Document Type : Research Article
Authors
1 University of Tehran
2 Islamic Azad University, Mashhad Branch
Abstract
Introduction: The analysis of extreme events such as last frost dates are detrimental phenomena which influence in various branches of engineering, such as agriculture. The analysis and probability predicting of these events can be decrease damage of agriculture, horticulture and the others. Furthermore, this phenomenon can have a relation with other thermal indexes. The analyzing of last frost dates of all synoptic stations of Khorasan Razavi province is subject of this article. The frequency analysis applied to eight distributions. Then the relationship between last frost dates and termal index were studied. Best relation was between minimum temperature and return periods of last frost dates.
Materials and Methods: The analyzing of last frost dates (origin is 23th september) of all synoptic stations of Khorasan Razavi province is subject of this article. First data of each station were screening. The basic properties such as homogeneity, randomness, stationary, independence and outliers must be test. The eight distribution distribution Normal, Gumbel type 1, Gamma 2-parameter, Log normal 2 or 3 parameters, Generalized Pareto, Generalized extreme values and Pearson Type 3 fitted to data and the parameters estimated with 7 methods by the name of the several types of Moments (5 methods), maximum likelihood and the maximum Entropy. The Kolmogorov – Smirnov goodness of fit test can compared the best distribution. The return periods of last frost dates are major application in frequency analysis. There is maybe a relationship between periods and termal index such as min., max. and mean temperature. This relationship can be adapted by regression methods.
Results and Discussion: The statistical analysis for prediction probabilities and return periods of the last frost dates for all synoptic stations in Khorasan Razavi province and the relationship between annual temperature indicators and this phenomenon is the aim of this article. The origin dates of this phenomenon are 23th September. First, data were screened. Then basic hypothesis test were applied which including the Runtest (randomness), the Mann-Whitney test (homogeneity and jump), the Wald-Wolfowitz test (independence and stationary), the Grubbs and Beck test (detection Outliers) and the three sigma methods (Outlier). The results were: 1-The Golmakan, Kashmar and Torbatejam had lower Outliers that will not cause any problem in data analysis by their skewness. 2- The independence of all stations was accepted at the 10% level. 3-The Gonabad data was not homogeneous and removed. Eight probability distributions (Normal, Gumbel type 1, 2-parameter gamma, 2 and 3 parameters log-normal, the generalized Pareto, the generalized extreme values and the Pearson type 3) were applied. The skewness coefficients for all stations were more than 0.1 so Normal distribution was rejected. Also the7 methods of estimation (five different methods of moments, maximum likelihood and maximum entropy methods) were used. The ks fit test was applied. The ks for some stations were closed together at several estimations methods. The results are as follows: GPA (4 times), PT3 (4 times), LN2 (4 times), GA2 (3 times). The obtained results were: 1- The shortest duration of frost date was belonged to the Sarakhs station, but the longest return periods were not same. 3- The interior station ranges were 32 to 50 days for all return periods, with a mean of 41, standard deviation 9.3 and the coefficient of variation 5.9%, which represents the damping of the phenomenon within the station. 4-Pearson type 3, which has been recommended by some researchers, can not be generalized. 5- The major method of estimation was MOM (8 cases). The relationship between the last frost days and other meteorological factors such as, minimum, average and maximum temperature were investigated in this paper. The linear relationship between last frost days and the average annual minimum temperature were the best-fit.
Conclusion: The last frost dates analyzing of all Khorasan Razavi province synoptic stations is subject of this article. The data screening and basic tests were applied and data accepted as random samples. The 8 distributions with 7 methods of estimation were fitted to data. The best fitted distribution at all stations mainly included GPA, PT3, LN2. The major estimation method was MOM. The relationship between last frost periods and minimum temperature was the best linear models. So, we can predict the return period from this temperature as well.
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