Fractal Dimension Probability Distribution Of TC Edge

In the past50years, the study on the dynamics of TC moving is just’ in view of the effect one factor alone (such as experimental steering, asymmetric structure of TC or nonsymmetrical convective system of TC), that is in single-factor framework. Elsberry pointed out the defect of just considering single factor effect. He said that the forecasting of TC road was more complicated than forecasting in ideal single-factor framework, it was a difficult nonlinear problem. Elsberry’ research gives some new ways on studying of dynamics of TC moving. In the other side, the influence of TC complex structure on TC track has been considered except nonsymmetrical convective system of TC.As the forecasting of TC road is a difficult nonlinear problem, we need to combine forecasting of TC road with Nonlinear Theory. It was generally acknowledged that Nonlinear Theory includes Chaos Theory, Fractal Theory, and Theory of self-organization et.al. We use the fractal theory that belong to nonlinear theory in this paper, and then quantitatively describe the complex degree of TC using the fractal dimension of TC edge, and also estimate probability density function (PDF) of TC edge fractal dimension. From all above, we combine the forecasting of TC road with fractal.Obtain1295TC edges from1295IR1images of69TCs from2006to2010, and calculate the fractal dimension of the edges using compasses method. Sorting the1295TC edge fractal dimension in descending order and classified into five categories, denoted by A, B, C, D, E, which are in the same frequencies. The fractal dimension mean value of the five categories are1.21,1.26,1.29,1.33,1.40respectively. Then find5samples that nearest to the averages. The IR imageries and TBB contour map of the five samples show that the edges of TCs are more roughness, non-circular, and the structure of TC is more complicated, as the increase of the fractal dimension. All above indicate that the fractal dimension of TC edges can quantitatively describe the complex degree of TC to some extent.The fractal dimension of TC edge that reaches by calculation in chapter three is not a determinate number but random a variable as the factors that affect geometrical shape of TC edge are extremely complicated. There are two forms for describe the random variable: continuous functions such as probability density function, and statistics features such as mean and variance. We calculate the statistics features and estimate probability density function (PDF) of TC edge fractal dimension using the1295samples, and find out the normal distribution fitting of the fractal dimension of TC edge both in northwestern pacific and South China Sea passes the hypothetical testing under5%of the significance levels. Then the union doesn’t pass. The logarithmic normal distribution fitting of the three above pass the hypothetical testing under5%of the significance levels, and the Dmax of normal distribution fitting is bigger than the logarithmic normal one. So, we can conclude that the logarithmic normal distribution fit the asymptotic distributions of TC edge fractal dimension well, and it’s better than the Normal one.