Prediction method of regional tropospheric wet delay based on Conv-LSTM network

doi:10.11947/j.AGCS.2025.20240108

Abstract

Abstract:

The tropospheric zenith wet delay (ZWD) is time-varying and varies with geographical locations, which has become one of the main bottlenecks restricting the accuracy or timeliness of various spatial geodetic technologies. In view of this, a prediction method based on convolutional long-short term memory (ConvLSTM) network was exploited, during which a continuation of regional historical ZWD was conducted to enhance the spatial correlation, and an incremental training was adopted to improve the attention of spatio-temporal series to sudden changing signals; finally, taking the central European region as an example, the calculation effects of the sliding window conic extrapolation, the classical ConvLSTM and the method in this paper were compared. The results show that the short-term accuracy of the sliding window conic method is equivalent to that of the classical ConvLSTM; yet, when the prediction span increases, the accuracy of the former decreases sharply, while the latter is almost unaffected. After using the incremental improvement method, the accuracy is improved by 60% on the basis of the classical ConvLSTM method; after employing the “extension+increment” method, the systematic error is even further reduced by more than 50%.

Key words: space geodesy, tropospheric wet delay, prediction of spatio-temporal series, machine learning, incremental learning

CLC Number:

P228

Haopeng FAN, Bojiao ZHANG, Zhongmiao SUN, Jinkai FENG. Prediction method of regional tropospheric wet delay based on Conv-LSTM network[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(5): 795-804.

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ConvLSTM参数	设置情况	备注
输入矩阵尺寸	41×81×7	前两维为ZWD格网尺寸，第三维为历史步长
输出矩阵尺寸	41×81×7	前两维为ZWD格网尺寸，第三维为预测步长
训练数据样本	前480个历元	—
测试数据样本	后240个历元	—
卷积核尺寸	3×3	—
激活函数	ReLU	—
优化器	Adam	—
损失函数	MSE	—
循环训练次数	50	—
时空增量策略	方法1：经典方法	方法1：无特殊设置
	方法2：相邻历元作差	方法2：利用相邻历元差值作为ConvLSTM的输入信息
	方法3：延拓+相邻历元作差	方法3：将区域ZWD向上延拓至区域内最高点所在平面（根据试验区地形数据，最高点海拔为3114 m），作差后再输入ConvLSTM网络，对预测后的结果再向下延拓至地表

方法	预报步长	最小值/mm	最大值/mm	平均值/mm	标准差/mm
滑动窗口二次曲线	1	1.4	12.0	4.7	2.1
	3	5.1	38.1	15.6	6.8
	5	9.9	72.1	30.3	12.9
	7	17.0	116.6	49.0	20.5
经典ConvLSTM	1	0.8/2.1	4.4/12.8	1.8/5.5	0.7/1.9
	3	2.4/1.8	11.9/9.2	5.6/4.2	2.3/1.4
	5	3.5/2.6	18.0/12.0	8.0/6.6	3.3/2.2
	7	4.5/4.9	22.7/18.9	10.1/10.7	4.0/3.4