Multiple Flow Direction Algorithm Research Articles

Similarity analysis of flow route algorithms for extracting drainage network from grid-based terrain model

Flow routing algorithm,which is often used to calculate the terrain parameters such as catchment area,specific catchment area,topographic wetness index and so on,is a key point in distributed hydrologic models,soil erosion modeling and other geoscience fields.The results obtained by the flow routing algorithms have distinct effects on hydrological and soil erosion modeling process.So evaluating flow routing algorithms has become a focus in these fields. In this paper,five flow routing algorithms,which are known as D8(Deterministic eight-node),Rho8(Random eight-node),Dinf(D-infinite),MFD(Multiple flow direction algorithm),and DEMON(Digital Elevation Model Networks),are selected to compare and analyze quantitatively on two Digital Elevation Model(DEM) with 5m,10m and 25m horizontal resolution respectively.Coefficient of relative difference,cumulative frequency distributions and XY scatter plot of the Total Catchment Area(TCA) are designed to evaluate the similarities within the selected flow path algorithms.Also the effect of DEM resolution on TCA,obtained from the selected five algorithms,is fully discussed. The results of the paper are summarized as follows: 1) differences between catchment area values estimated by the selected five flow routing algorithms were the greatest along side slopes area,and the differences decreased where the terrain became more convergent or along the channel;2) the difference exists in any DEM with various resolutions,but is more sensitive to the high resolution DEM;and 3) multiple flow direction(MFD) algorithm is more suitable to estimate catchment area in complex terrain area than single flow direction(SFD) algorithm does that.So if the condition permits or accurate results are needed,high resolution DEM and fine MFD should be used effectively.This study also points out that the choice of flow routing algorithm has potentially important consequences for the calculation of upslope contributing areas,sediment transport capacity,topographic wetness,and several other topographic indices.

Spatial statistical properties and scale transform analyses on the topographic index derived from DEMs in China

The topographic index (TI), frequently used in approximately characterizing the spatial distribution of variable source areas within a watershed, has been widely applied in topography-based land-surface process schemes coupled in regional or global climatic models. The TI concept, however, was originally developed for studying hill-slope scale hydrological processes and was most commonly used in simulations from small- to medium-sized watersheds. It is still questionable whether the TI computed from coarse-resolution digital elevation models (DEMs) for large-scale hydrology and climate studies can effectively reflect the spatial distribution of soil moisture, surface saturation, and runoff generation processes in most areas. In this study, we first proposed an improved multiple flow direction algorithm (IMFD) for accurately computing the TI distribution. We then evaluated the IMFD algorithm quantitatively by using four types of artificial mathematical surfaces. Subsequently, we conducted statistical analyses on the TI distributions computed with IMFD from 90×90 m 2 and 1000×1000 m 2 resolution DEM blocks sampled from across the whole of China. We found there are linear relationships between the mean TI values computed from the two different resolution DEMs in three sampled blocks of different sizes, i.e., 0.1°×0.1°, 0.5°×0.5° and 1°×1°. Systematic analyses further suggested that the forms of these linear relationships are evidently affected by the algorithm used for the TI computation, while the size, location, and number of the selected TI samples have minor effects on them. Finally, we investigated the influence of DEM resolution on the spatial statistical properties of TI. From the viewpoint of terrain discretization and smoothing effects, we also discussed the mechanism and the reasons causing the similarity on TI at different spatial resolutions.

Effects of catchment discretization on topographic index distributions

Summary Digital elevation models (DEMs) are widely used in topographically-based hydrology models. Most researchers dealing with DEMs have worked exclusively with either grid or contour based techniques. Intercomparisons of these techniques are empirical in nature, few in number and limited to a small number of catchments. We examine the relative effects of these techniques on the distribution of the topographic index (TI) for nine idealised hillslope types and eight natural catchments (4.4–83 km2) in southeast Australia. In particular we investigate the underlying causes for the frequently observed increase in the TI with grid size. A simple analytical model for a parallel-planar hillslope indicates that median TI is asymptotic with respect to the number of grid cells and a linear function of grid size. We demonstrate that the latter result holds for hillslopes with more complex geometry. Using a multiple flow direction algorithm, we find that hillslope geometry and flow partitioning affect the spatial pattern of the TI and the rate of change (M) of median TI with grid size. This makes it impractical to recommend general guidelines for the value of the directional parameter in flow partitioning algorithms. For the natural catchments we show that median TI is also a linear function of grid size and that there is some evidence for a linear relationship between M and the inverse of the median topographic slope. Throughout the investigation we find that contour DEMs are less sensitive to changes in resolution than grid DEMs.

광릉수목원 내 산지사면에서의 토양수분 시계열 자료의 단변량 분석

Soil moisture is one of the essential components in determining surface hydrological processes such as infiltration, surface runoff as well as meteorological, ecological and water quality responses at watershed scale. This paper discusses soil moisture transfer processes measured at hillslope scale in the Gwangneung forest catchment to understand and provide the basis of stochastic structures of soil moisture variation. Measured soil moisture series were modelled based upon the developed univariate model platform. The modeling consists of a series of procedures: pre-treatment of data, model structure investigation, selection of candidate models, parameter estimation and diagnostic checking. The spatial distribution of model is associated with topographic characteristics of the hillslope. The upslope area computed by the multiple flow direction algorithm and the local slope are found to be effective parameters to explain the distribution of the model structure. This study enables us to identify the key factors affecting the soil moisture distribution and to ultimately construct a realistic soil moisture map in a complex landscape such as the Gwangneung Supersite.

A new triangular multiple flow direction algorithm for computing upslope areas from gridded digital elevation models

Gridded digital elevation data, often referred to as DEMs, are one of the most widely available forms of environmental data. Topographic analysis of DEMs can take many forms, but in hydrologic and geomorphologic applications it is typically used as a surrogate for the spatial variation of hydrological conditions (topographic indices) and flow routing. Here we report on a new flow routing algorithm and compare it to three common classes of algorithms currently in widespread use. The advantage of the new algorithm is that unrealistic dispersion on planar or concave hillslopes is avoided, whereas multiple flow directions are allowed on convex hillslopes. We suggest that this new triangular multiple flow direction algorithm (MD∞) is more appropriate for a range of flow routing and topographic index applications.

A comparison of geographical information systems–based algorithms for computing the TOPMODEL topographic index

The performance of six geographical information systems (GIS)‐based topographic index algorithms is evaluated by computing root‐mean‐square errors of the computed and the theoretical topographic indices of three idealized hillslopes: planar, convergent, and divergent. In addition to these three idealized cases, two divergent hillslopes with varying slopes, i.e., concave (slopes decrease from top to bottom) and convex (slopes increase from top to bottom) are also tested. The six GIS‐based topographic index algorithms are combinations of flow direction and slope algorithms: i.e., single flow direction (SFD), biflow direction (BFD), and multiple flow direction (MFD) plus methods that determine slope values in flat areas, e.g., W‐M method [Wolock and McCabe, 1995] and tracking flow direction (TFD) method. Two combinations of horizontal resolution and vertical resolution of the idealized terrain data are used to evaluate those methods. Among those algorithms the MFD algorithm is the most accurate followed by the BFD algorithm and the SFD algorithm. As the vertical resolution increases, the errors in the computed topographic index for all algorithms decrease. We found that the orientation of the contour lines of planar hillslopes significantly influences the SFD's computed topographic index. If the contour lines are not parallel to one of eight possible flow directions, the errors in the SFD's computed topographic index are significant. If mean slope is small, TFD becomes more accurate because slope values in flat areas are better estimated.

A phenomenon-based approach to upslope contributing area and depressions in DEMs

Description of the terrain surface through digital elevation models (DEMs) strongly depends on data collection methods and DEM data structures. For efficiency and availability reasons regular point distributions are most common, which yield artefacts such as depressions and preferential flow directions. These facts need to be considered when natural phenomena are modelled, as is shown for handling depressions and for estimation of flow paths and upslope contributing areas. Analysis of the main reasons for the occurrence of depressions shows that they usually better reflect the terrain than their surroundings. Thus, the most common remedial method of raising depressions is rejected. Algorithms that ‘cut’ a flow path from the depression through its bounding barrier are favoured instead. Several flow routing algorithms are evaluated for their behaviour in regular grids. It is shown that the multiple flow direction (mfd) algorithm that distributes water from a grid cell to the lower of its eight neighbours proportionally to their elevation differences (slope) exhibits correct flow directions and the best rotation invariance. It is suggested that the estimation of upslope contributing areas (TCAs) is undertaken in two steps: first, a high quality flow direction data set is derived by a well-behaved mfd algorithm or by subgrid modelling of flow paths; secondly, the upslope contributing areas are obtained by counting the upslope elements. © 1998 John Wiley & Sons, Ltd.

Comparison of Single and Multiple Flow Direction Algorithms for Computing Topographic Parameters in TOPMODEL

Single flow direction (sfd) and multiple flow direction (mfd) algorithms were used to compute the spatial and statistical distributions of the topographic index used in the watershed model TOPMODEL. An sfd algorithm assumes that subsurface flow occurs only in the steepest downslope direction from any given point; an mfd algorithm assumes that subsurface flow occurs in all downslope directions from any given point. The topographic index in TOPMODEL is ln (a/tan β), where In is the Napierian logarithm, a is the upslope area per unit contour length, and tan β is the slope gradient. The ln (a/tanβ) distributions were computed from digital elevation model (DEM) data for locations with diverse topography in Arizona, Colorado, Louisiana, Nebraska, North Carolina, Oregon, Pennsylvania, Tennessee, Vermont, and Virginia. The means of the ln (a/tan β) distributions were higher when the mfd algorithm was used for computation compared to when the sfd algorithm was used. The variances and skews of the distributions were lower for the mfd algorithm compared to the sfd algorithm. The differences between the mfd and sfd algorithms in the mean, variance, and skew of the ln (a/tan β) distribution were almost identical for the various DEMs and were not affected by DEM resolution or watershed size. TOPMODEL model efficiency and simulated flow paths were affected only slightly when the ln (a/tan β) distribution was computed with the sfd algorithm instead of the mfd algorithm. Any difference in the model efficiency and simulated flow paths between the sfd and mfd algorithms essentially disappeared when the model was calibrated by adjusting subsurface hydraulic parameters.

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

AbstractWhen 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.