自回归移动平均模型的电离层总电子含量短期预报

摘 要：本文在充分考虑乘积性季节模型的情况下，利用差分法对电离层总电子含量（Total Electron Content，TEC）样本序列进行平稳化处理后，采用时间序列分析中的求和自回归移动平均模型（简称ARIMA，Autoregressive Integrated Moving Average)对TEC值序列进行预报分析。以欧洲定轨道中心（CODE）提供的2008-2012年电离层TEC值为样本数据，分析了该方法在电离层平静期、活跃期预报高、中、低不同纬度电离层TEC值的精度以及TEC样本数据的长短对预报精度的影响等。实验结果表明：在电离层平静期和活跃期预报6天的平均相对精度可达83.3%和86.6%；而平均预报残差分别为0.18±1.9TECU和0.69±2.6TECU，其中预报残差小于3TECU分别达到90%和81%以上；而且两个时期都具有纬度越高相对精度越低而绝对精度越高的规律。此外，预报精度会随TEC样本序列长度增加而提高，但40天左右为其最佳样本长度，如超过此长度，其精度会逐渐降低；而相同样本数据的预报精度会随预报长度的增加而减小，初期并不明显，但超过30天其相对精度将随时间明显降低。

Short-term TEC Prediction of Ionosphere Based on ARIMA Model

Abstract: With a fully consideration of the Multiplicative Seasonal model, we transform a seasonal time series for ionspheric Total Electron Content (TEC) into a stationary time series by seasonal differences and regular differences firstly, then use Autoregressive Integrated Moving Average (ARIMA) model from the time series analysis theory to model the stationary TEC values so as to predict the TEC series. Using the TEC data from 2008 to 2012 provided by the Center for Orbit Determination in Europe (CODE) as sample data, we analysed the precision of this method in the prediction of ionosphere TEC value which varies from high latitude to low latitude in both quiet and active period. The effect of TEC sample’s length on the predicted accuracy is analyzed, too. Results from numerical experiments show that in ionospheric quiet period the average relative prediction accuracy of 6 days are up to 83.3% with an average prediction residual errors of about 0.18±1.9TECu, while it changes to 86.6% with an average prediction residual errors of about 0.69±2.6TECu in ionospheric active period. For the former, above 90% of predicted residual is less than ±3TECu while the latter is only about 81%. Two periods show the same law that the higher the latitude, the higher the absolute precision, and the lower the predicted relative accuracy. In addition, the prediction accuracy will improve with the increase of TEC sample sequences length, but it will gradually reduce if the length exceed the optimal length about 40 days. On the other hand, with the same TEC sample, the predicted days increase, the predicted accuracy decreases. Though it’s not obvious in the beginning, it will be significantly reduced over 30 days.