We test the TIP method on six sites in England, selected for the availability of airborne lidar data in the form of gridded 1 m resolution rasters, provided by the UK Environment Agency (http://environment.data.gov.uk/ds/survey/), and for the diversity of their morphologies and tidal ranges. Dataset metadata are available freely on the Environment Agency website (https://data.gov.uk/dataset/lidar-composite-dtm-1m1). For each site, marsh platforms were digitised on an unfiltered and non-degraded DEM at a scale of 1:500, using the open-source software QGIS (step 6 in Fig. ). Source data were flown in 2012 for all sites, unless noted otherwise. The locations of the selected sites are shown in Fig. .

Shell Bay, Dorset (S1), is a shallow bay with a spring tidal range of 2.4 m, located in Poole Harbour, a limited entrance bay (sensu ) protected from strong waves. The marshes in Shell Bay display jagged outlines, indicative of low wave and tidal current stress . The Stour Estuary marshes (S2) 6 km upstream of the mesotidal Stour mouth are subject to a spring tidal range of 3.8 m and fluviotidal currents due to their estuarine fringing position (sensu ) and therefore display more linear boundaries. The Stiffkey marshes (S3) are back-barrier marshes , which experience a 4.7 m spring tidal range and display signs of erosion and accretion. These recent perturbations to the marsh surface provide an interesting challenge for topographic detection of marsh extents. The macrotidal Medway estuary marshes (S4, spring tidal range of 6.4 m) were chosen due to the presence of numerous channels in the tidal flats. In order to test the ability of our method in regions with extreme tidal ranges, we also analysed two megatidal sites: Jenny Brown's Point marshes (S5, spring tidal range of 9.2 m) and the Parrett estuary (S6, spring tidal range of 11.8 m), where sand dunes, different elevations inside the tidal flats, fallen blocks, and sunken platforms will test the limits of the method's ability to correctly delineate marshes in these environments.

The TIP method isolates marsh platforms from a DEM up to their seaward limits by detecting the topographic signature generated by the development of salt marshes. The definition of landward boundaries can vary significantly with context and may be defined by a vegetation zonation change , agricultural parcels, or infrastructure . Topographic input data are therefore clipped to the landward limit of the platform, at the discretion of the user. In the preparation stage, local slope is calculated from the DEM by fitting a second-order polynomial surface with a window radius of 3 times the horizontal resolution of the DEM, selected because it is the minimum radius needed to calculate slope with this method. The DEM may be passed through a Wiener filter to reduce noise from lidar datasets and/or degraded by averaged subsampling before the determination of slope to match complementary datasets. The effect of enabling these optional treatments is further discussed in the results section. Although methods exist to account for vegetation cover in the DEM , we chose not to apply these corrections as we wanted to ensure that the TIP method can be applied without information on the vegetation assemblages at a given site.

Tidal flats and salt marshes occur mostly on low energy coasts , characterised by low local relief and slopes. They therefore display similar local slope values, and this parameter alone is insufficient to differentiate between tidal flats and marsh platforms. Likewise, although marsh platforms are locally higher than tidal flats and channels, this may not be the case for complex depositional environments (e.g. marshes sheltered by a sand spit), where long-shore declivity may cause portions of the tidal flats to be higher than distant emergent platforms. Therefore, elevation alone, though it may be used to visually identify salt marsh platforms, is insufficient for objective platform detection. We address this problem by investigating transition features such as channel banks and erosion scarps, which are outliers in both slope and elevation rasters. These features are commonly defined by steep local slopes, particularly in mature and eroding systems . Furthermore, scarps connect marsh platforms to tidal flats and therefore represent a distinct break in elevation between the two. In this study, we focus on the identification of scarps and steep channel banks as a precursor to the detection of platforms, referred to as step 4 in Fig. .

To reduce computational costs, we delineate an initial search space to initiate the detection of scarps by isolating steep areas of the landscape, weighted by their elevation. We first calculate the relief of each pixel, Ri:

Ri=zi-zmin, where zi (dimension L) is the elevation of the pixel and zmin (L) is the minimum elevation in the DEM. We then divide this relief by the maximum relief in the DEM to get a dimensionless relief at each pixel, Ri*:

Ri*=Rizmax-zmin.

A similar procedure is followed for slope, where Rs (dimensionless) is determined by the slope at a pixel, Si minus the minimum slope Smin:

Rsi=Si-Smin, and the dimensionless version is calculated as

Rsi*=RsiSmax-Smin.

We then multiply these two metrics at each pixel to create the dimensionless parameter Pi* at each pixel:

Pi*=Ri*Rsi*.

This dimensionless product is useful for highlighting steep areas at high elevations (Fig. ): the higher the value of Pi*, the steeper and higher the pixel. Pi* could vary between 0 and 1, where a value of 0 would mean that a pixel was at both the lowest elevation and gradient in the DEM, and vice versa for a value of 1.

We use the properties of the probability distribution function (pdf) of P* to define the first search space, which we call Ss*. With the exception of macrotidal sites S5 and S6, the pdf of P* decreases monotonically with increasing P*, and at sites S5 and S6 the pdf decreases monotonically after a peak value (Fig. a). When f(P*) < max(f(P*)) and P* > max(P*), the derivative of the pdf is negative and increasing; i.e. the slope of the pdf curve becomes gentler with increasing P*. We therefore define the threshold value P*th where the slope of the pdf is equal to a threshold slope, Spthresh, on the declining limb of the pdf curve (Fig. a). In this study, we optimise the threshold value Spthresh to improve the classification of each site, as described in the results section. The first search space, Ss*, is defined as those pixels where P* > P*th, as shown in Fig. b. The search space Ss* is also schematically represented as grey cells in Fig. a (step 4.1)

We then define a square kernel K3 of three cells in width around each cell in Ss*. If more than one cell of K3 is included in Ss*, the cell containing the local slope maximum in K3 is flagged as a first-order scarp cell Sc1. If one given K3 already contains an Sc1 cell that is not the central cell, the central cell will be flagged as an Sc1 if, and only if, it is the next local maximum in K3. This results in patchwork of first-order scarp cells (step 4.2 in Fig. a).

For each first-order scarp cell (Sc1), we then flag two second-order cells (Sc2) as neighbouring cells with the next steepest slopes contained in the search space and not in contact with each other (red outlines in Fig. b). If two Sc1 cells are adjacent, only the cell with the higher slope will be flagged as a Sc2 cell (step 4.3 in Fig. b). This generates a patchwork of first-order cells (black outlines Fig. b) flanked by one or two second-order cells (red outlines in Fig. b). Starting from the second-order cells (Sc2), we prolong the scarps by finding the cell with the steepest slope that is not adjacent to another identified scarp cell of two lesser orders, within a K3 kernel centred on the previously identified cell. For example, on the third iteration, Sc3 cells are identified in a K3 kernel centred on a Sc2 cell and must not be adjacent to an Sc1 cell. Generally, Scn cells are identified in a K3 kernel centred on a Scn-1 cell and must not be adjacent to an Scn-2 cell. This routing procedure is applied in all kernels containing no more than two scarp cells and repeated until no cells fit the conditions or the order n is equal to 100 (blue outlines, step 4.4 in Fig. b).

This procedure produces a large number of potentially misidentified scarps, as small creeks within the platform and in higher portions of the tidal flat tend to be selected during this procedure. We use a further algorithm to thin these scarps and eliminate creeks. The first procedure eliminates low-elevation scarps. We first define a kernel of nine cells in width K9 (i.e. a square kernel of 81 pixels with the pixel being interrogated at its centre) and compare its maximum elevation max(ZK9) to the 75th percentile q75 of the entire DEM. Cells that do not satisfy the condition max(ZK9) >ZKthresh×q75 are discarded from the final ensemble of scarps (step 4.5 in Fig. c), where ZKthresh is a parameter which we optimise below. Each K9 kernel containing less than eight flagged cells is then discarded from the ensemble of scarps; after this procedure finishes, we are left with the final ensemble of scarps (step 4.6 in Fig. d).

We identify marsh platforms based on the final ensemble of scarps (step 5 in Fig. ). The final ensemble of scarps becomes a new search space (Ss2). We then create a square kernel three cells in width (K3) around each cell in this new search space. Using this kernel we identify first-order platform cells, Pc1, which are defined as all cells within K3 that have higher elevation values than the central cell of the kernel (i.e. those that are higher in elevation than the cells in the final scarp ensemble). We do this because platform cells are located at higher elevations than the scarp cells separating them from tidal flats. We use a kernel rather than a simple blanket elevation threshold over the entire DEM because longitudinal elevation variations may cause some tidal flat cells to be higher than scarp cells. Each Pc1 cell that is not adjacent to at least two other Pc1 cells is considered a product of isolated situations and eliminated from the ensemble of platform cells.

Following this initial selection of platform cells, we proceed to iteratively fill the platforms. At this point, the initial ensemble of platform cells, Pc1, is clustered around the final ensemble of scarps since we have only used a three-pixel-wide kernel centred on scarp cells to create the ensemble of Pc1 cells. We then iterate using a filling algorithm. The first iteration uses the cells Pc1, the second Pc2, and so on. In each iteration of Pcn cells, new cells are identified using two kernels, one being larger than the other. First, we define a local elevation condition using an 11-pixel-wide kernel K11: we find the maximum elevation in this kernel and then subtract 20 cm to define the minimum local elevation for a platform pixel. The 20 cm leeway is applied to account for local elevation variations on the platforms. The algorithm will not identify separate platforms separated by scarps less than this elevation threshold, so on microtidal marshes this threshold can be lowered. We address this limitation in the discussion and Appendix. The threshold is necessary to prevent the algorithm from excluding pools and slight depressions in the platform surface.

We then use a three-pixel-wide kernel (K3) within K11 to identify any cells in the next iterations' platform ensemble (Pcn+1). These cells must meet two conditions: (i) they are higher than the local elevation threshold identified with the 11-pixel kernel, and (ii) their distance to the nearest cell in the final scarp ensemble is greater than their distance to platform cells from previous iterations. The first condition is simply to ensure the platform is indeed a low-relief surface, and the second is to ensure the iterative process fills the platform away from the scarps. The second condition is also necessary to ensure the platform filling process does not cross scarps. This iterative process is repeated until n reaches an arbitrary value of 100, found to be sufficient to fill the entirety of the platform surface area for our sites.

This process results in platform surfaces that are spatially continuous, but in some instances sections of the tidal flat with relatively high elevations may also have been identified as marsh platforms. These areas are lower than marsh platforms by the height of the scarp separating them. We filter these cells by using the elevation properties of the entire DEM. A number of authors have shown that there is a gap in the probability distribution of elevations in intertidal landscapes that separates the majority of tidal flats from the majority of marsh platforms in microtidal environments e.g.. Such a separation, demonstrated by the decrease in probability between the grey and blue surfaces in Fig. , is also observed in our meso- and macrotidal sites, including megatidal environments such as the Parrett estuary (Fig. ). We search for this separation using the probability distribution of elevation, pdf(z), of all cells Pcn, divided in 100 elevation bins. We determine that the most frequent elevation bin, zmax(pdf(z)), is the most likely to contain cells correctly assigned to the platform ensemble, as the relief of marsh platforms is lower than that of tidal flats. Therefore, only elevations lower than zmax(pdf(z)) may contain cells misidentified as marsh platforms.

We then must identify which cells from the population of cells lower than zmax(pdf(z)) form part of the platform, and which do not. To do this, we truncate low elevations that have a low probability (red curves in Fig. ) to remove the long tail of low elevations from our initial platform identification. We take the probability distribution of the elevation of the remaining platform cells and calculate the mean probability pdf‾ (i.e. we average the probability from the 100 bins). We then search for rzthresh consecutive elevation bins that lie below the elevation of the maximum probability elevation that have lower probabilities than this average. The reason we use consecutive bins is that we do not want the minimum elevation to be determined by a single low-probability elevation that has spuriously arisen from the binning process. Once we find rzthresh consecutive elevation bins meeting these criteria, we remove all cells lower than and including the highest cell that lies within the rzthresh consecutive bins. We optimise the parameter rzthresh below.

Having eliminated these low-elevation, low-probability cells, we also mark all cells higher than zmax(f(z)) as platform cells. This may still out leave pools and pans, and platform edges remain jagged. Our final procedure aims to eliminate these artifacts using the following procedure: for a given value of the order n, we search in the ensemble of Pcn cells for cells that are surrounded by more than six Pc cells of any order within a K3 kernel. The two or less empty cells in K3 are then attributed the order n-1. By iterating through values of n, starting with the order 100 and finishing with the order 2, we progressively fill pools and jagged borders of the platform (Fig. a). Choosing six as the minimal number of platforms cells in each K3 necessary to execute this “reverse filling” procedure, we ensure that no headlands are generated. We then integrate scarp cells that are connected to platform cells into the platform ensemble with an order greater than 100. We then repeat the “reverse filling” process (Fig. b) and execute low-elevation elimination procedure (see blue curves in Fig. ) to obtain the final platform ensemble.

In order to evaluate the performance of the TIP method, we compare its outputs to manually digitised platforms for all of our test sites (step 7 in Fig. ). For each grid cell in the detected (automatically processed) and the reference (manually digitised) outputs, we assign the boolean value “true” to the marsh platform and “false” to the tidal flat. The results are classified as follows: true positives correspond to matching true cells in the tested and reference outputs, true negatives to matching false cells, false positives to true cells in the tested output that are false in the reference output, and false negatives to false cells in the tested output that are true in the reference output. The performance of the method is then evaluated using three metrics based on the numbers of true positive (TP), true negative (TN), false positive (FP), and false negative (FN) cells, respectively. The accuracy (Acc) describes the likelihood of cells in the tested raster corresponding to the reference raster:

Acc=TP+TNTP+TN+FP+FN.

We also test the performance of the method by reporting two other metrics: the precision, Pre, and the sensitivity, Sen . The precision represents the likelihood of the tested raster overestimating the positives compared to the reference:

Pre=TPTP+FP.

Conversely, the sensitivity, Sen, represents the likelihood of the tested raster missing positives compared to the reference:

Sen=TPTP+FN.

If the results of the TIP method perfectly matched that of the manual digitisation, all three metrics would have a value of 1.

The TIP method contains three user-defined, non-dimensional parameters occurring in sequence during the detection process. The first parameter, Spthresh, determines the threshold value P*th for the high-pass filter leading to the selection of the initial search space, shown in Fig. a. The parameter Spthresh influences the solution of the equation dfdP*=Spthresh. The second parameter, ZKthresh, determines the condition on the refinement of existing scarps in the high-pass filter max(ZK9)>ZKthresh×q75, schematically represented in Fig. . The third parameter, rzthresh, is used in the platform dispersion process to determine which percentage of the elevation range below pdf‾ is maintained in the platform ensemble. In this study, these parameters were set to maximise the average accuracy (Acc‾) across test sites (Fig. ): the optimised values (Spthresh=-2.0, ZKthresh=0.85, rzthresh=8) were used for the subsequent performance analysis. Users may modify these parameters as directed in the code documentation to better fit their study sites.

Figure  shows the performance of the TIP method for all six sites, discriminating between the use or absence of a Wiener filter and evaluating how the resolution of the topographic data influences the results. We also provide the full performance metrics in Appendix A (Tables  to ). We find the method's accuracy to be on average 94.8 % at the data's native resolution of 1 m, whether we apply a Wiener filter (Fig. a2) or not (Fig. a1). Degrading the DEM resolution still results in accuracy of above 90 %, although it decreases to around 60 % for microtidal site S1 at a resolution of 3 m. Applying a Wiener filter to the data causes a slight decrease in accuracy and precision (Fig. b2), but an increase in sensitivity (compare Fig. c2 to c1). Examining the results of all of the metrics shows that resolution degradation up to 3 m, as well as the use of a Wiener filter, primarily causes an increase in false positives and therefore an overestimation in the extent of the marsh platform. For sites S2 to S6, we observe little change in performance metrics with resolution degradation up to 3 m.

We suggest that all three performance metrics should be used when optimising the TIP method for a study site, as no combination of two metrics provides comprehensive insight into TIP uncertainties. Furthermore, although average accuracies remain above 85 % for resolutions of 4 to 5 m, we recommend caution when using the method at these resolutions, particularly in micro- to mesotidal settings where features may be smoothed beyond the method's recognition capacities. Use of the TIP method is not recommended for resolutions coarser than 5 m due to the very low accuracies observed for our test sites, making this method adapted to high-resolution data sources such as airborne lidar or photogrammetry.

In order to examine the performance of the method in sites with varying morphological characteristics, we compare the probability distribution functions of elevation from the digitised platforms to the platforms detected using the TIP method (Fig. ). Figure a–f show that a left-hand tail is present for the digitised platforms, whereas platforms detected by TIP show a sharp decrease in the pdf at these elevations: this indicates the presence of more false negatives than false positives at the lowest elevations of the marsh platform. This suggests that the TIP method excludes more features with a low elevation than manual digitisation, which correspond to tidal creeks and sunken terraces at the edge of the platform. However, this does not imply that the TIP method cannot identify multiple terraces within a platform, as shown by the multiple local maxima in the detected pdf in Fig. d and f.

We also show maps of the TIP method's performance for each test site in order to explore this spatial variability in feature detection (Fig. ). For instance, the dominance of false positives over false negatives in Fig. a (site S1) suggests that the method tends to overestimate the extent of jagged, low-relief marsh platforms, which are common in the sheltered microtidal bays characterising this site. This is the product of two factors: (i) identified scarps are not always complete in microtidal environments, as scarps tend to be small and therefore liable for elimination by our elevation threshold (see Fig. , step 4.5); and (ii) the reverse dispersion process (see Fig. ) is then likely to encroach on the tidal flat. This phenomenon is exacerbated by coarse grids or de-noised datasets (e.g. Fig. a1 and a2) where high slope values are smoothed and filtered out in the scarp detection process. In our meso- to macrotidal sites S2 to S4 (Fig. b–d), the method results in false negatives corresponding to the location of tidal creeks. These creeks were purposefully included in the marsh platform during the digitisation process but were identified as part of the tidal flat by the TIP method. This result indicates that our method often characterises creek banks as platform scarps due to their morphological similarity.

Other coastal landforms may generate false positives, as seen in Fig. c–f. In these cases, the position of the scarp line differs between the digitised and the TIP-detected platforms due to elevated portions of the tidal flat being adjacent to the marsh platform. This suggests that some areas of the tidal flat are topographically closer to the platform than to the rest of the tidal flat and may represent areas likely to be colonised by pioneer vegetation, even though they might not be vegetated at the time of data acquisition. Conversely, sunken platforms or fallen blocks that are not delineated by scarps may generate false negatives, as seen in the central area of Fig. e.

Although the TIP method was tested using salt marshes located in England, the scarp and platform association is a common feature to many salt marshes around the world, making the TIP method applicable over a wide range of geographic areas. Furthermore, the TIP method does not require the precise topography of the platform to function, making it relatively insensitive to unequal removal of vegetation between different DEM sources. The presence of vegetation induces positive errors in the DEM, which counter-intuitively may be useful when applying the TIP method, as this artificially increases the platform height and therefore the scarp slope. Examples of sites outside the United Kingdom are included in Fig.  and were selected to demonstrate the versatility but also the limits of the TIP method.

As discussed in Sect. , the TIP method currently excludes tidal creeks from the marsh platform, leading to discrepancies when compared to manual digitisation. Therefore, we would expect the TIP method to underperform on highly dissected marsh platforms. As a proxy for the dissection of the platform by tidal creeks, we digitise tidal creek centrelines from the DEM. We then calculate the total length of tidal creeks included in the digitised platform divided by the platform surface area. We refer to this quantity as the dissection index (DI). In Fig. , we examine the capacity of the TIP method to determine the area and perimeter of marsh platforms according to their dissection index. We find that for all test sites, TIP-detected area remains within 10 % of the digitised area, whereas TIP-detected perimeter increases steadily with dissection index, confirming that the exclusion of tidal creeks by the TIP method is consistently stricter than by digitisation. However, neither the TIP method nor manual digitisation offers an objective solution to detect tidal creeks. For a comprehensive analysis of marsh platforms, we recommend that objective platform detection be used in conjunction with objective creek detection methods such as those developed by and . Furthermore, future developments of the TIP method will include an objective creek detection method adapted from these publications, as well as channel network extraction methods developed for fluvial channels by , to ensure that tidal creeks are detected as separate objects.

The morphological characteristics of prograding marshes are different from those of established platforms: consequently, vegetation patches and pioneer zones are not the object of the TIP method. Specifically, prograding margins and vegetation patches tend to have a relief and slope that are close to those of the tidal flat, making their outlines invisible to the scarp routing process. The combined absence of scarps and low relief of prograding marshes then interfere with the 20 cm leeway included in the platform filling process and cause an excess of false positives. Users may reduce this leeway to improve accuracy (see Fig. b1), but we discourage the use of the TIP method to identify vegetation patches and prograding margins. However, these dynamic features are the centrepiece of salt marsh development and would benefit from reproducible monitoring methods. Future research may build on the works of to determine characteristic morphologies of prograding marshes, thus providing the necessary groundwork to enable reproducible monitoring.

As well as providing us with the ability to automate the delineation and analysis of marsh platforms across multiple sites, our method also allows the objective detection of change in marsh extent through time, with important implications for habitat monitoring or carbon storage evaluation. We test the capacity of the TIP method to monitor temporal change through the example of site S6, which was affected by heavy rainfall in the summer of 2007, resulting in high discharge in rivers such as the Parrett. The 1 m lidar data distributed by the Environment Agency shows that between March and October 2007 the north-eastern corner of site S6 underwent significant erosion. Blue pixels indicating loss of elevation (between March and October) in Fig. a bear the characteristic shape of slope failures and intersect the both the automatically and manually detected platform outline of March 2007, showing that the October platform outline is further inland.

This retreat of the marsh platform is observed both by the objectively classified (Fig. b) and the manually digitised platforms (Fig. c). However, whereas the digitisation effort focuses on the large bank failures, the TIP method also detects small changes in the DEM at the platform margin (visible in Fig. a and b) and may detect them as changes in marsh platform extent. Consequently, despite a close correspondence between TIP-determined marsh outlines and digitised outlines (Fig. a) near the bank failures, the digitised volume loss is only 81 % of the objectively detected volume loss. Pioneer zones, characterised by shallow slopes and rapid, uneven elevation changes, are also likely to generate small topographic differences between the DEMs.