A comparision of interpolation methods for producing digital elevation models at the field scale

Digital elevation models have been used in many applications since they came into use in the late 1950s. It is an essential tool for applications that are concerned with the Earth's surface such as hydrology, geology, cartography, geomorphology, engineering applications, landscape architecture and so on. However, there are some differences in assessing the accuracy of digital elevation models for specific applications. Different applications require different levels of accuracy from digital elevation models. In this study, the magnitudes and spatial patterning of elevation errors were therefore examined, using different interpolation methods. Measurements were performed with theodolite and levelling. Previous research has demonstrated the effects of interpolation methods and the nature of errors in digital elevation models obtained with indirect survey methods for small‐scale areas. The purpose of this study was therefore to investigate the size and spatial patterning of errors in digital elevation models obtained with direct survey methods for large‐scale areas, comparing Inverse Distance Weighting, Radial Basis Functions and Kriging interpolation methods to generate digital elevation models. The study is important because it shows how the accuracy of the digital elevation model is related to data density and the interpolation algorithm used. Cross validation, split‐sample and jack‐knifing validation methods were used to evaluate the errors. Global and local spatial auto‐correlation indices were then used to examine the error clustering. Finally, slope and curvature parameters of the area were modelled depending on the error residuals using ordinary least regression analyses. In this case, the best results were obtained using the thin plate spline algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

Smoothing of digital elevation models and the alteration of overland flow path length distributions

DEM smoothing is a common pre-processing technique used to remove undesirable roughness from a DEM. However, it is hypothesized that smoothing straightens and reduces the length of overland flow paths, which is an important factor controlling modelled time-to-peak flow. Currently, there is a lack of research comparing how different smoothing techniques alter the distribution of overland flow path length. Four low-pass filtering techniques were applied to three fine-resolution LiDAR DEMs of varying relief: the mean filter, the median filter, the Gaussian filter, and the feature-preserving DEM smoothing (FPDEMS) filter, each with different degrees of smoothing. Downslope-distance-to-stream distributions were then derived using D8 and D∞ flow directions and statistically compared to distributions derived from the unsmoothed DEM for each study site. The results indicate that the alteration of flow path length distributions as a result of smoothing is complex. Mean flow path lengths may decrease or increase in response to smoothing, depending on landscape relief and the derivation of flow directions, and generalized flow paths may become longer. The largest increase in mean flow path lengths was 19.2 m using the 21 × 21 median filter and D8 flow directions in the high-relief study site, relative to an unsmoothed mean length of 138.6 m in this site. The largest decrease in mean flow path length was 48.9 m using the 21 × 21 mean filter and D∞ flow directions in the low-relief study site, relative to an unsmoothed mean length of 290.9 m in this site. Furthermore, minimal flow path length alterations were achieved with the Gaussian filter when gentle smoothing is required, and with the FPDEMS filter when moderate to aggressive smoothing is required. These results suggest that an appropriate smoothing method should be chosen based on the relief of the landscape and the degree of smoothing required.     

The production of digital elevation models for experimental model landscapes

Automated digital photogrammetry was used to produce digital elevation models of experimental model landscapes under controlled laboratory conditions as part of a series of rainfall erosion experiments looking at the evolution of landforms in response to erosion. The method allowed the elevations of the experimental landscapes to be studied in great detail on a regular grid digital terrain map with relatively very little effort. Digital photogrammetry produced elevation data at a resolution of 6 mm with a standard deviation of 2·0 mm over an experimental catchment relief of approximately 200 mm; this resolution is considerably better than that achievable by conventional manual photogrammetry. The density of grid points was sufficiently high that small‐scale details such as knickpoints developing in channels were represented. The method can facilitate the study of both experimental and natural landscapes in great detail. Copyright © 2001 John Wiley & Sons, Ltd.     

Efficient hybrid breaching‐filling sink removal methods for flow path enforcement in digital elevation models

Digital elevation models (DEMs) that are used in hydrological applications must be processed to remove sinks, mainly topographic depressions. Flow enforcement techniques include filling methods, which raise elevations within depressions, breaching, which carves channels through blockages, and hybrid methods. Despite previous research demonstrating the large impact to DEMs and subsequent analyses of depression filling, it is common practice apply this technique to flow enforcement. This is partly because of the greater efficiency of depression filling tools compared to breaching counterparts, which often limits breaching to applications of small‐ to moderate‐sized DEMs. A new hybrid flow enforcement algorithm is presented in this study. The method can be run in complete breaching, selective breaching (either breached or filled), or constrained breaching (partial breaching) modes, allowing for greater flexibility in how practitioners enforce continuous flow paths. Algorithm performance was tested with DEMs of varying topography, spatial extents, and resolution. The sites included three moderate sized DEMs (52 000 000 to 190 000 000 cells) and three massive DEMs of the Iberian Peninsula, and the Amazon and Nile River basins, the largest containing nearly one billion cells. In complete breaching mode, the new algorithm required 87% of the time needed by a filling method to process the test DEMs, while the selective breaching and constrained breaching modes, operating with maximum breach depth constraints, increased run times by 8% and 27% respectively. Therefore, the new algorithm offers comparable performance to filling and the ability to process massive topographic data sets, while giving practitioners greater flexibility and lowering DEM impact. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation of digital channel network derivation methods in a glaciated subalpine catchment

The digital elevation model (DEM) has become an essential tool for an increasing array of mountain runoff analyses, particularly the derivation and mapping of stream channel networks. This study examines how well commonly applied DEM‐based channel derivation methods at different spatial resolutions can represent the channel network for a glaciated Rocky Mountain headwater catchment. The specific objectives are to (1) examine how differences in gridded DEM resolution affect spatially distributed values of local slope, specific contributing area, and topographic wetness index derived from both eight and infinite directional flow algorithms, (2) map the actual stream channel network to examine the influence of surface variables on channel initiation, and (3) assess accuracy of DEM‐derived networks compared with the field surveyed network. Results show that for the same contributing area threshold, increasing grid cell size leads to increased channelization of modeled networks. A plot of local slope versus contributing area reveals a negative relationship similar to that of prior studies in un‐glaciated areas but with breaks in slope at contributing areas that are too small to represent thresholds for channelization. Field survey results and evaluation of DEM‐derived channel networks suggest that channel network formation is not clearly related to surface topographic variables at Loch Vale. Digitally derived channel networks do not accurately predict low order channel locations, but approximations of the channel network with drainage density and headward extent of channelization similar to the observed network can be derived with both a 1 m and 10 m DEM using a contributing area threshold of approximately 4x10⁴ m². Copyright © 2014 John Wiley & Sons, Ltd.     

A simple algorithm for generating streamflow networks for grid‐based,macroscale hydrological models

A simple algorithm for generating streamflow networks for macroscale hydrological models (MHMs) from digital elevation models (DEMs) is presented. Typically these hydrological models are grid based, with the simulated runoff produced within each cell routed through a stream network which connects the centers of cells in the direction of the major streams. Construction of such stream networks is a time consuming task, which has generally been done by hand with the aid of maps. Results indicate that the algorithm works satisfactorily in areas of both high and low relief, and for a wide range of model cell resolutions, although some manual adjustments may be necessary. Copyright © 1999 John Wiley & Sons, Ltd.     

Gully erosion in Mangatu Forest,New Zealand,estimated from digital elevation models

The methodology and errors involved in determining the amount of sediment produced during two (19·5 and 33·2 year) periods by 11 (c. 0·01 − >0·20 km²) gullies within a 4 km² area in the headwaters of the Waipaoa River basin, New Zealand, using sequential digital elevation models are described. Sediment production from all gullies within the study area was 0·99 ± 0·03 × 10⁶ t a⁻¹ (2480 ± 80 t ha⁻¹ a⁻¹) during the period from 1939 to 1958. It declined to 0·62 ± 0·02 × 10⁶ t a⁻¹ (1550 ± 50 t ha⁻¹ a⁻¹) during the period from 1958 to 1992, when many of the smaller gullies were stabilized by a programme of afforestation, which commenced in 1960. Both figures are very high by global standards. The two largest (the Tarndale and Mangatu) gully complexes together generated 73 and 95 per cent of the sediment in the specified time periods, but the latter amount is equivalent to only c. 5 per cent of the total annual sediment load of the Waipaoa River. © 1998 John Wiley & Sons, Ltd.     

A combined algorithm for automated drainage network extraction from digital elevation models

Drainage networks are the basis for segmentation of watersheds, an essential component in hydrological modelling, biogeochemical applications, and resource management plans. With the rapidly increasing availability of topographic information as digital elevation models (DEMs), there have been many studies on DEM‐based drainage network extraction algorithms. Most of traditional drainage network extraction methods require preprocessing of the DEM in order to remove “spurious” sink, which can cause unrealistic results due to removal of real sinks as well. The least cost path (LCP) algorithm can deal with flow routing over sinks without altering data. However, the existing LCP implementations can only simulate either single flow direction or multiple flow direction over terrain surfaces. Nevertheless, terrain surfaces in the real world are usually very complicated including both convergent and divergent flow patterns. The triangular form‐based multiple flow (TFM) algorithm, one of the traditional drainage network extraction methods, can estimate both single flow and multiple flow patterns. Thus, in this paper, it is proposed to combine the advantages of the LCP algorithm and the TFM algorithm in order to improve the accuracy of drainage network extraction from the DEM. The proposed algorithm is evaluated by implementing a data‐independent assessment method based on four mathematical surfaces and validated against “true” stream networks from aerial photograph, respectively. The results show that when compared with other commonly used algorithms, the new algorithm provides better flow estimation and is able to estimate both convergent and divergent flow patterns well regarding the mathematical surfaces and the real‐world DEM.     

The influence of elevation error on the morphometrics of channel networks extracted from DEMs and the implications for hydrological modelling

Stream network morphometrics have been used frequently in environmental applications and are embedded in several hydrological models. This is because channel network geometry partly controls the runoff response of a basin. Network indices are often measured from channels that are mapped from digital elevation models (DEMs) using automated procedures. Simulations were used in this paper to study the influence of elevation error on the reliability of estimates of several common morphometrics, including stream order, the bifurcation, length, area and slope ratios, stream magnitude, network diameter, the flood magnitude and timing parameters of the geomorphological instantaneous unit hydrograph (GIUH) and the network width function. DEMs of three UK basins, ranging from high to low relief, were used for the analyses. The findings showed that moderate elevation error (RMSE of 1·8 m) can result in significant uncertainty in DEM‐mapped network morphometrics and that this uncertainty can be expressed in complex ways. For example, estimates of the bifurcation, length and area ratios and the flood magnitude and timing parameters of the GIUH each displayed multimodal frequency distributions, i.e. two or more estimated values were highly likely. Furthermore, these preferential estimates were wide ranging relative to the ranges typically observed for these indices. The wide‐ranging estimates of the two GIUH parameters represented significant uncertainty in the shape of the unit hydrograph. Stream magnitude, network diameter and the network width function were found to be highly sensitive to elevation error because of the difficulty in mapping low‐magnitude links. Uncertainties in the width function were found to increase with distance from outlet, implying that hydrological models that use network width contain greater uncertainty in the shape of the falling limb of the hydrograph. In light of these findings, care should be exercised when interpreting the results of analyses based on DEM‐mapped stream networks. Copyright © 2007 John Wiley & Sons, Ltd.     

Residual relief separation: digital elevation model enhancement for geomorphological mapping

Geomorphologically mapped data form a primary set of observations that can be used to infer former environmental conditions. Thus, objective and consistent mapping of landforms from remotely sensed data (e.g. satellite imagery, digital elevation models (DEMs)) is paramount for reconstructing palaeoenvironments. This paper proposes a technique, ‘residual relief separation’, to enhance landforms in DEMs prior to visualization and digital mapping. This is applied to a ～600 km² region surrounding Lough Gara, Ireland, where drumlins (～200 m wide) overlie a regional relief of hills (～10 km wide). Here, residual relief separation uses this difference in width‐scale. Regional relief is approximated by a 1 km wide median filter, then subtracted to leave the drumlins in a ‘residual’ topography. In a second step, the residual relief is normalized to allow for amplitude variations in the drumlins across the area (～5–40 m high). Finally, visualization uses a simple black‐to‐white colour scale for height. Although not numerically outperforming other visualization techniques, this method performs equally well, and as the data are not ‘illuminated’ there is no azimuthal bias. Additional benefits include the relatively simple calculation, intuitive visual comprehension, no emphasis of noise, and the possibility of using any desired visualization technique after the landscape has been topographically manipulated. Copyright © 2008 John Wiley & Sons, Ltd.     

Multiple flow direction algorithms for runoff modelling in grid based elevation models: An empirical evaluation

When pathways for groundwater flow are defined in grid based elevation models, the grid structure creates some obstacles as it only allows for eight flow directions. Earlier algorithms have used arbitrarily designed flow distributions, which have resulted in either too diverging or too converging flow patterns. This study defines a computationally simple distribution function, where the converging nature (x) can be altered. A material of reference flow distributions was produced through simulation in four elevation models. The distribution function was tested for different values on x, against the reference. The results show a stable correlation pattern between the tested function and the reference. Optimum values on x were found, which suggest that the flow distribution from a grid cell should be weighted with the slope gradient raised to the power of 4–6.     

Spectral filtering as a method of visualising and removing striped artefacts in digital elevation data

Spectral filtering was compared with traditional mean spatial filters to assess their ability to identify and remove striped artefacts in digital elevation data. The techniques were applied to two datasets: a 100 m contour derived digital elevation model (DEM) of southern Norway and a 2 m LiDAR DSM of the Lake District, UK. Both datasets contained diagonal data artefacts that were found to propagate into subsequent terrain analysis. Spectral filtering used fast Fourier transformation (FFT) frequency data to identify these data artefacts in both datasets. These were removed from the data by applying a cut filter, prior to the inverse transform. Spectral filtering showed considerable advantages over mean spatial filters, when both the absolute and spatial distribution of elevation changes made were examined. Elevation changes from the spectral filtering were restricted to frequencies removed by the cut filter, were small in magnitude and consequently avoided any global smoothing. Spectral filtering was found to avoid the smoothing of kernel based data editing, and provided a more informative measure of data artefacts present in the FFT frequency domain. Artefacts were found to be heterogeneous through the surfaces, a result of their strong correlations with spatially autocorrelated variables: landcover and landsurface geometry. Spectral filtering performed better on the 100 m DEM, where signal and artefact were clearly distinguishable in the frequency data. Spectrally filtered digital elevation datasets were found to provide a superior and more precise representation of the landsurface and be a more appropriate dataset for any subsequent geomorphological applications. Copyright © 2007 John Wiley & Sons, Ltd.