Journal of Landscape Studies 2 (2009), 57 – 68 Received: 18 December 2009; Accepted: 6 January 2010; Published online: 9 January 2010 Journal of Landscape Studies How to extract river networks and catchment boundaries from DEM: a review of digital terrain analysis techniques Vojtěch Barták* Department of Applied Geoinformatics and Spatial Planning, Faculty of Environmental Sciences University of Life Sciences Prague, Kamýcká 129, 165 21, Prague, Czech Republic Abstract Raster digital elevation models (DEMs) are a source of data with rapidly increasing quality and availability. Although they are used in a wide range of research and application fields, including hydrological modelling, river basin management, geomorphological modelling, soil science, plant ecology, and landscape characterization, only a few of the methods for processing DEMs described in the literature are accessible in commonly-used GIS software. A review of hydrologicallyoriented digital terrain analysis (DTA) techniques is provided. Apart from computation of basic terrain attributes, the main tasks are extraction of the automated river network and catchment boundaries. The basic approach is overland flow simulation using the predetermined flow directions from each cell to one or several of its neighbours. Such an approach requires treatment of the problematic parts of DEM, where the flow directions cannot be determined due to the absence of any lower neighbour (i.e. closed depressions and flat areas). Except in the case of two recently developed computer programs (DEMETERR and TAS), the available GIS software does not offer a satisfactory range of usable methods. Further development of programs like ArcGIS or GRASS is therefore necessary to fill this gap. Key words: Digital terrain analysis; Raster DEMs; Overland flow algorithms; Catchment delineation; River network extraction. 1. Introduction Raster digital elevation models (DEMs) are a source of data with rapidly increasing quality and availability. They are used in a wide range of research and application fields, particularly hydrological modelling, river basin management, geomorphological modelling, soil science, plant ecology, and landscape characterization (Moore et al., 1991). Unfortunately, only a few of the methods for processing DEMs described in the literature are accessible in commonly-used GIS software. Moreover, the accessible methods are sometimes the oldest and worst ones. Recently, two programs with satisfactory algorithm choice have been developed: DEMETERR (Barták, 2008) and * Corresponding autor; E-mail: [email protected] Available online at: www.centrumprokrajinu.cz/jls/ TAS (Lindsay, 2005), both focused on hydrological applications. The aim of this paper is to provide a review of hydrologically-oriented digital terrain analysis (DTA) techniques. Most of them are motivated by models of catchment rainfall-runoff response and river basin management needs, so the main tasks are to identify the river network and the positions of the catchment boundaries. The oldest methods were based on local topography evaluation (i.e. determining ridge and valley lines; see Tribe, 1992), but since the early 1980s the main approach has been to model overland flow (Mark, 1984; O’Callaghan et Mark, 1984; for a review, see 57 V. Barták: Journal of Landscape Studies 2 (2009), 57 – 68 Bertolo, 2000). In the present context, the term “overland flow” does not refer to any real outflow process, but to the theoretical water flow over the completely uncovered and impermeable terrain, generated by the initial unit rainfall regularly spaced over the entire DEM. The overland flow simulation consists of two basic steps. The first is the assignment of flow directions along which the water flows from a particular cell to one or several of its eight neighbours. The second step is flow accumulation computation, i.e. determining the upslope area draining through the particular cell. The results from the latter step are the size and the position of the catchment (often referred to as the contributing area or upslope drainage area) corresponding to each cell. Since the assignment of proper flow directions is a necessary step for the successful solution of these tasks, those cells that have no lower neighbour are problematic parts of the DEM. On such cells the flow directions remain undefined, so the resulting drainage network is discontinuous. Such problematic DEM parts are of two types, closed depressions and flat areas, and both must be treated before simulating the overland flow. 2. Primary and secondary terrain attributes Moore et al. (1991) distinguish between primary and secondary terrain attributes derivable from a DEM. The primary attributes are computed directly from elevations, while the secondary attributes are defined as a compound of the primary attributes. Further, the primary attributes may be computed using either the values of the eight neighbours (i.e. the surrounding cells) for each DEM cell, or larger cell neighbourhoods. Examples of primary attributes are the terrain slope, the aspect, or the horizontal and vertical curvature; the contributing area is an example of a secondary attribute. The slope, aspect and curvature can be calculated for the particular cell from the elevations of its eight neighbours, using the first and second discrete derivatives (for details, see e.g. Gallant et Wilson, 1996). Another way is to compute the slopes between the cell and its neighbours (as the ratio between the vertical and horizontal distance), and then use the steepest slope (i.e. greatest downhill slope), or their weighted mean, where the weights are proportional to the slope magnitude (Quinn et al., 1991). These methods directly correspond to certain methods for computing 58 contributing areas, which are described in the next section. A well-known example of secondary terrain attributes is the topographic index (sometimes called the wetness index), which indicates the tendency of the site to soil saturation (Quinn et al., 1995). It is defined as log(a/S), where a is the contributing area of the cell and S is the slope. For a comprehensive list of primary and secondary terrain attributes, see Moore et al., 1991. 3. Assigning flow directions 3.1. SFD8 The simplest method for assigning flow directions is to determine the flow direction from a given cell to that of its neighbours, to which the slope is steepest (Fig. 1). Such an approach is called SFD8 (Single Flow Direction chosen from 8 possibilities), and the first references are in Mark (1984) and O’Callaghan et Mark (1984). Figure 1. The SFD8 algorithm. The large numbers denote the elevations, the small numbers denote the slope from the central cell, and the arrow represents the determined flow direction. The slope from the cell to its neighbour is computed as the difference in elevation divided by the horizontal distance (cell size for cardinal neighbours and cell size multiplied by the square root of 2 for diagonal neighbours), and is considered as positive downhill. The basic feature of this approach is that the flow is always represented as convergent. No splitting of the flow to several directions is allowed. This may be regarded as an advantage as well as a disadvantage, depending on the aim of the V. Barták: Journal of Landscape Studies 2 (2009), 57 – 68 analysis. An additional and clearly undesirable feature is that the flow is biased towards one of the eight possible directions, so the result is strongly dependent on the grid orientation of the DEM. 3.2. MFD8 The MFD8 (Multiple Flow Directions chosen from 8 possibilities) algorithm was developed as a modification of SFD8 to represent flow divergence. The water flow from the cell is divided among all the neighbours to which there exists a positive (i.e. downhill) slope (Fig. 2). Figure 2. The MFD8 algorithm. The thickness of the arrows symbolizes the proportion of flow falling on the particular neighbour. et al. (1991). The generalization to p ≠ 1 (or 1.1) was given by Holmgren (1994) and Quinn et al. (1995). Note that the higher the values of parameter p, the greater the similarity of the MFD8 algorithm to SFD8 (theoretically if p →∞ then both algorithms merge). In other words, the exponent p controls the degree of flow convergence. 3.3. SFD∞ This approach (Single Flow Direction chosen from infinite possibilities) was proposed by Tarboton (1997). The algorithm chooses the direction of the steepest slope from the (theoretically) infinite range from 0˚ to 360˚. It proceeds by constructing eight triangles with vertices in the centres of the cell and its two (mutually adjacent) neighbours (Fig. 3), and subsequently identifies the steepest slope direction on the planes determined by the triangles. The greatest of these slopes is then chosen and, if it does not go directly to the centre of one of the neighbours, the flow is apportioned to the corresponding two neighbours, so that the amount of flow falling on the particular neighbour is inversely proportional to the deviation of the direction to the neighbour from the determined steepest slope direction (angles α1 and α2 in Fig. 3). The proportion of the flow assigned to the i’th neighbour is computed using the ratio S ip , ∑ S jp 0 < j ≤8 (1) where Si is the slope from the cell to its i’th neighbour, the summation is over the neighbours to which a positive slope exists, and p is a parameter that can be considered as constant or spatially variable (for the latter, see Quinn et al., 1995 and Kim et Lee, 2004). The original formulation of (1) with p = 1.1 was proposed by Freeman (1991), and with p = 1 and slopes multiplied by the so-called “contour length” (coefficient greater for diagonal neighbours than for cardinal neighbours) by Quinn Figure 3. The SFD∞ algorithm. The dots are the centres of the cells, the arrow is the flow direction. Note that this example does not use the topography from Figures 1 and 2. The fact that the flow is mostly divided into two directions has led some authors to consider this algorithm as “multiple flow” with the representation of divergent flow. However, the original aim (Tarboton, 1997) was to represent 59 V. Barták: Journal of Landscape Studies 2 (2009), 57 – 68 flow convergence, but without the undesirable bias towards cardinal and diagonal directions. Flow divergence obviously occurs, but it is always constrained to the two adjacent neighbours. 3.4. MFD∞ The MFD∞ method (Multiple Flow Direction chosen from infinite possibilities), developed by Seibert et McGlynn (2007), is a straightforward generalization of SFD∞, in the sense that MFD8 is a generalization of SFD8. As in SFD∞, the algorithm seeks the steepest slope directions on the eight triangle-generated planes. Then, however, it does not choose the steepest slope but all the positive and locally steepest slopes (Fig. 4). The flow apportioning between the chosen directions is realized by (1), and the corresponding flow part for each such direction is subsequently divided into two mutually adjacent neighbours, in the same manner as in SFD∞. appear much more realistic than those generated by SFD8, the random nature of the algorithm, providing different results with the same data, together with flow lines inconsistent with the topography, are usually considered as undesirable. Another method is the so-called DEMON (Digital Elevation MOdel Networks) algorithm, developed by Costa-Cabral et Burges (1994). The DEM values are placed in the corners of the cells rather than in their centres, and the flow directions are determined on the plane fitted to the four elevations of each cell. The flow is then represented by flow tubes of variable width, so a low degree of flow dispersion on a divergent topography is allowed. This algorithm represents a quite different approach than those described above, but its use is restricted due to the presence of complicated topographies requiring special treatments (Tarboton, 1997). The idea of a spatially variable degree of flow divergence led Pilesjö et al. (1998) to develop the Form Based algorithm. This consists of three basic steps. First, each cell is indicated as undisturbed (simple), complicated (consisting of several valleys) or flat, according to the configuration of its lower and higher neighbours. Then, a different flow mechanism is carried out on the each such cell type. On complicated cells, the flow is apportioned between the valleys, in proportion to their width. On undisturbed cells, the terrain shape is evaluated as convex or concave, and then the MFD8 method or the modified SFD∞ method is chosen. 4. Flow accumulation and watershed delineation Figure 4. The MFD∞ algorithm. The dark lines and dots delineate the triangles on which the locally steepest slopes are determined. The arrows represent the determined flow directions. 3.5. Other methods Apart from the algorithms described above, some other flow direction assignment methods have been proposed in the literature. In order to avoid the bias of SFD8 toward one of the eight possible directions, Fairfield et Laymarie (1991) suggested a modification that introduces a random component into the slope calculation procedure. Although their method (named Rho8) leads to flow lines that 60 Once the flow direction has been defined for each cell, we can simulate the flow accumulation and compute the contributing areas. One possible method (O’Callaghan et Mark, 1984) is as follows. At the beginning, the flow accumulation value is set to 1 for each cell. Then the DEM is scanned row-by-row and, for each cell, the number of its inflows (i.e. the neighbours whose flow direction is directed towards it) is counted. Subsequently, the DEM is repeatedly scanned (row-by-row) and, during each iteration, the cells with no inflow are determined and their flow accumulation values are distributed among their neighbours (by one of the methods described above). Simultaneously, the numbers of inflows of such neighbours are decreased by one. This implementation has O(n2) V. Barták: Journal of Landscape Studies 2 (2009), 57 – 68 asymptotic complexity. The complexity O(n) can be obtained when the neighbours whose number of inflows has dropped to zero are stored in the stack and the computation then proceeds at the first cell on the stack (while the stack is nonempty; see Barták, 2008). Thus an iterative row-by-row scan is avoided. Another approach, with asymptotic complexity O(nlogn), uses a priority queue and searches the DEM “from highest to lowest”. For watershed delineation, the position of the outlet must be known. Such an outlet may be represented by a single cell or by a group of cells. The catchment consists of all the cells draining through the flow directions to the outlet. Such cells can be found in exactly the same way as the flow accumulation described in the previous section, with two differences. Firstly, only the directions are traced and no flow partitioning has to be carried out. Secondly, the output is a list of cells belonging to the catchment rather than their count. depression has a “bottom” (consisting of cells with no lower neighbour), and a “catchment” (consisting of cells from which the flow paths terminate at the bottom). The lowest cell on the boundary of a catchment (i.e. the point through which the water will overflow when the depression is filling) is often called the “pour point”, and the depression itself can be defined as consisting of all the cells from its catchment whose elevation is lower than the elevation of the pour point (Fig. 5). 5. Removing closed depressions Closed depressions (often called sinks or pits) are cells or groups of cells completely surrounded by cells of higher elevation. This means that no flow direction can be assigned to such cells, since no positive slope is determined. Most landscapes are modelled by fluvial and erosion processes, and the presence of closed depressions in the DEM is usually due to data errors, such as errors from interpolation or measurement (Florinsky, 2002). Sometimes, however, they can reflect real terrain features (e.g. volcanic craters). Modellers often treat them as spurious features that must be removed from the DEM, otherwise they cause discontinuities in the drainage network determined by the flow directions, and thus prevent the successful solution of other DTA tasks (e.g. catchment delineation or river network extraction). An interesting attempt to develop a method for distinguishing between actual and spurious depressions is presented in Lindsay et Creed, 2006. Before describing methods for removing depressions, it is necessary to discuss their identification in the DEM, since they must usually be identified before they are removed, and since various complex depressions, such as nested or cascade-organized depressions, make this procedure surprisingly complicated. Some terminology is needed for the discussion. Each Figure 5. The vertical section of the DEM with a depression. The oldest methods for finding depressions are based on the following two-phase procedure (Jenson et Domingue, 1988; Martz et De Jong, 1988). In the first phase, the bottoms are found by row-by-row scanning; in the second phase, the catchment (and the pour point on its boundary) is found for each bottom. This type of procedure has asymptotic complexity O(n2), where n is the number of cells in the DEM, and since they treat each depression separately, their real complexity depends on the number and the complexity of the depressions. Soille et Gratin (1994) and later (without any reference to their paper!) also Wang et Liu (2006), suggested a more effective procedure. It uses a “from lower to higher” and “from the edges inwards” search, based on the priority queue data structure (also known as a binary heap), rather than a row-by-row scan. Only one search is needed and all the depressions and pour points are easily identified, with asymptotic complexity O(nlogn) (complexity of the priority queue). 61 V. Barták: Journal of Landscape Studies 2 (2009), 57 – 68 5.1. Filling The simplest and probably best known method for removing depressions from the DEM, first proposed by Jenson et Domingue (19898) and Martz et DeJong (1988), is to “fill” them by increasing the elevations of the depression cells up to the elevation of the pour point (Fig. 6). The theoretical background is the assumption that the depressions are caused by an underestimation of the elevations in the depressions. The depressions can be effortlessly filled during the priority-queuebased depression search described above (Soille et Gratin, 1994; Wang et Liu, 2006). Figure 7. An example of depression carving. The medium-thick line is the original topography before carving, the thickest line is the new topography after carving. Although this method is sometimes adequate, and removes the depressions by decreasing the elevations of only few cells, in the case of small deep depressions it can sometimes cause unrealistic long deep “channels” consisting of the decreased cells. In such cases, the filling approach would probably be better. 5.3. Combinations Figure 6. An example of depression filling. The thick line is the original topography before filling, the dotted line is the new topography after filling. An obvious disadvantage of this method is that the filled depressions create large flat areas, where the problem of assigning the direction of flow arises again. Such regions must be further treated by some method for removing flats (see the next section). 5.2. Carving An alternative assumption about the origin of depressions can be that they are due to an overestimation of the elevations in the neighbourhood of the pour point, where the overestimated cells have formed a “dam”. The proper solution is therefore to decrease rather than increase the elevations of the affected cells (Fig. 7). This approach (sometimes called “breaching”) was proposed independently (and with some differences) by Rieger (1998), Jones (2002) and Soille et al. (2003). The latest implementation is also based on priority-queue-search, and thus shares its complexity. 62 A logical extension of the approaches described here is to combine them, with the particular method being chosen according to its impact (or cost). The cost may be measured as the number of changed cells (the area cost), as the total change in elevations (the volume cost), or as a combination of these two. The last of these options is adopted in the IRA (Impact Reduction Approach) method proposed by Lindsay et Creed (2005), in which the cost is computed for each of the two methods (filling as well as carving) applied to the whole DEM, and then the method with the lower cost is chosen. A straightforward improvement to such a method would be to decide between filling and carving for each depression separately. Unfortunately, this cannot be done easily due to the presence of complex depressions (Barták, 2008). However, there are two methods that solve each depression separately, and, moreover, enable us to treat some part of the depression by carving and the rest by filling (Fig. 8). The first method was proposed by Martz et Garbrecht (1999), who called it “outlet breaching” (sometimes referred to as “constrained breaching”). The procedure tries to decrease the elevations of some cells in the neighbourhood of the pour point, before filling is performed. Soille V. Barták: Journal of Landscape Studies 2 (2009), 57 – 68 (2004) suggested a more sophisticated method based on mathematical morphology in which the proportion of carving and filling is set in such a manner that the resulting cost is the lowest possible. Although they generate more realistic terrains, both methods have the awkward feature that they are usually iterative, since in raising the elevations some new (mostly small and shallow) depressions may occur. This leads to a relatively high cost, containing elevation changes on the cells which were originally not in any depression. On the other hand, the advantage of such methods is that the flat areas and the depressions can be treated simultaneously by the same procedure. 6. Treatment of flat areas Figure 8. Combination of filling (arrows up) and carving (arrows down). 5.4. Physically-based methods These methods try to create a terrain which is more realistic than the flat areas generated by filling or carving procedures. The first and very simple approach is to fill the depressions in a manner similar to the filling technique, but the elevations of the cells in the depression are increased not at the pour point elevation but slightly higher. The method is called SDI (Spatially Distributed Elevation Increment; Tianqi et al., 2003), which reflects the fact that the increment added to the pour point elevation is spatially distributed in order to generate a gently inclined plane. An important assumption is that the DEM is relatively simple and is roughly inclined to one of its corners, so the resulting slope orientation of the plane originating from the particular depression corresponds to this DEM inclination. The second, truly physically-based method is PEM4PIT (Physical Erosion Model for PIT filling; Grimaldi et al., 2007). It simulates filling-up of the depressions by erosion, the intensity of which is consistent with the surrounding topography. The elevations of the cells in the depressions are changed so that the new topography satisfies the mass continuity equation for steady state topography, reflecting the equilibrium between tectonic, fluvial and diffusion processes in the landscape. Flat areas (or “flats”) are cells or groups of cells completely surrounded by cells with the same (or higher) elevation (Fig. 9). They are often present in DEMs due to data rounding on a relatively flat topography, or as a result of a particular depression-removing procedure. Apart from methods that treat flats together with depressions (both of the physically-based methods described above, and the carving implementation proposed by Jones, 2002), the literature offers two other usable approaches, both constructing the improved topography of the flat according to the surrounding topography. Figure 9. An example of a flat. The numbers denote the elevations. The flat is bordered by the thick line. The light grey cells have the flat elevation, the dark grey cells are higher, and the white cell is lower than the flat elevation. 6.1. Towards the lower gradient The first method, originally proposed by Jenson et Domingue (1988) and improved by Soille et Gratin (1994), is to construct a topography inclined towards the lower neighbours of the flat (Fig. 10). 63 V. Barták: Journal of Landscape Studies 2 (2009), 57 – 68 In the first step, the cells not adjacent to any lower cell are increased by a sufficiently small increment. This step is then repeated, until there is no cell with a lower neighbour. The increment must be determined in such a way that the elevations in the flat will not exceed the elevation range of the surrounding topography. mathematical morphology, which implicitly solves such cases and therefore does not require any additional step. Figure 11. From the upper gradient computed on the flat from Figure 9. The meanings of the symbols are as in Figure 10. Figure 10. Towards the lower gradient computed on the flat from Figure 9. In the picture on the left, the numbers denote the number of elevation increments added to the particular cell. The picture on the right shows the resulting flow directions (determined by the SFD8 algorithm). 6.2. Combined gradient The obvious result of the previous method is a simple inclined plane, in which the subsequently determined flow paths form non-realistic parallel lines (Fig. 10). To represent some degree of flow convergence, Garbrecht et Martz (1997) suggested a method combining the gradient “towards lower” topography with the gradient “from higher” topography. The first is computed in exactly the same way as in the preceding method. The computation of the second is analogous: in the first iteration the cells which are adjacent to some higher cell and are not adjacent to any lower cell are increased. Then the algorithm iteratively increases the cells not adjacent to any lower cell (for the result, Fig. 11). The final step is the summation of both gradients (i.e. of the number of increments added to each cell through any of the preceding steps, Fig. 12). An additional step is usually required, due to certain special cases where new (but always small and simple) depressions occur (Fig. 12, left). Such a step consists of computing the “towards lower” gradient on this new flat, with a half elevation increment. Soille et al. (2003) proposed an improved version of this algorithm, based on 64 7. River network extraction Sometimes it may be desirable to estimate the position of the river network from the DEM, even when the “real” position (i.e. the topographic map) is known, because the real position often does not agree with the DEM topography. Spatially distributed hydrological models that compute the outflow from a catchment using flow directions determined on the DEM cells should distinguish between “river cells” and “hill cells”, and represent the outflow from these two cell types in a different way, e.g. with flow divergence (multiple flow algorithms) on the hills and flow convergence (single flow algorithms) in the streams. Even in river basin management, when subcatchment Figure 12. The final step of the combined gradient algorithm. The numbers in the picture on the left are the sums of the numbers from Figures 10 and 11. The picture on the right shows the resulting flow directions. The flow direction of the central cell was determined through an additional step, since after summation of the total increments a new flat arose on this cell (see Garbrecht et Martz, 1997). (i.e. the number of increments added to the central cell will be 3.5). V. Barták: Journal of Landscape Studies 2 (2009), 57 – 68 delineation is required, there is a need for information about the position of the outlets (and thus the position of the river network). In all these tasks, the position of the river cells must be compatible with the remaining DEM topography so that the water will not be forced to flow uphill. Regardless of its real nature, the river network estimated from the DEM typically consists of lines that are one cell in width. Thus the methods for river network extraction must decide for each cell whether it is a river cell or not. Such a decision may be made using the real position of the river network (the so-called “blue lines” in the maps), or may be fully automatic, using the DEM as an exclusive source of information. The first approach, often referred to as “enforcement” or “burning” (see e.g. Soille et al., 2003; Turcotte et al., 2001), proceeds by overlaying the blue lines over the DEM and changing the elevations of the cells intersecting with blue lines. In this paper, the latter, fully automatic, approach is discussed. 7.1. Local curvature methods The oldest methods for fully automated river network extraction are based on satisfying some terrain shape criteria that are typical for river valleys. Each cell is analyzed within the moving window (usually 3x3 cells in size), and the shape of the corresponding terrain is examined. One possible way is to make several vertical cuts in different directions and then to analyze these cuts as to whether they are V-shaped, which is assumed to determine a river valley. Another way is to measure the degree of terrain convergence on each cell by counting the number of its neighbours that are higher than the inspected cell. The best known example is the Peucker et Douglas (1975) algorithm, which scans the DEM by 2x2 sized windows, and within each group of four cells the highest cell is marked. Then the river cells are determined as the cells that remain unmarked. An extensive review of local curvature methods along with a detailed discussion is provided by Tribe (1992), who noted that these apparently simple methods often require an additional step, which makes them much more complicated. The typical resulting networks are namely discontinuous, full of inappropriately determined river cells, and are too wide, so that there us a need for a step that connects them (e.g. using previously determined flow directions) and thins them. An interesting algorithm solving all these obstacles was proposed by Meisels et al. (1995). 7.2. Flow accumulation methods The basic concept of this approach is that river cells can be determined as cells in which the flow accumulation (i.e. the contributing area) is high enough for the transition of hillslope processes to fluvial processes (Mark, 1984). Therefore the cell may be considered as a river cell if its contributing area exceeds some predefined threshold value. If the SFD8 algorithm is used, the obvious advantage of such an approach will be that the resulting river network is fully connected. The particular methods differ in the way the threshold value is determined. The simplest method is to consider the area threshold as spatially constant (Mark, 1984; Jenson et Domingue, 1988; Martz et Garbrecht, 1982; Quinn et al., 2005; and many others). The corresponding theoretical background was given by Tarboton et al. (1992). Such approaches have been criticized for insufficient density of the resulting networks in the higher parts of a landscape, and for inappropriate positions of river initiations (see e.g. Montgomery et Foufoula-Georgiou, 1993). One possible solution is to consider the area threshold as dependent on the slope values. Generally, the higher the slope, the lower the sufficient area threshold. In practice, several authors (Montgomery et Foufoula-Georgiou, 1993; Montgomery et Dietrich, 1994; Ijjasz-Vasquez et Bras, 1995; and others) argue that the appropriate variable whose critical value has to be determined is aS2, where a is contributing area and S is slope. This threshold often leads to discontinuous networks, so subsequent network connecting according to flow directions is usually required. A substantial disadvantage of this approach is that the proper estimation of a local slope is a very difficult task, due to its strong scale dependency. Therefore Roth et al. (1996) suggested replacing the slope by the so-called “relative subcatchment elevation”, which is defined for each cell as the mean elevation over its contributing area (i.e. its catchment) minus the elevation of the cell. They argue that this variable exhibits a behaviour similar to that of the local slope multiplied by the contributing area; however, the estimation is less affected by uncertainty due to its summation over a 65 V. Barták: Journal of Landscape Studies 2 (2009), 57 – 68 larger area. An alternative method for extracting networks with a higher density in the higher parts of a landscape was developed by Tarboton et Ames (2001). Their area threshold value is determined by using the “weighted contributing areas” rather than the normal contributing areas. The weights reflecting local curvature enter into the computation of the contributing areas, so that the initial amount of water is greater in the cells located at the convergent topography. The simplest option is to set this amount to two for the cells determined as river cells by the Peucker&Douglas algorithm, and to one for the rest, and then to compute the contributing areas in exactly the same way as described in section 2.2. 7.3. Determining threshold values Irrespective of how the type of threshold was chosen, the proper determination of its value is an additional and non-trivial question. The simplest method is to visually compare the resulting network with the “blue lines” (e.g. Mark, 1984; Jenson et Domingue, 1988; Martz et Garbrecht, 1992). When the blue lines are converted to an appropriate raster, we can improve this comparison by minimizing the spatial differences between the extracted and mapped river cells (for such an optimization using a genetic algorithm, see Kim et Lee, 2004). Montgomery et Foufoula-Georgiou (1993) suggested using information about the real position of the river sources for calculating the critical value of aS2. If no such additional information is available, the determination should use some criterion based only on elevations. One way is to analyze the slopecontributing area plot and determine the break points corresponding to river initiations (Tarboton et al., 1991; Ijjasz-Vasquez et Bras, 1995); however, there is no agreement concerning the proper break point. A completely different approach was developed by Tarboton et al. (1991). It is based on fulfilling some empirical laws (often called Horton’s laws) describing the self-similar and scale-invariant morphology of real river networks. One such law is called the “constant drop law”, and can be formulated as follows: the average elevation drop along river reaches with the same Strahler order is approximately constant across the Strahler orders. According to Tarboton 66 et al. (1991), the lowest threshold value leading to a network that satisfies the constant drop law can be considered as the proper value. The authors called this procedure “constant drop analysis”, and an evaluation made by Barták (2008) proved its usability. 8. Final remarks A brief outline of available DTA techniques has been presented. The algorithms for particular tasks often differ substantially, and the individual choice depends on the aim of the analysis to be carried out. Mostly, it is not a matter of saying which method is generally the best or the proper one. For example, the SFD8 algorithm, which is unable to represent divergent flow, is more appropriate for watershed delineation than multiple algorithms, since flow dispersion leads to overlapping of adjacent catchments. Therefore, the availability of a suitable range of methods is desirable. Unfortunately, this is not the typical case, since just one method or a limited number of methods for a particular task can be accessed in widely-used commercial or noncommercial software (e.g. ArcGIS, Olivera et al., 2002; GRASS, GRASS Development Team, 2008; TAPES, Gallant et Wilson, 1996; etc.). Two exceptions are DEMETERR (Digital Elevation Models and their Elementary TERRain analysis; Barták, 2008) and TAS (Terrain Analysis System; Lindsay, 2005), which are however in an early stage of development. Further development and upgrading of extensive GIS programs, such as ArcGIS and GRASS, is therefore more than urgent. Acknowledgements This work has been supported by an IGA CULS grant. I thank Barbora Matoušková for substantially improving the manuscript. I thank Petra Šímová and Vladimír Puš for initializing this work. References Barták, V. 2008. Algoritmy pro zpracování digitálních modelů terénu s aplikacemi v hydrologickém modelování. Diploma thesis [online]. 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