2.1.

HJ-1A/1B Charge-Coupled Device Data

Multitemporal optical images from the HJ-1A/1B charge-coupled device (CCD) cameras are used in this study. The satellite constellation of HJ-1A/1B was launched on September 6, 2008, which was designed for environmental and disaster monitoring and forecasting. It is an ideal observation platform for daily monitoring of the environment and of the phenomena occurring over land and coastal oceans. The CCD cameras on-board HJ-1A/1B can acquire optical data in four channels covering the visible spectra from 430 to 900 nm, with a spatial resolution of 30 m and a swath width of 360 km. HJ-1A/1B CCD image data have been widely used in monitoring the environment and natural disasters, in terms of extracting disaster background information and assessing disaster damage.²⁴

For this study, a total of 250 HJ-1A/1B images acquired from April 2009 to April 2012 were collected and investigated. Among them, 41 images containing sun glitter signals from submarine bottom topography in the TB were identified. Six cloud-free HJ-1A/1B CCD images were finally selected and processed to map and measure the sand waves in the TB. These six images are listed in Table 1. Figure 2 shows one of the six images covering the study area in true color imaged by HJ-1B CCD on May 15, 2009.

Table 1

HJ-1A/1B CCD images used in this study.

Fig. 2

The true color image covering the study area acquired by HJ-1B CCD on May 15, 2009. The subimage at the upper-right corner is the enlarged region in the yellow box, showing lots of bright and dark stripes induced by submarine sand waves.

2.2.

Sun Glitter Imaging Mechanism of Submarine Bottom Topography

According to previous research,⁶ the signals of sun glitter radiation in ocean surface images are mainly dominated by the wind speed in suitable imaging geometry when there are no effects from submarine bottom topography. However, when the sand waves are present and the water depth is considerably shallow, the sand wave hypsography will cause the current to change, influencing the sea surface flow field and sea surface roughness, and, in turn, affecting sun glitter signal intensity. The sun glitter radiation from the submarine sand waves will add to the background, and the sun glitter radiation of the region with submarine sand waves will appear conspicuously different from the adjacent region without sand waves. The response of sun glitter radiation to submarine bottom topography can be decomposed into the following four physical processes:⁷ (1) forced modulation of the sea surface current due to submarine bottom topography; (2) modulation of the sea surface wave spectrum due to the changes in surface currents, through wave–current interaction, (3) impact of the sea surface roughness due to the changes in sea surface wave spectrum, and (4) modulation of the sun glitter radiation caused by the sea surface roughness.

2.3.

Determination of Sand Waves

According to the imaging model of Alpers and Hennings,²⁵ referred to as the AH model, when the tidal flow direction is almost normal to the ridge, the sea surface roughness of the sand wave’s upstream face (smooth face) is relatively smaller than that of the sand wave’s downstream face (rough face). This implies that one side of the ridge has a smooth face and the other has a rough face. At a suitable imaging geometry, the smooth and the rough faces appear as bright and dark stripes in sun glitter images, respectively. In Fig. 3(a), which illustrates a case of a sun glitter image of HJ-1B containing sand-wave information, the sand waves appear as bright and dark stripes. Figure 3(b) shows pixel values along the red profile covering some sand waves as shown in Fig. 3(a). This also displays the change in pixel values while covering the sand-wave ridge. Figure 3(c) demonstrates corresponding water depths from MB along the same profile as in Fig. 3(a), which was obtained by R2Sonic 2024 broadband multibeam echo sounder device from May 25 to June 28 in 2012. Figures 3(b) and 3(c) show that the water depths and the pixel values vary asynchronously along the profile. In this case, it is evident that the location of a sand-wave ridge is between two adjacent bright and dark stripes, as shown in Fig. 3(b). Based on the sun glitter imaging mechanism of submarine sand waves, the sand waves and their ridges can be readily identified and drawn with the help of an image processing software, such as the ArcGIS platform. Figure 3(d) shows all the sand-wave ridges identified from the HJ-1B image shown in Fig. 3(a). Limited by the spatial resolution of HJ-1A/B CCD imagery (30 m), our results indicate that a sand wave can be determined when its ridge length and wavelength are $>200$ and 100 m, respectively.

Fig. 3

Schematic determination of sand waves. (a) Sand-wave features in sun glitter image of HJ-1B and a red profile. (b) Pixel values along the profile in (a). (c) Water depths along the profile in (a). (d) Sand-wave ridges identified from (a). In the subimage (d), the length of L is the wavelength, the curve length from point “1” to “2” labeled by black arrow, and the direction of arrow labeled as D is the direction of the ridge curve labeled by black arrow.

Following the determination of sand waves and their ridges, the directions, wavelengths, and ridge lengths of the sand waves can be measured and calculated. The distance between two adjacent sand-wave ridges is considered the sand-wave wavelength, the direction perpendicular to the sand-wave ridge is the sand-wave direction, and the ridge length is measured along the sand-wave ridge. The direction and ridge length of each sand wave are calculated by spatial topology analysis on the ArcGIS platform.

2.4.

Statistical Analysis of Sand Waves

Based on the sand waves and their parameters, their spatial distribution is statistically analyzed. The schematic process of statistical analysis of sand waves is shown in Fig. 4, which involves a simple assumption that the original direction is the north and the direction angle increases clockwise, so the eastern direction is referred to as 90 deg. First, the study area is divided into $10\mathrm{km}\times 10\mathrm{km}$ cells. A cell of HJ-1B sun glitter image and the corresponding sand waves are shown in Figs. 4(a) and 4(b), respectively. Then, the average wave direction of each cell is calculated by averaging all the sand-wave directions in the cell. The average direction is regarded as a representative direction of all the sand waves in the cell, as shown in Fig. 4(c). Third, a typical profile with the cell representative direction is selected, covering all the sand waves in the cell [Fig. 4(d)]. The average wavelength of the cell is obtained by averaging the sand-wave lengths along a typical profile. The average density (${\mathrm{km}}^{-2}$) is calculated from the ratio of the sand-wave number to area ($100{\mathrm{km}}^2$).

Fig. 4

Schematic diagram of statistical analysis of sand waves. (a) A cell of 10 km by 10 km of HJ-1B sun glitter image. (b) The sand waves determined from the image of (a). (c) The representative sand-wave direction of the cell. (d) A typical profile along the direction of (c), and the representative wavelength calculated by averaging the individual wavelength along the profile.

3.1.

Spatial Distribution of Sand Waves

The sand waves in the TB are determined and mapped using the six HJ-1A/1B images listed in Table 1, leading to the identification of a total of 4604 sand waves, which are within 117°14’ and 119°26’E, and 22°32.5’ and 23°49’N, with an east-west span of up to 228 km and a north-south span of 145 km (Fig. 5). An envelope of all the sand-wave ridges is rendered in order to obtain the distribution range of the sand waves in the TB and its area. The area of the TB has, thus, been estimated to be $\mathrm{16,400}{\mathrm{km}}^2$, which is significantly larger than the previously reported value ($\sim \mathrm{13,000}{\mathrm{km}}^2$).¹⁴ Further details of the sand waves in the TB are revealed by our analysis, especially in the northeastern, western, and northwestern parts, where little investigation has previously been carried out. With the advantage of a large swath and high temporal repeatability of HJ-1A/1B, the sand waves can be mapped more comprehensively and the highest degree of accuracy thus far is achievable for the calculation of the sand-wave spatial cover.

Fig. 5

Spatial distribution of the sand waves in TB. An envelope by the dashed line indicates the boundary of TB.

3.2.

Spatial Characteristics of Sand Waves

The spatial distribution of the sand-wave direction in the TB is illustrated in Fig. 6(a), and its histogram and probability rose diagram are shown in Figs. 6(b) and 6(c), respectively. The results from statistical analysis show that the sand-wave directions follow a normal distribution and range from 132 to 264 deg clockwise from the north (same as below), with an average direction of 190 deg and a standard deviation (STD) of 20.4 deg. In terms of the spatial distribution, the directions in the northwestern area of the TB are mostly $>190\mathrm{deg}$ and those in the southeastern area are predominantly $<190\mathrm{deg}$.

Fig. 6

Spatial distribution (a), histogram (b), and probability rose diagram (c) of sand-wave directions in TB.

A total of 1449 sand-wave wavelengths in the TB are obtained by applying the method described in Sec. 2.4. The spatial map and histogram of the wavelengths are shown in Fig. 7. The results from statistical analysis reveal a skewed distribution of the sand-wave wavelengths, which range from 76 to 2151 m, with a peak at 500 m and an average of 721 m. Regarding the spatial distribution, the wavelengths in the northwestern area of the TB are mostly $>700\mathrm{m}$, while those in the southeastern area are mostly $<700\mathrm{m}$.

Fig. 7

Spatial distribution map (a) and histogram (b) of sand-wave wavelengths in TB.

Following the method described in Sec. 2.4, the average densities of 10-km grids are calculated, the distribution and density of which are shown in Fig. 8. Statistical analysis shows that the density also has a skewed distribution. The average density ranges from 0.035 to $1.090{\mathrm{km}}^{-2}$, with an average of $0.359{\mathrm{km}}^{-2}$ and an STD of $0.221{\mathrm{km}}^{-2}$, which implies that in the TB there are at least three or four sand waves in a 10-km grid (of $100{\mathrm{km}}^{-2}$), and at the most 109 sand waves. Regarding the spatial distribution, the density of the southeastern area of the TB is relatively higher. Moreover, the density along the boundary of the TB is lower, generally $<0.200{\mathrm{km}}^{-2}$.

Fig. 8

Spatial distribution (a) and histogram (b) of sand-wave density in TB.

The ridge length of each sand wave is calculated by spatial topological analysis. All the sand-wave ridges in the TB are illustrated in Fig. 9(a), and the histogram of the ridge length distribution is shown in Fig. 9(b). Statistical analysis shows that ridge length has a strongly skewed distribution, being mostly $<3000\mathrm{m}$. The ridge length ranges from 254 to 19,992 m, with the peak distribution at $\sim 1500\mathrm{m}$ and the average at 2453 m. Spatially, the sand waves with a ridge length $<3000\mathrm{m}$ are distributed in the whole area of the TB, and those with a ridge length $>10\mathrm{km}$ are observed in three regions, namely, the northwestern, the southwestern, and the northeastern regions.

Fig. 9

Spatial distribution (a) and histogram (b) of sand-wave ridge length in TB.

5.1.

Regional Division of the Taiwan Banks

As shown in Figs. 6 to 9, the direction, wavelength, density, and ridge length of the sand waves differ from one region to another. Figure 11 illustrates the distribution of direction and wavelength of the sand waves in the 10-km grid. The sand waves in the northwestern subregion of the TB display a northeast-southwest direction, while those in the southeastern subregion are oriented in a north-south direction.

Fig. 11

Spatial distributions of direction and wavelength of the sand waves in 10-km grid. TB can be divided into two subregions in terms of direction and wavelength of the sand waves. The direction and length of each red double-head arrow represent the average direction and average wavelength of sand waves in a 10-km grid, respectively.

Two different subregions in the TB in terms of direction and wavelength of the sand waves is, therefore, obvious (Fig. 11). The northwestern and southeastern subregions have areas of $\sim 7400{\mathrm{km}}^2$ and $9000{\mathrm{km}}^2$, respectively. There are 1495 sand waves in the northwestern subregion, which is about one third of the total number of sand waves in the TB. There are 3109 sand waves in the southeastern subregion.

5.2.

Statistical Analysis of Sand Waves

Following the division of the TB into two subregions, some statistical analyses of sand-wave direction, wavelength, density, and ridge length in the two subregions were performed and the results are listed in Table 2.

Table 2

Direction, wavelength, density, and ridge length of sand waves in the two subregions of the Taiwan Banks.

The count histogram of directions and the probability rose diagram in the subregions are illustrated in Fig. 12. The sand waves in both subregions follow a normal distribution. In the northwestern subregion, the sand waves are mainly aligned in the northeast-southwest direction, with an average direction of 210 deg, while $>50\%$ of the directions range from 200 to 220 deg. The average direction in the southeastern subregion is 180 deg and $>50\%$ of the directions range from 170 to 190 deg.

Fig. 12

Count histogram (a) and probability rose diagram (b) of sand-wave directions in the two subregions.

The wavelengths in the two subregions have distinct distributions, as illustrated by the histograms (Fig. 13). The wavelengths in the northwestern subregion are between 600 and 1250 m, while those in the southeastern subregion are relatively shorter, between 350 and 900 m. The average wavelength in the northwestern subregion is 950 m, much longer than that in the southeastern subregion (610 m). The histogram also reveals that the wavelength of 900 m is a dividing crest. The wavelengths $<900\mathrm{m}$ in the southeastern subregion are significantly more abundant than in the northwestern subregion, while those $>900\mathrm{m}$ are more abundant in the northwestern subregion than in the southeastern subregion.

Fig. 13

Count histogram of sand-wave wavelength in the two subregions.

The count histograms of density in the two subregions illustrate that the average density in the southeastern subregion ranges from 0 to 1.1, with an average of 0.438, while that in the northwestern subregion ranges from 0.1 to 0.7, with an average of 0.294 [Fig. 14(a)]. Overall, the density in the southeastern subregion is comparatively higher. Both density and wavelength can describe the sand-wave development. A scatter diagram of wavelength versus density is plotted in Fig. 14(b). In the low-density areas, the wavelengths vary widely from 200 to 2000 m. However, in the areas of higher density, the sand waves consistently have shorter wavelengths. Therefore, although there are fewer sand waves in the low-density area, their wavelengths may be long or short. In the high-density area, the sand waves are more abundant, and the wavelengths (distance between two adjacent sand-wave ridges) are shorter.

Fig. 14

Count histogram of sand-wave density in the two subregions (a) and wavelength versus density of the sand waves in the two subregions.

The average ridge lengths of the sand waves and their ranges in the two subregions are similar (Table 2, Fig. 15), but long ridges are more abundant in the northwestern subregion. The ridge-length frequency distribution for each subregion is determined by plotting the exceedance probability versus length. This parameter represents the probability ($y$ axis) that a given sand wave will be equal to or greater than a given length²³ [$x$ axis; Fig. 15(b)]. For each subregion, the ridge-length frequency distribution shows a large number of short sand-wave ridges and a small number of longer structures. However, the northwestern subregion contains fewer long sand-wave ridges. For example, a given sand-wave ridge in the northwestern subregion has a 10% probability ($\text{exceedance probability}>0.90$) of being equal to or longer than 6000 m. A ridge in the southeastern subregion, however, has an equivalent probability of being only 4500 m (or longer). In other words, the ridge lengths $>5\mathrm{km}$ account for 12.5% in the northwestern subregion and only 7.8% in the southeastern subregion. The ridge lengths $>10\mathrm{km}$ account for 2.1 and 0.4% in the northwestern subregion and southeastern subregion, respectively.

Fig. 15

Count histogram of sand-wave ridge length in the two subregions (a) and log-log plot of ridge length versus exceedance probability (b). In (b), the $y$ axis represents the probability that a given ridge is equal to or longer than a given area ($x$ axis). Exceedance probability is calculated based on the observed length frequency distribution of sand waves in each subregion.

5.3.

Hydrodynamic Influence on Sand Waves

The tidal nature of the bottom current is an important factor in the heterogeneous distribution of sand-wave features in the TB. The large-scale sand waves represent certain obstacles for the bottom current. Interactions between currents and sand waves may affect sand-wave features, such as direction, wavelength, density, and ridge length. The direction of current, PAC speed, and PAR of the current are three important parameters of the current regime. Here, quantitative analyses of bottom-current data against various sand-wave parameters are presented.

The average direction of PAC and the average direction of sand waves are derived from each 10-km grid, and they have a considerable correlation ($R^2=0.7643$; Fig. 16). In the northwestern subregion, the two directions are in the northeast-southwest direction, while in the southeastern subregion, they are along the north-south direction. According to previous studies,^28–30 the current in the northwestern subregion is dominated by a coastal current along the mainland coast in the northeast-southwest direction, while the current in the southeastern subregion flows closely along the north-south direction in most seasons. Results obtained by Shao confirmed that the sand-wave directions are generally aligned along the current directions in the TB.⁷ Therefore, the current is the dominant force for sand-wave formation in the TB, and its dominant direction controls the sand-wave orientation.

Fig. 16

Plot of direction of sand wave versus direction of principal axis current (PAC). There is a strong positive correlation ($R^2=0.7643$) between the two directions.

The PAC strength is another important factor for sand-wave shape and distribution. The quantitative relationships between PAC speed and wavelength, density, and ridge length are shown in Fig. 17, which do not show any significant correlations. All three correlation coefficients are low ($R^2=0.2673/R^2=0.1933/R^2=0.0310$). Wavelength has a very weak negative correlation with the PAC speed, whereas density has a very weak positive correlation. A larger current speed could induce a stronger disturbance on the bottom sediment, and the sediment particles may be frequently resuspended and deposited. The physical process has an impact on the formation of sand waves, resulting in smaller spacing and higher density.

Fig. 17

Plots of PAC speed versus wavelength (a), density (b), or ridge length (c). All three correlation coefficients are very low.

Another parameter of current regime is the PAR of the current, which is used to describe the frequency of varying current directions. The quantitative relationships between PAR and wavelength, density, and ridge length are shown in Fig. 18, where no significant correlations are observed. The highest correlation coefficient is only 0.1340 ($R^2$) between PAR and density. The plot depicts a weak trend, namely, a slowly increasing density with increasing PAR. It is also evident that both longer wavelengths and ridge lengths are distributed in the lower PAR area. For example, almost all the wavelengths $>1300\mathrm{m}$ and ridge lengths $>4000\mathrm{m}$ are located in the area with PAR $<0.3$. In these smaller PAR areas, the PAC is strong and the current direction is more stable. The more stable direction is an advantage for the formation of larger sand waves (longer wavelength and ridge length), and therefore, it is one of the essential conditions. In contrast, the higher PAR could induce a stronger disturbance on the bottom sediment, and the sediment particles may frequently get resuspended and deposited under the current with varying directions. The result shows that shorter wavelength and ridge length as well as higher density exist in higher PAR areas.

Fig. 18

Plots of current principal axis ratio versus wavelength (a), density (b), or ridge length (c). All three correlation coefficients are very low.

The above correlation analysis indicates that the direction of the sand waves is consistent with the direction of the dominant current. Even when the dominant current and PAR do not significantly determine the shape, size, and distribution of the sand waves, hydrodynamic conditions still influence sand waves to a certain degree.

5.4.

Water Depth Influence on Sand Wave

In addition to the controlling effect of the tidal current, water depth is another important influencing factor on sand waves. Previous research on the TB had revealed that longer-wavelength sand waves exist in the deeper water region, and shorter-wavelength sand waves exist in the shallow water region.⁷ For example, the western TB has deeper water depths, with an average depth of 35 m, longer wavelength (1000 to 1800 m), and lower amplitude ($<6\mathrm{m}$), while the eastern TB has relatively a shallower water depth ($<15\mathrm{m}$), shorter wavelength (500 to 1000 m), and higher amplitude (average of 15 m). The current study, based on comprehensive sand-wave information, attempts to discuss the distribution of sand waves in different water depths and analyze the correlation between water depth and wavelength, density, and ridge length.

By overlaying the boundary of the sand waves on the water-depth map obtained from nautical charts [Fig. 19(a)], it is revealed that the water depths of the sand-wave region primarily range from 10 to 50 m, with an average of 23.3 m. Most of the area with a depth from 10 to 30 m is covered by sand waves. The probability of a different water-depth area is calculated and shown in Fig. 19(b). Among them, the highest probability is 43% at a depth range from 20 to 30 m, which covers about half of the area in the TB. The next depth range is from 10 to 20 m, $\sim 38\%$, and is mainly located in the western TB. The area deeper than 30 m is $\sim 17\%$ and is distributed along the boundary of the TB. There is only an $\sim 2\%$ area shallower than 10 m in the central TB.

Fig. 19

Spatial distribution of water depth and boundary in TB (a) and probability of different depths in TB (b).

The average water depths of 10-km grids are derived and used to analyze the correlation between water depth and wavelength, density, and ridge length. The results are plotted in Fig. 20. Among them, the density has a certain negative correlation with the water depth ($R^2=0.4677$), which indicates that the density in shallow water is higher than that in deep water. Though the other two correlation coefficients are very low, the scatter diagrams still reveal that numerous sand waves are developed in shallow water (10 to 20 m) and that the sand waves with long wavelengths or ridge lengths are located in water with a depth close to 30 m. Considering the above analysis, shallow water depth might be a necessary condition for intensive sand waves, but large-scale sand waves need a moderate depth, e.g., 30 m.

Fig. 20

Plots of water depth versus wavelength (a), density (b), or ridge length (c). Only the sand-wave density has certain negative correlation with water depth ($R^2=0.4677$).