The Typhoon Tracks Analysis using Tri-plots and Markov chain

Based on the fractal dimension, the tri-plots can classify two large and not equal sizes of the time series datasets. The tri-plots measure three function values which include two self-plots and one cross-plot. The self-plot affords the character of one individual dataset. The cross-plot describes the relation between two datasets. Originally, the tri-plots just can get the relation in two datasets, but we can use tri-plots many times for multi-datasets. The time series data like typhoon trajectories, we are interested in the differences among the different annual events, e.g. ENSO and La Niña. In here, we propose the tri-plots method to analyze and classify different annual typhoon trajectories. On the other hand, the Markov chain is used to deal with the time series data in data mining filed. Markov chain establishes the probability relation between two consecutive time steps and estimate one model for one trajectory. Basically, every trajectory has own probability model. We can repeat this process until all datasets finished computing. In implementation, we combine several trajectories to be one trajectory in order to corresponding the physical meaning and saving executing time. After all trajectories of all datasets finished estimating their own model, the dissimilarity matrix can be given by comparing all trajectory models pairs, that is, the dissimilarity matrix describes the relations between the trajectories. So, we use the Markov chain to be another alternative method for different annual events trajectories classification problems. After the calculation of the tri-plots, the ENSO and La Niña years typhoon tracks can be separated by the classifier, the smooth support vector machines SSVM , which can get the training error about 0.023~0.268 and the testing error about 0.271~0.334. For Markov chain with the threshold of the pace , the SSVM classifier can get the training error around 0.031~0.173 and the testing around 0.181~0.287. Moreover, the tri-plots or Markov chain concentrate the information of all events to one distribution figure that presents the dissimilarity of these typhoon trajectories or depicts which years should be probably regarded as one group. We believe that they can be very helpful for realizing ENSO and La Niña atmospheric circulation and for establishing typhoon databases. In other words, we think tri-plots and Markov chain can be use to find the intrinsic patterns in other traditional weather data. Key word: fractal dimension, tri-plots, self-plot, cross-plot, Markov chain, smooth support vector machines