A prediction method for LOD based on combined LSTM and WLS

doi:10.11947/j.AGCS.2026.20250346

Abstract

Abstract:

The length of day (LOD), a crucial component of Earth orientation parameters (EOP), arises from fluctuations in Earth's rotation rate due to internal and external forces. These variations manifest as increases or decreases in LOD, directly influencing the timescale of the diurnal cycle. This study employs five distinct methods—least squares auto regressive (LSAR), weighted least squares auto-regressive (WLSAR), long short-term memory (LSTM) combined with polynomial curve fitting (PCF) extrapolation and least squares (LS) extrapolation, a hybrid LSTM and LS model (LSTM+LS), and a hybrid LSTM and weighted least squares model (LSTM+WLS), corresponding to schemes 1 to 5 in this study—to predict the LOD time series from January 1, 2016, to December 31, 2020, based on the EOP 20 C04 dataset released by the International Earth Rotation Service (IERS). The proposed scheme 5 (LSTM+WLS) in this study involves applying WLS method to the LOD data corrected for solid Earth zonal tidal effects to derive extrapolated, fitted, and residual terms. The residual term is then predicted using an LSTM model incorporating effective angular momentum (EAM) data. Finally, the LOD predictions are obtained by combining the predicted residuals, extrapolated terms, and solid Earth zonal tidal corrections. Compared to the other four schemes, scheme 5 demonstrates superior performance in 10-day predictions, achieving a mean absolute error (MAE) of 0.127 3 ms, representing improvements of 5.7%, 5.0%, 2.6%, and 4.6%, respectively. For 30-day predictions, it slightly outperforms schemes 1 and 2 while performing comparably to Schemes 3 and 4. In 90-day predictions, the MAE reaches 0.167 0 ms, with improvements of 8.0%, 8.8%, 15.3%, and 13.3% over the other schemes. Overall, the proposed LSTM+WLS model exhibits excellent performance in short-term LOD forecasting.

Key words: length of day, LSTM, LSAR, Earth orientation parameters, effective angular momentum

CLC Number:

P228

Jingxuan LIU, Xuexi LIU, Kefei ZHANG, Chao YANG, Suqin WU, Shouqing ZHU, Fudong GUO. A prediction method for LOD based on combined LSTM and WLS[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(3): 477-489.

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外推天数	PCF+LS	LS	WLS
10天	0.010 2	0.012 3	0.013 0
30天	0.028 9	0.029 8	0.032 2
90天	0.073 2	0.071 3	0.065 2
180天	0.140 7	0.132 0	0.109 1
360天	0.292 2	0.251 3	0.188 7

参数	10天	30天	90天	180天	360天
编码器	10	10	512	256	256
				128	128
				256	256
解码器	14	14	256	128	128
解码器	7	7	256	64	64
全连接层数	无	无	无	Dense（128，ReLU）	Dense（128，ReLU）
全连接层数	无	无	无	Dense（128，ReLU）	Dense（128，ReLU）
优化器	Adam	Adam	Adam	Adam	Adam
损失函数	MSE	MSE	MSE	MSE	MSE

预测天数	公报A	方案一	方案二	方案三	方案四	方案五	方案五相对于其他方案预报精度的提升
预测天数	公报A	方案一	方案二	方案三	方案四	方案五	公报A	方案一	方案二	方案三	方案四
10天	0.128 4	0.134 5	0.133 7	0.130 6	0.133 1	0.127 3	0.9%	5.7%	5.0%	2.6%	4.6%
30天	0.204 7	0.160 7	0.160 6	0.155 3	0.155 8	0.156 7	30.6%	2.6%	2.5%	－0.9%	－0.6%
90天	0.240 7	0.180 4	0.181 7	0.192 6	0.189 2	0.167 0	44.1%	8.0%	8.8%	15.3%	13.3%
180天	0.302 5	0.184 5	0.176 8	0.257 4	0.239 0	0.212 3	42.5%	－13.1%	－16.7%	21.2%	12.6%
360天	0.537 5	0.242 2	0.208 2	0.364 7	0.316 7	0.262 8	104.5%	－7.8%	－20.8%	38.8%	20.5%