联合半参数和长短期记忆神经网络的全球电离层TEC短期预报

Global ionospheric TEC short-term prediction by combing semiparametric and long-short term memory networks method

半参数球谐函数(Semiparametric Spherical Harmonic,Semi-SH)模型能减少电离层预报模型误差以及残余周期带来的系统误差.但是半参数球谐函数模型中窗宽参数的选取会带来一定的估计偏差,本文利用长短期记忆神经网络(Long-Short Term Memory Networks,LSTM)在非平稳性时间序列预报中的良好适应性,提出了一种联合Semi-SH与LSTM(Semi-SH-LSTM)的全球电离层TEC短期组合预报模型,适用于1—5天的短期预报.Semi-SH-LSTM模型通过预报球谐函数系数解算全球电离层TEC,利用二次多项式和半参数核估计方法分别拟合球谐系数趋势项和周期项,最后基于LSTM对拟合残差进行补偿预报.本文利用欧洲定轨中心(Center for Orbit Determination in Europe,CODE)球谐函数系数产品,采用单天预报和多天预报两种实验方案验证Semi-SH-LSTM模型的有效性.实验结果表明,相比于Semi-SH模型和综合半参数与自回归模型,Semi-SH-LSTM模型的单天全球TEC预报残差RMS值分别提升了12.6%和13.1%;误差小于1 TECU占比分别提升了4.9%、4.6%.基于Semi-SH-LSTM模型的多天全球TEC预报残差RMS值分别提升了10.5%和8.5%,误差小于1 TECU占比提升了3.9%和3.2%.同时,半参数LSTM组合预报模型每预报一天耗时约在2 h以内.

Semiparametric Spherical Harmonic(Semi-SH)model can reduce the ionospheric forecast model errors and the systematic errors caused by residual period.However,the estimation of window width parameter in the Semi-SH model can bring some estimation bias,this study takes the advantage of the favorable adaptability of Long-Short Term Memory Networks(LSTM)in non-stationary time series forecasting,and proposes a global ionospheric total electron content(TEC)short-term forecast model by combing Semi-SH and LSTM models,referred to as Semi-SH-LSTM model,which is suitable for short-term forecast of 1—5 days.This model calculates the global ionospheric TEC through predicting spherical harmonic(SH)coefficients.It uses quadratic polynomial and semiparametric kernel estimation methods to fit the trend and periodic terms of SH coefficients and finally uses LSTM in compensation prediction for the fitting residuals.The spherical harmonic function coefficient products of the Center for Orbit Determination in Europe(CODE)are performed in this study,and the validity of the Semi-SH-LSTM model is verified by using two experimental schemes as single-and multi-day prediction.Experimental results indicate that compared with the Semi-SH and combined Semi-SH and AR models,the RMS of prediction residual of the single-day global ionospheric TEC based on Semi-SH-LSTM model is improved by 12.6% and 13.1%,respectively,and the corresponding proportion of residual less than 1 TECU is improved by 4.9% and 4.6% respectively.For the multi-day global ionospheric TEC prediction,Semi-SH-LSTM model can improve the RMS of residual by 10.5% and 8.5%,and the residual proportion less than 1 TECU by 3.9% and 3.2% respectively.Meanwhile,the Seni-SH-LSTM model takes about 2 h per day to forecast.