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Influence of survey strategy and interpolation model on DEM quality
Geomorphology 112 (2009) 334–344
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Geomorphology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / g e o m o r p h
Influence of survey strategy and interpolation model on DEM quality George L. Heritage a,⁎, David J. Milan b, Andrew R.G. Large c, Ian C. Fuller d a JBA Consulting, The Brew House, Wilderspool Park, Greenhalls Avenue, Warrington, WA4 6HL United Kingdom (Research Fellow, Built and Human Environment Research Institute, University of Salford, Manchester, M5 4WT, United Kingdom) b Department of Natural and Social Sciences, University of Gloucestershire, Cheltenham, GL50 4AZ, United Kingdom c School of Geography, Politics and Sociology, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom d School of People, Environment and Planning, Massey University, Palmerston North, New Zealand
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Article history: Received 20 February 2009 Received in revised form 24 June 2009 Accepted 25 June 2009 Available online 14 July 2009 Keywords: Terrestrial laser scanning LiDAR Gravel-bed rivers DEM Interpolation Survey strategy
a b s t r a c t Accurate characterisation of morphology is critical to many studies in the field of geomorphology, particularly those dealing with changes over time. Digital elevation models (DEMs) are commonly used to represent morphology in three dimensions. The quality of the DEM is largely a function of the accuracy of individual survey points, field survey strategy, and the method of interpolation. Recommendations concerning field survey strategy and appropriate methods of interpolation are currently lacking. Furthermore, the majority of studies to date consider error to be uniform across a surface. This study quantifies survey strategy and interpolation error for a gravel bar on the River Nent, Blagill, Cumbria, UK. Five sampling strategies were compared: (i) cross section; (ii) bar outline only; (iii) bar and chute outline; (iv) bar and chute outline with spot heights; and (v) aerial LiDAR equivalent, derived from degraded terrestrial laser scan (TLS) data. Digital Elevation Models were then produced using five different common interpolation algorithms. Each resultant DEM was differentiated from a terrestrial laser scan of the gravel bar surface in order to define the spatial distribution of vertical and volumetric error. Overall triangulation with linear interpolation (TIN) or point kriging appeared to provide the best interpolators for the bar surface. Lowest error on average was found for the simulated aerial LiDAR survey strategy, regardless of interpolation technique. However, comparably low errors were also found for the bar-chute-spot sampling strategy when TINs or point kriging was used as the interpolator. The magnitude of the errors between survey strategy exceeded those found between interpolation technique for a specific survey strategy. Strong relationships between local surface topographic variation (as defined by the standard deviation of vertical elevations in a 0.2-m diameter moving window), and DEM errors were also found, with much greater errors found at slope breaks such as bank edges. A series of curves are presented that demonstrate these relationships for each interpolation and survey strategy. The simulated aerial LiDAR data set displayed the lowest errors across the flatter surfaces; however, sharp slope breaks are better modelled by the morphologically based survey strategy. The curves presented have general application to spatially distributed data of river beds and may be applied to standard deviation grids to predict spatial error within a surface, depending upon sampling strategy and interpolation algorithm. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Digital elevation modelling of morphological features is widely used throughout geomorphology. In fluvial geomorphology, detailed topographic data of bed and floodplain surfaces are required in process-based numerical models (Booker et al., 2001; French, 2003; Ferguson et al., 2003; Milan, 2009) and cellular models (DoeschlWilson and Ashmore, 2005; Coulthard et al., 2007) where a definition of morphology and surface roughness can be critical to flow, sediment transport predictions, and channel change estimation. Digital elevation model (DEM) differencing is being increasingly used to identify and quantify morphological change, to determine scour and fill ⁎ Corresponding author. Tel.: +44 1925 437020; fax: +44 1925 437029. E-mail address: [email protected] (G.L. Heritage). 0169-555X/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2009.06.024
volumes, and to provide detailed spatial and temporal insights into the locations of scour and fill (Brasington et al., 2000; Lindsay and Ashmore, 2002; Brasington et al., 2003; Fuller et al., 2003a, Lane et al., 2003; Milan et al., 2007; Rumsby et al., 2008). As such, the application of DEMs in fluvial geomorphology is becoming increasingly utilised in the field of morphological budgeting at the reach scale (Ashmore and Church, 1998) and as a tool to elucidate a process (Fuller et al., 2003b; Fuller and Hutchinson, 2007; Fuller and Marden, 2008). The quality of the DEM is fundamental to the success of the above approaches and has been shown to be influential to the output of the flow simulations (Milan, 2009) and in the derivation of accurate volumetric estimates of channel change (Fuller et al., 2005). Meaningful interpretation of sediment volumes and the spatial distribution of scour and fill derived from DEM differencing must consider error within the surface. During DEM differencing, the magnitude of the
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error propagated between two surfaces can exceed the vertical change under consideration, particularly subtle scour or fill (i.e.,± 0.25 m). Lane et al. (1994) and Lane (1998) suggested that DEM quality is a function of (i) the quality of the individual data points within the surface, (ii) the density of data points used to represent the surface, and (iii) the distribution of data points within the surface. Both (ii) and (iii) are related to the field sampling strategy and to the hardware used to collect the data. Hancock (2006) further indicated that the interpolation method used to produce the DEM may also influence the character of the DEM, although limited attention has been given towards the suitability of the interpolation algorithm used to model the spatial dataset. To address this gap, we use a detailed and accurate terrestrial laser scan (TLS) based three-dimensional data set to clarify the importance of (i) field sampling strategy, i.e., where points are surveyed relative to the morphology, and (ii) data interpolation techniques used in the production of the DEM. Errors associated with various combinations of survey strategy and interpolation technique and the influence of local topographic variability error are also explored. 2. Methodology 2.1. Study area and acquisition of surface control data The study focused upon a 9900-m2 area of point bar on the River Nent at Blagill in the North Pennine uplands, Cumbria, UK (Fig. 1). The River Nent drains an upland catchment of 29.4 km2 before flowing into the River South Tyne west of Alston. The geology of the basin consists of sedimentary rocks, principally sandstone, shale, and limestone that have undergone extensive base metal mineralisation. The river may be described as wandering in nature, following the criteria set out by Church (1983). The study is sited within one of two instability zones 0.2–0.3 km in length, which are separated by a stable single-thread reach of 150 m (Fig. 1). Channel metamorphosis has been documented at this site since the 1700s as a result of system loading with fines generated by mining activity (Macklin, 1986), with more recent channel response being described by Chappell et al. (2003). Anthropogenic activity has had an unexpected benefit: this section of the River Nent has been classified as an Special Site of Scientific Interest (SSSI) by English Nature because of the wandering nature of the channel and the metalophyte plant community that thrives on the floodplain. Planform change and bar activity is evident in both the upstream and downstream instability zones creating a dynamic assemblage of morphologic units. 2.2. DEM validation Quantifying the accuracy of DEMs generated from survey data is difficult since validation requires comparison between the derived DEMs and a second, more accurate surface (Wood, 1996; Brasington et al., 2000, 2003). Usually the acquisition of this surface is impossible, therefore DEM validation is often based on quantifying model uncertainty through diagnostic surface visualisations or field “ground truthing” (Wood, 1996; Wechsler, 2000). However, this study was able to obtain the control surface using a terrestrial laser scanner that is capable of producing a surface accurate to the grain scale, i.e., the D50 surface roughness in gravel-dominated systems (Heritage and Hetherington, 2005; Heritage et al., 2006; Heritage and Milan, 2009). An LMS Z-210™ scanning laser manufactured by Riegl Instruments (Horn, Austria) was used to collect topographic data for the control DEM. The instrument works on the principle of “time of flight” measurement using a pulsed eye-safe infrared laser source (~0.9 µm wavelength) emitted in precisely defined angular directions controlled by a spinning mirror arrangement. A sensor records the time taken for the emitted laser light to be reflected from the incident surface. Angular measurements are recorded to an accuracy of 0.036o in the vertical and 0.018o in the horizontal.
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Survey control was facilitated by RiScan Pro™ survey software that is capable of visualising the large volumes of point cloud data generated by repeat scans in the field. Scans were generally restricted to 240o in front of the scanner, and scans were collected with substantial overlap ensuring that the surface of the study reach was recorded from several directions. The effect of this approach is to increase the point resolution across the surface (and the data volume) and to reduce the possibility of unscanned areas because of the shadowing effect of larger roughness elements along the line of each scan. Before scans were taken, a total of 20 reflectors were placed on and around the study reach. These reflectors were tied into the project coordinate system using an EDM theodolite and were automatically located by the RiScan Pro™ software and matched to the project coordinates using a common point configuration algorithm. A total of 253,000 points were recorded across the point bar surface with median spacing of 0.09 m (lower and upper quartiles = 0.05 and 0.13 m). Terrestrial laser scan data accuracy was evaluated through the collection of 186 independent prominent surface point coordinates using an EDM theodolite obtained at the same time as the TLS survey. There was good agreement between the two data sets, with a median error of − 0.003 m, 72% of the TLS elevation values were within ± 0.05 m of the theodolite points (Fig. 2), and this value was used as the threshold of accurate detection for the surface control DEM. The TLS data were subsequently used to generate a 0.05-m resolution DEM of the point bar surface. Delauney triangulation with linear interpolation was employed as an exact interpolator. 2.3. Spatial sampling technique A TOPCON EDM theodolite (accuracy ± 5 mm) was used to gather data from the study reach using several different sampling regimes: (i) cross section; (ii) bar outline only (in order to highlight the issue of low survey density within a geomorphic unit); (iii) bar and chute outline, and (iv) bar and chute outline with spot heights on uniform surfaces (Fig. 3). A fifth sampling strategy (v) aimed to simulate the spatial sampling resolution that can be obtained using aerial LiDAR. In the absence of the actual aerial LiDAR data, this was achieved through degradation of the TLS control data. By extracting closest point data based on a 2-m regular grid from the TLS data, an equivalent resolution scan to that obtained through airborne LiDAR by Charlton et al. (2003) was achieved. Random errors in the range ± 0.15 m were added to each of the data points, thus replicating the reported errors on aerial LiDAR in a similar environment (Charlton et al., 2003). Data from all of these survey strategies were then used to generate equivalent resolution (0.05 m) DEMs using a range of interpolation algorithms. Five different common interpolation procedures were applied to each of the data sets using Surfer™ GIS: (i) inverse distance to a power (squared); (ii) kriging using the default point kriging variogram options in Surfer; (iii) kriging using a variogram produced from the survey data; (iv) minimum curvature, and (v) Delauney triangulation with linear interpolation (TINs). 3. Results 3.1. Spatial variations in vertical error DEMs for each sampling strategy and interpolation technique were subtracted from the surface control DEM created using TLS data. Digital elevation models of elevation difference (DoDs) in excess of the error within the TLS surface control DEM of the bar surface (±0.05 m) were produced (Fig. 4). Average aerial elevation error statistics for the bar surface as a whole are summarised in Table 1, ranked vertically by standard deviation of the errors. Standard deviation values demonstrate that the simulated aerial LiDAR survey strategy has the lowest overall error regardless of the interpolation technique. This is followed by the bar and chute with spot height
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Fig. 1. Study location, Blagill, River Nent, Cumbria. (a) Catchment map, and (b) aerial photograph of reach (Googleearth.com).
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Fig. 2. Terrestrial laser scanner data accuracy, evaluated through the collection of 186 independent prominent surface point coordinates using an EDM theodolite, obtained at the same time as the TLS.
strategy associated with the kriging algorithm. Errors are greatest when the minimum curvature algorithm is used, particularly where the survey data consisted of cross section or basic bar outline only. Spatial differences in the degree of survey and interpolation error are evident (Fig. 4). The channel and chute features tend to have their depth overestimated, and the bars tend to have their height overestimated. Errors appear lowest overall for the aerial LiDAR and bar-chute-spot height sampling strategy, regardless of the interpolation technique, a feature evident for each of the interpolation
procedures used. For the cross section survey strategy, errors are lowest close to the cross section points and highest in areas where there is no measured data (between the sections). The head of the point bar has high positive elevation errors in the order of 0.7 m when a bar outline and chute-bar sampling strategy was employed, using a minimum curvature or triangular linear interpolation as the interpolator (Fig. 4d,e). High negative errors are also evident at the tail of the bar feature for the bar outline and chute-bar sampling strategies, when minimum curvature was used as the interpolator (Fig. 4e). The
Fig. 3. Point bar site on the River Nent, demonstrating a) DEM of bar surface based upon TLS data, and b) the position of sample points used to create DEMs for different sampling strategies. The bar is orientated west–east.
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greatest channel and chute errors are exhibited in the DoDs produced using only bar outline and a chute-bar sampling regime with no spot heights, with kriging using the variogram derived from the field data as the interpolator. 3.2. Net elevation and volumetric error Volumetric error was calculated by subtracting each of the DEMs in Fig. 4 from the control surface produced from the TLS data (Fig. 3a), after first removing the ± 0.05-m error associated with the TLS
surface. The results shown in Fig. 5 indicate that the aerial LiDAR resolution survey displays the lowest vertical and volumetric errors out of all the sampling regimes. Volumetric survey errors ranged between 400 and 1100 m3 across the 9900-m2 point bar survey area; this is equivalent to an average vertical error of between 0.04 and 0.11 m. Mean volumetric errors are between 350 and 400 m3 across the 9900-m2 point bar survey area. Notably the bar-chute-spot height survey obtained using a total station can provide comparable errors to those obtained using simulated aerial LiDAR, if point default value kriging or triangulation with linear interpolation is used as the
Fig. 4. Surface error maps: (a) inverse to a distance power, (b) default kriging, (c) kriging using variogram produced from the field data, (d) minimum curvature, and (e) Dalauney triangulation TIN. The blank area shown on the DEM represents an area where there were no laser returns from the bed surface, due to ponding of water in a chute channel. The maps are orientated west–east.
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Fig. 4 (continued).
interpolation algorithm. The inverse distance squared algorithm was consistently poor, giving a total volumetric error of between 800 and 1100 m3 for all sampling regimes with the exception of aerial LiDAR. Bar-chute, bar outline, and cross section sampling regimes gave the poorest volumetric errors (generally in excess of 600 m3 regardless of interpolation method); however, the choice of interpolation algorithm does seem to make an important difference to the accuracy of the surface. This is particularly evident for the cross section sampling regime, where errors were as low as 450 m3, when triangulation with linear interpolation was used.
The location of survey points and hence survey strategy is important and should be sensitive to the morphology under consideration (e.g., Chappell et al., 2003). Greatest vertical error is likely to be found at breaks of slope, such as bank edges, unless the top and base of the slope are surveyed and subsequently honoured by the interpolator. Interpolation algorithms are normally used to approximate the surface elevation based upon the elevation of the surrounding measured data. If measured data are sparse in regions of high topographic variation, then the topography is generally more poorly modelled by the interpolator. Hence, more data is needed where there are
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Fig. 4 (continued).
relatively large changes in elevation over short distances (e.g., bank edges). Conversely, fewer points are required over flatter surfaces (e.g., bar tops). To date in fluvial geomorphology however, DEM error has only been considered to be uniform in nature across the DEM (e.g. Brasington et al., 2000, 2003; Lane et al., 2003; Milan et al., 2007).
3.3. Vertical error and local surface variability The spatial distribution of field survey and data interpolation error was further explored through an investigation of the relation between local form roughness as defined by standard deviation of bed
Table 1 Combined survey and interpolation error statistics for the point bar surface at Blagill on the River Nent, Cumbria.
Kriging (variogram) Kriging (default value) Inverse distance Triangular linear interpolation Minimum curvature Kriging (default value) Kriging (variogram) Triangular linear interpolation Minimum curvature Triangular linear interpolation Kriging (default value) Kriging (default value) Inverse distance Kriging (default value) Triangular linear interpolation Inverse distance Triangular linear interpolation Inverse distance Kriging (variogram) kriging (variogram) Inverse distance Kriging (variogram) Minimum curvature Minimum curvature Minimum curvature
Aerial Aerial Aerial Aerial Aerial Spots and morphology Spots and morphology Spots and morphology Spots and morphology Cross sections All morphology Basic morphology Cross sections Cross sections All morphology Spots and morphology Basic morphology Basic morphology Cross sections Basic morphology All morphology All morphology Basic morphology All morphology Cross sections
Mean
Median
Minimum
Maximum
First quartile
Third quartile
StDev
Skew
Kurtosis
0.002 0.002 − 0.003 0.001 0.006 0.034 0.056 0.035 0.017 − 0.010 0.098 0.083 − 0.040 − 0.063 0.102 0.098 0.078 0.071 − 0.053 0.088 0.148 0.135 0.050 0.057 − 0.015
0.003 0.003 − 0.001 0.002 0.006 0.001 0.023 0.009 − 0.007 0.009 0.068 0.066 − 0.020 − 0.024 0.069 0.064 0.059 0.089 − 0.025 0.131 0.163 0.167 0.013 0.011 − 0.002
− 1.152 − 1.152 − 1.100 − 1.203 − 1.213 − 1.259 − 1.120 − 1.290 − 1.384 − 1.503 − 1.259 − 1.341 − 1.421 − 1.414 − 1.290 − 1.348 − 1.357 − 1.389 − 1.325 − 1.131 − 1.350 − 1.049 − 1.695 − 1.525 − 1.692
1.267 1.267 1.072 1.339 1.374 1.548 1.415 1.508 1.644 1.226 1.575 1.506 1.299 1.242 1.548 1.405 1.397 1.428 1.298 1.290 1.462 1.436 2.576 2.679 1.408
− 0.078 − 0.078 − 0.088 − 0.081 − 0.083 − 0.067 − 0.064 − 0.059 − 0.084 − 0.093 − 0.056 − 0.058 − 0.194 − 0.207 − 0.051 − 0.081 − 0.062 − 0.100 − 0.230 − 0.111 − 0.060 − 0.083 − 0.089 − 0.103 − 0.182
0.083 0.083 0.085 0.086 0.094 0.088 0.138 0.092 0.072 0.097 0.227 0.217 0.123 0.098 0.236 0.232 0.204 0.251 0.133 0.295 0.347 0.345 0.162 0.175 0.188
0.184 0.184 0.188 0.189 0.197 0.213 0.213 0.216 0.238 0.238 0.250 0.251 0.256 0.258 0.260 0.264 0.265 0.268 0.271 0.280 0.282 0.283 0.297 0.304 0.351
− 0.155 − 0.155 − 0.236 − 0.121 − 0.022 1.428 1.042 1.118 1.426 − 0.425 0.506 0.029 − 0.344 − 0.514 0.372 0.642 0.036 − 0.241 − 0.342 − 0.358 −0.033 − 0.150 0.678 1.039 − 0.488
4.625 –4.298 3.424 4.484 4.664 6.094 3.337 5.857 6.784 2.786 2.084 2.044 0.515 0.556 1.867 0.952 2.105 0.860 0.110 − 0.125 0.196 − 0.274 4.396 4.274 0.957
Data are sorted vertically by the standard deviation of the errors.
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Fig. 5. Error summary for different survey sampling strategies and interpolation methods (inverse distance to a power-IDP, kriging using the default point kriging variogram options in Surfer-PK, kriging using a variogram produced from the survey data-BK, minimum curvature-MC, Delauney triangulation with linear interpolation-TIN), based upon the DEMs of difference presented in Fig. 4: (a) vertical error, (b) volumetric error.
elevations in a 0.1-m radius moving window. The approach calculated the local standard deviation of all points occurring within the 0.1-m radius search window of every point in the TLS point cloud data set; these values were then averaged across a 0.1-m regular grid corresponding to point records in the DoD data. The spatially variable error displayed in each of the DoDs in Fig. 4 could then be directly associated with the standard deviation grid. During the moving window processing, a zero value for the local standard deviation was recorded for areas with less than eight data points present within the window. This was the case for areas where very few laser returns from the bed from ponding of water in chute channels on the bar surface (shown on the DoDs in Fig. 4 as a blank area on the inside of the point bar). Breaks of slope such as bank edges and bar edges will have greater local form roughness in comparison to bar surfaces. Local form roughness, as defined by the areal averaged standard deviation values, is plotted against vertical error for each survey strategy and interpolation algorithm in Fig. 6. Clearly, as local form roughness increases so the error associated with the specific survey and the interpolation algorithms also rises, indicating that the interpolation algorithms are unable to accurately model increasingly complex surfaces because of the lack of local data. Errors across the flatter surfaces are generally smallest for the simulated aerial LiDAR data set; however, sharp slope breaks characterised by a higher local standard deviation are better modelled by the morphologic-based survey methodologies where appropriately located data facilitate more accurate interpolation. An important finding of this analysis suggests that the focused nature of the morphology-based techniques identifies slope breaks better than the grid-based aerial survey techniques, allowing the interpolators to better model these features. Densifying the surface data collected will also improve the interpolation accuracy and the local variation is better represented in
the data set. Issues with the survey error resulting in the erroneous interpolation of nonexistent surface variation at low roughness levels require consideration; however, continued improvements to the density and accuracy of the airborne LiDAR data will undoubtedly lead to better surface representation as a result. 4. Discussion 4.1. Field data sampling strategies to detect morphological changes The methods by which river beds are surveyed has changed in response to both hardware and software developments, particularly in the last 10 years. Traditionally, topographic data have been collected to elucidate morphological change using a cross section two-dimensional approach (e.g. Brewer and Passmore, 2002). Morphological change was quantified by superimposing successive cross sections to identify areas of scour and fill (Maizels, 1979; Ashworth and Ferguson, 1986; Fenn and Gurnell, 1987; Ashworth and Ferguson, 1994). When cross sections are linked together, information on three-dimensional volumetric changes can be calculated (Goff and Ashmore, 1994; Ham and Church, 2000; Fuller et al., 2003b, 2005). This approach, however, is subject to error propagated between cross sections (Lane et al., 1994; Brasington et al., 2000; Westaway et al., 2000), as typical distance between cross sections can be tens of metres or more. When spaced closer together (b5 m), data from cross sections have been used to produce DEMs (e.g., Milan et al., 2001). This study further highlights problems in using cross section data for DEM generation. Morphological-based survey approaches have gradually become established with the advent of more sophisticated field survey hardware such as total stations and differential GPS. The benefits of adopting the morphological
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Fig. 6. Surface DEM error as a function of local surface topographic variation.
approach to river bed survey are clear: survey of morphological outlines, cut banks, breaks of slope, and inclusion of spot heights on uniform surfaces reduces DEM error. Other advances in hardware, such as aerial LiDAR (e.g., Charlton et al., 2003), terrestrial laser scanning (Heritage and Hetherington, 2005; Milan et al., 2007; Heritage and Milan, 2009), and synoptic remote sensing (Lane et al., 2003), provide high resolution, fully distributed, three-dimensional data of a surface. While the spatial coverage of TLS data is good, evidence suggests a much greater range of error associated with individual point elevations. This may be due to several factors including (i) returning laser light reflected off of
multiple targets, such as vegetation inside the footprint of the laser being interpreted as the ground surface; (ii) the lateral spread of the laser footprint over the sloping terrain; (iii) the inappropriate use of the first return signal; (iv) the influence of strong reflectors adjacent to weaker reflecting surfaces and (v) aerosol returns (see Heritage and Large, 2009, for a full overview). In this study, the focused nature of the morphology-based techniques was able to identify slope breaks better than the grid-based aerial survey techniques allowing the interpolators to better model these features. The increased grid point resolution achievable as LiDAR technology advances will reduce this difference.
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Table 2 Rating relationships for predicting vertical error from local surface variability, for different sampling strategies and interpolation algorithm.
Aerial LiDAR All morphology outline Basic morphology Cross section Morphology and spot heights
Default kriging
Variogram kriging
Inverse distance to a power
Minimum curvature
y = 0.4988x+ 0.0282 y = 0.3366x + 0.1532 y = 0.3513x + 0.1434 y = 0.407x + 0.095 y = 0.3967x + 0.0939
y = 0.2474x + 0.2045 y = 0.272x + 0.1788 y = 0.3962x + 0.1095 y = 0.3685x + 0.1045
y = 0.5001x + 0.0298 y = 0.2789x + 0.2015 y = 0.3234x + 0.1594 y = 0.4123x + 0.096 y =0.0676x + 0.0805
y = 0.3747x + 0.1648 y = 0.4093x + 0.1517 y = 0.3899x + 0.1606 y = 0.3983x + 0.1086
4.2. Interpolation algorithms The interpolation algorithm that is used to model spatial data can influence the accuracy/quality of the surface produced (Goovaerts, 2000, 2001; Lloyd and Atkinson, 2001; Siska and Hung, 2001; Kastens and Staggenborg, 2002; Chaplot et al., 2006; Yue et al., 2007). The choice of algorithm is in part dependent upon the nature of the morphological surface under investigation. While in fluvial geomorphology, TINs (e.g. Butler et al., 1998; Brasington et al., 2000; Vallé and Pasternack, 2006; Milan et al., 2007; Rumsby et al., 2008;) or kriging (Fuller et al., 2003a; Nicholas, 2003) are the most common interpolation algorithms used, Fuller and Hutchinson (2007) in a comparison found TINs to be more reliable. Furthermore, the solution of TINs can be computationally efficient and well suited to discontinuous shapes (such as ridges), and breaks of slope (Moore et al., 1991). The findings of this study further support the use of TINs as the best interpolator in fluvial environments, although the choice of the interpolation algorithm is not as important as survey strategy. Ground-based surveys that map morphological features such as bar edges, augmented by additional spot heights, can provide comparably low errors to higher density surveys such as those obtained from aerial LiDAR. However, the interpolation method is also important; the results obtained across the point bar surface on the River Nent support the use of TINs or point kriging. Error can be introduced to the survey if an inappropriate point sampling regime is used, e.g., merely surveying bar and chute outlines or bar outlines. The outline of the features, top and base of breaks of slope and spot heights on flat surfaces, should be surveyed. Strong relationships exist between local surface topographic variation and DEM error. The nature of this relationship also shows variations dependent upon the field survey strategy and the interpolation algorithm used (Fig. 6; Table 2). Following an assessment of the spatial surface topographic variability (a relatively straightforward procedure with commercial spatial analysis software packages), we suggest the application of one of the curves presented in Fig. 6, dependent upon the sampling strategy and interpolation algorithm used. 5. Conclusions This study used an independent terrestrial laser-scanned survey to model the surface of a cobble-gravel point bar in a river draining an upland part of the Pennine orefield in northern England. This represents the most comprehensive and accurate data set collected for a gravel-bed river system against which field survey and the data interpolation techniques may be compared. Comparison of DEMs created using a variety of field sampling strategies and interpolation algorithms with the base data set allow the following general conclusions to be drawn from the study: (i) DEM error is strongly influenced by the position of survey points relative to the morphology being surveyed; (ii) choice of the interpolation algorithm is less important; (iii) TINs using bar-chute-spot data represented the best overall combination for morphologically based surveys;
Triangulation with linear interpolation y = 0.4432x + 0.0434 y = 0.3647x + 0.1489 y = 0.3488x + 0.1465 y = 0.4274x + 0.0808 y = 0.4109x + 0.0911
(iv) error across a modelled surface is not uniform and is a function of local form roughness; and (v) results from the error analysis have generated a series of equations for each survey strategy / interpolation combination, that may be applied to regular grid files to produce a grid of spatially distributed error. We recommend use of the appropriate equation to assess the error associated with regular grid files during the process of DEM differencing. Finally, in light of the results outlined above, we recommend that, in addition to spot height data, ground-based surveys should focus on morphological features such as bar edges and other breaks in slope, as this approach provides similar errors to grid-based surveys such as those obtained from aerial LiDAR. Acknowledgements We would like to thank the landowners at Blagill, Mr. and Mr. Graham, for allowing access to their land. We are also grateful for the comments of three anonymous reviewers.
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French, J.R., 2003. Airborne LiDAR in support of geomorphological and hydraulic modelling. Earth Surface Processes and Landforms 28, 321–335. Fuller, I.C., Hutchinson, E., 2007. Sediment flux in a small gravel-bed stream: response to channel remediation works. New Zealand Geographer 63, 169–180. Fuller, I.C., Marden, M., 2008. Connectivity in steepland environments: gully-fan coupling in the Tarndale system, Waipaoa catchment, New Zealand. In: Schmidt, J., Cochrane, T., Phillips, C., Elliott, S., Davies, T., Basher, L. (Eds.), Sediment Dynamics in Changing Environments. IAHS Publ. 325,Wallingford, UK, pp. 275–282. Fuller, I.C., Large, A.R.G., Milan, D.J., 2003a. Quantifying development and sediment transfer following chute cutoff in a wandering gravel-bed river. Geomorphology 54, 307–323. Fuller, I.C., Large, A.R.G, Charlton, M.E., Heritage, G.L., Milan, D.J., 2003b. Reach-scale sediment transfers: an evaluation of two morphological budgeting approaches. Earth Surface Processes and Landforms 28, 889–903. Fuller, I.C., Large, A.R.G., Heritage, G.L., Milan, D.J., Charlton, M.E., 2005. Derivation of reach-scale sediment transfers in the River Coquet, Northumberland, UK. In: Blum, M., Marriott, S., Leclair, S. (Eds.), Fluvial Sedimentology VII, IAS Special Publication, vol. 35. Wiley-Blackwell, Chichester, UK, pp. 61–74. Goff, J.R., Ashmore, P.E., 1994. Gravel transport and morphological change in braided Sunwapta River, Alberta, Canada. Earth Surface Processes and Landforms 19, 195–213. Goovaerts, P., 2000. Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall. Journal of Hydrology 228, 113–129. Ham, D.G., Church, M., 2000. Bed-material transport estimated from channel morphodynamics: Chilliwack River, British Columbia. Earth Surface Processes and Landforms 25, 1123–1142. Hancock, G.R., 2006. The impact of different gridding methods on catchment geomorphology and soil erosion over long timescales using a landscape evolution model. Earth Surface Processes and Landforms 31, 1035–1050. Heritage, G.L., Hetherington, D., 2005. Towards a protocol for laser scanning in fluvial geomorphology. Earth Surface Processes and Landforms 32, 66–74. Heritage, G.L., Milan, D.J., 2009. Terrestrial laser scanning of grain roughness in a gravelbed river. Geomorphology. doi:10.1016/j.geomorph.2009.03.021. Heritage, G.L., Hetherington, D., Large, A.R.G., Fuller, I., Milan, D.J., 2006. Terrestrial laser scanner based roughness quantification using a random field approach. In: Devereux, B.J., Amable, G.S., Fuller, R.M. (Eds.), Understanding a Changing World: Integrated Approaches to Monitoring, Measuring and Modeling the Environment. Proceedings of RSPSoc 2006: Understanding a Changing World, 5–8 September 2006, Fitzwilliam College, University of Cambridge, UK. The Remote Sensing and Photogrammetry Society (RSPSoc). Heritage, G.L., Large, A.R.G., 2009. Fundamentals of laser scanning. In: Heritage, G.L., Large, A.R.G. (Eds.), Laser Scanning for the Environmental Sciences. Wiley-Blackwell, Chichester, UK, pp. 21–35. Kastens, T., Staggenborg, S., 2002. Spatial interpolation accuracy. Kansas State Precision Conference. Great Bend. www.agmanager.info/crops/prodecon/precision/default.asp. Lane, S.N., 1998. The use of digital terrain modelling in the understanding of dynamic river systems. In: Lane, S.N., Richards, K.S., Chandler, J.H. (Eds.), Landform Monitoring, Modelling and Analysis. John Wiley and Son Ltd., Chichester, UK, pp. 311–342. Lane, S.N., Chandler, J.H., Richards, K.S., 1994. Developments in monitoring and modelling small-scale river bed topography. Earth Surface Processes and Landforms 19, 349–368. Lane, S.N., Westaway, R.M., Hicks, M., 2003. Estimation of erosion and deposition volumes in a large, gravel-bed, braided river using synoptic remote sensing. Earth Surface Processes and Landforms 28, 249–271.
Lindsay, J.B., Ashmore, P.E., 2002. The effects of survey frequency on estimates of scour and fill in a braided river model. Earth Surface Processes and Landforms 27, 27–43. Lloyd, C.D., Atkinson, P.M., 2001. Assessing uncertainty in estimates with ordinary and indicator kriging. Computers and Geosciences 27, 929–937. Macklin, M.G., 1986. Channel and floodplain metamorphosis in the River Nent, Cumberland. In: Macklin, M.G., Rose, J. (Eds.), Quaternary River Landforms and Sediments in the North Pennines, England. Field Guide, British Geomorphological Research Group/Quaternary Research Association, pp. 19–33. Maizels, J.K., 1979. Proglacial aggradation and changes in braided channel patterns during a period of glacial advance: an alpine example. Geografiska Annaler 61A, 87–101. Milan, D.J., 2009. Terrestrial laser-scan derived topographic and roughness data for hydraulic modelling of gravel-bed rivers. In: Heritage, G.L., Large, A.R.G. (Eds.), Laser Scanning for the Environmental Sciences. Wiley-Blackwell, Chichester, UK, pp. 133–146. Milan, D.J., Heritage, G.L., Large, A.R.G., Charlton, M.E., 2001. Stage-dependent variability in shear stress distribution through a riffle-pool sequences. Catena 44, 85–109. Milan, D.J., Hetherington, D., Heritage, G.L., 2007. Application of a 3D laser scanner in the assessment of a proglacial fluvial sediment budget. Earth Surface Processes and Landforms 32, 1657–1674. Moore, I.D., Grayson, R.B., Ladson, A.R., 1991. Digital terrain modelling: a review of hydrological, geomorphological, and biological applications. Hydrological Processes 5, 3–30. Nicholas, A.P., 2003. Investigation of spatially distributed braided river flows using a two-dimensional hydraulic model. Earth Surface Processes and Landforms 28, 655–674. Rumsby, B.T., Brasington, J., Langham, J.A., McLelland, S.J., Middeton, R., Rollinson, G., 2008. Monitoring and modelling particle and reach-scale morphological change in gravel-bed rivers: applications and challenges. Geomorphology 93, 40–54. Siska, P.P., Hung, I.K., 2001. Propagation of errors in spatial analysis. Papers and Proceedings of the Applied Geography Conferences, vol. 24. University of North Texas, pp. 284–290. Vallé, B.L., Pasternack, G.B., 2006. Field mapping and digital elevation modelling of submerged and unsubmerged hydraulic jump regions in a bedrock step-pool channel. Earth Surface Processes and Landforms 31, 646–664. Wechsler, S.P., 2000. Effect of DEM uncertainty on topographic parameters, DEM scale and terrain evaluation. State University of New York College of Environmental Science and Forestry. Syracuse, New York, USA. Westaway, R.M., Lane, S.N., Hicks, D.M., 2000. The development of an automated correction procedure for digital photogrammetry for the study of wide, shallow, gravel-bed rivers. Earth Surface Processes and Landforms 25, 209–226. Wood, J., 1996. Scale-based characterization of digital elevation models. In: Parker, D. (Ed.), Innovations in GIS 3. Taylor and Francis, London, UK. Yue, T., Du, Z., Song, D., Gong, Y., 2007. A new method of surface modelling and its application to DEM construction. Geomorphology 91, 161–172.
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Geomorphology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / g e o m o r p h
Influence of survey strategy and interpolation model on DEM quality George L. Heritage a,⁎, David J. Milan b, Andrew R.G. Large c, Ian C. Fuller d a JBA Consulting, The Brew House, Wilderspool Park, Greenhalls Avenue, Warrington, WA4 6HL United Kingdom (Research Fellow, Built and Human Environment Research Institute, University of Salford, Manchester, M5 4WT, United Kingdom) b Department of Natural and Social Sciences, University of Gloucestershire, Cheltenham, GL50 4AZ, United Kingdom c School of Geography, Politics and Sociology, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom d School of People, Environment and Planning, Massey University, Palmerston North, New Zealand
a r t i c l e
i n f o
Article history: Received 20 February 2009 Received in revised form 24 June 2009 Accepted 25 June 2009 Available online 14 July 2009 Keywords: Terrestrial laser scanning LiDAR Gravel-bed rivers DEM Interpolation Survey strategy
a b s t r a c t Accurate characterisation of morphology is critical to many studies in the field of geomorphology, particularly those dealing with changes over time. Digital elevation models (DEMs) are commonly used to represent morphology in three dimensions. The quality of the DEM is largely a function of the accuracy of individual survey points, field survey strategy, and the method of interpolation. Recommendations concerning field survey strategy and appropriate methods of interpolation are currently lacking. Furthermore, the majority of studies to date consider error to be uniform across a surface. This study quantifies survey strategy and interpolation error for a gravel bar on the River Nent, Blagill, Cumbria, UK. Five sampling strategies were compared: (i) cross section; (ii) bar outline only; (iii) bar and chute outline; (iv) bar and chute outline with spot heights; and (v) aerial LiDAR equivalent, derived from degraded terrestrial laser scan (TLS) data. Digital Elevation Models were then produced using five different common interpolation algorithms. Each resultant DEM was differentiated from a terrestrial laser scan of the gravel bar surface in order to define the spatial distribution of vertical and volumetric error. Overall triangulation with linear interpolation (TIN) or point kriging appeared to provide the best interpolators for the bar surface. Lowest error on average was found for the simulated aerial LiDAR survey strategy, regardless of interpolation technique. However, comparably low errors were also found for the bar-chute-spot sampling strategy when TINs or point kriging was used as the interpolator. The magnitude of the errors between survey strategy exceeded those found between interpolation technique for a specific survey strategy. Strong relationships between local surface topographic variation (as defined by the standard deviation of vertical elevations in a 0.2-m diameter moving window), and DEM errors were also found, with much greater errors found at slope breaks such as bank edges. A series of curves are presented that demonstrate these relationships for each interpolation and survey strategy. The simulated aerial LiDAR data set displayed the lowest errors across the flatter surfaces; however, sharp slope breaks are better modelled by the morphologically based survey strategy. The curves presented have general application to spatially distributed data of river beds and may be applied to standard deviation grids to predict spatial error within a surface, depending upon sampling strategy and interpolation algorithm. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Digital elevation modelling of morphological features is widely used throughout geomorphology. In fluvial geomorphology, detailed topographic data of bed and floodplain surfaces are required in process-based numerical models (Booker et al., 2001; French, 2003; Ferguson et al., 2003; Milan, 2009) and cellular models (DoeschlWilson and Ashmore, 2005; Coulthard et al., 2007) where a definition of morphology and surface roughness can be critical to flow, sediment transport predictions, and channel change estimation. Digital elevation model (DEM) differencing is being increasingly used to identify and quantify morphological change, to determine scour and fill ⁎ Corresponding author. Tel.: +44 1925 437020; fax: +44 1925 437029. E-mail address: [email protected] (G.L. Heritage). 0169-555X/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2009.06.024
volumes, and to provide detailed spatial and temporal insights into the locations of scour and fill (Brasington et al., 2000; Lindsay and Ashmore, 2002; Brasington et al., 2003; Fuller et al., 2003a, Lane et al., 2003; Milan et al., 2007; Rumsby et al., 2008). As such, the application of DEMs in fluvial geomorphology is becoming increasingly utilised in the field of morphological budgeting at the reach scale (Ashmore and Church, 1998) and as a tool to elucidate a process (Fuller et al., 2003b; Fuller and Hutchinson, 2007; Fuller and Marden, 2008). The quality of the DEM is fundamental to the success of the above approaches and has been shown to be influential to the output of the flow simulations (Milan, 2009) and in the derivation of accurate volumetric estimates of channel change (Fuller et al., 2005). Meaningful interpretation of sediment volumes and the spatial distribution of scour and fill derived from DEM differencing must consider error within the surface. During DEM differencing, the magnitude of the
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error propagated between two surfaces can exceed the vertical change under consideration, particularly subtle scour or fill (i.e.,± 0.25 m). Lane et al. (1994) and Lane (1998) suggested that DEM quality is a function of (i) the quality of the individual data points within the surface, (ii) the density of data points used to represent the surface, and (iii) the distribution of data points within the surface. Both (ii) and (iii) are related to the field sampling strategy and to the hardware used to collect the data. Hancock (2006) further indicated that the interpolation method used to produce the DEM may also influence the character of the DEM, although limited attention has been given towards the suitability of the interpolation algorithm used to model the spatial dataset. To address this gap, we use a detailed and accurate terrestrial laser scan (TLS) based three-dimensional data set to clarify the importance of (i) field sampling strategy, i.e., where points are surveyed relative to the morphology, and (ii) data interpolation techniques used in the production of the DEM. Errors associated with various combinations of survey strategy and interpolation technique and the influence of local topographic variability error are also explored. 2. Methodology 2.1. Study area and acquisition of surface control data The study focused upon a 9900-m2 area of point bar on the River Nent at Blagill in the North Pennine uplands, Cumbria, UK (Fig. 1). The River Nent drains an upland catchment of 29.4 km2 before flowing into the River South Tyne west of Alston. The geology of the basin consists of sedimentary rocks, principally sandstone, shale, and limestone that have undergone extensive base metal mineralisation. The river may be described as wandering in nature, following the criteria set out by Church (1983). The study is sited within one of two instability zones 0.2–0.3 km in length, which are separated by a stable single-thread reach of 150 m (Fig. 1). Channel metamorphosis has been documented at this site since the 1700s as a result of system loading with fines generated by mining activity (Macklin, 1986), with more recent channel response being described by Chappell et al. (2003). Anthropogenic activity has had an unexpected benefit: this section of the River Nent has been classified as an Special Site of Scientific Interest (SSSI) by English Nature because of the wandering nature of the channel and the metalophyte plant community that thrives on the floodplain. Planform change and bar activity is evident in both the upstream and downstream instability zones creating a dynamic assemblage of morphologic units. 2.2. DEM validation Quantifying the accuracy of DEMs generated from survey data is difficult since validation requires comparison between the derived DEMs and a second, more accurate surface (Wood, 1996; Brasington et al., 2000, 2003). Usually the acquisition of this surface is impossible, therefore DEM validation is often based on quantifying model uncertainty through diagnostic surface visualisations or field “ground truthing” (Wood, 1996; Wechsler, 2000). However, this study was able to obtain the control surface using a terrestrial laser scanner that is capable of producing a surface accurate to the grain scale, i.e., the D50 surface roughness in gravel-dominated systems (Heritage and Hetherington, 2005; Heritage et al., 2006; Heritage and Milan, 2009). An LMS Z-210™ scanning laser manufactured by Riegl Instruments (Horn, Austria) was used to collect topographic data for the control DEM. The instrument works on the principle of “time of flight” measurement using a pulsed eye-safe infrared laser source (~0.9 µm wavelength) emitted in precisely defined angular directions controlled by a spinning mirror arrangement. A sensor records the time taken for the emitted laser light to be reflected from the incident surface. Angular measurements are recorded to an accuracy of 0.036o in the vertical and 0.018o in the horizontal.
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Survey control was facilitated by RiScan Pro™ survey software that is capable of visualising the large volumes of point cloud data generated by repeat scans in the field. Scans were generally restricted to 240o in front of the scanner, and scans were collected with substantial overlap ensuring that the surface of the study reach was recorded from several directions. The effect of this approach is to increase the point resolution across the surface (and the data volume) and to reduce the possibility of unscanned areas because of the shadowing effect of larger roughness elements along the line of each scan. Before scans were taken, a total of 20 reflectors were placed on and around the study reach. These reflectors were tied into the project coordinate system using an EDM theodolite and were automatically located by the RiScan Pro™ software and matched to the project coordinates using a common point configuration algorithm. A total of 253,000 points were recorded across the point bar surface with median spacing of 0.09 m (lower and upper quartiles = 0.05 and 0.13 m). Terrestrial laser scan data accuracy was evaluated through the collection of 186 independent prominent surface point coordinates using an EDM theodolite obtained at the same time as the TLS survey. There was good agreement between the two data sets, with a median error of − 0.003 m, 72% of the TLS elevation values were within ± 0.05 m of the theodolite points (Fig. 2), and this value was used as the threshold of accurate detection for the surface control DEM. The TLS data were subsequently used to generate a 0.05-m resolution DEM of the point bar surface. Delauney triangulation with linear interpolation was employed as an exact interpolator. 2.3. Spatial sampling technique A TOPCON EDM theodolite (accuracy ± 5 mm) was used to gather data from the study reach using several different sampling regimes: (i) cross section; (ii) bar outline only (in order to highlight the issue of low survey density within a geomorphic unit); (iii) bar and chute outline, and (iv) bar and chute outline with spot heights on uniform surfaces (Fig. 3). A fifth sampling strategy (v) aimed to simulate the spatial sampling resolution that can be obtained using aerial LiDAR. In the absence of the actual aerial LiDAR data, this was achieved through degradation of the TLS control data. By extracting closest point data based on a 2-m regular grid from the TLS data, an equivalent resolution scan to that obtained through airborne LiDAR by Charlton et al. (2003) was achieved. Random errors in the range ± 0.15 m were added to each of the data points, thus replicating the reported errors on aerial LiDAR in a similar environment (Charlton et al., 2003). Data from all of these survey strategies were then used to generate equivalent resolution (0.05 m) DEMs using a range of interpolation algorithms. Five different common interpolation procedures were applied to each of the data sets using Surfer™ GIS: (i) inverse distance to a power (squared); (ii) kriging using the default point kriging variogram options in Surfer; (iii) kriging using a variogram produced from the survey data; (iv) minimum curvature, and (v) Delauney triangulation with linear interpolation (TINs). 3. Results 3.1. Spatial variations in vertical error DEMs for each sampling strategy and interpolation technique were subtracted from the surface control DEM created using TLS data. Digital elevation models of elevation difference (DoDs) in excess of the error within the TLS surface control DEM of the bar surface (±0.05 m) were produced (Fig. 4). Average aerial elevation error statistics for the bar surface as a whole are summarised in Table 1, ranked vertically by standard deviation of the errors. Standard deviation values demonstrate that the simulated aerial LiDAR survey strategy has the lowest overall error regardless of the interpolation technique. This is followed by the bar and chute with spot height
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Fig. 1. Study location, Blagill, River Nent, Cumbria. (a) Catchment map, and (b) aerial photograph of reach (Googleearth.com).
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Fig. 2. Terrestrial laser scanner data accuracy, evaluated through the collection of 186 independent prominent surface point coordinates using an EDM theodolite, obtained at the same time as the TLS.
strategy associated with the kriging algorithm. Errors are greatest when the minimum curvature algorithm is used, particularly where the survey data consisted of cross section or basic bar outline only. Spatial differences in the degree of survey and interpolation error are evident (Fig. 4). The channel and chute features tend to have their depth overestimated, and the bars tend to have their height overestimated. Errors appear lowest overall for the aerial LiDAR and bar-chute-spot height sampling strategy, regardless of the interpolation technique, a feature evident for each of the interpolation
procedures used. For the cross section survey strategy, errors are lowest close to the cross section points and highest in areas where there is no measured data (between the sections). The head of the point bar has high positive elevation errors in the order of 0.7 m when a bar outline and chute-bar sampling strategy was employed, using a minimum curvature or triangular linear interpolation as the interpolator (Fig. 4d,e). High negative errors are also evident at the tail of the bar feature for the bar outline and chute-bar sampling strategies, when minimum curvature was used as the interpolator (Fig. 4e). The
Fig. 3. Point bar site on the River Nent, demonstrating a) DEM of bar surface based upon TLS data, and b) the position of sample points used to create DEMs for different sampling strategies. The bar is orientated west–east.
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greatest channel and chute errors are exhibited in the DoDs produced using only bar outline and a chute-bar sampling regime with no spot heights, with kriging using the variogram derived from the field data as the interpolator. 3.2. Net elevation and volumetric error Volumetric error was calculated by subtracting each of the DEMs in Fig. 4 from the control surface produced from the TLS data (Fig. 3a), after first removing the ± 0.05-m error associated with the TLS
surface. The results shown in Fig. 5 indicate that the aerial LiDAR resolution survey displays the lowest vertical and volumetric errors out of all the sampling regimes. Volumetric survey errors ranged between 400 and 1100 m3 across the 9900-m2 point bar survey area; this is equivalent to an average vertical error of between 0.04 and 0.11 m. Mean volumetric errors are between 350 and 400 m3 across the 9900-m2 point bar survey area. Notably the bar-chute-spot height survey obtained using a total station can provide comparable errors to those obtained using simulated aerial LiDAR, if point default value kriging or triangulation with linear interpolation is used as the
Fig. 4. Surface error maps: (a) inverse to a distance power, (b) default kriging, (c) kriging using variogram produced from the field data, (d) minimum curvature, and (e) Dalauney triangulation TIN. The blank area shown on the DEM represents an area where there were no laser returns from the bed surface, due to ponding of water in a chute channel. The maps are orientated west–east.
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Fig. 4 (continued).
interpolation algorithm. The inverse distance squared algorithm was consistently poor, giving a total volumetric error of between 800 and 1100 m3 for all sampling regimes with the exception of aerial LiDAR. Bar-chute, bar outline, and cross section sampling regimes gave the poorest volumetric errors (generally in excess of 600 m3 regardless of interpolation method); however, the choice of interpolation algorithm does seem to make an important difference to the accuracy of the surface. This is particularly evident for the cross section sampling regime, where errors were as low as 450 m3, when triangulation with linear interpolation was used.
The location of survey points and hence survey strategy is important and should be sensitive to the morphology under consideration (e.g., Chappell et al., 2003). Greatest vertical error is likely to be found at breaks of slope, such as bank edges, unless the top and base of the slope are surveyed and subsequently honoured by the interpolator. Interpolation algorithms are normally used to approximate the surface elevation based upon the elevation of the surrounding measured data. If measured data are sparse in regions of high topographic variation, then the topography is generally more poorly modelled by the interpolator. Hence, more data is needed where there are
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Fig. 4 (continued).
relatively large changes in elevation over short distances (e.g., bank edges). Conversely, fewer points are required over flatter surfaces (e.g., bar tops). To date in fluvial geomorphology however, DEM error has only been considered to be uniform in nature across the DEM (e.g. Brasington et al., 2000, 2003; Lane et al., 2003; Milan et al., 2007).
3.3. Vertical error and local surface variability The spatial distribution of field survey and data interpolation error was further explored through an investigation of the relation between local form roughness as defined by standard deviation of bed
Table 1 Combined survey and interpolation error statistics for the point bar surface at Blagill on the River Nent, Cumbria.
Kriging (variogram) Kriging (default value) Inverse distance Triangular linear interpolation Minimum curvature Kriging (default value) Kriging (variogram) Triangular linear interpolation Minimum curvature Triangular linear interpolation Kriging (default value) Kriging (default value) Inverse distance Kriging (default value) Triangular linear interpolation Inverse distance Triangular linear interpolation Inverse distance Kriging (variogram) kriging (variogram) Inverse distance Kriging (variogram) Minimum curvature Minimum curvature Minimum curvature
Aerial Aerial Aerial Aerial Aerial Spots and morphology Spots and morphology Spots and morphology Spots and morphology Cross sections All morphology Basic morphology Cross sections Cross sections All morphology Spots and morphology Basic morphology Basic morphology Cross sections Basic morphology All morphology All morphology Basic morphology All morphology Cross sections
Mean
Median
Minimum
Maximum
First quartile
Third quartile
StDev
Skew
Kurtosis
0.002 0.002 − 0.003 0.001 0.006 0.034 0.056 0.035 0.017 − 0.010 0.098 0.083 − 0.040 − 0.063 0.102 0.098 0.078 0.071 − 0.053 0.088 0.148 0.135 0.050 0.057 − 0.015
0.003 0.003 − 0.001 0.002 0.006 0.001 0.023 0.009 − 0.007 0.009 0.068 0.066 − 0.020 − 0.024 0.069 0.064 0.059 0.089 − 0.025 0.131 0.163 0.167 0.013 0.011 − 0.002
− 1.152 − 1.152 − 1.100 − 1.203 − 1.213 − 1.259 − 1.120 − 1.290 − 1.384 − 1.503 − 1.259 − 1.341 − 1.421 − 1.414 − 1.290 − 1.348 − 1.357 − 1.389 − 1.325 − 1.131 − 1.350 − 1.049 − 1.695 − 1.525 − 1.692
1.267 1.267 1.072 1.339 1.374 1.548 1.415 1.508 1.644 1.226 1.575 1.506 1.299 1.242 1.548 1.405 1.397 1.428 1.298 1.290 1.462 1.436 2.576 2.679 1.408
− 0.078 − 0.078 − 0.088 − 0.081 − 0.083 − 0.067 − 0.064 − 0.059 − 0.084 − 0.093 − 0.056 − 0.058 − 0.194 − 0.207 − 0.051 − 0.081 − 0.062 − 0.100 − 0.230 − 0.111 − 0.060 − 0.083 − 0.089 − 0.103 − 0.182
0.083 0.083 0.085 0.086 0.094 0.088 0.138 0.092 0.072 0.097 0.227 0.217 0.123 0.098 0.236 0.232 0.204 0.251 0.133 0.295 0.347 0.345 0.162 0.175 0.188
0.184 0.184 0.188 0.189 0.197 0.213 0.213 0.216 0.238 0.238 0.250 0.251 0.256 0.258 0.260 0.264 0.265 0.268 0.271 0.280 0.282 0.283 0.297 0.304 0.351
− 0.155 − 0.155 − 0.236 − 0.121 − 0.022 1.428 1.042 1.118 1.426 − 0.425 0.506 0.029 − 0.344 − 0.514 0.372 0.642 0.036 − 0.241 − 0.342 − 0.358 −0.033 − 0.150 0.678 1.039 − 0.488
4.625 –4.298 3.424 4.484 4.664 6.094 3.337 5.857 6.784 2.786 2.084 2.044 0.515 0.556 1.867 0.952 2.105 0.860 0.110 − 0.125 0.196 − 0.274 4.396 4.274 0.957
Data are sorted vertically by the standard deviation of the errors.
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Fig. 5. Error summary for different survey sampling strategies and interpolation methods (inverse distance to a power-IDP, kriging using the default point kriging variogram options in Surfer-PK, kriging using a variogram produced from the survey data-BK, minimum curvature-MC, Delauney triangulation with linear interpolation-TIN), based upon the DEMs of difference presented in Fig. 4: (a) vertical error, (b) volumetric error.
elevations in a 0.1-m radius moving window. The approach calculated the local standard deviation of all points occurring within the 0.1-m radius search window of every point in the TLS point cloud data set; these values were then averaged across a 0.1-m regular grid corresponding to point records in the DoD data. The spatially variable error displayed in each of the DoDs in Fig. 4 could then be directly associated with the standard deviation grid. During the moving window processing, a zero value for the local standard deviation was recorded for areas with less than eight data points present within the window. This was the case for areas where very few laser returns from the bed from ponding of water in chute channels on the bar surface (shown on the DoDs in Fig. 4 as a blank area on the inside of the point bar). Breaks of slope such as bank edges and bar edges will have greater local form roughness in comparison to bar surfaces. Local form roughness, as defined by the areal averaged standard deviation values, is plotted against vertical error for each survey strategy and interpolation algorithm in Fig. 6. Clearly, as local form roughness increases so the error associated with the specific survey and the interpolation algorithms also rises, indicating that the interpolation algorithms are unable to accurately model increasingly complex surfaces because of the lack of local data. Errors across the flatter surfaces are generally smallest for the simulated aerial LiDAR data set; however, sharp slope breaks characterised by a higher local standard deviation are better modelled by the morphologic-based survey methodologies where appropriately located data facilitate more accurate interpolation. An important finding of this analysis suggests that the focused nature of the morphology-based techniques identifies slope breaks better than the grid-based aerial survey techniques, allowing the interpolators to better model these features. Densifying the surface data collected will also improve the interpolation accuracy and the local variation is better represented in
the data set. Issues with the survey error resulting in the erroneous interpolation of nonexistent surface variation at low roughness levels require consideration; however, continued improvements to the density and accuracy of the airborne LiDAR data will undoubtedly lead to better surface representation as a result. 4. Discussion 4.1. Field data sampling strategies to detect morphological changes The methods by which river beds are surveyed has changed in response to both hardware and software developments, particularly in the last 10 years. Traditionally, topographic data have been collected to elucidate morphological change using a cross section two-dimensional approach (e.g. Brewer and Passmore, 2002). Morphological change was quantified by superimposing successive cross sections to identify areas of scour and fill (Maizels, 1979; Ashworth and Ferguson, 1986; Fenn and Gurnell, 1987; Ashworth and Ferguson, 1994). When cross sections are linked together, information on three-dimensional volumetric changes can be calculated (Goff and Ashmore, 1994; Ham and Church, 2000; Fuller et al., 2003b, 2005). This approach, however, is subject to error propagated between cross sections (Lane et al., 1994; Brasington et al., 2000; Westaway et al., 2000), as typical distance between cross sections can be tens of metres or more. When spaced closer together (b5 m), data from cross sections have been used to produce DEMs (e.g., Milan et al., 2001). This study further highlights problems in using cross section data for DEM generation. Morphological-based survey approaches have gradually become established with the advent of more sophisticated field survey hardware such as total stations and differential GPS. The benefits of adopting the morphological
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Fig. 6. Surface DEM error as a function of local surface topographic variation.
approach to river bed survey are clear: survey of morphological outlines, cut banks, breaks of slope, and inclusion of spot heights on uniform surfaces reduces DEM error. Other advances in hardware, such as aerial LiDAR (e.g., Charlton et al., 2003), terrestrial laser scanning (Heritage and Hetherington, 2005; Milan et al., 2007; Heritage and Milan, 2009), and synoptic remote sensing (Lane et al., 2003), provide high resolution, fully distributed, three-dimensional data of a surface. While the spatial coverage of TLS data is good, evidence suggests a much greater range of error associated with individual point elevations. This may be due to several factors including (i) returning laser light reflected off of
multiple targets, such as vegetation inside the footprint of the laser being interpreted as the ground surface; (ii) the lateral spread of the laser footprint over the sloping terrain; (iii) the inappropriate use of the first return signal; (iv) the influence of strong reflectors adjacent to weaker reflecting surfaces and (v) aerosol returns (see Heritage and Large, 2009, for a full overview). In this study, the focused nature of the morphology-based techniques was able to identify slope breaks better than the grid-based aerial survey techniques allowing the interpolators to better model these features. The increased grid point resolution achievable as LiDAR technology advances will reduce this difference.
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Table 2 Rating relationships for predicting vertical error from local surface variability, for different sampling strategies and interpolation algorithm.
Aerial LiDAR All morphology outline Basic morphology Cross section Morphology and spot heights
Default kriging
Variogram kriging
Inverse distance to a power
Minimum curvature
y = 0.4988x+ 0.0282 y = 0.3366x + 0.1532 y = 0.3513x + 0.1434 y = 0.407x + 0.095 y = 0.3967x + 0.0939
y = 0.2474x + 0.2045 y = 0.272x + 0.1788 y = 0.3962x + 0.1095 y = 0.3685x + 0.1045
y = 0.5001x + 0.0298 y = 0.2789x + 0.2015 y = 0.3234x + 0.1594 y = 0.4123x + 0.096 y =0.0676x + 0.0805
y = 0.3747x + 0.1648 y = 0.4093x + 0.1517 y = 0.3899x + 0.1606 y = 0.3983x + 0.1086
4.2. Interpolation algorithms The interpolation algorithm that is used to model spatial data can influence the accuracy/quality of the surface produced (Goovaerts, 2000, 2001; Lloyd and Atkinson, 2001; Siska and Hung, 2001; Kastens and Staggenborg, 2002; Chaplot et al., 2006; Yue et al., 2007). The choice of algorithm is in part dependent upon the nature of the morphological surface under investigation. While in fluvial geomorphology, TINs (e.g. Butler et al., 1998; Brasington et al., 2000; Vallé and Pasternack, 2006; Milan et al., 2007; Rumsby et al., 2008;) or kriging (Fuller et al., 2003a; Nicholas, 2003) are the most common interpolation algorithms used, Fuller and Hutchinson (2007) in a comparison found TINs to be more reliable. Furthermore, the solution of TINs can be computationally efficient and well suited to discontinuous shapes (such as ridges), and breaks of slope (Moore et al., 1991). The findings of this study further support the use of TINs as the best interpolator in fluvial environments, although the choice of the interpolation algorithm is not as important as survey strategy. Ground-based surveys that map morphological features such as bar edges, augmented by additional spot heights, can provide comparably low errors to higher density surveys such as those obtained from aerial LiDAR. However, the interpolation method is also important; the results obtained across the point bar surface on the River Nent support the use of TINs or point kriging. Error can be introduced to the survey if an inappropriate point sampling regime is used, e.g., merely surveying bar and chute outlines or bar outlines. The outline of the features, top and base of breaks of slope and spot heights on flat surfaces, should be surveyed. Strong relationships exist between local surface topographic variation and DEM error. The nature of this relationship also shows variations dependent upon the field survey strategy and the interpolation algorithm used (Fig. 6; Table 2). Following an assessment of the spatial surface topographic variability (a relatively straightforward procedure with commercial spatial analysis software packages), we suggest the application of one of the curves presented in Fig. 6, dependent upon the sampling strategy and interpolation algorithm used. 5. Conclusions This study used an independent terrestrial laser-scanned survey to model the surface of a cobble-gravel point bar in a river draining an upland part of the Pennine orefield in northern England. This represents the most comprehensive and accurate data set collected for a gravel-bed river system against which field survey and the data interpolation techniques may be compared. Comparison of DEMs created using a variety of field sampling strategies and interpolation algorithms with the base data set allow the following general conclusions to be drawn from the study: (i) DEM error is strongly influenced by the position of survey points relative to the morphology being surveyed; (ii) choice of the interpolation algorithm is less important; (iii) TINs using bar-chute-spot data represented the best overall combination for morphologically based surveys;
Triangulation with linear interpolation y = 0.4432x + 0.0434 y = 0.3647x + 0.1489 y = 0.3488x + 0.1465 y = 0.4274x + 0.0808 y = 0.4109x + 0.0911
(iv) error across a modelled surface is not uniform and is a function of local form roughness; and (v) results from the error analysis have generated a series of equations for each survey strategy / interpolation combination, that may be applied to regular grid files to produce a grid of spatially distributed error. We recommend use of the appropriate equation to assess the error associated with regular grid files during the process of DEM differencing. Finally, in light of the results outlined above, we recommend that, in addition to spot height data, ground-based surveys should focus on morphological features such as bar edges and other breaks in slope, as this approach provides similar errors to grid-based surveys such as those obtained from aerial LiDAR. Acknowledgements We would like to thank the landowners at Blagill, Mr. and Mr. Graham, for allowing access to their land. We are also grateful for the comments of three anonymous reviewers.
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