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.     

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.     

Evaluating preprocessing methods of digital elevation models for hydrological modelling

With the introduction of high‐resolution digital elevation models, it is possible to use digital terrain analysis to extract small streams. In order to map streams correctly, it is necessary to remove errors and artificial sinks in the digital elevation models. This step is known as preprocessing and will allow water to move across a digital landscape. However, new challenges are introduced with increasing resolution because the effect of anthropogenic artefacts such as road embankments and bridges increases with increased resolution. These are problematic during the preprocessing step because they are elevated above the surrounding landscape and act as artificial dams. The aims of this study were to evaluate the effect of different preprocessing methods such as breaching and filling on digital elevation models with different resolutions (2, 4, 8, and 16 m) and to evaluate which preprocessing methods most accurately route water across road impoundments at actual culvert locations. A unique dataset with over 30,000 field‐mapped road culverts was used to assess the accuracy of stream networks derived from digital elevation models using different preprocessing methods. Our results showed that the accuracy of stream networks increases with increasing resolution. Breaching created the most accurate stream networks on all resolutions, whereas filling was the least accurate. Burning streams from the topographic map across roads from the topographic map increased the accuracy for all methods and resolutions. In addition, the impact in terms of change in area and absolute volume between original and preprocessed digital elevation models was smaller for breaching than for filling. With the appropriate methods, it is possible to extract accurate stream networks from high‐resolution digital elevation models with extensive road networks, thus providing forest managers with stream networks that can be used when planning operations in wet areas or areas near streams to prevent rutting, sediment transport, and mercury export.     

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.     

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.     

Landform‐oriented flow‐routing algorithm for the dual‐structure loess terrain based on digital elevation models

The loess landform in the Loess Plateau of China is with typical dual structure, namely, the upper smooth positive terrain and the lower cliffy negative terrain (P–N terrain for short). Obvious differences in their morphological feature, geomorphological mechanism, and hydrological process could be found in the both areas. Based on the differences, a flow‐routing algorithm that separately addresses the dual‐structure terrain would be necessary to encompass this spatial variation in their hydrological behaviour. This paper proposes a mixed flow‐routing algorithm to address aforementioned problems. First, the loess landform surface is divided into P–N terrains based on digital elevation models. Then, specific catchment area is calculated with the new algorithm to simulate the water flows in both positive and negative terrain areas. The mixed algorithm consists of the multiple flow‐routing algorithm (multiple‐flow direction) for positive areas and the D8 algorithm for negative areas, respectively. The approach is validated in two typical geomorphologic areas with low hills and dense gullies in the northern Shaanxi Loess Plateau. Four indices are used to examine the results, which show that the new algorithm is more suitable for loess terrain in simulating the spatial distribution of water accumulation, as well as in modeling the flow characteristics of the true surface by considering the morphological structures of the terrain. Copyright © 2013 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.     

Hydraulics of interrill overland flow on rough,bare soil surfaces

A set of laboratory experiments on bare, rough soil surfaces was carried out to study the relationship between soil surface roughness and its hydraulic resistance. Existing models relating roughness coefficients to a measure of surface roughness did not predict the hydraulic resistance well for these surfaces. Therefore, a new model is developed to predict the hydraulic resistance of the surface, based on detailed surface roughness data. Roughness profiles perpendicular to the flow are used to calculate the wet cross‐sectional area and hydraulic radius given a certain water level. The algorithm of Savat is then applied to calculate the hydraulic resistance. The value for the equivalent roughness, which is used in the algorithm of Savat, could be predicted from the roughness profiles. Here, the tortuosity of the submerged part of the surface was used, which means that the calculated roughness depends on flow depth. The roughness increased with discharge, due to the fact that rougher parts of the surface became submerged at higher discharges. Therefore, a single measure of surface roughness (e.g. random roughness) is not sufficient to predict the hydraulic resistance. The proposed model allows the extension of the flow over the surface with increasing discharge to be taken into account, as well as the roughness within the submerged part of the surface. Therefore, the model is able to predict flow velocities reasonably well from discharge and roughness data only. Copyright © 2000 John Wiley & Sons, Ltd.     

Computing spatially distributed sediment delivery ratios: inferring functional sediment connectivity from repeat high‐resolution digital elevation models

High‐resolution digital elevation models (DEMs) from repeat LiDAR (light detection and ranging) or SfM (structure from motion) surveys have become an important tool in process geomorphology. The spatial pattern of negative and positive changes of surface elevation on raster DEMs of difference (DoD) can be interpreted in terms of geomorphic processes, and has been used for morphological budgeting. We show how the application of flow routing algorithms and flow accumulation opens new opportunities for the analysis of DoD. By accumulating the values of the DoD along downslope flowpaths delineated on a DEM, these algorithms lend themselves to computing the net balance, i.e. sediment yield (SY), for the contributing area of each cell. Doing the same for the negative subset of the DoD yields a minimum estimate of erosion (E) within the contributing area. The division of SY by E yields (a maximum estimate of) the sediment delivery ratio (SDR), that is the proportion of material eroded within the contributing area of each cell that has been exported from that area. The resulting SDR is a spatially distributed measure of functional sediment connectivity. In this letter, we develop the computationally simple approach by means of an example DoD from a lateral moraine section in the Upper Kaunertal Valley, Austrian Central Alps. We also discuss advantages, assumptions and limitations, and outline potential applications to connectivity research using field‐, laboratory‐, and model‐based DoD. Copyright © 2018 John Wiley & Sons, Ltd.     

A cross-scale comparison of drainage basin characteristics derived from digital elevation models

The feasibility of using small-scale digital elevation models (DEMs) to extract various drainage basin characteristics was evaluated by comparing basin parameters derived from the 1:250 000 DEMs with those from the 1:24 000 DEMs. Twenty basins ranging approximately from 150 km² to 1000 km² in West Virginia, a geologically complex region, were examined in this study. The basin parameters examined included those commonly used in hydrology and geomorphology such as elevation, slope, stream length, drainage density, relief ratio and ruggedness number. Our results suggested that the 1:250 000 DEMs can provide accurate estimates for elevation-based and stream-length-based basin parameters, but not for slope-based parameters. After examining the differences between the DEM-derived basin parameters from the two different scales, we found that the performance of the 1:250 000 DEMs was not significantly influenced by basin size, while terrain complexity seems to be an important factor of accuracy of the estimated basin parameters. Copyright © 1999 John Wiley & Sons, Ltd.     

An improved method for single flow direction calculation in grid digital elevation models

This paper presents improvements to the global D8 (GD8) method for calculating single flow directions in a grid digital elevation model. Flow directions computed from grid digital elevation models serve as the foundation for much of the analysis and modeling of hydrological processes that are driven by topographic gradients. The literature includes both single flow direction methods, where flow goes to only one downslope cell, and multiple flow direction methods that apportion flow among multiple downslope cells. Among single flow direction methods, the standard D8 method, in which the flow direction is set based on the steepest local slope, results in bias on surfaces that do not align with the grid directions. Efforts to address this problem have led to the development of extended methods that account for elevation values further upslope in determining flow directions. We have identified discrepancies in one such method, GD8, and have examined ways to resolve these discrepancies. An improvement to GD8, named iGD8, is presented that allows replacing a reference cell from which path deviations are accumulated and that considers horizontal path deviation rather than global slope as a flow direction criterion. The improved method is found to be effective in resolving the problems encountered with GD8 and to be more efficient than a previously proposed alternative method (least transversal deviation (LTD) based D8, namely D8‐LTD) that uses recursive searching for the largest upstream area when multiple flow paths converge. The proposed improved GD8 method offers the opportunity for improved analysis and modeling of topographically driven hydrological processes by providing better foundational flow directions for these analyses.     

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.     

The effects of topographic depressions on multiscale overland flow connectivity: A high‐resolution spatiotemporal pattern analysis approach based on connectivity statistics

In watershed modelling, the traditional practice of arbitrarily filling topographic depressions in digital elevation models has raised concerns. Advanced high‐resolution remote sensing techniques, including airborne scanning laser altimetry, can identify naturally occurring depressions that impact overland flow. In this study, we used an ensemble physical and statistical modelling approach, including a 2D hydraulic model and two‐point connectivity statistics, to quantify the effects of depressions on high‐resolution overland flow patterns across spatial scales and their temporal variations in single storm events. Computations for both models were implemented using graphic processing unit‐accelerated computing. The changes in connectivity statistics for overland flow patterns between airborne scanning laser altimetry‐derived digital elevation models with (original) and without (filled) depressions were used to represent the shifts of overland flow response to depressions. The results show that depressions can either decrease or increase (to a lesser degree and shorter duration) the probability that any two points (grid locations) are hydraulically connected by overland flow pathways. We used macro‐connectivity states (Φ) as a watershed‐specific indicator to describe the spatiotemporal thresholds of connectivity variability caused by depressions. Four states of Φ are identified in a studied watershed, and each state represents different magnitudes of connectivity and connectivity changes (caused by depressions). The magnitude of connectivity variability corresponds to the states of Φ, which depend on the topological relationship between depressions, the rising/recession limb, and the total rainfall amount in a storm event. In addition, spatial distributions of connectivity variability correlate with the density of depression locations and their physical structures, which cause changes in streamflow discharge magnitude. Therefore, this study suggests that depressions are “nontrivial” in watershed modelling, and their impacts on overland flow should not be neglected. Connectivity statistics at different spatial scales and time points within a watershed provide new insights for characterizing the distributed and accumulated effects of depressions on overland flow.     

Problems in automated recognition of valley features from digital elevation models and a new method toward their resolution

Valley recognition methods given in the literature fail to produce valley networks suitable for locating valley heads for one of two main reasons: (a) they are based on the concept of [higher than] or (b) they are based on contributing area thresholds. In this paper a new method for recognizing valley bottoms is presented. This is based on two improvements of Carroll's (1983) method, and produces a network that reflects the topography well. The network is used to locate valley heads. Once located, the valley heads are delineated using criteria suggested by geomorphologists and hydrologists. The resultant valley heads are generally well recognized although two problems are evident: (a) there are a number of commission errors; and (b) the valley heads recognized by the method are too small.