تعیین بهترین تابع توزیع احتمال برای برآورد بارش فصل رشد برنج در مناطق عمده برنجکاری کشور

ABSTRACT
Despite the water supply, rainfall has multiple and conflicting roles during the rice cultivation period and choosing the appropriate distribution of the probability of its occurrence is an important step in planning water resources management and adjusting the planting calendar and reducing damage in rice farming. In this research, to determine the most appropriate distribution of rainfall probability during the rice-growing season, from the data of eight synoptic stations of the southern coast of the Caspian Sea, including the stations of Astara, Bandar Anzali, Rasht, Ramsar, Babolsar, Qarakhil, Nowshahr and Gorgan with a statistical period of 30 the year (1991-2020) was used. After quality control and homogenizations, Bernoulli-log-normal, Bernoulli- Weibull and Bernoulli-gamma distributions were fitted to the rainfall data in the daily time range (in windows of three days without overlap) as well as the length of the rice-growing season. Kolmogorov-Smirnov goodness of fit test (K-S) and Akaike's index (AIC) were used to identify the most suitable one. The obtained results showed that the Bernoulli-Gamma distribution is the most suitable probability distribution for estimating the rainfall of the rice-growing season in the southern shores of the Caspian Sea. After the Bernoulli-Gamma distribution, the Bernoulli-Weibull distribution showed a better fit, especially for Nowshahr station located in the central part of Mazandaran province. The findings of this research can be used to quantify the amount of expectation and risk caused by rain during the rice-growing season.
Extended Abstract
Introduction
Precipitation is one of the key components of the hydrological cycle and one of the determining features of the climate change of the planet of earth. The southern coast of the Caspian Sea is one of the wettest regions of Iran, where precipitation, in it as most important climatic element and atmospheric phenomenon, has a complex temporal and spatial distribution. Knowledge of the probability distribution of rainfall and determining the model of rainfall distribution during the year and its temporal changes provide a suitable basis for planning water resources in different sectors. Statistical probability distributions can be very successful in generating data at points without stations. According to the amount of rainfall received in the study area during the rice-growing season, only 30 to 50% of the water requirement of rice is provided through rainfall and the rest must be compensated through irrigation. However, in some years, only a small part of rain plays a very important role in determining the fate of the product in those years. Therefore, since in the relatively short period of the growing season of rice planting to harvesting, the role of precipitation is constantly changing, choosing an appropriate statistical distribution that can well describe the temporal distribution of precipitation data during the rice growing season in the southern shores of the Caspian Sea will be crucial for water resources planning and cropping calendar adjustment in the growing season. Therefore, the main goal of this study will be to find the appropriate statistical distribution of precipitation events during the rice cultivation period on the shores of the Caspian Sea.
 
Methodology
The area studied in this research is the southern shores of the Caspian Sea (Caspian), which in terms of country divisions includes the three provinces of Gilan, Mazandaran and Golestan. Past studies have shown that the variable distribution of precipitation skewed to the right. Therefore, among statistical distributions, distributions like gamma, Weibull and log-normal can be suitable. Most of these distributions have values greater than zero and since the number of days with zero rainfall is high in the region and period under investigation, therefore, in this research, Bernoulli-Gamma, Bernoulli-Weibull and Bernoulli-Log normal distributions were studied to fit the rainfall of the rice-growing season. In each of the mentioned distributions, first the probability of precipitation occurrence was modeled using Bernoulli distribution with parameter p (probability of having non-zero precipitation) and then the intensity of non-zero precipitation was modeled with Weibull, gamma or log normal distribution. Fitting was performed for data in non-overlapping 3-day time windows.
 
Results and Discussion
The results showed that the highest amount of rainfall received in the western parts of the southern shores of the Caspian Sea occurs in the autumn season and especially in September, which gradually changes to the eastern coast of the rainfall regime and in the winter season (March to October) the maximum amount of precipitation is received. Examining the time distribution pattern of rainfall in the studied stations shows that in September, the highest amount of rainfall occurs in the third quartile. In all studied stations, the minimum coefficient of variation was in March and September. This shows that the distribution of precipitation during these months is appropriate and indicates the dominance of precipitation systems in these months. The coefficient of variation has gradually increased towards the warmer months of the year. This indicates that the distribution of daily rainfall during the warm months of the year such as June, July and August (reproductive stages to harvest) is much more irregular than other months of the growing season. The probability distribution of precipitation for different months varies according to the geographic location, the distribution of unevenness in the study area. The month-to-month variability of precipitation distribution in the Caspian region is high, and rainfall-producing systems are concentrated on the coastline in limited months in autumn and winter. This has caused the precipitation in the coastal parts of the Caspian Sea to be more concentrated and have a more irregular time distribution. At the same time, towards the southern parts of the Caspian Sea, corresponding to the heights of Alborz, the time distribution of rainfall is more uniform and the difference of rainfall distribution from month to month is less. Therefore, the rainfall distribution in the study area during the rainiest months follows the Gamma and Weibull distribution. While in the months of June and July, parts of the eastern coast of the Caspian Sea are dominated by normal log distribution. The results of fitting different probability distributions on the daily rainfall of the studied stations on the southern shores of the Caspian Sea showed that the gamma distribution was superior to other probability distributions and the estimates of this method were closer to reality. Among the studied stations, Rasht and Bandar Anzali stations had the best fit with gamma distribution. In these stations, gamma distribution showed a better fit in more than 50% of the days of the rice-growing season. In the stations of Astara, Babolsar, Gharakhil, the gamma distribution also showed a better relative fit with most of the rainy days of the rice-growing season. Meanwhile, in Nowshahr station, the distribution of Weibull had a better fit in 44.2% of the rainy days of the rice-growing season. For Ramsar station, located in the western part of Mazandaran province, two Weibull and Gamma distribution functions had a better fit with the rainy days during the rice-growing season, in which Gamma distribution was the best fit in 43% of the days and Weibull distribution in the other 43%.
 
Conclusion
In this research, an attempt was made to investigate the appropriate statistical distribution of rainfall during the rice-growing season in the southern shores of the Caspian Sea. The results of various types of probability distributions showed that the dominant distribution of non-zero precipitation in the study area is of gamma type and the Weibull distribution is in the next stage. The occurrence of precipitation in July and June has the highest coefficient of monthly precipitation changes in the northern regions, and practically, such occurrence of precipitation cannot be relied upon in seasonal planning. At this point in time, the occurrence of long rains due to the continuation of cloudy hours and days with high relative humidity may also cause an outbreak of rice pests and diseases. However, the most decisive role of rainfall can be considered the rains at the end of the growing season (from reproductive period to harvest), which, in addition to disrupting the harvesting process, can have consequences such as cracking of the grain, staining and even complete destruction of the product. Also, during the months of June and July, which coincide with the flowering and clustering stages of rice in the study area, the frequency of distributions is relatively equal which indicates the irregularity of rainfall in this stage of growth in the studied area. The findings of this research can be used to quantify the amount of expectation and risk caused by rain during the rice-growing season.
 
Funding
There is no funding support.
 
Authors’ Contribution
All of the authors approved the content of the manuscript and agreed on all aspects of the work.
 
Conflict of Interest
Authors declared no conflict of interest.
 
Acknowledgments
We are grateful to all the scientific consultants of this paper.