A temporal waterline approach to mapping intertidal areas using X-band marine radar

Abstract Mapping the morphology of intertidal areas is a logistically challenging, time consuming and expensive task due to their large expanse and difficulties associated with access. A technique is presented here that uses standard marine navigational radar operating at X-band frequency. The method uses a series of time-exposure radar images over the course of a two-week tidal cycle to identify the elevation of the wetting and drying transitions at each pixel in the radar images, thereby building up a morphological map of the target intertidal area. This “Temporal Waterline” method is applied to a dataset acquired from Hilbre Island at the mouth of the Dee Estuary, UK, spanning March 2006 to January 2007. The radar gathered data with a radial range of 4 km and the resulting elevation maps describe the intertidal regions of that area. The results are compared with airborne LiDAR data surveyed over the same area and within the radar survey time period. The residual differences show good agreement across large areas of beach and sandbanks, with concentrations of poor estimations around points that are shadowed from the radar or likely to suffer from pooling water. This paper presents the theoretical framework of the method and demonstrates its stability and accuracy. The Temporal Waterline radar method is aimed at providing a useful tool for the monitoring and operational management of coastlines.

1. Introduction 1.1. The importance of mapping intertidal morphology

*Manuscript
Coastal, shallow water environments are important to commercial activities as they are often the site of ports, harbours and recreational areas which represent high value assets in the provision of various ecosystem services and are the foundation of many local and national economies. These shallow water systems are also incredibly dynamic and their morphology is known to change significantly during high energy storm events, and more gradually during more average conditions. The nature, extent and timescales of such changes at a variety of intertidal areas around the world has been well documented (Fisher and Stauble, 1977;Fitzgerald et al., 1994;Morton et al., 1995;Nicholls and Marston, 1939;Sexton and Moslow, 1981;Stone et al., 1996). Changes in morphology can compromise navigation channels and inlets in a variety of ways (FitzGerald et al., 2000) and can have significant financial consequences; the United States spends more than $100 million annually on Federal channel maintenance, dredging between 50 and 100 million m 3 of sand (Rosati and Kraus, 2000). At a regional level, strategic ports located in morphologically dynamic areas such as river deltas can experience significant navigation channel disruption due to sedimentation. An example of this is Port Harcourt located in the Bonny River estuary which empties into the Niger Delta region, Nigeria. This Port is a crucial gateway to the oil-producing region, and the complicated system of sandbars and shoals combined with dynamic bank and shoreline erosion present navigational risks to shipping operating in the vicinity of the port. Often the series of exposed jetties in the Bonny River estuary are isolated as the shoreline is eroded (Diop et al., 2014). This area is too large and exposed to monitor manually with ease and therefore a method of remotely monitoring the health and morphology of the coastline in dynamic areas such as this could be highly effective. Another example of a vulnerable area is the mouth of the Amazon River, where sandbanks are known to encroach upon the critical navigation channels. Sand bank migration rates of up to 250 m/year have been observed here (Fernandes et al., 2007), causing significant disruption to the operation of the ports. terrain vehicle. The use of vessel-based multibeam echo sounder surveys is constrained by expense and inefficiency of operation over large areas and the limited swath width in shallow waters (Gao, 2009). Airborne LiDAR (Light detection and ranging, Lyzenga (1985)) is a non-imaging technique using laser pulses to detect the range to the ground at low water or the water surface in wet areas.
More advanced versions can distinguish the signals from the water surface and the secondary reflection from the sea bed provided water clarity is sufficiently good. In recent years, airborne LiDAR has become the tool of choice for surveying large intertidal areas and multiple surveys flown over the same area can be used to accurately monitor changes in bathymetry (Guenther et al., 2000). Although these techniques have improved significantly in accuracy and applicability over recent decades, they remain expensive, relatively time consuming and rarely run over the same area on a routine basis. Consequently, data recorded in dynamic areas quickly becomes obsolete until the next survey. When used in this manner these methods provide only snapshots of episodic morphological change over relatively long timescales. In order to compliment these accurate and focused surveys, a method that provides constant, long-term monitoring over a wide area of the coast would provide unprecedented insight into the episodic, seasonal and interannual variability of intertidal areas.
An effective and long-established method of monitoring shoreline position and nearshore beach processes is to use video camera analysis of the nearshore and swash zones (Aarninkhof et al., 2003(Aarninkhof et al., , 2005Holland et al., 1997;Holman et al., 1993;Holman and Stanley, 2007;Plant and Holman, 1997;Santiago et al., 2013;Sobral et al., 2013). Video monitoring has been used successfully to monitor stretches of intertidal beach at a number of sites around the world, such as during a large European research project CoastView (Davidson et al., 2007) and improvements continue to be made, including automated methods that are capable of updating bathymetric maps on a daily basis (Uunk et al., 2010). The use of thermal infrared cameras allows such methods to be performed using data collected both during the day and at night to derive intertidal DEM (Digital Elevation Models) (Gaudin et al., 2009). Video cameras mounted on towers along a shoreline have also been used successfully in combination with in situ sensors to measure morphological change and sediment transport (Austin and Masselink, 2006) and these passive optical sensors have been proven to be accurate and effective in their deployment.

Depth mapping with marine X-band radar
Marine radar generally operates well in low visibility, has excellent temporal and spatial coverage and is able to provide similar data to that of a camera at slightly lower resolution but to a significantly greater range and regardless of light conditions (Dankert and Horstmann, 2007). X-band radar has become an integral part of the nearshore remote sensing infrastructure in recent years (Holman and Haller, 2013). Operationally, it has been used extensively to determine 2-D wave spectra in offshore areas for both commercial and scientific applications for many years now (Nieto Borge and Guedes Soares, 2000;Reichert et al., 1999), for the most part using techniques based on those developed by Young et al. (1985). The visibility of ocean waves on the radar imagery and the ability to record sequences of these images of the waves allows their wavelength and period to be determined. If currents are neglected, various techniques can be used to fit the water depth that best explains the observed wave behaviour (Bell, 1999(Bell, , 2008Bell et al., 2006;Flampouris et al., 2009;Hessner et al., 1999).
If the data are from areas where currents cannot be neglected, it becomes necessary to find the best fit to the location of the wave dispersion surface in the full 3D wavenumber-frequency domain in terms of the water depth and the two components of the current vector. Again, there are various approaches to both determining (and sometimes filtering) the frequency wavenumber spectrum and also a number of approaches to finding the best fit of the current vector and depth to the observed wavenumber spectrum (Senet et al., 2008;Hessner et al., 2009Hessner et al., , 2014Nieto Borge et al., 2004, 2008Serafino et al., 2010). Such techniques have been used successfully to map currents at tidal energy test sites in Scotland UK (Bell et al., 2012, McCann & Bell, 2014. Recently, the additional complication of correcting for vessel movement has started to be addressed in order to allow bathymetry mapping using radar data from a moving vessel, and water depth maps down to a water depth of approximately 50 m have been shown to be possible (Bell and Osler, 2011).
The overriding stipulation for these wave inversion techniques is that clear wave fields must be visible to the radar in order for the analysis to work accurately. Such techniques also inherently involve the analysis of data windows of several hundred metres square in order to allow the determination of the wave properties required to reliably determine both water depth and currents.
Thus a degree of spatial averaging is involved that makes that approach less useful for the mapping of often high spatially variable intertidal areas.
The Temporal Waterline method detailed in the following sections is not as reliant on the presence of coherent wave patterns on the radar data and operates at a pixel level rather than involving spatial averaging. The combination of the products of water line and wave inversion methodologies is planned for future work.

The Temporal Waterline Method
The method presented in this paper builds upon known principles, an early version of which was described by Admiral Sir R.H. Bacon who commanded the UK Dover Patrol from 1915-1917. During this time he correctly theorised that aerial photographs taken at regular timed intervals over a shoreline could be used in conjunction with a known tidal levels measured from a submarine to create a series of contour lines that described elevations above Chart Datum, and thus describe the beach profile (Bacon, 1932). This knowledge was critical in the planning of amphibious landings and military operations in the nearshore area. This underlying principle has been applied to a variety of remote sensing methods, such as Synthetic Aperture Radar (SAR) by Koopmans & Wang (1994) who picked out the waterlines of the intertidal areas of the Wadden Sea and assigned those contours to water elevations based on a tidal model. Mason and Davenport (1995) carried out a similar exercise with SAR images of the extensive intertidal regions of the Morecambe Bay area of the UK. An iterative process was later used between the tidal model and updating bathymetry to arrive at more precise tidal elevations for the detected waterlines (Annan, 2001).
The waterline approach to intertidal mapping has also been applied to marine radar data. Takewaka (2005) showed that beach elevations could be determined by associating the strong radar echo due to waves breaking on the shoreline with the tidal elevation recorded nearby. Beach slopes were also calculated from a number of records separated in time. However, the analysis used by Takewaka sometimes required manual intervention to correct the waterline estimate and hence was inappropriate for automated application to large datasets and long time series.
Repeated analysis of the same area over varying timescales allows the measurement and quantification of sediment transport (Mason and Garg, 2001;Mason et al., 1999;Ryu et al., 2008).
The source of images is commonly SAR from either satellite or survey aircraft, because the active sensing ability of SAR allows penetration of cloud cover and the gathering of images during poor weather, a quality shared by X-band radar. It is also possible to use traditional optical satellite images to detect waterlines (Ryu et al., 2002), the availability of which can be intermittent, thus reducing the temporal resolution of the method and leading to increased interpolation errors in the final map. Recently this method has been used to map large areas of the coast of China with mean vertical errors in the measurements between 29 -42cm (Liu et al., 2013). The technique was also applied using SAR images to map the change in topography on tidal flats along the Wadden Sea German coast between 1996 and 1999. The elevation values in this region were compared to those gathered by survey vessel, the mean error was 20cm in 1996 and 21cm in 1999 (Heygster et al., 2010).
The X-band radar waterline method described here differs from those already discussed by moving the waterline detection from the spatial domain of identifying the discrete waterline in individual images, to the temporal domain where the transitions between wet and dry are associated with the best match between pixel intensity records and the tidal signal which would cause that wetting/drying pattern over a given time period (Bell, 2014). This takes advantage of the excellent temporal update rates possible with ground-based remote sensing but could equally be applied to a range of remote sensing data types, given a sufficient number of images. More importantly, it circumvents the need for the waterlines in individual images to be clear and unambiguous -which is often not the case. Most published methods contain extensive details of error correction methods to deal with discontinuities in contour lines in individual images or handle ambiguous water lines. With the temporal approach these are unnecessary, and thus the method is easily automated and inherently more robust.

Experiment description
Radar image data were collected using a Kelvin Hughes 9.4GHz horizontally polarised X-band marine radar mounted on a 15 m mast (Figure 1), itself approximately 15m above chart datum, at Hilbre Island, northwest UK at the mouth of the River Dee ( Figure 2). This site offers good visibility of the estuary and the north western beach of the Wirral peninsula. The Dee estuary is a funnel-shaped, macrotidal estuary on the border between North Wales and England with a maximum spring tidal range of more than 10 m. The site features particularly interesting geomorphology, with a progressively accreting saltmarsh to the south-east, migrating tidal channels within the central sandbanks and shifting intertidal bed features along the beach. The waves within Liverpool Bay and the mouth of the Dee estuary are locally generated and fetch limited within the eastern Irish Sea such that significant wave height (H s ) is less than 5.5 m, the peak wave period (T p ) is less than 12 s, and the mean period less than 8 s (Wolf et al., 2011). The main channel of the River Dee splits into two deep channels around 12 km downstream from a canalised section leading to the City of Chester, the Hilbre channel to the east and the Welsh channel to the west, which feed into the Eastern Irish Sea (Moore et al., 2009).

Radar data collection and pre-processing
Hilbre Island, where the radar was located, is cut off from the mainland for the upper half of every tidal cycle and has no grid-connected electricity supply. In order to provide power to the ranger station on the island, a 2 kW wind turbine and off-grid battery storage system with diesel generator back-up was installed by Wirral Borough Council, which provided power most of the time. The remote nature of the site made maintenance and monitoring of both the power systems and the radar system a challenge and numerous gaps exist in the dataset as a result. Despite these challenges, several years of radar data were collected before a number of factors made the data collection impractical to continue.
The radar data used in the present work were gathered over 10 months from March 2006 to January 2007. Further archives of radar data up to 2009 exist and will form the basis of future work investigating episodic, seasonal and interannual changes within the estuary. The 2.4 m radar antenna was mounted approximately 30 m above chart datum and set to short pulse (~60 ns pulse length) in order to cover a 4 km range radius. The data were then sampled at 40 MHz with a radial resolution of 3.75 m using an OceanWaves GmbH Wamos system linked to the internet via a long range wi-fi link to the mainland. The antenna rotated at 25 rpm yielding an image every 2.4 s. The raw data were then interpolated from polar coordinates onto a Cartesian grid to enable georeferencing and proper visualisation of the results. This process includes the removal of small variations in antenna rotation rate that would otherwise cause an azimuthal error of several degrees in the location of nominally static targets if a uniform antenna rotation rate was assumed.
Strictly speaking, the polar to Cartesian conversion should also account for the slant range associated with the elevation of the radar antenna above ground level -a simple calculation using Pythagoras' theorem. However, as the ground level is the unknown quantity in this analysis, one can either assume an approximate elevation that accounts for the majority of the slant range error or include no correction. The option of no correction was chosen in this case as an antenna elevation of approximately 25-30 m coupled with a Cartesian pixel size of 5m means that the slant range error only becomes greater than the pixel size for points within approximately 100 m of the radar in a region where data is being recorded to a range of almost 4 km.
If precision in the nearest 100 m was of principle concern, the simplest method would be to perform the waterline method with no slant range correction, and once the elevation of each pixel had been identified, apply a correction to the radial range of each pixel based on the slant range appropriate to that elevation and range. A detailed correction for this effect was considered an unnecessary over complication in the present work considering the likely marginal gains in positional accuracy. It may however be implemented as a refinement in future work if necessary.
Images produced from radar data show not only detected hard targets such as ships and land, but also many reflections from the sea surface. This is known generally as "sea clutter" and is a product of Bragg scattering from centimetre-scale capillary waves on the sea surface interacting with the projected electromagnetic energy (Valenzuela, 1978) and sea spikes, a scattering phenomenon occurring when radar waves interact with steep or breaking waves at low grazing angles (Coakley et al., 2001;Fuchs et al., 1999;Ja et al., 2001;Trizna and Hansen, 1991). This sea clutter is inconsequential for the most part if wind speed is low (<3 m/s). As the sea surface is not roughened sufficiently, significant wave heights less than 1 m are also difficult to detect with radar. This radar frequency is also used by weather radars and thus rainfall is also visible on marine X-band radar and can potentially obscure the sea clutter (Bell et al., 2012). Figure 3 shows a snapshot of radar image data collected from Hilbre Island. The hard coast of the Wirral mainland is clearly defined to the east and sea clutter is also detected, particularly along the shoreline to the northeast where breaking waves give higher radar returns.
The intensity of a pixel in a radar image is dependent on the strength of the radar returns from that location (Richards, 2005) and in marine radars is uncalibrated and usually logarithmically amplified.
The raw value of the returned signal is stored as an unsigned 12-bit integer by the particular digitisation system used here.
Sequential radar images recorded once per antenna rotation provide movies of waves (when visible) propagating up to the shore, and the interface between wet areas and dry areas varies from wave to 21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 wave. In order to stabilise this fluctuating signal and define a "waterline" representative enough for this analysis, the radar images from each ten minute burst (of 256 images) are temporally averaged, smoothing the wave signatures and yielding an image that is analogous to a time-exposure in photography, in which the limit of the interface between land and ocean is more easily distinguished ( Figure 4); The time exposure radar images used in this work represent just over 10 minutes of data that were gathered either every hour or every 30 minutes, depending on the operating regime. Figure 4 shows a sample time exposure image used in this method. This image represents a period at low tide and so a great deal of beach is exposed between the shoreline and the seawalls and dunes along the peninsula to the east of Hilbre Island. The tidal sandbanks to the west are also exposed at low tide and the repeated wave breaking along the margins of the Hilbre channel picks out the general shape of the sandbank margins.

Tidal elevation data
The aim of the presented method is to map the intertidal area, which follows a cycle of wetting and drying governed primarily by the tides and varied local beach morphology. A partial record of tidal elevation was available from an old tide gauge located on the northernmost tip of Hilbre Island close to where the radar was located. This tide gauge, which is thought to have existed in various forms for up to 130 years, was refurbished in its present form by the Mersey Docks and Harbour Corporation (now Peel Ports) during the 1970s. It consisted of an obsolete float gauge with chart plotter. The stilling well for the float was cut into the sandstone bedrock of the island and connected to a subtidal location off the northern end of the island via a lead pipe. A pressure sensor was also located in the stilling well coupled to a VHF transmitter from which data were automatically relayed to both the Mersey Docks and Harbour Corporation and to the Proudman Oceanographic Laboratory (now the National Oceanography Centre). When the Proudman Oceanographic Laboratory moved from its original site at Bidston Observatory to Liverpool in 2004, the range became too great for line of sight reception of the VHF signal, so a VHF receiver was connected directly to the radar digitiser 3 4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 PC on Hilbre Island to pick up the tide gauge data from then on whenever the radar was operating.
Unfortunately the inlet pipe had degraded and became increasingly prone to blockages and siltation in recent years, compromising data quality. It was finally discontinued by Peel Ports in favour of an offshore radar level gauge in 2010.
The available Hilbre Island tide gauge data is shown in Figure 5a with the period that overlaps with the study period of the present work shown in blue. Figure  The incomplete and at times unreliable nature of this record made it unsuitable for use in this application where a robust and continuous time series of water levels was required. An alternative approach was therefore adopted taking advantage of the nearest UK National Tide Gauge Network class 'A' tide gauge outside Gladstone Dock, Liverpool. The residual meteorological contribution to the tide at Liverpool was determined by subtracting the predicted tide from the measured tide. This is shown in Figure 5c with the period corresponding to the present study highlighted in blue. The assumption was made that this meteorological component of the water level was a geographically wide area effect that could also be used as an approximation for the meteorological component of the water level at Hilbre Island, 15 km to the west. This was then added to the predicted tide for Hilbre Island to provide the required water level for the radar waterline analysis, shown in Figure 5d with the study period again highlighted in blue. In order to verify that this "synthetic tide" was a better representation of the water elevation than tide predictions alone, tidal records from mid-September 2006 to mid-February 2007 were subjectively selected as a period when the Hilbre Island tide gauge was not suffering from significant issues with pipe blockages -i.e. when obvious anomalies in the tide gauge data and residuals were not evident. It should be noted that the authors cannot be certain that even this section of the data was not contaminated by pipe blockages, only that any such effects were small .  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 The tidal residuals for both Liverpool Gladstone Dock and Hilbre Island were calculated by subtracting the tidal predictions from the measured water levels. As expected, a scatter plot of the residuals from one gauge compared with the other in Figure 6 shows a strong linear relationship between the residuals from the two tide gauges, with an R 2 correlation of 0.9, a standard deviation of less than 0.10 m and a Root Mean Square (RMS) difference of 0.10 m.
Over the same period, the RMS tidal residual of the Gladstone Dock data was 0.37 m, suggesting that if a similar residual was present on the Hilbre water levels then by applying the tidal residual from Gladstone Dock to the tidal prediction for Hilbre Island should provide a significantly more accurate water level than using predictions alone. The residuals from the Hilbre tide gauge data with respect to the tidal predictions alone were compared with the remaining signal when the synthetic tide (comprising the Hilbre tidal prediction plus the Gladstone Dock residual) were subtracted, shown in Figure 5e. With predictions alone, the Hilbre Island RMS residual for the test period of September 2006 -February 2007 was found to be 0.38 m, while the use of the synthetic tide was found to reduce this to 0.1 m. This represents a reduction in the difference of almost a factor of 4, confirming that this approach of adding the residual from the Liverpool tide gauge to that of the Hilbre Island tidal predictions yields a significantly more accurate representation of the water levels at that site than predictions alone. A subsection of the tidal data are shown in Figure 7, with the tide prediction marked as the red dotted line, the Hilbre tide gauge data, which was considered valid during that period, marked in blue, and the synthetic tide marked as the black dots. The points marking the synthetic tide can be seen to overlay the tide gauge data (cyan line) almost perfectly.
Reflectivity data were also supplied in a similar format. In order to more closely match the resolution of the radar data, the 1m gridded elevation data from the LiDAR were mean gridded on a 5 m grid and elevations were adjusted from Ordinance Datum Newlyn (ODN) to Admiralty Chart Datum (ACD) corresponding approximately to Lowest Astronomical Tide by adding 4.93 m to the ODN values for the comparisons presented here.
Examination of the original 1m gridded data showed clear evidence of elevations related to the water surface in wet areas, thus elevation values below 2.5 m relative to chart datum were eliminated from the comparison as potentially contaminated data points. Examination of the reflectivity values in these wet areas showed high reflectivity when the laser beam was pointing near vertical, and very low reflectivity data at lower grazing angles. Features with similar reflectivity signatures could be identified by eye in the bottom of channels in the sand flats and sand banks, indicating a strong likelihood that such areas contained pooling water, even near low tide when the survey was conducted. Filtering out such areas from the LiDAR survey was not attempted as no unique criteria could be determined for that purpose.

The Temporal Waterline Method
The initial step in this method is to gather time series of individual radar pixel intensities from each time exposure image across the chosen timescale, in this case two weeks, as shown in Figure 8. For each x and y coordinate of the time exposure image ሺ‫ܫ‬ ̅ ሻ, the (mean) pixel intensity (P) is retrieved from that location; this is then repeated for each time exposure image, with the values being separated by Δt -in this case either 30 or 60 minutes.
The resulting plot (Figure 9d) shows the raw pixel intensities throughout a two week period, where periodic episodes of high and low intensities generally indicate tidal cycles of wetting and drying.
The value of the radar pixel intensity at the peaks will not be regular as it is a function of local weather and surface conditions. These include including wind speed (which roughens the sea surface), wave height and wave direction relative to the radar antenna location, which contribute to varied backscatter of radar energy from the sea surface.
The two week length of the analysis period was chosen to include a full spring-neap cycle, thus maximising the vertical intertidal range able to be detected by this method, while maintaining a reasonable temporal resolution through a year. It would be possible to reduce the analysis period to approximately a week and still maximise the intertidal range experienced at a site, provided the analysis period was precisely half the exact spring-neap cycle length and synchronised such that each analysis period covered either the interval from neap to spring or from spring to neap. Periods less than this could also be used, perhaps even a single tidal cycle, but there would be times when the analysis period would be focussed only on the smaller intertidal range at neaps, which does not make best use of this overall approach.
In order to relate the tidal variation in pixel intensity at a given location to an elevation, a set of water levels was chosen reflecting the potential tidal range of the deployment area; for Hilbre Island this was 0.5-10 m in 10 cm increments. For each of these elevations, the synthetic tidal record was used to determine whether a pixel at that elevation would be either covered by the tide, or exposed at the times corresponding to each radar record. This yielded a binary pulse sequence unique to each elevation, illustrated in Figure 9b. Peaks in the absolute gradient of that binary pulse sequence ( Figure 9e) represent the points of transition between wet and dry at a given elevation.
The example pixel intensity time series shown in Figure 9d is not a clean binary pulse sequence like the one generated by the tidal record in Figure 9c, due to changing weather and surface conditions over the two week analysis period. Further, the presence of strong radar reflectors such as rocks in some pixels can exhibit a high radar cross section that is then reduced by inundation with water, thus inverting the expected pulse sequence.
In order to allow a more like for like comparison between the binary sequences of Figure 9c and the analogue time series in Figure 9d, we attempt to normalise the analogue time series. The absolute gradient of the time series is calculated and the gradient peaks selected (representing sharp changes in intensity) using a robust peak-finding algorithm described by Yoder (2009); these peak values were then normalised and other non-peak values reduced to zero (Figure 9f). Similarly, the absolute gradient is also taken of the binary wet-dry pulse sequences, illustrated in Figure 9e.
It is then a straightforward matter to step through each possible elevation and determine a measure of similarity between the theoretical and measured pulse sequences. In this case we use the normalised cross correlation to calculate R, the correlation coefficient at each elevation being: The normalised correlation coefficient (R) for each water-level number (N) is calculated using equation (1), where P is the pixel intensity gradient record and T is the record of tidal state change gradients, σ P and σ T indicate the standard deviation of P and T, respectively.
Each tidal elevation value now has a correlation coefficient (R) value defining the strength of the relationship between the record of pixel intensity gradients and the expected wetting and drying pattern at a given individual pixel location (Figure 10). The maximum coefficient is used to indicate the tidal elevation of the waterline and the process is repeated for all pixel intensity records from every pixel location in the input image sequence. The results are then used to populate a matrix which builds up a map of intertidal pixel elevations above chart datum.
It can be seen from Figure 9d and the derived pulse sequence in Figure 9f that there are times when the transition between wet and dry is not evident in the data, probably due to very calm weather conditions. If one attempted to apply the conventional approach of identifying a physical waterline in the radar images from records around that time, it would not be possible because that information is not contained within the data. However, by taking the temporal approach to the problem, provided there are at least some measurable wet-dry transitions during the two week time period, the absence of even days of wetting and drying transitions can be tolerated as can the occasional erroneous identification of a transition caused by for heavy rain for example.
Pixel records from areas which are submerged even at low tide (subtidal areas) generally yield low correlation coefficients with the predicted wetting & drying pulse sequences. These areas are filtered out by setting a simple threshold in the correlation coefficient as a quality control. The resulting maps can be used to visualise the mean elevations over a single spring neap cycle.

Results
The Temporal Waterline method described above was used to process radar data from  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 Radar data collection is inhibited through shadowing , a phenomenon common in the analysis of ocean waves with low-grazing angle radar (Lynch and Wagner, 1970;Mattie and Harris, 1978). Even with the radar being sited on a tower, the large radial range over which data has been recorded means that some intertidal areas will still be shadowed from the radar signal, and these areas also exhibit low correlations. Clear, unobstructed line of sight to the intertidal area of interest is therefore an important consideration when selecting a deployment site. A subjectively chosen correlation threshold of 0.3 was used to filter out the values generally corresponding to subtidal and shadowed areas as a quality control process. Land areas and the islands have been masked out and set to an arbitrary elevation above the maximum tide.
A single waterline map is shown in Figure 12 illustrating the mean intertidal bathymetry over a twoweek period; successive analyses over a longer time period will be useful in isolating and monitoring the movement of bed features over different timescales. The intertidal sand flats of West and East Hoyle Bank are clear in Figure 12, as are the banks of the large central channel. This is one of two channels into the Dee estuary which connect to the canalised River Dee and the city of Chester 20km higher up the estuary. A striking result is that the wreck of the Greek cargo ship SS Nestos displayed in Figure 13, stranded and sunk on the sandbank in 1941, can be seen clearly to the north, with an elevation of ~3.5 m at low tide.

Temporal filtering and smoothing of elevation values
The elimination of pixels by any quality control process would lead to unwanted gaps in individual elevation maps. It would not be appropriate to spatially interpolate the missing values as the gradient of complex beach profiles is rarely linear and assuming such could lead to significant errors in further processing (Holman and Bowen, 1979).
However, the existence of multiple sequential records allows an alternative approach to be taken to mitigate and filter points with intermittent poor correlations. A weighted temporal smoothing of the time series of each pixel was applied to the ten months of results. The square of the correlation  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 coefficients was used to weight each elevation at each two-week time step in a five point running smoothed fit using a robust smoothing algorithm by Garcia (2010). This has the effect of strongly smoothing the resulting time series of elevations while emphasising points with good correlations and de-emphasising those with weak correlations. An example of the results of smoothing the data in this way can be seen later in Figure 16b 4.2 Physical meaning of the waterline The algorithm described here operates in the time domain rather than the spatial domain, hence it is not immediately obvious how the derived waterline relates to an individual record. Figure 14 gives an example of how the derived waterline relates to both the LiDAR survey and the wave signatures on an individual radar record along a cross shore transect. The record started at 06:00 on the 6 th October 2006 and finished at around 06:10 after recording 256 images under relatively low wave conditions, just before a significant wave event. A cross-shore transect from the radar backscatter time series, and corresponding to transect 2 in Figure 15, is shown in the plot as it progresses through just over 10 minutes of data. The left hand side of the plot corresponds to the onshore (dry) sand flats while the right hand side has the sea clutter of the waves approaching from right to left.
The tidal elevations at the start, middle and end of the record were 2.97 m, 3.11m and 3.29m respectively. Figure 14a shows how the radar backscatter profile evolves over the ten minutes, with the wave breaker line clearly evident around x = 550 m, and the change in water level on the location of the breaking waves on the beach profile is immediately evident, with the breaker line having moved approximately 25m as the water level rose by over 30cm during that time. Shoreward of the breaker line to the left, there are some strong backscatter targets that appear to move around, and inspection of the full radar image sequence verified that these are almost certainly sea birds moving around either singly or in groups on the sands. Figure 14b shows the temporal mean of that backscatter profile. The cyan line marked on both plots indicates the location where the still water level with respect to the LiDAR survey in the middle (at 06:05 am) of the radar record would  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 lie. The red, green and blue lines mark the corresponding derived average waterlines from the 2 week period ending on the 8 th October 2006, and at the start, middle and end of the 06:00 -06:10 6 th October 2006 record respectively. The line corresponding to the middle of the radar record in time (green line) is close to the peak of the backscatter associated with the breaker line, which corresponds well with the peak of the breaker backscatter used as the criterion for defining the water line used by Takewaka (2005).
Since the waterline derived here relates to the peak in the shore breaker zone, it is slightly offshore of that which might be expected from the LiDAR elevation plus still water level at that time, which is the factor generating the slight overestimate in overall beach elevations described later. Figure 15 shows the location of five cross-shore transects extracted from the processed dataset.

Changes in beach transects
These transects capture most of the foreshore beach extending from the subtidal boundary to the backshore where the gradient decreases. Transect 5 is the northernmost, with transect 1 being closest to the Island. Figure 16 shows the results of extracting these transects every two weeks from 10 months of data, each row represents elevations along the transect from on to offshore. Noisy data appears most prominently across all transects around time step 10 and 17 (29/07/2006 and 4/11/2006). This could be the result of very calm weather during the two-week sample periods, resulting in a smoother sea surface (i.e. less sea clutter) and lower correlation coefficients. The mean offshore significant wave heights for these time steps were 0.66 m and 0.82 m according to the CEFAS Wavenet buoy (WMO ID:62287) in Liverpool Bay compared to a mean of 0.92 m and a maximum of 4.89 m seen in January 2007 (these wave data are accessible from http://www.cefas.defra.gov.uk). Waves of this height (<1 m) are difficult to detect with marine radar (although the wave heights will have increased as the waves shoal), so it is unsurprising that the data are poor for these periods. From Figure 15 it is clear that transect 5 runs close to a channel in the sand flats where shadowing inhibits the radar line of sight. Figure 17 shows the start and end transects from the ten months of data, which demonstrate that there is evidence of changes to the beach level during that time and that those changes in beach profile are quantifiable from the waterline derived topographic maps. Although there are small sections of the beach that move seawards and that appear to be associated with the crests of large bedforms, the overall pattern of change is a mean shorewards migration of the beach profile, which may be a seasonal effect rather than a long term trend of erosion. Table 1 lists the mean changes both in elevation along the transects and horizontally in terms of the cross shore translation of the beach profile from the beginning to the end of the ten-month period. This idea will be explored in further work.

Fixed elevation control points
The changes observed in these transects demonstrate that the method is capable of determining surprisingly small changes in beach elevations provided the changes are real and not artefacts of seasonal changes in wave height. To investigate this possibility, a number of rocky outcrops in the intertidal zone were chosen as control points that should not vary in elevation. If the results showed that that these targets did not vary in elevation through the ten months of the study period, then it would be reasonable to assume that changes in the elevations of potentially mobile sandy areas nearby during the same period are genuine.
The locations of these control points are shown in Figure 18. One site is located on Hilbre Island itself, another on a rock Platform close to the Island, one from Hilbre Middle Eye, and the final site is from the rock armour protecting the recreational marine lake at West Kirby.
The time series of waterline-derived elevations for each control point are displayed, with waterline elevation relative to Admiralty Chart Datum (m) on the y axis and time in two week intervals along the x axis. The plots show that radar derived elevations at these control points are relatively stable across 10 months, and thus it is concluded that the elevation changes observed in the sandy areas are almost certainly genuine.

Relationship between the waterline elevation and the absolute intertidal elevation
It should be emphasised that the elevations determined by this method are those of the waterline relative to the tidal water level. This is not the same as the absolute elevation that might be surveyed by LiDAR or other survey methods. However, the purpose of beach transects and surveys themselves should be considered before a discussion of relative accuracies of one method against another. The purpose of many beach transect monitoring campaigns is to determine to what position the combination of waves and tides might reach, damage sea defences and potentially overtop beaches and sea walls. Conventional surveys are carried out to absolute elevation datums, then tidal elevations can be combined with models of wave setup and runup to estimate how high up the beach the water would reach under various conditions. Waterline methods potentially supply this information directly, without the need for the modelling step, so absolute accuracy of the waterline derived elevations relative to a survey may be less important than the long term stability of the technique.  Figure 19b shows the LiDAR survey itself. The general shape, location and elevations of the coastline and sandbanks detected by the waterline method are in mostly in good agreement with the LiDAR survey. There is an area of particularly poor results to the southwest of the study area in Figure 19a where the radar method overestimates bed elevation by in excess of 5 m in places. These areas were therefore removed in order to prevent contamination of further analysis. A combination of the shadowing effect of the sandbanks at midto low tide and the increasing lack of sea clutter at locations further into the sheltered estuary is thought to be the cause of the concentrated area of poor results. It is, however, significant that the present processing and filtering techniques do not remove these poor elevations and the pixel records in these areas often have seemingly valid matches with a given tidal elevation. Identifying the reason for this and addressing the issue is a priority for future work.
In order to quantify the differences between the LiDAR and radar elevation plots, the LiDAR values at each point were subtracted from the radar derived values. Figure 20 shows these residuals. The majority of the radar-derived elevations lie within ± 1 m of the corresponding LiDAR elevations, with the overall pattern indicating that the waterline derived elevations are slightly higher than the survey elevations. Intuitively this might be expected due to contributions from wave setup and runup. However, the steeper beachfaces within 2 km of the island show surprisingly good agreement with the LiDAR survey, which may indicate that the wave runup and setup may not be the only factors involved in the differences.
Consistent differences between survey and waterline elevations with strong correlation values are evident over the flatter areas of the sand banks. This suggests there may be additional effects that add to the elevation of the water, such as pooling of the water between sediment features. Figure 21 shows a comparison between the waterline derived elevations and the corresponding LiDAR transects. These reveal that the sloping parts of the transects leading down to the low water mark are relatively well matched between LiDAR and waterline. However, the flatter areas bounded by sediment bars or sand waves appear have water trapped behind the bedforms, supporting the idea that water is pooling on the sand flats and creating some of the differences between LiDAR and waterline maps. As has already been noted, the reflectivity data associated with the LiDAR elevations also indicated pooling of water in these areas, even at low water.
This is an effect known to exist by the authors, based on numerous trips walking to the island. As the tide goes out, it takes a considerable time for the water to drain off the flatter areas, and it is often advisable to wait an hour or two beyond the time when the tide has nominally gone out to allow sufficient water to drain off the sand flats before setting off for the island on foot.
These factors indicate that the simplification of applying the water level associated with the tide gauge location on Hilbre Island across the whole domain is probably an over-simplification.

Close-range (< 3 km range) accuracy
In order to better compare the features present in the LiDAR and radar-derived elevations and the spatial distribution of differences at the closer range, Figure 22 shows a subsection of the data covering the area of the northeastern beach in more detail. Figure 22   Further errors might be expected due to the simplification that the tidal elevation relating to the location of the Hilbre Island tide gauge defines the water level across the entire analysis area. The  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 true pattern of water elevation across this complex macro-tidal environment must be expected to degrade with range from the measurement location. Moore et al. (2009), explored the differences in tidal asymmetry across the estuary via a numerical modelling study, showing stronger asymmetry over the sand banks compared with the channels, which confirms that our assumption of a uniform tidal elevation across the site at any particular moment is almost certainly an over-simplification.
Attempts to apply a more realistic 2-D tidal elevation pattern either using a tidal propagation model or empirically may be explored in future work. In particular, the issue of pooling water taking time to drain off the sand flats might suggest that although the transition time of the rising tide may be relatively accurate across the study site, that of the falling tide may be delayed reltive to the tide gauge location.
Some differences between the radar derived elevations and the survey are also to be expected due to the different temporal scales of the two surveys. LiDAR is a near instantaneous snapshot in time whereas radar-derived elevations represent the mean conditions over a two week period in this case. Thus numerical comparisons must be considered in this light and a perfect match should not be expected. Significant changes to the shape and location of the sedimentary features have been observed to occur overnight by the authors, so the superficial features of the intertidal sand flats must be assumed to be varying slightly even from tide to tide under dynamic conditions. Such observations reinforce the value of what could be considered a more representative average measure of intertidal elevations than the snapshots provided by surveys such as LiDAR. bar features, while areas of high change that are less linear may highlight areas subject to spatially discrete erosion or accretion. Overall, the plot illustrates that the majority of the area exhibits relatively little change over the ten months, with isolated areas of mobile features representing largely superficial changes to that part of the estuary.

Discussion
This new method of deriving maps of the intertidal zone, although relatively effective and simple in concept, relies on a number of assumptions that are probably over-simplifications at present.
The use of a single instantaneous tidal elevation across a complex estuarine environment is acknowledged by the authors to be a simplification of reality, and appropriate tidal propagation models may in future provide a more realistic spatially varying water level distribution across large areas. In particular, increasing tidal asymmetry across the sand flats and sand banks may be adversely affecting results in this complex area as a result of this assumption.
The present study was conducted in a macro-tidal estuary, in which there are extensive intertidal areas. At sites where a more modest intertidal zone is expected, consideration must be given to the expected width of the intertidal zone relative to the radar pixel size. If the intertidal beach width is narrow relative to the radar pixel size of 5-10 m, then X-band radar may not possess the appropriate horizontal resolution for the task. Instead, millimetre wave radar such as the 77 GHz version used by Bell et al (2006) may be more appropriate as such systems are capable of sub-metre range resolution and have been demonstrated to respond well to the breaking waves and beach run-up that categorises the water line. Optical camera systems are also likely to work well with this technique and can provide similar sub-metre resolution within a reasonable range of the camera, albeit in daylight and good visibility.
Further, if the vertical tidal range is narrow, the elevation intervals used in the analysis could be made finer than the 0.1 m intervals used here. Even in micro-tidal areas, meteorological effects can introduce significant water level changes in excess of the astronomical tides, and the additional contribution of these would undoubtedly assist the success of the technique at such sites.
The accuracy of the method at the limits of the tidal range also requires further consideration. This is because the number of waterline transitions close to the water level limits of the spring-neap cycle will reduce, from the peak of a uniform two transitions per tidal cycle, i.e. over 50 transitions in 14 days, down to single figures and then none as the water level approaches and goes beyond the limits. Looking for a correlation between the radar derived signatures and a tidally derived signal with only a few transitions will inevitably result in a less reliable match, and it would be prudent to implement a threshold in the number of wet-dry transitions below which any derived elevations are considered at least suspect if not invalid, regardless of the quality of the numerical match achieved.
It may be that the mean low water and mean high water levels would provide standardised thresholds for this application in the future.
The temporal update rate was set to two-week intervals corresponding to a single spring-neap cycle and chosen to maximise the tidal range during each temporal analysis window. Further work may investigate reducing this interval to approximately a week or even less but should be synchronised to span neaps to springs or springs to neaps to ensure the maximum tidal ranges were experienced during each analysis period.

Conclusions
A new method of analysing the location of waterlines in remotely sensed data has been presented.
The method differs from established methods by moving the problem from the spatial domain to the time domain and looking for matches in the expected temporal pattern of transitions between wet and dry areas over a spring-neap cycle. This is inherently more robust and easier to implement automatically than attempting to identify the precise physical waterline in individual remotely sensed images. The accuracy relative to a LiDAR survey varies from an overestimate of 0.12 m within the first 0.75 km from the radar, to an approximate 0.5 m overestimate further from the radar, although these comparisons are complicated by the complex nature of the macrotidal estuary used as the test case.
The tidal water level used for the analysis is assumed to be flat across the study area at any instant in time, which is almost certainly an over-simplification, and the application of a modelled 2-D water level that took into account the tidal asymmetry over sand flats and sand banks may improve the absolute accuracy in future.
The method provides a map of the elevation of the waterlines relative to the tidal reference, rather than the absolute elevation of the bed. The analysis of pixels corresponding to a number of rocks demonstrated that elevations of the derived waterlines relating to those rocks are relatively stable through the 10 months of processed data. In contrast, inspection of a number of beach transects showed gradual evolution of those transects during the study period, with all beach transects exhibiting a slight lowering of the beach face during the 10 months from March 2006 to January 2007. Hence, the waterline elevations can be viewed as a very effective measure of intertidal change yielding volumetric changes that could be used in conjunction with a single validation survey to relate such changes to absolute elevations if necessary.
Despite these simplifications, the results are remarkably stable through time, suggesting that the method would be suitable for the autonomous monitoring of changes to large intertidal areas over sustained periods of months to years.