Temperature profile inversion in the South China Sea under the constraint of depth-fixed temperature
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摘要: 为快速获取大范围、准实时的海洋内部结构，海面遥感数据被广泛应用于构建温度剖面垂直结构，但卫星遥感仅能获得较为准确的海洋表面或者近表层数据。为了提高全海深温度剖面的反演精度，本文以水下固定深度处温度为约束，通过径向基函数神经网络生成海表面温度和海平面高度异常等海表遥感数据与温度剖面之间的非线性映射，并对约束深度选取的理论依据进行讨论。南海海域温度剖面的反演结果表明，第1阶经验正交函数系数可以表征温跃层的垂直位移，而第1阶经验正交函数基函数极值点对应深度处的温度与第1阶经验正交函数系数之间具有强相关性。当增加该深度处温度为约束时，温跃层的反演精度比仅使用海面遥感数据约提高0.35℃，反演温度剖面的平均均方根误差约为0.33℃。Abstract: In order to quickly obtain a large-scale, quasi-real-time internal structure of the ocean, sea surface remote sensing data are widely used to construct the vertical structure of the temperature profiles, but satellite remote sensing can only obtain relatively accurate ocean surface or near-surface data. In order to improve the accuracy of temperature profile inversion, this paper takes the depth-fixed temperature as the constraint, and the nonlinear mapping between the temperature profiles and the sea surface remote sensing data such as sea surface temperature (SST) and sea level anomaly (SLA) is generated through the radial basis function (RBF) neural network, and discuss the theoretical basis for constrained depth selection. The inversion results of the temperature profiles in the South China Sea show that the first empirical orthogonal function (EOF) coefficient can characterize the vertical displacement of the thermocline. And there is a strong correlation between the temperature at the depth corresponding to the extreme point of the first EOF and the first EOF coefficient. Therefore, when the temperature at this depth is added as a constraint, the inversion accuracy of the thermocline is about 0.35℃ higher than that of only using sea surface remote sensing data, and the mean root mean square error of temperature profile inversion is about 0.33℃.
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图 2 1 200 m以浅的温度剖面
Fig. 2 Measure temperature profiles at depths shallower than 1 200 m
图 3 训练集与测试集站位的空间分布
Fig. 3 Spatial distribution of stations in the training and test sets
图 4 训练集（a）、测试集（b）温度剖面及训练集和测试集平均温度剖面（c）
灰色实线为实测温度剖面，黑色实线为平均温度剖面
Fig. 4 Temperature profiles in the training set (a) and test set (b), and mean temperature profiles of training and test sets (c)
The gray solid line represents the measured temperature profile, while the black solid line represents the average temperature profile
图 6 位置信息和遥感数据反演温度剖面的均方根误差
Fig. 6 Root mean square error of temperature profile inversion using position information and remote sensing data
图 7 不同约束温度下的温度剖面重构误差与第1阶EOF基函数的对比（归一化后）
Fig. 7 Comparison of the temperature profile reconstruction error at different confinement temperatures and the first EOF (after normalization)
图 8 训练集和测试集第1阶EOF基函数（a），温度剖面的方差（b）及 均方根误差随深度的变化（c）
Fig. 8 The first EOF (a) , variance of the temperature profiles (b) and root mean square error with depth (c) of training set and test set
图 9 第1阶EOF系数、24.5℃等温线及各剖面68 m处温度（归一化后）
Fig. 9 The first EOF coefficient, 24.5°C isotherm and temperature at 68 m of each profile (after normalization)
图 10 使用两种方法反演温度剖面的均方根误差
Fig. 10 Root mean square error of the temperature profile inversion using two methods
图 11 温度剖面反演误差随深度的分布
a. 使用位置信息和遥感数据；b. 以T68 m为约束；c. 均方根误差随深度的变化
Fig. 11 Distribution of temperature profile inversion error with depth
a. Using position information and remote sensing data; b. constrained by T68 m; c. root mean square error with depth
表 1 前6阶EOF方差贡献率及累计方差贡献率
Tab. 1 First six EOFs variance contribution and cumulative variance contribution
EOF阶次 训练集 测试集 方差贡献率/
%累计方差贡献率/
%方差贡献率/
%累计方差贡献率/
%1 68.99 68.99 69.15 69.15 2 12.02 81.01 11.82 80.97 3 7.24 88.25 7.81 88.78 4 4.05 92.30 3.96 92.74 5 2.64 94.94 2.55 95.29 6 1.55 96.49 1.91 97.20 
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表 2 深度浮动对反演温度剖面的均方根误差（RMSE）影响
Tab. 2 Influence of depth fluctuation on root mean square error (RMSE) of temperature profile inversion
实验a RMSEn RMSEm 最大值 平均值 最大值 平均值 未考虑深度浮动 0.555 3 0.367 4 0.948 3 0.3307 1 0.555 8 0.365 9 0.946 2 0.330 1 2 0.556 2 0.367 1 0.947 6 0.330 5 3 0.556 1 0.367 8 0.954 1 0.330 9 4 0.557 6 0.366 8 0.953 5 0.330 5
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表 3 温度测量误差对反演温度剖面的均方根误差（RMSE）影响
Tab. 3 Influence of temperature measurement error on root mean square error (RMSE) of temperature profile inversion
实验b RMSEn RMSEm 最大值 平均值 最大值 平均值 1 0.573 7 0.364 7 0.959 5 0.329 0 2 0.557 7 0.366 3 0.949 7 0.330 1 3 0.555 8 0.367 5 0.948 3 0.330 8 4 0.554 9 0.366 9 0.947 0 0.330 3
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表 4 深度浮动和温度测量误差对反演温度剖面的均方根误差（RMSE）影响
Tab. 4 Influence of depth fluctuation and temperature measurement error on root mean square error (RMSE) of temperature profile inversion
实验c RMSEn RMSEm 最大值 平均值 最大值 平均值 1 0.575 4 0.369 3 0.949 2 0.333 9 2 0.556 7 0.366 8 0.951 1 0.330 3 3 0.555 2 0.370 0 0.941 9 0.333 9 4 0.556 2 0.366 9 0.952 1 0.330 5
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