MARKOVmodel and normalize distribution applied in probably of drought and wet period ،MASHAD-IRAN

جغرافیاوتوسعه ناحیه ای

Article 5, Volume 11, Issue 1 - Serial Number 20, September 2013   

Document Type: scientific-research article

DOI: 10.22067/geography.v11i20.30752

Authors

Parvin Kahrobaeian^* ; Anise Iranmanesh; Hossine Mohammady

Abstract

Extended abstract
1- Introduction
Rainfall increase or decrease in each area that normal rain cause drought or flood. This phenomen impacts of social and economic. drought forecast through dynamic and synoptic methods and statistical models is possible.In this paper with markov model and normal distribution of rainfal mashad synoptic station in 30 period year is statistical analyze and dry - wet periods can be predicted to be determined. On the other possibilities will increase in the dry and wet seasons, so that the probability of drought in spring 40.2 percent, while wet it 23.4 will be of chi square test verdict on the superiority of the Markov chain relative to the normal distribution in the region. In most cases, climate events such as droughts , wet years , floods, thunderstorms can not be definitively established , because the statistical methods , it is considered as a random process. Precipitation simply can not be predicted, and any forecast from phenomen, if it is possible to predict the statistics and data about the past. In statistical models to determine are relationship between input of data and time and based on the laws of probablitiy to occur some events are more likely. Sometimes it's just one of the many possible scenarios that can happen. After statistical models, due to ease of use and practicality are good. athough Gumbel and Pearson models are used extensively in the analysis of drought prediction, but Markov chain model have one of the best and most efficient predicted by models of climate sciences.
2- Theoretical framework
A simple mathematical methods (such as matrix multiplication), possibilities of solving the associated processes are very easy, so large applications in predictions more periods of drought and wet climatology. studies on the diagnosis of the drys drought and drought periods are several aspects to be considered, One of these Markov model is to predict probablitiy of drought. Droughts and wet years using Markov chain has a higher accuracy, because the frequency of precipitation makes in the mathematical model. In this model, we formed a p ,square matrix ,this matrix is a square matrix with elements Pij(t) is expressed as follows:

P[ x(t-1) = I , x(t) = j ]
Pij(t) = P [ x(t) = j / x(t-1) = i ] = --------------------------------
P [x(t-1) = I ]

For all pairs i and j, the chain may be out of state i at time t-1 to r-mode and 1, 2 , 3 = j to change at time( t) . So with unknown status at( t-1) at time( t) corresponding to the transition probabilities (pi) and the(pir) , ...(pir) is displayed:


3- Methodology
This study is an applied one using statical-analytical methods , and used mashhad synoptic stations of data over the period 30 years of rainfall .Data was analyzed using SPSS software pakage.Rainfall of data analyze using Markov chain model and calculated matrix and the probabilities of wet and dry periods. Based on the Markov chain , probablity of annual and seasonal drought to obtain useful information from seasonal rainfall forecasts.
4- Discussion and conclusion
The study area included Mashhad city , khorrasane razavi province , with data rainfall 30 period.Research findings show Markov chain using a statistical model can efficiently detect likely from dry periods determined annually and seasonals. After computing mean and standard deviation of rainfall Mashhad station and fitting them to the normal distribution, was determined the classes climate between dry (D) and wet conditions (W).Therefore, the intervals specified were determined between D and W in the Markov model of climate conditions and. The thresholds are calculated based on the mean and standard deviation of annual rainfall. Conclusion findings show probablity of long-term droughts 45.6 percent, the probability of occurrence of wet periods 9 percent and probability of average rainfall (moderate conditions) 45.5 percent.Drought probability is (sum probability of dry and semi-dry conditions) for the 50.7 percent and probability of wet annual only 19 percent, and in 30.3% is normal average rainfall .
The long-term seasonal probablity occurrence of droughts in autumn, winter and spring, respectively: 56.7, 46 , 47.6 per cent, While probablity of occur wet seasons, respectively: 2.7,6.2, 6.1 percent. It is expected to be higher risk of droughts.

Keywords

drought; Markov chain; Normal distribution rainfal; Ststistical method; Drought and wet period; Mashad