Retrieving shallow bathymetry by integrating spatial autocorrelation features with machine learning
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摘要: 基于多光谱影像的水深反演方法是获取近岸水深信息的高效手段，然而反演精度低一直是制约其广泛应用的瓶颈。本文聚焦于实测水深与多光谱数据自身的空间自相关特性，提出在机器学习框架下将学习样本的空间自相关特征与统计互相关特征相结合，以提高水深反演精度。西沙北岛海域的实验结果表明：在实测数据量较小的情况下，相比传统机器学习，顾及自相关特征的新方法可获得18%的精度提升；而当实测数据量充足时，精度提升可达到27%。结果表明，将数据源的空间自相关特征融入机器学习算法中，可显著提升多光谱水深反演结果的精确性，进而为浅海海洋研究提供有效数据支撑。Abstract: Retrieving shallow water depth based on multispectral satellite imagery is highly cost-effective. However, the extensive application of satellite-derived bathymetry has been restricted by its low prediction accuracy. To improve about the accuracy of the retrieved bathymetry, spatial autocorrelation features within the in situ depth measurements and the multi-spectral image are focused in this research. To this end, we develop a machine learning method combining with spatial autocorrelation features and statistical intercorrelation features of learned samples. The experimental results of Xisha Beidao show that compared with the traditional machine learning, the accuracy of the new method is improved by 18% when the number of in situ depths is small. On the contrary, when the number of in situ depths is large, an improvement of 27% in root mean square error is achieved. This demonstrates that incorporating the spatial autocorrelation features of data sources into the machine learning can significantly improve the prediction accuracy, and then provide effective data support for shallow ocean research.
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Key words:
- bathymetry retrieval /
- random forest /
- machine learning /
- spatial autocorrelation
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图 3 北岛地理位置（a）及原位水深点测量分布（b）
Fig. 3 Location of Beidao (a) and distribution of in situ depth measurements (b)
图 5 全局的全局莫兰指数及半方差的变化
Fig. 5 Global Moran’s I and semivariance with different lags of variable
图 6 对数比值（a）、普通克里金（b）、随机森林（c）和空间自相关随机森林（d）模型反演水深散点图（训练数量为150）
Fig. 6 Scatter diagram of predicted depth values by Stumpf (a), ordinary Kriging (b), random forest (c), and spatial autocorrelation random forest (d) models (the number of training data points is 150)
图 7 对数比值（a）、普通克里金（b）、随机森林（c）和空间自相关随机森林（d）模型的残差散点图（训练数量为150）
Fig. 7 Scatter diagram of residual error by Stumpf (a), ordinary Kriging (b), random forest (c), and spatial autocorrelation random forest (d) models (the number of training data points is 150)
图 8 训练样本量500时残差分布直方图（a）和不同训练数据占比下的均方根误差（b）
Fig. 8 The histogram of error distribution when the training sample is 500 (a) and root mean square error for different training data shares (b)
图 9 反演的陆域与水下地形图（a）和地貌细节图（b）
a图分辨率为2 m；b图左列为卫星影像，右列为反演的海底地形
Fig. 9 Bathymetry retrieval of onshore and inversion bathymetric topographic map (a) and geomorphic details (b)
The resolution is 2 m in a; the left are the satellite images and the right are the retrieved bathymetric topographies in b
表 1 研究区变量的全局莫兰指数、Z值和P值
Tab. 1 Global Moran’s I, normalized Z value and P value of variables in the study area
环境变量 莫兰指数 Z值 P值 水深 0.511 8.853 0.001 蓝光波段 0.631 10.967 0.001 绿光波段 0.501 8.954 0.001 红光波段 0.301 5.531 0.001 
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表 2 验证数据测试精度对比
Tab. 2 Accuracy comparison of different methods
方法 均方根误差/m 平均绝对误差/m 决定系数 对数比值模型 2.067 1.608 0.797 普通克里金模型 1.894 1.487 0.845 随机森林模型 1.635 1.058 0.888 空间自相关随机森林模型 1.338 0.998 0.923
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