Global ionospheric TEC prediction model integrated with semiparametric kernel estimation and autoregressive compensation
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摘要:
针对电离层半参数球谐函数模型中窗宽参数选择引起的估计偏差，本文在传统的电离层球谐函数模型中引入半参数核估计和自回归（Autoregressive model，AR）模型，分别用于分离球谐函数模型的系统误差和窗宽参数引起的估计偏差，提出一种全球电离层总电子含量（Total Electron Content，TEC）组合预报模型.首先，利用多项式拟合法剔除球谐系数的趋势项；然后利用频谱分析法提取球谐系数的周期，引入半参数核估计平差模型求解模型参数，建立半参数球谐函数（Semiparametric-Spherical Harmonic，Semi-SH）模型；最后将Semi-SH模型拟合残差用AR模型补偿预报.实验结果表明，组合预报模型相比单一的Semi-SH模型有较大的提升，全球TEC预报值与欧洲定轨中心（Center for Orbit Determination in Europe，CODE）发布的TEC值相比，单天预报残差小于1 TECU、3 TECU和5 TECU占比分别为54.30%、93.40%和98.61%；组合模型滑动预报5天相对精度在低、中、高纬度地区分别提高了2.14%、1.32%和2.32%.
Abstract:Aiming at the estimation deviation caused by the selection of window width parameters in the ionospheric semi-parametric spherical harmonic function model, the semi-parametric kernel estimation and the autoregressive (AR) model are introduced to the traditional ionospheric harmonic function model, which are used to separate the systematic error of spherical harmonic function model and the estimation deviation of window width parameters respectively. A combined model for the forecasting of global ionospheric total electron content (TEC) is proposed in this paper. Firstly, the trend term of the ionospheric spherical harmonic coefficient is eliminated by polynomial fitting. Secondly, the spectral analysis method is used to extract the period of the ionospheric spherical harmonic coefficient, and the semiparametric kernel estimation adjustment model is introduced to solve the model parameters. Based on the aforementioned work, the semiparametric-spherical harmonic model (Semi-SH) is established. Finally, the prediction is carried out after using the AR model to compensate the Semi-SH model fitting residual error. The results indicate that the combined forecasting model based on the semi-parametric kernel estimation and the AR model shows certain advantages than the ordinary Semi-SH model. For validation, the TEC values obtained with the proposed model are compared with those issued by the Center for Orbit Determination in Europe (CODE), and the daily forecasting residuals of global TEC less than 1 TECU, 3 TECU and 5 TECU account for 54.30%, 93.40%, and 98.61% respectively. For the 5-day sliding forecast, the relative accuracy of the combined model are improved by 2.14%, 1.32% and 2.32% in low-, mid- and high-latitude regions respectively.
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Key words:
- Ionospheric TEC /
- Semiparametric model /
- AR model /
- Combined forecast
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图 1
C1PG值(a)、Semi-SH模型(b)和组合模型(c)单天预报残差全球分布图
Figure 1.
The global map of residuals of C1PG (a), Semi-SH (b) and combined model (c) value with respect to CODG value
图 2
Semi-SH模型和组合模型预报RMS统计
Figure 2.
RMS statistics of Semi-SH value and combined model value relative to CODG value
图 3
Semi-SH模型(a)和组合模型(b)预报残差密度统计
Figure 3.
Semi-SH model (a) and combined model (b) forecast residual probability density statistics
图 4
Semi-SH模型、组合模型预报值与CODG值对比
Figure 4.
Comparison of Semi-SH model, combined model forecast value with CODG value
表 1
C1PG模型、Semi-SH模型和组合模型预报值残差分析
Table 1.
C1PG model, Semi-SH model and combined model prediction residual analysis
模型 北半球RMS(TECU) 南半球RMS(TECU) 全球RMS(TECU) |Δ|＜1 TECU(%) |Δ|＜3 TECU(%) |Δ|＜5 TECU(%) C1PG 1.45 2.15 1.84 45.06 89.71 98.50 Semi-SH 1.35 1.96 1.69 53.13 92.04 98.24 组合模型 1.23 1.88 1.59 54.30 93.40 98.61 
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表 2
Semi-SH模型和组合模型预报精度对比
Table 2.
Comparison between the prediction accuracies of the Semi-SH model and the combined model
纬度 模型 评定指标 天数 均值 1 2 3 4 5 15°S Semi-SH RMS(TECU) 2.57 3.54 3.43 2.37 1.80 2.74 P(%) 84.25 85.26 84.79 86.58 86.72 85.52 组合模型 RMS(TECU) 1.22 3.62 3.10 2.48 1.56 2.40 P(%) 91.19 86.48 86.47 85.71 88.45 87.66 50°S Semi-SH RMS(TECU) 1.11 2.80 1.32 1.71 1.78 1.74 P(%) 89.38 80.10 85.07 83.78 79.30 83.53 组合模型 RMS(TECU) 1.01 2.70 0.98 1.69 1.83 1.64 P(%) 91.72 80.95 89.06 82.65 79.88 84.85 70°S Semi-SH RMS(TECU) 0.86 1.01 1.32 1.19 1.97 1.27 P(%) 89.90 86.60 82.07 85.04 80.12 84.75 组合模型 RMS(TECU) 0.79 0.83 1.07 1.06 1.47 1.04 P(%) 91.08 88.97 85.20 86.44 83.66 87.07
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