基于多种度量的电离层TEC混沌预测分析

Analysis of chaotic properties and prediction of ionospheric total electron content based on different measurements

利用东经120°,北纬45°上空的2008年年积日101～150d时间段内共600个电离层格网TEC数据为时间序列样本,分析了该点上空电离层TEC参数的混沌特性,发现其关联维数为2.2632,嵌入维数为5,最大Lyapunov指数为λ=0.0833,表明该点上空电离层TEC时间序列具有混沌的特征,存在混沌现象.采用加权一阶局域法对TEC时间序列进行预测时,在有效预报尺度内,利用各种度量进行预报得到的中误差都随着预报天数的增加而逐渐增大,但预报的相对误差却是在一定幅度范围内上下波动.采用四种距离度量以及皮尔森相关系数和Jaccard相似系数进行预报,其预测结果或者平均中误差较大,或者平均相对误差较大,结果不理想.其中,采用标准化欧氏距离得到的平均中误差最大,达到5.107TECU,而采用皮尔森相关系数得到的平均中误差最小,为5.078TECU;对于平均相对误差而言,由切比雪夫距离得到的平均相对误差最大,为0.185,而Jaccard相似系数得到的平均相对误差最小,为0.166.而采用余弦相似度得到的预测结果,其平均中误差和平均相对误差都很小,分别为5.079TECU和0.167.因此,在一阶局域混沌预测时,采用余弦相似度作为衡量相空间轨迹的差异性是较为合适的.

The chaotic properties of ionospheric total electron content based on the 600 TEC data from 101 to 150 day of 2008 over 45N, 120E are analyzed in the paper. Calculation results show that the correlation dimension is 2. 2632, embedding is 5 and largest Lyapunov exponent is 0. 0833. The weighted one-rank local-region forecasting method is used triumphantly to forecast the time series of TEC in the paper. The forecasting results show that the standard deviations are more with the accretion of forecasting scale while relative errors fluctuating in certain scope range. The forecasting mean standard deviations and mean relative errors are unsatisfactory using four distance measurements, Pearson correlation coefficient and Jaccard similarity coefficient. In general, the max mean standarddeviation is 5. 107 TECU which is computed by standardized Euclidean distance while the min mean standard deviation is 5. 078 TECU computed by Pearson correlation coefficient. For mean relative errors, the max value is 0. 185 computed by Chebyshev distance while the min value is 0. 166 computed by Jaccard similarity coefficient. However, It is comforting that cosine similarity has a better precision of forecasting, the mean standard deviation and mean relative error respectively are 5. 079 TECU and 0. 167. So cosine similarity can measure accurately the phase space of the different tracks and is a better measurement using weighted one-rank local-region method to forecast time series.