Analysis On The Relationship Between The Time Series Of Weather And Climate In Liaoning Province Based On Fract Ional Derivative

In this paper,the daily,monthly and annual average temperature from 1951 to 2010 in ten cities(Shenyang,Dalian,Anshan,Fushun,Jinzhou,Yingkou,Fuxin,Chaoyang,Dandong,Benxi)of Liaoning province were used to analyze the characteristics of autocorrelation and long-trail probability distribution for these time series by using the autocorrelation function and the normalized probability density function.Next,Making use of the normalized histogram of probability density distribution fitting curve in three different time scale(the daily,monthly and annual)to compare the difference of extreme weather and extreme climate in ten cities.Furthermore,the fractional derivative relationships between monthly,annual average temperature anomaly and daily average temperature anomaly were established by using structure function method.The main research conclusions are as follows:(1)The time series of daily,monthly,annual average temperature anomaly in all ten cities present the characteristics of non-memory,short-term memory and long-term memory,respectively.Therefore,Get the conclusions:Weather data has no memory,can be considered to white noise sequence;Climate data has memory,of which yearly climate data has better memory namely the long-range correlation.,compared with monthly climate data.And the climate data of temperature in different areas present different memory.The monthly memory of the areas near the Liaodong gulf and the western is better than the northern and eastern.The yearly memory in the west and south is slightly larger than the northern and eastern.(2)In this paper,research shows that there is a fractional order derivative relation between the monthly,yearly and daily average temperature anomaly series.Calculated the corresponding derivative order are Dandong 0.532 and 0.646,Dalian 0.516 and 0.929,Fushun 0.504 and 0.598,Chaoyang 0.524 and 0.524,Benxi 0.523 and 0.658,Shenyang 0.524 and 0.524,Yingkou 0.505 and 0.798,Jinzhou 0.52 and 0.52,Fuxin 0.526 and 0.725,Anshan 0.523 and 0.805.From the point of the value of 'q' all the values of 'q' are between 0 and 1,belongs to the fractional order derivative.From the numerical point of view,the value of 'q' in year scale is greater than that in month scale.In month scale,the difference of'q' in 10 areas is very slight.In year scale,the result presents the values of q' in western and southern are larger than which in northern and eastern.This conclusion is consistent with the characteristics of the Memory in geographical regions.(3)Comparing the normalized probability density distribution of weather time series with which of climate time series,get the conclusion:The normalized probability density distribution of monthly and yearly average temperature time series have longer tails than which of daily data.Among them,yearly sequence presents obviously the longest tail characteristics.It suggests that the normalized probability density distribution of climate time series has the characters of long tail.It means that the possibility of extreme weather events is bigger than extreme weather events.The weather extreme temperature events in different regions of Liaoning province have no obviously regional differences,while the possibility of climate extreme events in the western and southern is greater than the area in the north and east of Liaoning province.Also,the view is consistent with the characteristics of the memory in different regions.