. 11a).These series of conditions have induced 36 mm of precipitation at an average station. The above pattern has caused greater precipitation to occur in this period in the West, Southwest, Northeast, and western part of Caspian Sea than in other regions. The spatial distribution of precipitation in this period well demonstrates that it has spread widely over most parts of the country (Fig. 11c).
3.4 Case 2
Like the above instances, the sinuosity pattern for March 2003 has caused heavy precipitation over Iran, leading to prolonged persistent precipitation during a seven-day period of blocking. Some of the stations have recorded 100 mm of precipitation within this period, when the largest amounts of precipitation have concerned regions located along Zagros Mountains, in the Northwest, and along the Caspian coasts, in that order, indicating unstable conditions over different regions from the Southwest to the North. Sinuosity has amounted in this period to 1.48, bringing about unstable conditions as precipitation in Eastern Mediterranean under the influence of westerlies extended to 15-20°N. Over the Mediterranean, blocking has caused the flows to be split into two branches, northern and southern. The latter has extended southward to lower latitudes as a result of blocking in Fig. 12a. The sinuous flow pattern from the West to the East, involving sinuosity over Eastern Atlantic and Western and Eastern Mediterranean, indicates an increase in wave power and in upward shift in the upper layers of the atmosphere. Upon widespread precipitation over the country, the greatest humidity can be observed over the western half. The mid-layer trough is located in average at 35°N upon precipitation in the region. The spatial location of this trough over Eastern Mediterranean and Northern Red Sea, well justifies the increase in humidity for heavy precipitation (Fig. 12c).
3.5 Case 3
The 500hPa geopotential height pattern indicates the high meridian extension at 30°E up to 40°N, which has intensified pressure gradient over the eastern half of Northern Atlantic, indicating great divergence in temperature, pressure, and wind speed. The decrease in meridian flows in Western Mediterranean has led to a tilted trough axis and an increase in wavelength. Stack extension from Southeastern to Northeastern Mediterranean has amplified the Eastern Atlantic trough, evolved with the increase in mid-layer trough flows in Eastern Mediterranean(Fig. 12a). The rise in the amplitude and depth of 500hPa flows can well be observed in the geopotential height pattern, causing an increase in the occurrence of blocking. There have also been particular conditions in terms of precipitation over Iran in December 2004 due to the formation of the bipolar mid-layer cut off low pattern in Eastern and Western Mediterranean with a sinuosity value of 1.49, when an extensive part of the country has received precipitation. In certain regions, total precipitation has amounted to more than 100 mm upon formation of this pattern. Moreover, the values of specific humidity upon precipitation indicate moisture flux from the Southern waters, particularly Indian Ocean and Oman Sea, with the requirements for heavy precipitation met despite the intense conditions for upward shift in the middle layers of the atmosphere. Maximum humidity is observed in the western half of Iran as 8 g/kg (Fig. 12b).
3.6. Case 4
As mentioned in the examination of the previous pattern, widespread and ultraheavy precipitation has occurred over the country in March 2019, when the persistence of instability and increase in atmospheric sinuosity with multiple days of duration have caused ultraheavy precipitation to occur in the western and northeastern parts of Iran as sinuosity has been amplified, and cut off lows have taken shape in the middle layers of the atmosphere. At certain stations, the recorded precipitation has amounted to more than 300 mm in Fig. 6c, which equals half of the annual precipitation for some of the stations (Alijani et al. 2019). A daily sinuosity rate of 1.6 can be observed for this period, which is regarded as a wet one with high precipitation. Instability has been experienced in this period in a large number of regions in Iraq, Saudi Arabia, and Turkey as well as in Iran. An examination of the geopotential height pattern indicates the formation of a highly powerful cut off low over the Mediterranean, where the increase in the prevalence of flows and trough deepening have intensified instability over the country. The geopotential height pattern demonstrates that two troughs have taken shape over Eastern and Western Mediterranean, which have become distinguishable following a stack extension in Western Mediterranean. The trough in the East has split westerly Bifurcation, due to the 500hPa blocking. The southern branch of westerlies, in Eastern Mediterranean, has induced cut off lows, the appropriate location of which along with their stretch over Red Sea and the humidity of the Mediterranean has brought about moisture flux from Red Sea. This scarce pattern has caused the highest precipitation to occur over the western parts of Iran. The flows correlated as a result of the developed pattern have amplified humidity upon heavy precipitation in the lower layers of the atmosphere, and plenty of moisture has arrived in the region from the Mediterranean, Red Sea, Persian Gulf, and Oman Sea upon persistence of precipitation. Maximum humidity is observed as more than 8 g/kg as the pattern induces precipitation over the western half of Iran, which occurs in larger amounts than that induced by other patterns. The location of cut off lows and the persistence and high intensity of precipitation in March 2019 has caused widespread and heavy precipitation to occur over the country (Fig. 14c).
3.7 Blocking
As stated earlier, the blocking pattern and the low middle layers of the atmosphere have played a major role in the occurrence of widespread and heavy precipitation over Iran. Fig. 15a shows the best case of widespread and extreme precipitation occurring over the country following the formation of mid-layer cut off lows. Under these conditions, cutoff lows have caused deep troughs to take shape in the middle layers of the atmosphere, the outermost contour of which has been located at 15°N. The lows have covered a spatial range around 15°N 10°E. For the study period, the occurrence of widespread and heavy precipitation has been consistent with the location of cut off lows within 20°N-35°N, 20°E-40°E, which has led to extreme precipitation over Iran in most cases. This demonstrates that the location of cut off lows plays an important role in the persistence and intensified occurrence of heavy precipitation over the country.
An analysis of their frequency of occurrence within the 500hPa 10°N-60°N 0 -70°E kernel indicates that they have occurred with an increasing trend throughout the study period. Increase in the frequency of cut off lows is highly consistent with 500hPa sinuosity. One of the most important factors that can control the frequency, intensity, and duration of cut off low activity is westerly flow, the variation and gradient in which leads to the separation of cut off lows. A low-pressure closed cyclonic eddy separated from the main jet stream (Singleton et al. 2007), a cut off low functions as a system that interrupts westerly flow upon occurrence of wet and dry periods (Muñoz and Schultz 2021). During the study period, cut off lows have occurred more frequently as 500hPa sinuosity has increased, and far more frequently in the 2000-2020 period than in 1979-1999, particularly in 2000-2003, 2015, and 2019. This highlights the role of sinuosity in the occurrence of atmospheric blocking. Furthermore, the frequency of blocking could have a significant impact on the intensity of heavy precipitation in Iran due to its arid and semi-arid climate and the showery nature of precipitation therein (BabaieFini and Farajzadeh 2002). Given the importance of blocking in the occurrence of precipitation over Iran, it is essential to conduct further studies on the role of climate change in the variation in atmospheric patterns effective on the occurrence of blocking.
The relationship between Extreme and Comprehensive precipitation and sinuosity in Iran
Figure 17 shows the relationship between monthly sinuosity rate and precipitation during the study period using Pearson’s correlation coefficient at the confidence level of 95%. As can be observed, there has been a positive relationship between widespread precipitation and sinuosity over a large part of Iran. In other words, precipitation has assumed an increasing trend there as atmospheric sinuosity has risen. The relationship has been far closer in all the months in the western and northern halves and the Southwest than in the other regions. Moreover, the rate of correlation between precipitation and 500hPa sinuosity has been higher over the western half of the country in March and November than in the other months. More regions have received precipitation in February along with increase in sinuosity, and there has been poorer relationship between widespread precipitation and sinuosity in the southern and southeastern regions. In all the months under examination, there has been maximal relationship between sinuosity and widespread precipitation in the western half and northern parts of Iran. It can be stated in general that the variation in sinuosity provides an appropriate index for investigation of the impact of variation in westerly flows on the occurrence of precipitation over the country, as heavy precipitation over Iran has increased with a rise in sinuosity.