عنوان مقاله [English]
Introduction: The analysis of extreme events such as first frost dates are detrimental phenomena which influence in various branches of engineering, such as agriculture. The analysis and probability predicting of these events can decrease damage of agriculture, horticulture and the others. Furthermore, this phenomenon can have a relation with other thermal indexes. The analyzing of first 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 first frost dates and thermal index were studied. Best relation was between minimum temperature and return periods of first frost dates.
Materials and Methods: The analyzing of first frost dates (origin is March 21) of all synoptic stations of Khorasan Razavi province is subject of this article. At first data of each station were screening. The basic properties such as homogeneity, randomness, stationary, independence and outliers must be tested. The eight 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 be used to compare the best distribution. The return periods of first frost dates are major application in frequency analysis. There is maybe a relationship between periods and thermal 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 first 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 date of this phenomenon is March 21. 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 Sabzevar, Mashhad and Gonabad had lower Outliers that will not cause any problem in data analysis by their skewness. The first frost data of all station were without upper outlier. 2- The independence of all stations was accepted at the 10% level. 3-All stations were Randomness, Independence and homogeneous and lack of jump. 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). Generalized Pareto distribution had the best fitted to data (60% of cases compared to the other functions). The results significantly indicated that the occurrence of first frost on the first day of process is in place. The first frost in the period of 2 years at all stations, not occur earlier than Aban(October 28). The 100-year return period event does not occur earlier than first of Mehr(September 22). There is no significant relationship between first frost in the period of 2 years with other factors such as altitude, latitude, longitude, temperature and precipitation as well.
Conclusion: Date of the first fall frost is one of the unfavorite climate influences that cause reduction in crop products. The purpose of this paper is to analysis the frequency occurrence of first frost day in several Khorasan’s synoptic stations as study area. Screening and initial basic tests such as randomness homogenity, independence, etc. were done. Eight distribution function, namely Normal, Gumbel type 1, Gamma 2 parameters, Log normal 2 and 3 parameters, Generalized Pareto and Pearson type III were fitted to data with five probability distributions methods (Ordinary Moments, Maximum Likelihood method, Modified Moments, Probability Weighted Moment and Maximum Entropy). Goodness of fit test was Kolmogorove-Smirnov test. PWM and ModM methods revealed relatively superior results compared to the rest of methods. Generalized Pareto distribution had the best fitted to data (60% of cases compared to the other functions). The results significantly indicated that the occurrence of first frost on the first day of process is in place. The first frost in the period of 2 years at all stations, not occur earlier than Aban. The 100-year return period event does not occur earlier than first of Mehr. There is no significant relationship between first frost in the period of 2 years with other factors such as altitude, latitude, longitude, temperature and precipitation as well.