Variation In Frequency And Share of Duration of Rainy Days In Iran’s Precipitation

In any region, climate change can be manifested in the form of various characteristics of climatic elements. To investigate the possible precipitation variations, as a sign of climate change in Iran, in the present study, the frequency of duration of rainy days was examined as a precipitation characteristic. To this end, gridded data of precipitation were used for the period of 1971-2016, and days with the precipitation of more than 1 mm were considered as rainy days. Considering the frequency of the rainy days, it was revealed that during the study period, one to thirty six-day duration of precipitation occurred in the country. One-day duration had the highest frequencies and covered the vastest area, while thirty six-day duration had the lowest frequencies and covered the smallest area. Accordingly, the one-day duration played the most significant role in annual precipitation. The share of these types of rainfalls in the low-precipitation parts of the country was more than 80% and in some areas. The findings also revealed that there was an increasing frequency of short-term, especially two-day duration, in large parts of the country, and a decrease in the long-term duration. The results showed that latitude and longitude, respectively, had the most significant impact on the frequency distribution of the duration of rainy days. Latitude had a direct effect (except in terms of the share of one-day duration of annual precipitation) and longitude had an inverse effect (except in the share of one-day duration of annual precipitation).


Introduction
As one of the most important climatic elements in Iran, precipitation has always had its own unique complexities. These complexities are mainly due to the location and geographical features of the country, something which have caused inequalities in the temporal and spatial distribution of precipitation (Alijani et al. 2014). The significance role of precipitation in water supply has drawn the attention of climatologists to this climatic element, its characteristics and changes. One of the most important features of precipitation in Iran is the temporal and spatial variations of rainy days and their duration, which have been examined only in few studies to date.
A rainy day refers to a day with at least one millimeter of precipitation (Douguedroit 1987; Romero et al. 1998 A study examining dry periods in Russia conducted by Ye and Fetzer (2019) indicated that there is a tendency toward longer dry periods in Russia due to the higher temperatures in summer. Nazaripour  Due to variations in precipitation behavior and its characteristics in recent years leading to flood and drought risks in Iran, investigation into precipitation is of utmost importance. One of the important characteristics of precipitation in Iran is the duration of rainy days. In this study, the frequency of precipitation duration and its variations were studied based on regression methods for the period of 1970 to 2016.

Study area
Iran is located in the southwest of Asia and in the desert belt of the planet, where most of the arid and semi -arid regions of the world are located (Alizadeh 2009).
Therefore, the large parts of the center, and the east and southeast of the country are arid areas.

Data
The daily precipitation data of 2188 synoptic, climatic and rain gauge stations of the Meteorological Organization were obtained for the period of 1951 to 2018 (i.e. 24837 days, equaling 68 years). These data were converted into a matrix of time-place mode.
In this case, the dimensions of the matrix were 24837 rows (time; days) and 2188 columns (place; meteorological station). The average number of active stations per day is 488. For various reasons, the number of active stations was not constant during the under study period. The spatial density of the stations decreased from west to east and from north to south (Fig 1). The spatial density of the station varied between zero and 4 per 100 km 2 .

Methods
To determine Iran's long-term precipitation data, it is necessary to convert the data from stations into gridded data through the interpolation process. In this study, the duration of precipitation in Iran was evaluated. To this end, days with a precipitation rate of higher than 1 mm were considered as rainy days. After determining the rainy days, the frequency of rainy days was also examined.
Consecutive days with precipitation of more than 1 mm were identified as precipitation sequences. After identifying precipitation duration, two approaches were considered to analyze the findings: ). is the y-intercept of trend line and  is the slope of the trend line.  and  are usually calculated by the least squares method.
2. Spatial analysis and modeling of rainy days and their duration were performed based on multivariate regression. Using regression equations, in addition to quantifying the effect of geographical coordinates (longitude (  ) and latitude ( )) and topographic factors (altitude ( h ), slope direction ( A ) and slope rate ( S )), as independent factors, the effect of each factor on the studied element can be obtained decreases from west to east and from north to south. The maximum precipitation was observed in the Caspian region and the Zagros ridges. Fig 2B also shows the average frequency of rainy periods in the country. It should be noted that in this study, the rainy period is from 1 to n days during which it was raining continuously. Each rainy period is separated from the next by at least 1 dry day. As can be seen from fig 2B, most of the rainy periods were observed on the northern coast of the country. After the northern coasts, the northwestern, northeastern parts and highlands of the Zagros had the highest numbers of rainy periods. The central, eastern and southeastern parts had the lowest precipitation periods. Therefore, it can be indicated that rainy periods, like annual rainfall, had a decreasing spatial trends from west to east and from north to south. Asakereh et al (2020) attributed the spatial trend of precipitation in Iran to the reduction of energy and rainfall of Mediterranean cyclones as well as the leeward effect of Zagros and Alborz ranges. In addition to the geographical coordinates, this decreasing trend can also be associated to the altitude.

Fig 2 Long -term average of annual precipitation (A: thick line is the spatial average of precipitation) and annual average of frequency of rainy periods (B) 3.2 Frequency of durations of rainy days
Analysis of precipitation rate in Iran during the study period showed that the rainy days can last from 1 to 36 days. The findings of the study showed that during the study period, the whole country has 1-4 rainy days' duration and more than 80% of the country had 5 to 7 rainy days' duration. As the number of consecutive rainy days increases, the precipitation area decreases. Therefore, in more than 13 days' duration, the receiving area diminishes to less than 10% (Table 1). This can be due to the locality of heavy rains. Therefore, in this paper, the duration that covers extensive areas are examined. Fig 3 shows the average frequency of 1 to 10-day duration in the study period.   (Table 1).
In two-day duration, the maximum frequency of precipitation was limited to the northern coasts of the country. The frequency of this duration, nevertheless, was less than one-day duration. It is noteworthy that the Zagros and Alborz ranges had significant influence on this duration. Therefore, the highlands of Zagros and Alborz had an average of more than six sets of two-day duration of precipitation per year.
This frequency increased at higher altitudes by 10 or more days.
The three-day duration of precipitation occurred most frequently in the northern coasts of the country. However, there was less duration in the eastern parts of the coast and the central parts, especially the western coasts, the frequency of three-day duration of precipitation was the highest. The Zagros and Alborz heights also played an important role in this duration, and at higher heights, the frequency of three-day duration of precipitation increased.
From four to ten-day duration of precipitation, in the northern coasts of the country (especially, in the southwest of the Caspian Sea) the frequency of duration reached the maximum. It should be noted, however, that as the number of precipitation days increased, their frequencies and areas decreased (Fig 3). Also, the frequency of higher duration was limited to the highlands. Darand (2018) also showed the role of altitudes in the duration of precipitation in Kurdistan province, Iran.
During the study period, the duration of precipitation ≥4 days was not observed in a large southern and eastern part of the country, and this duration was more common in the northern, northwestern parts and highlands.  precipitation with one to three-day duration in the eastern regions was more prevalent, while precipitation with longer duration of more than 3 days in the western half of the country was more common. In the northern coasts as well as in the highlands of the Zagros, one-day duration of precipitation had the lowest share of annual precipitation ( Fig 5). These areas were the rainiest areas of the country, respectively ), in which the precipitation showed a decreasing trend in one-day duration.
Therefore, it can be noted that the minimum duration in low-precipitation areas and longer duration in higher-precipitation areas include significant shares of precipitation rates. The results of a study by Nazaripour et al. (2011) are also in line with those of the present study. As the precipitation period lengthens, the share of annual precipitation duration decreases. Therefore, in the maximum duration, this share reaches the lowest possible value and is only slightly higher than zero. Precipitation with minimal duration appears to be due to large-scale atmospheric systems, as short duration of precipitation affects a wider area and accounts for more annual precipitation. Nazaripour (2014) also showed that short duration of precipitation include the majority of rainfall and rainy days throughout Iran and long duration include a limited number of rainfalls locally.

Trend of Maximum duration of rainy days
During the study period, the highest duration in the country was 36 consecutive days of rainfall. In some parts of the country, the highest duration was 4 days, mostly in the central parts of the country. In a large part of the country, the maximum duration of precipitation in the under investigation period was fewer than 10 days. In small parts of the west, northwest and north of the country, the maximum duration was more than 25 days. In these areas, the maximal duration experienced a decreasing trend. In areas where the maximal duration was short, the number of maximal duration increased. It should be noted that the largest increasing trend of maximal duration could be observed in the northwestern border areas and the northern coasts of the country. The decreasing trend of maximal duration may be due to the fact that in these areas, precipitation occurred in a limited number of days. This means that a significant share of the precipitation in these areas occurs in one or a few days (minimum frequency) (Fig 6). This can cause climatic hazard and lead to floods. 22.6% of the country had an increasing trend and 77.4% had a decreasing trend of annual maximal duration.  also showed a decreasing trend in the frequency of rainy days based on high percentiles of precipitation. According to their study, the frequency of dry days had an increasing trend. An increase in dry days can reduce precipitation duration.

Fig 6 The longest precipitation duration (days) during the under study period and the trend of the longest precipitation duration (days/year) 3.5 Spatial analysis and modeling of precipitation duration
Multivariate regression was used to investigate the effect of spatial factors on the frequency of precipitation duration. Spatial factors used in this study are latitude and longitude, altitude, slope and terrain slope. For the sake of brevity, only the multivariate regression equation for one to ten-day duration and the share of one to ten-day duration of annual precipitation were included in Tables 2 and 3. As can be seen from Table 2, latitude and longitude were the most important factors affecting the spatial distribution of the frequency of one to ten-day duration, respectively. The  Table 3). The share of one-day duration in annual precipitation decreased as the latitude increased and it increased as the longitude increased, which indicates the importance of the role of one-day precipitations in water supply of arid regions of the country. In other cases of duration of rainy days, the opposite was true.

summery and Conclusion
In this study, precipitation gridded data were used for the period of 1971 to 2016 and a daily data matrix was formed for 16436 days. In addition, the frequency of rainy days was investigated as a characteristic of precipitation and its variations were analyzed. The study showed that during the under study period, the country's precipitation had duration of 1 to 36 days. One-day duration had the highest number of repetitions and covered the widest area, while thirty six-day duration had the lowest number of repetitions and covered the smallest area. Due to the importance of shorter duration, one to ten-day duration were analyzed in this study. The findings showed that one-day duration had the highest share in annual precipitation. In some parts of the central, eastern and southeastern areas, all annual precipitation resulted from oneday duration. In other words, areas with low precipitation received a high percentage of annual precipitation (in some parts, all annual precipitation) from one-day duration.
In areas with high-precipitation, one-day duration included a small share in the annual precipitation supply. The frequency of short-term duration, especially two-day duration, was increased in large parts of the country, and long-term duration was decreased in many areas. The share of short-term duration also increased. The results showed that latitude and longitude had the most significant impact on the frequency distribution of rainy-day duration, respectively.

Declarations:
-Conflict of Interest : The authors declare that there is no conflict of interest while conducting this research.
-Funding Statement: There was no specific grant for this research from any funding source.
-Author's Contribution: We, the authors, contributed to the research. Hossein Asakereh performed the study conception, design, and data analysis. Material preparation, data collection were performed by Saeideh Ashrafi. The first draft (in Persian) of the manuscript was written by Saeideh Ashrafi. The final versions of the manuscript (in English) was written by Hossein Asakereh.
-Availability of data and material: The data of daily precipitation was provided from Islamic Republic of Iran Meteorological Organization (IRIMO) which have been described in details under the heading of "2.2 data" in this manuscript.
-Code availability: MATLAB code used in this study for analyzing the data and preparing the required maps of the study area. The code is written according to the method is described in details under the heading of "2.3 Method" section.
-Ethics approval: The manuscript is original and is not submitted to another journal for simultaneous consideration neither have been published elsewhere in any form or language (partially or in full). Results are presented clearly, honestly, and without fabrication, falsification or inappropriate data manipulation. No data, text, or theories by others are presented as if we are the author's own.
-Consent to participate: We, the authors, understand that any information we submit for this study will be treated as confidential, and that we have all contributed to the research.
-Consent for publication: We, the authors, provide our consent for this research to be published in Theoretical and Applied Climatology journal, which include maps and information within the text.