Quantitative Analysis of the Waterline Method for Topographical Mapping of Tidal Flats : A Case Study in the Dongsha Sandbank , China

Although the topography of tidal flats is important for understanding their evolution, the spatial and temporal sampling frequency of such data remains limited. The waterline method has the potential to retrieve past tidal flat topography by utilizing large archives of satellite images. This study performs a quantitative analysis of the relationship between the accuracy of tidal flat digital elevation models (DEMs) that are based on the waterline method and the factors that influence the DEMs. The three major conclusions of the study are as follows: (1) the coverage rate of the waterline points and the number of satellite images used to create the DEM are highly linearly correlated with the error of the resultant DEMs, and the former is more significant in indicating the accuracy of the resultant DEMs than the latter; (2) both the area and the slope of the tidal flats are linearly correlated with the error of the resultant DEMs; and (3) the availability analysis of the archived satellite images indicates that the waterline method can retrieve tidal flat terrains from the past forty years. The upper limit of the temporal resolution of the tidal flat DEM can be refined to within one year since 1993, to half a year since 2004, and to three months since 2009.


Introduction
Tidal flats (also known as intertidal zones) are areas between the mean high tide and mean low tide lines [1].They are important coastal geomorphologic systems that provide habitats for wildlife, resources for land reclamation, and protection for the coast against extreme storm events [2,3].However, tidal flats have been considered economically unimportant areas in the past, and knowledge of their past topography is limited by the poor accessibility and significant temporal dynamics of the tidal flats, technical and financial limitations, and indifference.It is impossible to retrieve tidal flat topography of the past few years or even decades by using ground surveys, ship-based echo-sounding, airborne stereo-photogrammetry, airborne light detection and ranging (LiDAR), or airborne interferometric synthetic aperture radar (INSAR) [4][5][6][7].
The widely used waterline method, which uses a time series of satellite images taken during different tidal periods to map the topography of a tidal flat, may be the only method with the potential to retrieve digital elevation models (DEMs) of tidal flats from the past because of the massive number of archived satellite images taken by various types of satellites.Over the past forty years, numerous space-borne platforms with increasing spatial, temporal, and spectral resolutions have been deployed by the public and private sectors.For example, the Landsat 1-5 and 7 satellite series acquired and archived more than 434 terabytes of satellite images from 1972 to 2003 [8].Remotely sensed images have been estimated to be acquired at the rate of several terabytes per day [9].The large numbers of archived images that cover broad areas of the coasts provide sufficient data to map the topography of tidal flats [10][11][12][13][14][15][16][17][18][19][20].However, little is known about the factors that control the accuracy of DEMs that are based on the waterline method, possibly due to the lack of the synchronous validation data and the low utilization of archived satellite images.The lack of such knowledge may hinder researchers in constructing, interpreting, and applying tidal flat DEMs to understand the evolution of tidal flats.This study aims to close this knowledge gap and investigate the factors that influence the accuracy of DEMs that are based the waterline method.The article is organized as follows.The second section introduces the study area, the Dongsha Sandbank, and the data collection process.The third section describes the rationale of the waterline method and the factors that potentially influence the results.In the fourth section, the correlation between the accuracy of the resultant DEMs and the influencing factors is quantitatively analyzed.

Study Area
The Dongsha Sandbank (Figure 1) is one of the largest offshore sandbanks in the South Yellow Sea Radial Sand Ridges (SYSRSR), which are the largest tidal sand ridges on the Chinese continental shelf [21].The Dongsha Sandbank has an area of more than 1,267 km 2 above the sea chart datum [22,23].The Dongsha Sandbank is a macro-tidal area with an average tidal range of 3.9-5.5 m and exhibits an irregular semi-diurnal tide [24].During the high water periods, most of the Dongsha Sandbank is submerged in the sea [25].In addition, the Dongsha Sandbank suffers significant erosion during tropical storms, which occur in the summer and autumn [26].
The Dongsha Sandbank was selected as a test site to explore the sensitivity of the waterline method for three reasons.First, Dongsha Sandbank is a large offshore tidal sandbank, and typical landforms (such as bare tidal flats, tidal ridges, tidal creeks, and tidal basins) are well developed [22].Second, almost all of the available high-quality medium-resolution satellite images (a total of 705 images) taken by various sensors from 1973 to 2012 have been collected, and all of the available MODIS images have been collected.Third, other essential data from the Dongsha Sandbank, including hourly tidal gauge data from 1973 to 2012 and LiDAR DEMs measured in 2006, were collected by the research team.

Data Sets
The following materials were collected for the quantitative analysis of the waterline method: 1) Preview satellite images.A total of 2,494 preview satellite images that cover the study area were collected.The images were taken from common civilian medium spatial-resolution satellite sensors, including the Landsat Multispectral Scanner System (MSS), Thematic Mapper (TM), Enhanced Thematic Mapper Plus (ETM+), Japanese Marine Observation Satellite (MOS) Multispectral Electronic Self-Scanning Radiometer (MESSR), Japanese Earth Resources Satellite (JERS) Synthetic Aperture Radar (SAR), Indian Remote-Sensing Satellite (IRS) Linear Imaging Self-Scanning Sensor (LISS), Advanced Wide-Field Sensor (AWiFS), China-Brazil Earth Resources Satellite (CBERS) Charge Coupled Device (CCD), Chinese Beijing-1 CCD, Chinese HJ CCD, European Remote-Sensing Satellite (ERS) SAR, and the Environmental Satellite (Envisat) Advanced Synthetic Aperture Radar (ASAR).Details of the image sources are listed in Table 1.Of all the preview satellite images, 852 images are high-quality (cloud-free and containing clear waterlines).2) Medium spatial-resolution satellite images.A total of 231 medium-resolution satellite images taken during different tidal periods in 1973-1977, 1980-1981, 1990-1991, 2000, 2006, 2007, 2008, 2009, and 2010 were obtained from several sensors, including Landsat MSS/TM/ETM+, MOS-1 MESSR, SPOT HRV, IRS-P6 LISS/AWiFS, CBERS-1/2 CCD, Beijing-1 CCD, HJ-1 A/B CCD, JERS SAR, and ERS-1/2 SAR (Table 2).The spatial resolution of these satellite images varies from 10 m to 80 m.All the satellite images are of high-quality.1) Extract the waterlines from the time-series of satellite images.The locations (x, y) of the waterland boundary are extracted from the satellite images.
2) Simulate the water level at the time of satellite overpass.The water level (h) relative to a datum is calculated from transect data, tide gauge data, or a hydraulic model.
3) Assign a water level to each discrete waterline point.All of the waterlines are discretized to points and are then assigned water levels that correspond to the time of acquisition.
4) Interpolate the tidal flat DEM.All of the waterline points over a specific period are merged into a waterline-point dataset, and a gridded DEM is created using spatial interpolation techniques.
All of the topographic maps hereinafter were generated using an identical, homogeneous processing methodology, described above.

Potential Errors in the Waterline Method
The terrain of tidal flats is spatio-temporally dynamic due to variations in the tides, waves and other sedimentary factors [14].The waterline method is proposed based on the following assumptions: 1) a sufficient number of satellite images was taken over a short time period, so the variation in the topography over the tidal flats can be reasonably neglected [20]; 2) high-quality satellite images taken at various water levels were collected and can be used to construct a DEM over a given inter-tidal zone [19]; 3) the waterlines in a given satellite image accurately indicate the water level.Hence, the errors in tidal flat DEMs lie not only in the planar dimension (x, y) and the vertical dimension (z) but also in the temporal dimension (t).Errors in tidal flat DEMs generated using the waterline method may be introduced at each stage and can be caused by the number of the satellite images used or the characteristics of the tidal flat (Figure 2b).The errors are summarized as follows: 1) Positional error introduced during the geo-correction and waterline extraction processing of the satellite images.The error introduced in the geo-correction process may result in positional distortion of the waterlines in the satellite images.In most cases, the total root mean square error (RMSE) is less than 0.5 pixels because of the gentle topography in the intertidal zone [15].Moreover, errors in the positional accuracy may also arise from the waterline extraction process, in which the positional error depends on the waterline extraction method, the band combination, the influence of mixed pixels, and other factors.The waterline position can easily be identified in the near infrared or short wave infrared bands [29].Many waterline delineation methods have been proposed based on water's spectral characteristics in these two bands.However, it is difficult to find an appropriate method to delineate waterlines in multi-source and multi-temporal RS images.Moreover, the study region covers an area of more than 2100 km 2 , and the boundary between the water and the tidal flat varies spatially and temporally.To ensure the accuracy of the resultant tidal flat DEMs, on-screen digitization was used instead of automated waterline extraction methods.False-color composite (i.e., near infrared, red, and green spectral bands) are preferred because they best discern water from other land cover.Specifically, the near infrared bands include band 4 of the Landsat TM, CBERS-2 CCD, HJ CCD, IRS-P6 and AWiFS/LISS images and band 3 of the SPOT HRV and Beijing-1 CCD images; the red bands include band 3 of the Landsat TM, CBERS-2 CCD, HJ CCD, and IRS-P6 AWiFS/LISS images and band 2 of the SPOT HRV and Beijing-1 CCD images; and the green bands include band 2 of the Landsat TM, CBERS-2 CCD, HJ CCD, IRS-P6 AWiFS/LISS images and band 1 of the SPOT HRV and Beijing-1 CCD images.Digitization was performed according to the spectral and spatial characteristics of the tidal flats in the false-color composite images.Waterlines within the internal sandbank around tidal creeks were not considered in the analysis.The average positional error of the extracted waterlines is less than one pixel [17].Given that the mean slope of a typical intertidal zone ranges between 1-3 ‰, the total positional error (1.5 pixels) may result in vertical errors of 4.5-13.5 cm on a 30 m resolution satellite image.Furthermore, the positional error introduced in the geo-correction and waterline extraction of the images and its influence on the accuracy has been discussed in the literature [20,27,30]; hence, this factor is not a focus of this study.
2) Error introduced in the water level simulation process.The accuracy of the tidal level simulation depends on the complexity of the hydrodynamic conditions, the accuracy of the seafloor topography used in the hydrodynamic model, the characteristics of the simulation method (such as the cell size of the model and the open boundaries), and the accuracy of the calibration data [31].The error is usually a few tens of centimeters (approximately 10-30 cm) under reasonably calm weather conditions [11,31].In general, the waterlines can be treated as quasi-contour lines of the topography at a small scale.To apply the waterline method to broader regions, the spatial variation of the water level must be considered.This study covers an area of approximately 35 km × 60 km.A two-dimensional hydraulic model for the south Yellow Sea was constructed using Delft 3D (WL|Delft Hydraulics) to simulate the water level at the satellite overpass times.The average error in the tidal level simulation results is less than 30 cm [15].Moreover, it is difficult to simulate the regional water level at different accuracies to analyze the relationship between the accuracy of the resultant tidal flat DEM and the accuracy of the water level simulation results.Hence, the vertical error caused by the hydrodynamic model was regarded as constant in the following quantitative error analysis.
3) Error caused by the distribution of water levels.The distribution of water levels in the satellite images impacts the accuracy of tidal flat DEMs that are based on the waterline method.However, the tidal condition of the study area is complex; two tidal systems, the East China Sea progressive tidal wave and the Southern Yellow Sea rotary tidal wave, converge near the coastal waters of Jianggang [2].The tide in the study region is not synchronous (especially on the eastern and western sides of the Dongsha Sandbank), so it is difficult to analyze the distribution of the water level and its influence on the accuracy.Hence, the impacts of the distribution of water levels in the satellite images on the accuracy of the tidal flat DEMs are not fully considered in this study.
4) Error introduced in the DEM interpolation process.This factor is analyzed in Section 4.1.5) Error caused by the number of time-series satellite images used in the waterline method.This factor is analyzed in Section 4.2.
6) Error caused by the distribution of the water level.This factor is analyzed in Section 4.3.7) Error caused by the characteristics of the tidal flat (such as area and slope).This factor is analyzed in Section 4.4.

The Spatial Interpolation Approach and Its Impact on the Accuracy
The accuracy of the resultant DEMs depends on the spatial interpolation approaches that are used.This study used three spatial interpolation approaches, Inverse Distance Weighting (IDW), Ordinary Kriging (OK), and Thin Plate Spline (TPS), to generate three topographical maps of the Dongsha Sandbank (Figures 3a-c).These three approaches are integrated into the ArcGIS software (ESRI; http://www.esri.com).The waterline-point dataset was extracted from 40 images taken in 2006 (Table 2).In the IDW method, a variable search radius is adopted; the number of points used is set to 12, and the maximum distance is set at 1,000 m.In the OK method, a spherical model is used for the semivariogram, and the same search strategy as in the IDW is used.In the TPS approach, the weight is set to 0.1, and the number of points used is set to 12.
Few ground validation data are available because of the large area and muddy surface of the tidal flats, the closely spaced tidal creeks, and the complicated hydrodynamic conditions in the Dongsha Sandbank.Hence, a synchronous LiDAR DEM (Figure 3d) collected in 2006 (with a vertical accuracy of less than 15 cm) was used as validation data.Error maps were obtained by subtracting the LiDAR-DEM from the three resultant tidal flat DEMs, and the RMSE of each of the error maps was calculated.The RMSEs of the resultant DEMs interpolated by the IDW, OK, and TPS are 47.83, 45.27, and 44.79 cm, respectively.In this case, the TPS approach appears to have the best performance.Hence, in the following analysis, the resultant tidal flat DEMs are interpolated using the TPS approach.

The Number of Satellite Images Used and Its Impact on the Accuracy
The principle of the waterline method is to collect as many satellite images as possible that cover the study area over a given short time span because the tidal conditions are different in almost all of the images.When a larger number of satellite images was used, more waterlines recorded at different water levels could be extracted, which resulted in more detailed topographical information.This section describes the quantitative analysis of the relationship between the number of high-quality satellite images and the accuracy of the resultant tidal flat DEM.4a-k) were constructed based on different numbers of satellite images (from five to forty images).Figures 4a-k shows that the topographical information in the tidal flat DEMs is gradually refined as additional satellite images are used in the waterline method compared with the synchronous LiDAR DEM (Figure 4l, measured in April and May 2006).The tidal flat DEM derived from five satellite images (Figure 4a) only represents general topographic information (especially on the ridge of the sandbank); in contrast, the DEM derived from twenty satellite images (Figure 4f) provides more details of the tidal flat topography (such as sand ridges and tidal creeks), and the DEM derived from forty satellite images (Figure 4k) offers even more detailed topographical information.Note that the tidal flat DEM derived from 32 satellite images (Figure 4i) is quite similar to the LiDAR DEM (Figure 4l).
The synchronous LiDAR DEM (Figure 4l) measured in 2006 was also used as validation data.Figure 5a shows the strong linear correlation between the number of satellite images used and the RMSEs of the resultant DEMs (R 2 = 0.9238, n = 11).In general, the RMSE of the resultant DEM decreases as the number of satellite images increases.For example, the RMSEs of the resultant DEM retrieved from five, twenty, and forty satellite images are 62.43, 51.97, and 44.79 cm, respectively.Note that the RMSE appears to reach a saturation point (45.44 cm) at 32 satellite images and then increases slightly as the number of satellite images increases.For example, comparing the two tidal flat DEMs in Figure 4i and Figure 4j, although the number of satellite images increased by seven, the RMSE of the resultant DEM only decreased by 0.04 cm (blue ellipse in Figure 5a).The reason for this behavior will be analyzed in Section 4.3.In addition, previous studies have used different numbers of satellite images have been used to map the tidal flat topography in different locations.In the literature, ten satellite images have usually been recognized as being sufficient [32,33].In this case, the RMSE of the resultant DEM retrieved from twenty satellite images is 51.97 cm, even though twice as many satellite images were used as is generally considered sufficient.The high RMSEs may be due to the larger area of the study site (more than 620 km 2 ) than the areas investigated in other studies [32,33] and because the waterlines extracted from only ten satellite images do not completely cover our study site.A more detailed analysis will be presented in Section 4.4.

Characteristics of the Waterline and Their Impact on the Accuracy
In the construction of the gridded DEM, points with unknown elevations are interpolated from neighboring known points, and the regions of missing waterline points have an important influence on the interpolation.In general, the number of waterline points increases with the number of satellite images used.However, different parts of the tidal flat are submerged at different frequencies; the upper tidal flat is submerged less often than the lower tidal flat [17].Hence, the density of waterline points may not increase in proportion to the number of satellite images; the additional waterline points from the additional satellite images may overlap each other in the commonly submerged areas and be sparse in the rarely submerged areas.In other words, after reaching the saturation point, the additional waterline points may be redundant and add few height measurements to the DEM construction process, even though more satellite images were used.
To validate this hypothesis, we converted the eleven waterline-point sets that were used to interpolate the eleven tidal flat DEMs in Figures 4a-k into raster format with a 60 m × 60 m cell size.If a cell has a corresponding height waterline point, the cell is labeled, and the proportion of labeled cells is calculated.Figure 5b shows a strong positive linear correlation between the RMSE of the resultant DEMs and the proportion of labeled cells (R 2 = 0.9531, n = 11).Specifically, Figure 4h was interpolated from 88,095 waterline points (a coverage rate of 79.73%) that were extracted from 29 satellite images (the red circle in Figure 5b), while Figure 4i was interpolated from 94,667 waterline points (a coverage rate of 85.32%) extracted from 32 satellite images (the red circle in Figure 5a).The 6,572 additional waterline points resulted in a 5.59% improvement in the coverage rate, which contributed to a 1.89 cm improvement in the performance of the DEM inversion (the red circle in Figure 5b).Although the number of satellite images used increased from 32 to 39 (the blue circle in Figure 5a), the accuracy only improved by 0.04 cm, which can be attributed to the small improvement in the coverage rate of only 0.53% (the blue circle in Figure 5b).Hence, the coverage rate of the labeled cells is more important to the improvement of the RMSE of the corresponding tidal DEMs than the number of satellite images.Moreover, according the linear regression formula (y=-0.5126x+89.799)derived from the eleven samples (Figure 5b), the RMSE for a coverage rate of 100% will be 38.54cm.This relationship may vary in different regions of the tidal flat.If the linear relationship can be determined in a given region, the coverage rate of waterline points may be used as an indicator to estimate the error of the tidal flat DEMs based on the waterline method when no validation data are available.

Characteristics of the Tidal Flats and Their Impact on the Accuracy
Mason [34] mapped tidal flat DEMs in tidal zones with different slopes and indicated that the vertical error of a tidal DEM is sensitive to the slope of tidal flat.In the present study, an additional experiment was conducted to quantitatively explore the relationship between the accuracy and the slope.According to the LiDAR DEM measured in 2006, the maximum slope in the Dongsha Sandbank is 0.7 degree (approximately 1:80 slope), the minimum slope is 0 degree, and the average slope is 0.1 degree (approximately 1:550).We divided the LiDAR DEM into seventy levels according to the slope and calculated the RMSE of the tidal flat DEM derived from forty satellite images (Figure 4k) in the corresponding region.Figure 6a shows that there is a positive linear correlation (R 2 = 0.7693, n = 70) between the average slope of the tidal flat and the RMSE of the tidal flat DEM.In this case, the RMSE in the tidal flat area (slope < 0.2 degree) is less than 55 cm, and the RMSE decreases to less than 45 cm in flatter tidal flat areas (slope < 0.1 degree).Note that the tidal creeks and the neighboring regions usually have higher slopes; hence, a higher density of tidal creek systems may increase the error of the resultant tidal flat DEMs.In our case, the discrepancies along the tidal creeks are as high as 145 cm in some areas.Moreover, areas near the tidal creeks have higher mean absolute errors in the buffer area.Additional details about the tidal creeks and their influence on the accuracy of the resultant DEMs are discussed in the literature [17].The waterline method has been successfully applied to many intertidal flat zones around the world, including the intertidal zones of the coast of England [7,11,18,35,36], the Wadden Sea tidal flat along the German coast [12], the Amazon-derived mud bank in French Guiana [13], the tidal flats along the Korean coast [29], and the intertidal zones of the Chinese coast [20,37].Of these studies, only seven provide the area and the accuracy of the mapped tidal flat.The area of the mapped tidal flats in the seven cases varied from 1.5 to 620 km 2 , while the accuracy ranged from 14.0 to 44.79 cm. Figure 6b shows a positive linear correlation between area and accuracy (R 2 =0.7195, n=7), suggesting that the vertical errors of the tidal flat DEMs are positively correlated with the area of the region being studied.There are several possible explanations for this correlation.(1) The error in the resultant DEMs is sensitive to the spatial variability of the tidal flat.For instance, an ebb current in the tidal creek, which is supplied by the neighboring tidal flat surface and the upper reaches, has a significant impact on the morphological landscapes of the tidal flat.A larger catchment area of a tidal creek system will have a greater ebb discharge in the tidal creek and a more developed tidal creek system.A higher density of tidal creek systems may introduce additional errors in the tidal flat DEMs.(2) The difficult of constructing a hydraulic model increases as the area of the mapped tidal flat increases.The accuracy of the tidal flat DEMs depends on the performance of the hydraulic model, which depends on the data (such as the bathymetry data, the harmonic constant data at the open boundaries, and the calibration data).Hence, it is difficult to build a hydrodynamic model associated with a larger tidal flat area and to maintain the accuracy of the water level simulation.Note that the relationship between the area of the mapped tidal flat and the error of the resultant tidal flat DEMs may be influenced by the different validation approaches (e.g., transect validation, echo sounding data validation, and LiDAR DEM validation).

Potential Temporal Resolution of the Tidal Flat DEM Based on the Waterline Method
The terrain of tidal flats is spatio-temporally dynamic; hence, the temporal resolution of a given tidal flat DEM that is based on the waterline method is as important as the planar and vertical accuracies.The waterline method has not yet been developed to its full potential.To improve the accuracy of the waterline method, it is necessary to identify how rapidly and for how long to trace back the tidal flat terrains over the broad tidal flats.
A total of 852 high-quality satellite preview images of the study area were chosen based on a visual evaluation of the 2,494 preview images (Table 1).Of these high-quality preview images, 82.74% (i.e., 705 images) were acquired by optical sensors, which is more than four times as many as those acquired by SAR sensors.A quarterly frequency analysis was conducted of all 852 high-quality preview images.Figure 7a shows the frequency distribution of the common satellite sensors from 1973 to 2011 at quarterly intervals.Since the launch of Landsat-1, the number of high-quality medium spatial resolution satellite images has increased gradually.Since 1984, a sufficient number of highquality images (more than 20 images) that can be used to construct tidal flat DEMs are collected every two years.Since 2006, a sufficient number of images (more than 40 images) is collected each year, and since 2008, a sufficient number of images (approximately 20 images) is collected every quarter, which is mainly attributed to the 2-day revisit cycle of China's HJ-1A/B satellite.
In the availability analysis of the archive satellite images described above, some satellite-image sources were not included for several reasons: (1) images taken by the SPOT series satellites were not included because at least three scene images are needed to completely cover the middle Jiangsu coast; (2) images taken by the ASTER sensor on the Terra satellite were not included because the ASTER images are mainly collected based on user-demand and lack routinely archived data; (3) other SAR images, including images taken by TerraSAR-X, ALOS, RADARSAT-1/2, and Cosmo-SkyMed, were not included because these images are too expensive or difficult to access in China.The temporal resolution of the tidal flat DEMs may depend to a large degree on the number of available high-quality satellite images.Hence, we counted approximately 47 medium-resolution civilian satellite sensors (spatial resolution between 10 m and 100 m) that had been launched between 1972 and 2013 (Figure 6b) that could be used to estimate the upper limit of the temporal resolution of the tidal flat DEM based on the waterline method.In Figure 7b, the horizontal bars present the service time of the medium-resolution satellites.The red line indicates the annual sum of the available satellite images, which was estimated based on each satellite's revisiting cycle.According to [16], 16.72% of the 8,163 MODIS images taken by Terra and Aqua between 2000 and 2008 over the Jiangsu coast are of high-quality.The availability of SAR scenes for the waterline method is approximately 60% [12].Hence, the availability rate of high-quality satellite images was set to this proportion for the optical images, and the availability rate for the SAR images was 60%.The green line in Figure 7b represents the potential annual sum of available high-quality satellite images.If all of these potential medium-resolution satellite images are taken into account, the upper limit of the temporal resolution of the tidal flat DEM based on the waterline method should be improved significantly due to the increase in the number of sensors; the temporal resolution increases to one year since 1993 (more than 50 images per year), half a year since 2004 (more than 100 images per year), and three months since 2009 (more than 200 images per year).This increased temporal resolution makes it feasible to conduct research on the interannual, inter-seasonal, or even intra-seasonal trends of tidal flat evolution.In the future, this method may be able to detect short-term terrain changes caused by a single storm surge with the continued launching of more earth observation satellites.2).All of the important topographic features, such as sandbanks and tidal channels, can be identified and are positioned precisely on these maps.Note that the results for the first three phases of tidal flat DEMs are marginally satisfactory: in general, the elevation in the Dongsha Sandbank always decreases from the center to the margin, but some unnatural ripples are present near the center of the sand ridge in the resultant DEMs (red circles in Figures 7a-d).These features are primarily attributed to the long time span.However, these three phases of tidal flat DEMs based on the waterline method may be the sole topographical data available for tidal flat evolution trend analysis over the past decades.Three interesting phenomena can be observed from the eight phases of DEMs of the Dongsha Sandbank over the past 40 years: (1) the area of the exposed sandbanks decreased from 1973 to 2010; (2) the northern small sandbank had a southward movement tendency; (3) the western margin of the Dongsha Sandbank was straight during the twentieth century than became more curvy over the first ten years of this century.These findings agree with field observations.However, the evolutionary trend of the Dongsha Sandbank is not the main focus of this paper; the trends observed from the eight tidal DEMs were presented as circumstantial evidence to illustrate the feasibility of building DEMs of tidal flats from previous decades based on satellite images despite the lack of synchronous ground data.

Conclusions
This research quantitatively analyzed the relationship between the accuracy of DEMs that are based on the waterline method and the controlling factors.The three major conclusions of the study are as follows: 1) The number of satellite images used in the waterline method and the coverage rate of the waterline points are statistically correlated with the RMSEs of the resultant DEMs.In particular, the coverage rate of the waterline points is more closely related to the accuracy of the resultant DEMs than the number of images, which implies that increasing the number of satellite images used in the waterline method may only slightly improve the accuracy, while additional waterline points could significantly improve the accuracy of the DEMs.
2) The area and the slope of the tidal flats reflect the inherent spatial variability of the tidal flats.Tidal flat DEM inversion over a large-scale tidal flat with complex landforms requires denser waterlines and a higher coverage rate to delineate the micro-morphology and to account for regional loss.
3) The availability analysis of the archive satellite images indicated that the waterline method is able to recover tidal flat terrains from the past forty years.The upper limit of the temporal resolution of the tidal flat DEMs is one year since 1992, half a year since 2004, and three months since 2008, which makes the method practical for research on inter-annual, inter-seasonal, or even intra-seasonal trends of tidal flat evolution.

Figure 1 .
Figure 1.Location maps of the Dongsha Sandbank (a) in China and (b) in the SYSRSR; (c) HJ-1B Charge Coupled Device (CCD) false-color image of the study area using the near infrared (band 4), red (band 3) and green spectral bands (band 2) mapped to RGB, acquired at GMT 02:36, January 24, 2010.

Figure 2 .
Figure 2. (a) Diagram illustrating the waterline method; (b) potential errors in the waterline method.

Figure 3 .
Figure 3. DEMs of the Dongsha Sandbank in 2006 from different approaches.(a) Interpolated using the inverse distance weighting approach; (b) interpolated using the

Figure 4 .
Figure 4. DEMs of the Dongsha Sandbank in 2006 constructed using different numbers of satellite images.(a) Five images in May; (b) nine images from April to May; (c) 13 images

Figure 5 .
Figure 5. (a) Relationship between the number of satellite images used in the waterline method and the accuracy of the resultant DEMs; (b) relationship between the coverage rate of waterline points and the accuracy of the resultant DEMs.

Figure 6 .
Figure 6.(a) Relationship between the error of the resultant DEMs and the slope of the tidal flat; (b) relationship between the area of the tidal flat and the accuracy of the resultant DEMs.

Figure 7 .
Figure 7. Quarterly frequency of high-quality satellite images over the study area from 1973 to 2010.

Table 1 .
Summary of common satellite preview images.