Integration of machine learning and physical models for the reconstruction of mesoscale eddy sound speed profile
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摘要: 针对中尺度涡内声速剖面结构复杂且重构误差显著偏大的问题，本文采用多源卫星遥感数据和Argo剖面，结合随机森林算法和中尺度涡统一结构模型，提出了PIRF-DEN模型。通过将海表面温度、高度异常、盐度、密度等海表环境参数与Argo密度作为输入，建立了“水面-水下”声速映射关系。同时，基于中尺度涡统一结构模型重构涡旋内密度场，将海表环境参数和涡旋重构密度输入映射关系并重构了涡旋内声速剖面。研究结果表明，PIRF-DEN模型显著提高了声速剖面的重构精度，MAE和RMSE分别降至
0.8324 m/s和1.3869 m/s，较传统的sEOF-r方法降低了87.3%和83.7%，且声速重构精度和稳定性优于现有模型。-
关键词:
- 声速重构 /
- 随机森林 /
- 中尺度涡统一结构模型 /
- 垂向密度
Abstract: To address the issue of complex sound speed profile (SSP) structures and significantly large reconstruction errors within mesoscale eddies, this study proposes the PIRF-DEN model by integrating multi-source satellite remote sensing data and Argo profiles with a random forest algorithm and a unified mesoscale eddy structure model. By utilizing sea surface temperature, height anomaly, salinity, density, and other environmental parameters at the sea surface, along with Argo density data as inputs, the model establishes a "surface-to-underwater" sound speed mapping relationship. Additionally, it reconstructs the density field within eddies based on the unified mesoscale eddy structure model and incorporates both surface environmental parameters and reconstructed eddy densities into the mapping relationship to reconstruct the SSP within the eddies. The results demonstrate that the PIRF-DEN model markedly enhances the accuracy of SSP reconstruction, reducing the Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) to0.8324 m/s and1.3869 m/s, respectively. This represents an 87.3% and 83.7% reduction compared to the traditional sEOF-r method. Furthermore, the sound speed reconstruction accuracy and stability of the PIRF-DEN model surpass those of existing models. -
图 4 四种SSP重构方法在各深度层的声速MAE和RMSE
Fig. 4 The MAE and RMSE of sound speed for four SSP reconstruction methods across various depth layers
图 5 四种SSP重构方法在各Argo站位处的声速误差，其中1−4行分别为PIRF-DEN、RF、sEOF-RF和sEOF-r的声速平均误差，1−2列分别为四种方法的声速平均MAE和平均RMSE。
Fig. 5 Sound speed errors of the four SSP reconstruction methods at various Argo stations, where rows 1−4 represent the average sound speed errors for PIRF-DEN, RF, sEOF-RF, and sEOF-r, respectively, and columns 1−2 show the MAE and RMSE of sound speed for the four methods.
图 6 1号涡SSP重构效果一览图。其中(a)为1号涡及其内部Argo站位示意图，红线为其边缘轮廓，五角星的位置为其涡心所在位置，黑点为Argo观测站位；(b)为声速MAE分布；(c)为声速RMSE分布；(d)为四种方法重构的平均SSP与经验公式计算的平均SSP对比
Fig. 6 Summary of SSP reconstruction of vortex No. 1. (a) Schematic of Vortex No. 1 and Internal Argo Stations. The red line outlines the vortex boundary, the pentagram marks the vortex center, and black dots indicate Argo observation stations; (b) Sound Speed MAE Distribution; (c) Sound Speed RMSE Distribution; (d) Compare the mean SSP reconstructed by the four methods with the mean SSP calculated by the empirical formula
图 7 2号涡SSP重构效果一览图，各分图的具体含义与图9类似。
Fig. 7 Summary of SSP reconstruction of vortex No. 2, the specific meaning of each sub-diagram is similar to Figure 6.
图 8 3号涡SSP重构效果一览图，各分图的具体含义与图9类似
Fig. 8 Summary of SSP reconstruction of vortex No. 3, the specific meaning of each sub-diagram is similar to Figure 6
图 9 密度重构误差与SSP重构误差相关性，其中a～c分别代表1～3号涡
Fig. 9 The correlation between density reconstruction error and SSP reconstruction error, where a~c represent eddies 1 to 3, respectively
表 1 数据信息
Tab. 1 Data Information
数据名称 要素 时间分辨率 覆盖时间 空间分辨率 Argo 温度和盐度 1 d 1997年1月～
2024年3月— DUACS SLA 1 d 0.25°×0.25° GHRSST OISST 1 d 0.05°×0.05° CNR SSS和SSD 1 d 0.125°×0.125° ARMOR 3D 温度和盐度 1 w 0.25°×0.25° 
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表 2 前5模态的方差贡献率（%）
Tab. 2 Variance contribution rates (%) of the first five modes
模态数 1 2 3 4 5 方差贡献率 91.76 4.97 1.81 0.76 0.29
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表 3 四种SSP重构方法的评估系数
Tab. 3 Evaluation metrics for the four SSP reconstruction methods
评估系数 SSP重构方法 PIRF-DEN RF sEOF-RF sEOF-r MAE 0.83 3.66 5.84 6.56 RMSE 1.39 5.42 8.28 8.51
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表 5 观测涡旋信息
Tab. 5 Observation of vortex information
编号 涡旋类型 涡心坐标 半径/km 观测仪器 观测时间 站位数/个 1 反气旋涡 29.625°N, 147.168°E 101.38 Argo 2014.3.29 15 2 气旋涡 31.25°N, 157.625°E 63.14 XCTD 2014.6.26 12 3 反气旋涡 35.5°N, 155.5°E 99.34 XCTD 2022.6.23 11
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表 6 四种SSP重构方法在实测涡处的重构效果
Tab. 6 Reconstruction performance of the four SSP reconstruction methods at observed vortex locations
重构方法 MAE/(m/s) RMSE/(m/s) 1号涡 2号涡 3号涡 1号涡 2号涡 3号涡 PIRF-DEN 1.06 1.90 2.60 1.39 2.30 3.23 RF 0.80 5.53 2.88 1.01 5.92 3.38 sEOF-r 1.50 1.95 2.07 1.80 2.28 2.36 sEOF-RF 6.10 1.66 6.97 6.62 1.99 7.34
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