Optical remote sensing image characteristics of large amplitude convex mode-2 internal solitary waves: an experimental study
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Abstract: A series of experiments are designed to propose a new method to study the characteristics of convex mode-2 internal solitary waves (ISWs) in optical remote sensing images using a laboratory-based optical remote sensing simulation platform. The corresponding wave parameters of large-amplitude convex mode-2 ISWs under smooth surfaces are investigated along with the optical remote sensing characteristic parameters. The mode-2 ISWs in the experimentally obtained optical remote sensing image are produced by their overall modulation effect on the water surface, and the extreme points of the gray value of the profile curve of bright-dark stripes appear at the same location as the real optical remote sensing image. The present data extend to a larger range than previous studies, and for the characteristics of large amplitude convex mode-2 ISWs, the experimental results show a second-order dependence of wavelength on amplitude. There is a close relationship between optical remote sensing characteristic parameters and wave parameters of mode-2 ISWs, in which there is a positive linear relationship between the bright-dark spacing and wavelength and a nonlinear relationship with the amplitude, especially when the amplitude is very large, there is a significant increase in bright-dark spacing.
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Figure 1. A schematic diagram of the laboratory experiment designed to generate mode-2 internal solitary waves (ISWs) and detect them using optical remote sensing. See the text for an explanation of all parameters. CCD: charge-coupled device; LED: Light Emitting Diode.
Figure 2. An example time series diagram from Experiment 1. a. Waveforms of the internal solitary wave (ISW) from camera CCD2; b. optical remote sensing image of the ISW from camera CCD1 (y-axis is horizontal sampling width); c. y-axis is absolute gray value.
Figure 3. Details of parameter definitions describing a mode-2 internal solitary wave (ISW). a. Wave parameters of the mode-2 ISW; b. optical remote sensing characteristic parameters of the mode-2 ISW.
Figure 4. Gaofen-1 image taken north of Dongsha Islands on July 9, 2014. The blue box highlights a mode-1 internal solitary wave (ISW), and the red box highlights a mode-2 ISW. Profile data for the two ISWs are given in the insert figures. The mode-1 ISW shows dark-bright stripes, while the mode-2 ISW is the opposite.
Figure 5. Example diagram showing the matching of internal solitary wave (ISW) properties and profile curve of gray value of the associated remote sensing image. This time series was obtained from Experiment 12 (i.e., h1/H=0.288, C/H=4.29; the definitions of h1, H, C refer to Fig. 1). The left vertical axis represents the vertical sampling range in the tank, the right vertical axis represents the absolute gray value, and the horizontal axis represents the charge-coupled device camera shooting time. The blue boxes at the sampling time of about 30 s and 80 s represent the initial wave and reflected wave at the sampling location, respectively. The red curve is the profile curve of gray value recorded at the sampling location.
Figure 6. Wave parameter relationship diagrams for mode-2 internal solitary waves (ISWs). a. Relationship between average amplitude and initial step depth; b. relationship between average amplitude and average wavelength. The data points are the experimental data in this paper, and the solid black lines are the fitting of the experimental data. The black dotted lines are the experimental results of Brandt and Shipley (2014).
Figure 7. Schematic diagram of sampling location and imaging angle. A−D are all in the sun glint. Initial incident wave propagation from right to left.
$ \mathrm{\alpha } $ is the solar zenith angle, and$ \ {\beta } $ is the sensor zenith angle. LED: Light Emitting Diode; CCD: charge-coupled device.
Figure 8. Bright-dark spacing versus wavelength in internal solitary wave optical remote sensing images. a. The relationship between the bright-dark spacing and the wavelength of the upper interface; b. the relationship between the bright-dark spacing and the wavelength of the lower interface; c. the relationship between the bright-dark spacing and the average wavelength.
Figure 9. Relationship between bright-dark spacing and wavelength at different angles. The least-square fitting results of four sampling locations A (blue dotted line), B (red dotted line), C (orange dotted line), and D (green dotted line), and the fitting results of all data (black solid line) are presented.
Table 1. Experimental parameters for the 26 individual experiments performed in the study
No. H/cm h1/H h/H C/h 1 40 0.475 0.028 5.33 2 40 0.475 0.031 6.43 3 40 0.375 0.014 8.85 4 40 0.375 0.024 5.24 5 40 0.375 0.031 5.69 6 40 0.338 0.015 8.20 7 40 0.338 0.037 3.39 8 40 0.338 0.041 4.26 9 40 0.313 0.021 8.33 10 40 0.313 0.039 3.19 11 40 0.288 0.025 6.97 12 40 0.288 0.029 4.29 13 40 0.288 0.039 3.22 14 40 0.263 0.026 6.73 15 40 0.238 0.026 6.73 16 40 0.238 0.039 3.19 17 40 0.213 0.024 7.33 18 40 0.213 0.028 4.48 19 46 0.417 0.017 9.21 20 46 0.417 0.038 5.75 21 46 0.370 0.021 7.18 22 46 0.370 0.038 5.71 23 46 0.315 0.024 4.57 24 46 0.315 0.034 4.52 25 46 0.261 0.018 5.92 26 46 0.261 0.029 5.17 Note: H: total fluid depth; h1: upper layer thickness; h: characteristic thickness of the interface; C: initial step depth. 
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Table 2. Correlation coefficients between bright-dark spacing and wavelength at a series of locations along the tank
Location Solar zenith angle Sensor zenith angle Ru Rl Ra A 55.8° 51.3° 0.88 0.91 0.95 B 55.2° 53.3° 0.88 0.89 0.92 C 54.4° 55.5° 0.92 0.88 0.92 D 53.7° 57.5° 0.81 0.86 0.87
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