Evaluation the Ability of Markov Chain Model to Estimating and Regionalizing the Probability of Dry Days in Iran

Document Type : مقاله پژوهشی


Zanjan University


1. Introduction
Climate events behave as stochastic phenomena, which mostly could be predicted by using probability rule and stochastic process. The terms of "stochastic" and "probability" refer to uncertainty about the occurrence of phenomena (Asakereh 2011: 239). Accordingly, the climate events follow uncertainty in their behavior. Therefore, using probability rule in climatology could justify a lot of climate phenomena which semblance of unpredictable events. Due to this kind of usage of probability rules in climatology, the environmental management will be more successful based on climatic information. Because the probability rules, in fact, can help experts through extract constant rules from semblance of disorder or abnormal phenomena.
One of the stochastic models categories which are widely used in climatology is Markov Chain technique. For instance Grigorten (1966) used this technique to estimate the frequency and persistence of weather types during vast and different time interval. Feyerherm and Dean (1967) used Markov Chain technique to analyze the wet and dry spells in the Northern United States. Todorovic and Woolhiser (1974) applied Markov Chain model to investigate the possibility of rain in a sequence of days. Steam (1980) used this model in order to study the probability of rainfall occurrences in India and Nigeria.
In the current paper, the dry days were evaluated based on probability rules, stochastic process, and Markov Chain. Accordingly the ability of Markov model was validated.
2. Study Area
Iran is located in southwest of Asia with high mountains on its four sides, and borders the seas in south and north. Due to its location, besides intra-annual variations of precipitation, spatial differences also occur. In addition, the vast area of the country (approximately 1600000 ), its wide latitudinal extent (25 to 40 N), and its pronounced relief lead to the complex structure of the precipitation distribution over Iran.
The wide latitudinal extent of Iran causes it to be in many systems paths, which can activate its precipitation in a tempo- spatial fashion. Under given conditions, there are systems causing different precipitation; each operates on different space and time scales. These systems come not only from outside of the country (e.g. Mediterranean Sea) but from inside (high mountain systems) (Alijani, 1994).
The two highest mountain systems, Zagros and Alborz- Talish, which rise up to 4,557m and 5,670m above sea level, respectively, strikingly affect the temporal and spatial patterns of precipitation. Zagros, in the western part of Iran, is the most elevated mountain range, extending from north-west to southeast, while the northern highlands (Talish and Alburz) are extending from west-to-east along southern Caspian Sea.
3. Material and Methods
The data network of daily precipitation of Iran employed in current study, was obtained by interpolating the daily observations from 1961-2010 and 1436 (synoptic and climatological) stations which are recently achieved from Islamic Republic of Iran Meteorological Organization (IRIMO). Due to deprivation of station coverage in time and space and in order to have a complete coverage over Iran, the interpolation was carried out by the Kriging method (Asakereh 1387) that had the lowest root mean square errors when compared to other spatial interpolation methods. The Spatial data resolution was 15 15 km and the country was covered by 7187 pixels. Accordingly, Iran's precipitation had 18218× 7187 dimension and S-Mode matrix (time on the rows and location on columns).
Dry days analyses by using Markov model carried out on aforementioned database. Accordingly, precipitation estate was distinct based on precipitation amounts, thus, the day without any precipitation, considered as a dry day, and the days with any given values of precipitation indicated as a rainy day. The frequency matrix is formed and the probability matrix of rainy – dry days is created accordingly based on maximum likelihood method. This procedure is used for all 7187 pixels. Then the frequency of calculated dry days, and the frequency of observed dry days was compared in order to find the estimation error for each pixel. In the next step, the classification process took place by using hierarchical cluster analyses. In this process, the pixels with similar characters of dry days probability and similarity in error of Markov model estimator were put in the same class.
4. Results and Discussion
The monthly maps output of dry days based on Markov chain model were prepared. In order to validate this model, the number of observed dry days maps also were illustrated. To sum up, four months (January, April, July, and October) were analyzed as representative of four seasons.
As can be seen from Figures in current paper, there are many places (e.g. along Alborz an Zagros Mountains, Caspian sea coast, and in the western provinces) in January, the error of Markov model is pronounced. The deprivation of Markov model output during April is more distinguishable in southern parts of the country, while the minimum errors took place in northern coast, northwest of Iran, and in western parts of the country. The dry days during summer season (July) estimated by Markov model is the best estimation in compare to other seasons in which Markov model suggested. There are only small overestimated errors that did not exceed one day only. During September, the same result as the summer result took place except for the western parts, northwest, and some parts in Caspian Sea coasts.
According to probability of dry days based on Markov model and based on the model validity, pigeonhole of pixels took place. As it mentioned before, the process is taken place by using Cluster Analyses model. Therefore six zones, which are in agreement with geographical factors (e.g. Topography, Latitude and Longitude), were diagnosed over Iran:
The first zone coincidence with highest parts of Zagros Mountains, which covers only 9.2% of Iran territory. The second zone covered approximately 13.2% of the country, and dominant in northeast, northwest of Iran, and the southern part of Alborz Mountain. The third zone covered 19% of the country among some parts of northeast, Lalezar and Hezar mountain in Kerman province, and some parts in south of Iran. About half of Iran territory including central, eastern, and parts of south of the country, is covered by the forth class. The least coverage is the fifth class qualification. This class covered 2.3% of the country among center parts and the west of Caspian Sea coast. The sixth class including 5.8% of Iran territory is among east of Caspian Sea, and northwest of Iran.
5. Conclusion
Precipitation is one of the most important climatic elements that can characterize some main aspects of the climate of a region. One of more important aspect in precipitation changes is alteration in its occurrence and non- occurrence. Stochastic approaches, such as Markov chain model, are one of the appropriate approaches with which we can simulate precipitation estate. Accordingly the frequency matrix is formed and the probability matrix of rainy – dry days is created for each pixel over Iran, based on maximum likelihood method. Therefore the probably and frequency of Dry days were estimated based on persistence probability calculated based on succeed power on probability matrix. This value for each pixel was compared with the observed values for each pixel. The dry days of summer months showed more agreement with the estimate of Markov model in compare with other months. There was an attempt to pigeonhole Iran based on dry days probability, and its accurate values. Therefore, six classes were discovered. These classes are in agreement with geographical factors e.g. Topography, Latitude and Longitude.


جانسون. ریچارد. وویچرون. دین. دبلیو.ترجمه نیرومند، حسنعلی؛ 1379. تحلیل آماری چند متغیری کاربردی. مشهد: انتشارات دانشگاه فردوسی مشهد. ص 740.
جعفری بهی، خدابخش؛ 1378. تحلیل آماری دوره‌های تر و خشک بارندگی در چند نمونه اقلیمی ایران با استفاده از زنجیره مارکف. پایان‌نامه کارشناسی ارشد هواشناسی کشاورزی. دانشگاه تهران. دانشکده کشاورزی. گروه آبیاری. استاد راهنما دکتر سهراب حجام، ص87.
عساکره، حسین؛ 1387. کاربرد روش کریجینگ در میان یابی بارش. مجله جغرافیا و توسعه. شماره12. صص42-25، زاهدان.
عساکره، حسین؛ 1389. احتمال تواتر و تداوم یخبندان‌های زودرس و دیررس در شهر زنجان. مجله جغرافیا و برنامه‌ریزی محیطی.ش1. صص 16-1. اصفهان.
عساکره، حسین؛ 1390. مبانی اقلیم‌شناسی آماری. زنجان: انتشارات دانشگاه زنجان. ص548.
علیزاده، امین، آشگرطوسی، شادی؛ 1387. توسعه یک الگو برای پیش‌بینی و پایش خشکسالی (مطالعه موردی استان خراسان رضوی). مجله علوم و صنایع کشاورزی (ویژه آب‌وخاک). شماره1. صص234-224. مشهد.
علیجانی، بهلول و دیگران؛ 1389. بررسی تداوم روزهای یخبندان در ایران با استفاده از مدل زنجیره مارکوف. مجله پژوهش‌های جغرافیای طبیعی. شماره73. صص20-1، تهران.
علیجانی، بهلول، و دیگران؛ 1390. بررسی ساختار تداوم دو وضعیتی بارش‌های سالانه جنوب ایران با استفاده از الگو وضعیت نهان زنجیره مارکوف. مجله جغرافیا و توسعه. شماره25. صص20-1. زاهدان.
فرشادفر، عزت‌الله؛ 1384. اصول و روش‌های آماری چند متغیره. کرمانشاه: انتشارات دانشگاه رازی
Ana, A., Paulo, S., 2007. Prediction of SPI drought class transitions using Markov chain. Water Resources Management 21, 1813-1823.
Anagnostopoulou, Ch., Maheras, P., Karakostas, T.,Vafadis, M., 2003. Spatial and temporal analysis of dry spell in Greece, Journal of Geogrphy Research.74: p237-242.
Badraddin,Y., Mohammad, A.,1997. Climatic classification of Saudi Arabia: An application of factor – cluster analysis. Geojournal 41, 69-84.
Alijani, B., Mahmodi, P., Chogan, E., Bisheh niaser, M., 2011. Check the continuity of annual precipitation south conditions using hidden Markov chain model. Journal of Geography and Development 25, 1-20.
Alijani, B., Mahmodi, P., Rigi Chahi, E., Khosravi, P., 2010. Study of frost days in Iran continues using the Markov chain model. Journal of Geogrphy Researches 73, 1-20.
Alizadeh, A., AshgarTosi, Sh., 2008. Develop a model for forecasting and drought monitoring (Case study: Khorasan Razavi). Journal of Agriculture and Industries (specific water and soil) 1, 224-234.
Asakereh, H., 2008. Application of kriging method through rain routing. Journal of Geography and Development 12, 25-42.
Asakereh, H., 2010. The frequency stability and continuity of early frosts likely zanjan. Journal of Physical Geogrphy1, 1-16.
Asakereh, H., 2011. Fundamentals of statistical climatology. Zanjan university Zanjan, Pp548.
Farshadfar, E., 2005. Principles of multivariate statistical methods, Kermanshah,university Kermanshah, pp734.
Feyerherm, A.M., Dean, B., 1967. Goodness of a Markov chain model Frequency‎ of wet and dry days, Journal of Applied Meteorology 6, 770-787.
Grigorten, L, A., 1966. Statistics model of the frequency and duration of weather events, Journal of Applied Meteorology 5, 606-616.
Heli, Lu., Quangin, Sh.,Jiyuan, L., Junbang, W.,Shenbin, Ch.,Zhuogi, Ch., 2008. Cluster analysis on summer precipitation field over Qinghai–Tibet plateau from 1961 to 2004, Geographical science 18: 295-307.
Jaefrie Behi, KH., 1999. Statistical analysis of rainfall during the wet and dry climate with few examples of using Markov chain, Master Thesis Agricultural meteorology , university Tehran, Faculty Advisor:Sohrab Hejam, 1-87.
Janson, R., Vichren, W., translator: Niromand, H.A., 2000. Applied multivariate statistical analysis, Ferdowsi university of Mashhad, pp740.
Stem, R.D.,1980. The calculation of probability distribution for models of daily Precipitation. Archiv for meteorology geophysic and bioclimatologic 28, 137-147
Todorovic, P., Woolhiser, D. A., 1975. A statistical model of n-day precipitation. Journal of Applied Meteorology 14, 17-24.