Multiple Flow Direction Algorithm Research Articles

Proposal of a facet-to-facet multiple flow direction algorithm based on geometrical and mathematical analysis of physical dispersion over triangle facet

Flow direction algorithms have been widely used to extract crucial terrain attributes of great hydrological and geomorphological significance. However, essential distinctions between the empirically-designed strategies of typical algorithms and the natural rules of physical dispersions bring various problems (e.g. parallel channel, artificial dispersion), leading to the low size and extent precisions of estimated results. In this work, geometrical and mathematical analysis is conducted on the inherent characteristics of physical dispersions along slope lines on local terrains. On each 3 × 3 window of digital elevation model (DEM), center pixel is divided into eight non-overlapping sub-facets. Necessary and sufficient (NS) conditions of size relationships between the elevations of adjacent pixels are summarized to directly identify the receiving facets of a sub-facet. Then, strict mathematical relations are derived between slope direction of a sub-facet and flow proportions allocated to receiving facets. A strategy is designed to re-adjust receiving facets and flow proportions for the boundary flow of adjacent facets. Lastly, a multiple-flow-direction algorithm called TFGA is proposed with the NS condition of size relationships, mathematical relation of slope direction with flow proportion, and adjustment strategy of boundary flow. Case studies are conducted for investigating the total contributing areas (TCA) and specific contributing areas (SCA) estimated by TFGA. Results reveal all-side superiorities of TFGA to typical algorithms in spatial patterns, error indicators and statistic characteristics of estimated TCAs and SCAs. Particularly, TFGA improves size precision of estimated results by approximately one order of magnitude. In a conclusion, we highly recommend TFGA for digital elevation analysis.

Coupled sink and flow accumulation analyses with single flow direction and multiple flow direction algorithms

Abstract A static flood analysis (SFA) toolset is implemented with the purpose of performing simplified, event-based flood inundation modeling. The simulation process is divided into two steps: a topographic sink analysis of the terrain followed by flow accumulation (FA) of runoff volumes. Both procedures are coupled to account for sink storage effects. The sink analysis procedure determines the morphology of present sinks that are utilized during FA to calculate the sink storage by solving a mass balance, whereby inflows are captured in each sink according to their capacity and overflows are routed further downstream. Each sink is enriched with a set of hydrological attributes such as the total inflow, overflow, and flood depth. The flood depth is then utilized to determine the flood extent and flood depths of each sink. Two main options are made available for the FA procedure: either a single flow direction (SFD) or a novel formulation of the multiple flow direction (MFD) algorithm. Both methods were compared in terms of their accuracy with results from the TELEMAC-2D finite-volume solver for an urban inundation model. Both methods showed good agreement when compared with the validation results, with the MFD method performing marginally better than the SFD method.

Modification of the RUSLE slope length factor based on a multiple flow algorithm considering vertical leakage at karst landscapes

Heterogeneous karst surfaces exerted scaling effects whereby specific runoff decrease with increasing area. The existing RUSLE-L equations are limited by the default implicit assumption that the surface-runoff intensity is constant at any slope length. The objective of this study was to modify the L-equation by establishing the functional relationship between surface-runoff intensity and karst slope length, and to evaluate its predictive capability at different resolution DEMs. Transfer grid layers were generated based on the area rate of surface karstification and considered the runoff transmission percentage at the exposed karst fractures or conduits to be zero. Using the multiple flow direction algorithm united with the transfer grid (MFDTG), the flow accumulation of each grid cell was simulated to estimate the average surface-runoff intensity over different slope lengths. The effectiveness of MFDTG algorithm was validated by runoff plot data in Southwestern China. The simulated results in a typical peak-cluster depression basin with an area rate of surface karstification of 6.5% showed that the relationship between surface-runoff intensity and slope length was a negative power function. Estimated by the proposed modified L-equation ((alx(b+1)/22.13)m), the L-factor averages of the study basin ranged from 0.35 to 0.41 at 1, 5, 25 and 90 m resolutions respectively. This study indicated that the modified L-equation enables an improved prediction of the much smaller L-factor and the use of any resolution DEMs on karst landscapes. Particular attention should be given to the variation of surface-runoff intensity with slope length when predicting L-factor on hillslopes with runoff scale effect.

Do Model Results Vary under Different Routing Algorithms Based on a Distributed Ecohydrological Model?

Abstract Although several flow routing (FR) algorithms are developed for hydrological modeling, it is still uncertain how the selection of algorithms may affect model results. This study aims to explore the similarity and dissimilarity in model results among different FR algorithms characterized by single flow direction (SD) and multiple flow direction (MD). The Coupled Hydro-Ecological Simulation System (CHESS) was incorporated with six different FR algorithms (D8, D∞, MD∞, MD8, MFD-md, and RMD∞) and then applied for modeling ecohydrological processes for a semiarid mountainous watershed in the western United States during 1991–2012. Comparisons were made between the model results at the catchment and the grid scale. After slightly adjusting one of the most sensitive soil parameters, all algorithms behave similarly in simulating stream hydrographs. When averaged for the watershed, the modeled ecohydrological variables mostly do not differ significantly (<5%) among the six FR algorithms. Nevertheless, the simulated ecohydrological variables are spatially more autocorrelated under the more dispersive MD algorithms. In addition, there exist significant (>5%) cell-level differences in modeled soil moisture among different FR algorithms, with propagated influences on the simulated evapotranspiration and vegetation growth variables. In hillslopes, the cell-level differences in model results tend to increase significantly as the flows move to the streams. Overall, this study proves that the watershed-level differences in model results among FR algorithms are low after model calibration, while significant differences still occur at the cell level. Thus, observational data are essential for testing which routing algorithm captures better the reality of local ecohydrological processes. Significance Statement The consideration of flow routing is essential for accurately simulating land surface ecohydrological processes. However, less is known about how the selection of flow routing algorithms may affect the model results. Based on model experiments, we found that the model results under different algorithms do not significantly differ from each other when averaged for the watershed. However, significant differences in model results exist at the individual cell level. These findings are useful for guiding future modeling-related research and also suggest the importance of field studies for testing which routing algorithm can better represent local ecohydrological processes.

Comparison of long-term field-measured and RUSLE-based modelled soil loss in Switzerland

Long-term field measurements to asses model-based soil erosion predictions by water are rare. We have compared field measurements based on erosion assessment surveys from a 10-year monitoring process with spatial-explicit model predictions with the Revised Universal Soil Loss Equation (RUSLE). Robust input data were available for both the mapped and the modelled parameters for 203 arable fields covering an area of 258 ha in the Swiss Midlands. The 1639 mapped erosion forms were digitized and converted to raster format with a 2 m resolution. A digital terrain model using 2 m resolution and a multiple flow direction algorithm for the calculation of the topographic factors and the support practice factor was available for modelling with the RUSLE. The other input data for the RUSLE were determined for each field. The comparison of mapped and modelled soil loss values revealed a substantially higher estimation of soil loss values from modelling by a factor of 8, with a mean mapped soil loss of 0.77 t/ha/yr vs. modelled soil loss of 6.20 t/ha/yr. However, high mapped soil losses of >4 t/ha/yr were reproduced quite reliably by the model, while the model predicted drastically higher erosion values for mapped losses of <4 t/ha/yr. Our study shows the value of long-term field data based on erosion assessment surveys for model evaluation. RUSLE-type model results should be compared with erosion assessment surveys at the field to landscape scale in order to improve the calibration of the model. Further factors related to land management like headlands, traffic lanes and potato furrows need to be included before they may be used for policy advice.

An Improved Triangular Form‐Based Multiple Flow Direction Algorithm for Determining the Nonuniform Flow Domain Over Grid Networks

AbstractThe naturally existing diffusive flow provides revisited values for the multiple flow direction (MFD) algorithm for digital elevation models. However, since the flow is uniformly distributed over a grid cell, existing MFD algorithms can hardly force the flow to propagate within a finite region without arbitrary dispersion. In this study, an improved Triangular Form‐based Multiple Flow Algorithm called iTFM is proposed to limit the arbitrary dispersion by considering the nonuniform flow domain in a cell. In the new algorithm, flow is routed between facets rather than cells and drained to at most two downstream facets, which forces the flow to propagate over partial subregions of a cell, so that different facets in the cell may have different contributing areas. In addition, two alternative strategies including vector split (VS) and area split (AS) are evaluated to determine the flow split ratio for the two downstream facets in this study. Then, the algorithms combining different split strategies (i.e., iTFM‐VS, iTFM‐AS) are compared with eight existing algorithms over four numerical terrains and one physical terrain. The visual and quantitative assessment results show that iTFM‐AS can provide accurate total contributing areas and predicted flow domains for numerical terrains with resolutions ranging from 1 to 20 m. Moreover, the flow domains predicted by iTFM‐AS are in high agreement with the observed domains over the physical terrain with practical resolutions. Therefore, it can be concluded that the iTFM‐AS algorithm can better and more robustly define the dispersive flow domain.

An Improved D8‐LTD for the Extraction of Total Contributing Area (TCA) by Adopting the Strategies of Path Independency and Local Dispersion

AbstractD8‐LTD is a path‐based flow direction algorithm for estimating total contributing area (TCA). However, the precision of D8‐LTD TCA is seriously challenged by the incorporation of flow paths and basic hypothesis of allowing only one receiving pixel. To solve above problems, this work proposes an improved D8‐LTD by adopting the strategies of path independency and local dispersion (i.e., LTD‐PI‐LD). Two indicators are adopted to quantify size and extent precisions of estimated TCAs relative to theoretical TCA. Then, LTD‐PI‐LD is compared with several typical single‐flow‐direction (SFD) algorithms (i.e., D8, D8‐LTD, LTD‐PI) and multiple‐flow‐direction (MFD) algorithms (i.e., MFD‐Quinn, D∞) on synthetic surfaces. Results indicate that (1) TCA maps of D8 and D8‐LTD contain too many singular high‐TCA tubes and source pixels, which are caused by the incorporation of flow paths and converging characteristics of SFD algorithms. (2) In MFD algorithms, the problem of artificial dispersion triggers the mechanisms of cross compensation and mutual amplification, leading to high size precision but low extent precision in estimated TCAs. (3) Strategy of path independency prevents the occurrence of high‐TCA tubes and effectively reduces the number of source pixels. (4) Both size and extent precisions of D8‐LTD TCAs are largely improved by introducing the strategies of path independency and local dispersion. Of all algorithms, LTD‐PI‐LD obtains the highest/second‐highest size precision and the highest extent precision in estimated TCAs. As a whole, LTD‐PI‐LD shows advantages of high precision in estimated TCAs, low computation cost, high efficiency and robustness to DEM (Digital elevation model) resolution and terrain type.

A new approach for calculating the slope length factor in the Revised Universal Soil Loss Equation

This paper proposes a flow-path-network-triangular-facet-network (FPN_TFN) method based on a flow path network (FPN) and triangular facet network (TFN) constructed from a digital elevation model (DEM) to enhance the calculation of the slope length factor (<i>L</i>) in the Revised Universal Soil Loss Equation (RUSLE). First, the slope length was derived from a FPN, which is traced by the flow path network model. Then, a TFN was used to estimate the slope, and finally, <i>L</i> was obtained by combining slope length with slope using the equation in RUSLE. Experiments were conducted to (1) quantitatively validate the accuracy of the FPN_TFN method using 5 m DEMs that were generated from four mathematical surface models; and (2) qualitatively evaluate the error by using a 30 m DEM of a real-world mountainous region located in central Ganzi Tibetan Autonomous Prefecture of Sichuan Province, China. The performance of the four algorithms proposed by Moore and Burch (1986a), Böhner and Selige (2006), Desmet and Govers (1996), and Hickey (2000) were compared with that of the new approach. In the former two algorithms, two single flow direction and four multiple flow direction algorithms were selected for calculating the upslope contributing area (CA) and specific catchment area (SCA), such that 14 algorithms would be used for the comparison. The <i>L</i> estimates computed with the proposed algorithm were closer to the theoretical value. The root mean standard errors (RMSE) of the proposed algorithm are 79%, 96%, 69%, and 90% less than the same errors generated by the best of 14 comparison algorithms on the ellipsoid, inverse ellipsoid, saddle, and plane, respectively. The mean absolute errors (MEs) of the proposed algorithm are 0.83, 0.14, 1.00, and 0.39 m using the aforementioned order of surfaces, obviously lower than that of the comparison algorithms. The spatial error of the proposed algorithm is distributed between –1 and 1 for the inverse ellipsoid and plane surfaces, and falls mainly between –1 and 1 on the ellipsoid and saddle surfaces. They are still lower than that for the other algorithms. The new approach also produces better spatial distributions of <i>L</i> on the real-world mountainous region.

Some multiple flow direction algorithms for overland flow on general meshes

After recalling the most classical multiple flow direction algorithms (MFD), we establish their equivalence with a well chosen discretization of Manning–Strickler models for water flow. From this analogy, we derive a new MFD algorithm that remains valid on general, possibly non conforming meshes. We also derive a convergence theory for MFD algorithms based on the Manning–Strickler models. Numerical experiments illustrate the good behavior of the method even on distorted meshes.

Evaluating the area and position accuracy of surface water paths obtained by flow direction algorithms

The surface water path (SWP) extracted from digital elevation model (DEM) by flow direction algorithms is widely employed to obtain a variety of topographic variables used in hydrological modeling. Accurate SWPs can facilitate understanding the underlying mechanisms of water movement on Earth’s surface. However, the accuracy of extracted SWPs by different flow direction algorithms has not been systematically studied. In this work, two indicators are developed to measure the area and position errors of extracted SWPs relative to theoretical SWPs on four synthetic surfaces representing typical terrains of natural watersheds. Based on the formulas of the synthetic surfaces, theoretical true SWP can be derived for any grid cell on the DEM discretized from the synthetic surfaces. Several widely used flow direction algorithms including three single flow direction (SFD) algorithms (i.e. D8, Rho8 and D8-LTD approaches) and three multiple flow direction (MFD) algorithms (i.e. FDFM, MFD-md and D∞ approaches) are implemented to extract SWPs. Results suggest that significant distinctions can be detected in SWPs extracted by different flow direction algorithms. The SWPs extracted by SFD algorithms are always one-dimensional non-dispersive lines because SFD algorithms allow only one flow direction at each grid cell. In contrast, the SWPs extracted by MFD algorithms show excessive artificial dispersion. The average area error of extracted SWPs ranges from 16.3% to 75.2% on different synthetic surfaces and the minimum is obtained by FDFM approach for all synthetic surfaces. The average position error falls in the range of 46.0% to 161.4%. The maximum is gained by D8 or FDFM approach, and the minimum by D8-LTD or D∞ approach. The cross compensation of SWP area induced by artificial dispersion leads to relatively high area accuracy but relatively low position accuracy of MFD algorithms. In addition, increasing DEM resolution without capturing more topographic variability can decrease the area and position accuracy due to error accumulation from more steps of flow direction calculation. Our findings provide a beneficial insight into applying SWP-derived topographic variables to hydrological modeling.

Parallelizing Multiple Flow Accumulation Algorithm using CUDA and OpenACC

Watershed analysis, as a fundamental component of digital terrain analysis, is based on the Digital Elevation Model (DEM), which is a grid (raster) model of the Earth surface and topography. Watershed analysis consists of computationally and data intensive computing algorithms that need to be implemented by leveraging parallel and high-performance computing methods and techniques. In this paper, the Multiple Flow Direction (MFD) algorithm for watershed analysis is implemented and evaluated on multi-core Central Processing Units (CPU) and many-core Graphics Processing Units (GPU), which provides significant improvements in performance and energy usage. The implementation is based on NVIDIA CUDA (Compute Unified Device Architecture) implementation for GPU, as well as on OpenACC (Open ACCelerators), a parallel programming model, and a standard for parallel computing. Both phases of the MFD algorithm (i) iterative DEM preprocessing and (ii) iterative MFD algorithm, are parallelized and run over multi-core CPU and GPU. The evaluation of the proposed solutions is performed with respect to the execution time, energy consumption, and programming effort for algorithm parallelization for different sizes of input data. An experimental evaluation has shown not only the advantage of using OpenACC programming over CUDA programming in implementing the watershed analysis on a GPU in terms of performance, energy consumption, and programming effort, but also significant benefits in implementing it on the multi-core CPU.

A Network‐Based Flow Accumulation Algorithm for Point Clouds: Facet‐Flow Networks (FFNs)

Flow accumulation algorithms estimate the steady state of flow on real or modeled topographic surfaces and are crucial for hydrological and geomorphological assessments, including delineation of river networks, drainage basins, and sediment transport processes. Existing flow accumulation algorithms are typically designed to compute flows on regular grids and are not directly applicable to arbitrarily sampled topographic data such as lidar point clouds. In this study we present a random sampling scheme that generates homogeneous point densities, in combination with a novel flow path tracing approach—the Facet‐Flow Network (FFN)—that estimates flow accumulation in terms of specific catchment area (SCA) on triangulated surfaces. The random sampling minimizes biases due to spatial sampling and the FFN allows for direct flow estimation from point clouds. We validate our approach on a Gaussian hill surface and study the convergence of its SCA compared to the analytical solution. Here, our algorithm outperforms the multiple flow direction algorithm, which is optimized for divergent surfaces. We also compute the SCA of a 6‐km2‐steep, vegetated catchment on Santa Cruz Island, California, based on airborne lidar point‐cloud data. Point‐cloud‐based SCA values estimated by our method compare well with those estimated by the D∞ or multiple flow direction algorithm on gridded data. The advantage of computing SCA from point clouds becomes relevant especially for divergent topography and for small drainage areas: These are depicted with much more detail due to the higher sampling density of point clouds.

Electrical resistivity and spatial variation in agriculture terraces: statistical correlation between ert and flow direction algorithms

Abstract The construction of earthen embankment terraces in the Douro Region raises a set of problems related to hydrological processes. The main objective of this study is the evaluation of the spatial variation of electrical resistivity in agriculture terraces at Douro valley (Portugal). To achieve this objective, two variables are analysed, the soil electrical resistivity and the flow direction algorithm. In a field survey we recorded 13 electrical resistivity profiles. The contributing area was calculated with the algorithms D∞ (Deterministic Infinity Flow) and MFD (Multiple Flow Direction) and the results are the base of the internal runoff modelling, both supported by the digital elevation model with a spatial resolution of 1m2. A correlation between the spatial variation of the soil electrical resistivity represented by the standard deviation of the electrical resistivity for each profile and the average value of the contributing area coincident with each profile was established. The electrical resistivity standard deviation seems to be moderately well correlated according to the D∞ algorithm at about 1m of depth, and it has a good correlation at 1,5m to 2m of depth with the MFD algorithm. Taken together, the results show a significant positive statistical correlation between the electrical resistivity standard deviation and the contributing areas (MFD and D∞) depending on the soil depth.

Assessment of rainfall-generated shallow landslide/debris-flow susceptibility and runout using a GIS-based approach: application to western Southern Alps of New Zealand

Rainfall-triggered shallow slope failures are very common in the western Southern Alps of New Zealand, causing widespread damage to property and infrastructure, injury and loss of life. This study develops a geographic information system (GIS)-based approach for shallow landslide/debris-flow susceptibility assessment. Since landslides are complex and their prediction involves many uncertainties, fuzzy logic is used to deal with uncertainties inherent in spatial analysis and limited knowledge on the relationship between conditioning factors and slope instability. A landslide inventory was compiled using data from existing catalogues, satellite imagery and field observations. Ten parameters were initially identified as the most important conditioning factors for rainfall-generated slope failures in the study area, and fuzzy memberships were established between each parameter and landslide occurrence based on both the landslide inventory and user-defined functions. Three output landslide susceptibility maps were developed and evaluated in a test area using an independent population of landslides. The models demonstrated satisfactory performance with area under the curve (AUC) varying from 0.708 to 0.727. Sensitivity analyses showed that a six-parameter model using slope angle, lithology, slope aspect, proximity to faults, soil induration, and proximity to drainage network had the highest predictive performance (AUC = 0.734). The runout path and distance of potential future landslides from the susceptible areas were also modelled based on a multiple flow direction algorithm and the topographic slope of existing debris-flow deposits. The final susceptibility map has the potential to inform regional-scale land-use planning and to prioritize areas where hazard mitigation measures are required.

Comparison of Flow Direction Algorithms in the Application of the CTI for Mapping Wetlands in Minnesota

Topography has been traditionally used as a surrogate to model spatial patterns of water distribution and variation of hydrological conditions. In this study, we investigated the use of light detection and ranging (lidar) data to derive two Single Flow Direction (SFD) and five Multiple Flow Direction (MFD) algorithms in the application of the compound topographic index (CTI) for mapping wetlands. The CTI is defined here as ln [(α)/(tan (β)], where α represents the local upslope contributing area and β represents the local slope gradient. We evaluated the following flow direction algorithms: D8, Rho8, DEMON, D-∞ MD-∞, Mass Flux, and FD8 in three ecoregions in Minnesota. Numerous studies have found that MFD algorithms better represent the spatial distribution of water compared to SFD algorithms. CTI maps were compared to field collected and image interpreted reference data using traditional remote sensing accuracy estimators. Overall accuracy results for the majority of CTI based algorithms were in the range of 81–92 %, with low errors of wetland omission. The results of this study provide evidence that 1) wetlands can be accurately identified using a lidar derived CTI, and 2) MFD algorithms should be preferred over SFD algorithms in most cases for mapping wetlands.

Multiple Flow Direction Algorithm Based on Extending Neighborhood Terrain

Flow direction algorithm is an important research area in hydrological analysis. In this paper, a novel flow direction algorithm with varied trend of extending neighborhood terrain is introduced, which is based on the basic principle of multiple flow direction algorithms. The basic idea of the methodology is that the flow partitioning proportion from the central grid to every neighboring grid should be related with the extending neighborhood terrain, and the influence of the extending neighborhood terrain for the flow condition should be considered comprehensively. At the last, the novel multiple flow direction algorithm is applied to an experimental region lie in Liaohe river basin. As the results, the new method can identify the river network accurately, and is a kind of relatively reasonable multiple flow direction algorithm.

Parallelizing flow-accumulation calculations on graphics processing units—From iterative DEM preprocessing algorithm to recursive multiple-flow-direction algorithm

As one of the important tasks in digital terrain analysis, the calculation of flow accumulations from gridded digital elevation models (DEMs) usually involves two steps in a real application: (1) using an iterative DEM preprocessing algorithm to remove the depressions and flat areas commonly contained in real DEMs, and (2) using a recursive flow-direction algorithm to calculate the flow accumulation for every cell in the DEM. Because both algorithms are computationally intensive, quick calculation of the flow accumulations from a DEM (especially for a large area) presents a practical challenge to personal computer (PC) users. In recent years, rapid increases in hardware capacity of the graphics processing units (GPUs) provided in modern PCs have made it possible to meet this challenge in a PC environment. Parallel computing on GPUs using a compute-unified-device-architecture (CUDA) programming model has been explored to speed up the execution of the single-flow-direction algorithm (SFD). However, the parallel implementation on a GPU of the multiple-flow-direction (MFD) algorithm, which generally performs better than the SFD algorithm, has not been reported. Moreover, GPU-based parallelization of the DEM preprocessing step in the flow-accumulation calculations has not been addressed. This paper proposes a parallel approach to calculate flow accumulations (including both iterative DEM preprocessing and a recursive MFD algorithm) on a CUDA-compatible GPU. For the parallelization of an MFD algorithm (MFD-md), two different parallelization strategies using a GPU are explored. The first parallelization strategy, which has been used in the existing parallel SFD algorithm on GPU, has the problem of computing redundancy. Therefore, we designed a parallelization strategy based on graph theory. The application results show that the proposed parallel approach to calculate flow accumulations on a GPU performs much faster than either sequential algorithms or other parallel GPU-based algorithms based on existing parallelization strategies.

A novel multiple flow direction algorithm for computing the topographic wetness index

The topographic wetness index (TWI), frequently used in approximately characterizing the spatial distribution of soil moisture and surface saturation within a watershed, has been widely applied in topography-related geographical processes and hydrological models. However, it is still questionable whether the current algorithms of TWI can adequately model the spatial distribution of topographic characteristics. Based upon the widely-used multiple flow direction approach (MFD), a novel MFD algorithm (NMFD) is proposed for improving the TWI derivation using a Digital Elevation Model (DEM) in this study. Compared with MFD, NMFD improves the mathematical equations of the contributing area and more precisely calculates the effective contour length. Additionally, a varying exponent strategy is adopted to dynamically determine the downslope flow-partition exponent. Finally, a flow-direction tracking method is employed to address grid cells in flat terrain. The NMFD algorithm is first applied to a catchment located upstream of the Hanjiang River in China to demonstrate its accuracy and improvements. Then NMFD is quantitatively evaluated by using four types of artificial mathematical surfaces. The results indicate that the error generated by NMFD is generally lower than that computed by MFD, and NMFD is able to more accurately represent the hydrological similarity of watersheds.

A new GRASS GIS toolkit for Hortonian analysis of drainage networks

The aim of this paper is to present a new GRASS GIS toolset designed for Hortonian analysis of drainage networks. The r.stream toolset uses a multiple flow direction algorithm for stream network extraction as well as for calculating other hydrogeomorphological features in the catchment’s area. As all GRASS GIS toolsets, r.stream consists of several separate modules that can extract stream networks from a spectrum of accumulation maps, order the extracted network using several ordering methods, do advanced modeling of basin’s boundary, perform Hortonian statistics, calculate additional parameters such as flow path distance to watershed elements, partition ordered and unordered networks into near-straight-line sectors, and calculate sector directions. The package is free and open-source software, available for GRASS version 6.4 and later.

Determination of surface flow paths from gridded elevation data

Surface flow paths are obtained from gridded elevation data by connecting grid cell centers along predetermined flow directions. These flow directions are commonly determined using single and multiple flow direction algorithms. It remains, however, unclear whether multiple flow direction algorithms, which introduce artificial dispersion, can be used to describe surface flow paths and gravity‐driven processes across a terrain without causing unrealistic flow dispersion. To explore this issue, a unified algorithm for the determination of flow directions has been developed, and new methods for the validation of the resulting surface flow paths are introduced. The unified algorithm makes it possible, by setting appropriate parameters, to perform local or path‐based analyses and to experiment with different combinations of single and multiple flow directions in a morphologically significant manner. The new validation methods use drainage systems delineated from contour elevation data as a reference and take into consideration the overlap between these systems and those obtained from gridded elevation data. The unified algorithm is presented, and the results are evaluated for selected case studies in order to provide guidance on the use of surface flow path algorithms based on gridded elevation data.