Short-term Prediction of Ionospheric TEC Based on ARIMA Model

doi:10.11947/j.JGGS.2019.0102

Abstract

Abstract:

In order to achieve high short-term prediction accuracy of ionospheric TEC, first, we transform a seasonal time series for ionospheric Total Electron Content (TEC) into a stationary time series by seasonal differences and regular differences with a full consideration of the Multiplicative Seasonal model. Next, we use the Autoregressive Integrated Moving Average (ARIMA) model taken from time series analysis theory for modeling the stationary TEC values to predict the TEC series. Using TEC data from 2008 to 2012 provided by the Center for Orbit Determination in Europe (CODE) as sample data, we analyzed the precision of this method for prediction of ionospheric TEC values which vary from high to low latitudes during both quiet and active ionospheric periods. The effect of the TEC sample’s length on the predicted accuracy is analyzed, too. Results from numerical experiments show that during the ionospheric quiet period the average relative prediction accuracy for a six day time span reaches up to 83.3% with average prediction residual errors of about 0.18±1.9TECu. During ionospheric active periods it changes to 86.6% with an average prediction residual error of about 0.69±2.6TECu. For the quiet periods, above 90% of predicted residual is less than ±3TECu while during active periods, it is only about 81%. The two periods show that that the higher the latitude, the higher the absolute precision, and the lower the predicted relative accuracy. In addition, the results show that prediction accuracy will improve with an increase of the TEC sample sequences length, but it will gradually reduce if the length exceeds the optimal length, about 30 days. On the other hand, with the same TEC sample, as the predicted days increase, the predictive accuracy decreases. Athough the predictive accuracy is not apparent at the beginning, it will be significantly reduced after 30 days.

Key words: ARIMA; ionosphere prediction; time series analysis; prediction accuracy; TEC

Xiaohong ZHANG,Xiaodong REN,Fengbo WU,Qi LU. Short-term Prediction of Ionospheric TEC Based on ARIMA Model[J]. Journal of Geodesy and Geoinformation Science, 2019, 2(1): 9-16.

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Days	Δ<1TECU		1TECU≤Δ<2TECU		2TECU≤Δ<3TECU		Δ≥3TECU
Days	Quiet period	Active period	Quiet period	Active period	Quiet period	Active period	Quiet period	Active period
1	61.1%	39.6%	23.6%	20.2%	7.0%	13.2%	8.4%	27.1%
2	55.5%	40.3%	20.9%	22.9%	9.7%	18.0%	13.9%	18.8%
3	50.0%	43.1%	22.2%	27.1%	13.9	9.0%	13.9%	20.8%
4	43.1%	47.9%	36.1%	30.6%	15.3	6.3%	5.6%	15.3%
5	50.0%	46.5%	22.2%	18.1%	15.3	18.8%	12.5%	16.7%
6	43.0%	45.9%	33.3%	22.2%	15.3	10.4%	8.4%	21.5%
Mean value	50.0%	44.0%	26.0%	24.0%	13.0%	13.0%	10.0%	20.0%

Predicted days	Low latitudes			Middle latitudes			High latitudes
Predicted days	Δ_ave	σ	P_rel	Δ_ave	σ	P_rel	Δ_ave	σ	P_rel
1	0.41	2.46	89.14%	0.68	0.83	91.34%	0.41	1.04	86.12%
2	0.78	1.61	94.14%	2.1	1.79	83.10%	0.23	1.39	78.67%
3	1.22	2.15	90.39%	1.07	1.19	89.47%	-0.69	1.23	54.27%
4	0.85	1.5	89.51%	-0.27	1.11	86.83%	-0.5	1.17	73.08%
5	-0.91	2.62	86.16%	-0.21	1.31	88.14%	-0.55	1.43	69.19%
6	-0.26	2.5	88.71%	-0.53	1	90.23%	-0.71	1.26	69.58%
Mean value	0.35	2.14	89.68%	0.47	1.2	88.18%	-0.3	1.25	71.82%

Predicted days	Low latitudes			Middle latitudes			High latitudes
Predicted days	Δ_ave	σ	P_rel	Δ_ave	σ	P_rel	Δ_ave	σ	P_rel
1	1.44	3.5	89.11%	0.84	1.79	87.20%	0.82	1.76	80.98%
2	1.71	3	89.24%	0.9	1.49	88.98%	-0.01	1.53	78.84%
3	2.59	3.1	88.51%	0.52	1.63	88.99%	-0.58	1.26	81.59%
4	1.62	2.49	91.11%	0.62	1.15	90.88%	0.15	1.53	82.37%
5	1.08	2.84	88.83%	1.01	1.47	88.65%	0.02	1.28	85.68%
6	-0.36	3.98	88.94%	1.05	1.46	88.91%	0.52	1.54	80.60%
Mean value	1.35	3.15	89.29%	0.82	1.5	88.94%	0.15	1.48	81.68%