Simulation analysis for remote sensing inversion of wavelength and water depth by the Fast Fourier Transform method
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摘要: 利用海浪波峰和波谷位置的遥感影像信息差异，可以基于快速傅里叶变换（FFT）方法反演波长，进而反演近岸水深.本文采用理想波面数据和数值模拟波面数据代替遥感资料进行仿真研究，讨论资料分辨率和子图长度对海浪波长及水深反演的影响.研究结果表明：低分辨率资料反演波长和水深的效果差，但是当资料分辨率达到一定要求时，再提高资料分辨率对波长和水深反演结果没有影响.当波长不存在空间变化时，子图越大，波长反演误差越小.在非均匀变化的地形上，子图长度为4~8倍波长、并且小于或等于地形变化尺度时，波长和水深反演误差小，子图太大或太小时，波长和水深反演误差都增大.Abstract: Using the difference in remote sensing reflectivity between wave crest and trough, wavelengths can be inversed by the Fast Fourier Transform (FFT) method to derive the nearshore water depth. Remote sensing images with higher resolution are generally thought to induce less error in marine information inversion. In this study, remote sensing images were replaced by elevation data from ideal equations and numerical simulations to study the effect of data resolution on wavelength inversions and water depths. The results show that low-resolution data result in significant errors in the wavelengths and water depths. But variations in resolution make no difference in reversing the wavelengths and water depths as they reach certain levels. The sub-image size in the FFT method was also studied by simulation analysis. Larger sub-images generate less error in wavelength inversion if the wavelength doesn't vary spatially. On uneven topography, errors from wavelength and water depth inversions are small if the sub-image size is 4-8 times the wavelength and not more than the topography variation; however, when the sub-image is too large or too small, the errors will increase.
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图 1 不同分辨率的波面资料计算的波数能量谱
注: 波面资料的波长为70m, 子图为512m; (b)为(a)中红色框部分的放大显示图; 谱能量为归一化到0~255的值; (b)中重合点为0.25m, 0.5m, 2m, 8m, 16m和32m的谱能量峰值点
Fig. 1 Wavenumber spectrum calculated by elevation data using different resolutions
图 3 FUNWAVE对波浪水槽实验中(1)-(8)断面波高的模拟检验
注: 实线为计算值, 圆圈为水槽实验值
Fig. 3 Waveheight test to FUNWAVE simulating the wave flume experiment at sections of (1)-(8)
图 5 在斜坡地形上基于数值模拟仿真数据反演的波长和地形
注: (a)-(d)的子图长度分别为128、256、512、1 024m
Fig. 5 Wavelengths and topographies from inversions using the simulated elevation data on a slope
图 6 在斜坡地形上32m分辨率资料反演的波长和地形
Fig. 6 Wavelengths and topographies from inversions using the simulated elevation data with 32 m resolution on a slope
图 7 在沙坝地形上子图长度512 m反演的波长和地形
注: (a)-(d)的沙坝地形呈椭圆形, 其长半轴分别为125、250、500和1 000 m
Fig. 7 Wavelengths and topographies from inversions using the simulated elevation data on bars
表 1 波长为70m的理想波面资料反演的波长
Tab. 1 Wavelengths from inversions by elevation data at a wavelength of 70 m
m 子图长度 不同分辨率资料反演的波长 0.25m 0.5m 1m 2m 4m 8m 16m 32m 64m 64m 64 64 64 64 64 64 64 64 - 128m 64 64 64 64 64 64 64 64 - 256m 64 64 64 64 64 64 64 64 - 512m 73 73 73 73 73 73 73 73 512 1 024m 68 68 68 68 68 68 68 68 1 024 
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表 2 波长为90m的理想波面资料反演的波长
Tab. 2 Wavelengths from inversions by elevation data at a wavelength of 90 m
m 子图长度 不同分辨率资料反演的波长 0.25m 0.5m 1m 2m 4m 8m 16m 32m 64m 64m 64 64 64 64 64 64 64 64 - 128m 128 128 128 128 128 128 128 128 128 256m 85 85 85 85 85 85 85 85 256 512m 85 85 85 85 85 85 85 85 256 1 024m 93 93 93 93 93 93 93 93 205
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表 3 波长为110m的理想波面资料反演的波长
Tab. 3 Wavelengths from inversions by elevation data at a wavelength of 110 m
m 子图长度 不同分辨率资料反演的波长 0.25m 0.5m 1m 2m 4m 8m 16m 32m 64m 64m - - - - - - - - - 128m 128 128 128 128 128 128 128 128 - 256m 128 128 128 128 128 128 128 128 128 512m 102 102 102 102 102 102 102 102 128 1 024m 114 114 114 114 114 114 114 114 146
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表 4 组合波动(振幅之比1.2)的理想波面资料反演的波长
Tab. 4 Wavelengths from inversions by elevation data including two fluctuations with an amplitude ratio of 1.2
m 子图长度 不同分辨率资料反演的波长 0.25m 0.5m 1m 2m 4m 8m 16m 32m 64m 64m 64 64 64 64 64 64 64 64 - 128m 64 64 64 64 64 64 64 64 128 256m 64 64 64 64 64 64 64 128 128 512m 102 102 102 102 102 102 102 102 170 1 024m 68 68 68 68 68 68 68 102 170
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表 5 组合波动(振幅之比1.6)的理想波面资料反演的波长
Tab. 5 Wavelengths from inversions by elevation data including two fluctuations with an amplitude ratio of 1.6
m 子图长度 不同分辨率资料反演的波长 0.25m 0.5m 1m 2m 4m 8m 16m 32m 64m 64m 64 64 64 64 64 64 64 64 - 128m 64 64 64 64 64 64 64 64 - 256m 64 64 64 64 64 64 64 64 - 512m 73 73 73 73 73 73 73 73 512 1 024m 68 68 68 68 68 68 68 68 1 024
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表 6 在斜坡地形上利用数值模拟仿真数据反演水深的误差统计
Tab. 6 Errors of water depths from inversions using the simulated elevation data on a slope
子图长度 0-3 m水深段的误差统计 3-12 m水深段的误差统计 12-20 m水深段的误差统计 平均绝对
误差/m平均相对
误差/%平均绝对
误差/m平均相对
误差/%平均绝对
误差/m平均相对
误差/%128m 0.45 19.59 1.71 23.19 7.50 48.13 256m 0.29 12.34 1.65 19.02 2.24 15.22 512m 0.23 10.34 0.56 7.62 1.77 11.44 1 024m 0.48 21.43 0.35 4.89 1.21 7.20
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表 7 在沙坝地形上利用数值模拟仿真数据反演水深的误差统计
Tab. 7 Errors of water depths from inversions using the simulated elevation data on bars
沙坝尺寸 子图长度128 m时 子图长度256 m时 子图长度512 m时 子图长度1 024 m时 平均绝对
误差/m平均相对
误差/%平均绝对
误差/m平均相对
误差/%平均绝对
误差/m平均相对
误差/%平均绝对
误差/m平均相对
误差/%125m 1.37 27.91 0.79 16.37 1.27 30.12 3.05 72.04 250m 1.37 28.87 0.73 15.82 1.08 20.93 2.99 66.83 500m 0.95 19.39 0.70 15.36 0.47 10.64 1.21 23.14 1 000m 1.47 21.16 1.26 16.27 0.62 10.29 1.09 19.43
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