CATCHMENT DELINEATION AND CHARACTERISATION

CATCHMENT DELINEATION AND CHARACTERISATION A Review by Francesca Bertolo C atchment C haracterisation & M odelling An Activity of the EuroLandscape Project Space Applications Institute (SAI) Catchment Characterisation and Modelling EuroLandscape Project Space Applications Institute, Joint Research Centre Ispra (Va), Italy April 2000 Space Applications Institute Environment & Geo-Information Unit DG Joint Research Centre European Commission

ii Francesca Bertolo For further information concerning the Catchment Characterisation and Modelling activity or the EuroLandscape project you may contact: Dr. Jürgen Vogt, JRC-SAI-EGEO, email: juergen.vogt@jrc.it or Dr. Sten Folving, JRC-SAI-EGEO, email: sten.folving@jrc.it. Or visit our website on URL: http://www.egeo.sai.jrc.it JRC SAI EGEO

Catchment Delineation and Characterisation iii Table of Contents Preface v 1. Introduction...1 2. Digital Elevation Models...2 3. Catchment Delineation...5 3.1 Defining Drainage From Raster Datasets...6 3.2 The Problem of Flat Areas....11 3.3 The Channel Source Definition...12 3.4 About Errors...15 4. River and Catchment Ordering...16 5. Catchment Characterisation...19 6. Final Considerations...22 7. References...24 EuroLandscape CCM, April 2000

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Catchment Delineation and Characterisation v Preface Economic and environmental sustainability is one of the major goals of European policy. One of the basic pre-requisites to meet these goals is a sound knowledge of the different processes underlying economic and environmental evolution in the European territory. The documentation of the current situation and the study of relevant processes are, therefore, important issues for European institutions such as, for example, the Directorate General Environment (DG ENV), the European Environmental Agency (EEA), the European Statistical Office (EUROSTAT) or the Joint Research Centre (JRC) of the European Commission. In the frame of the 5 th Framework Programme on Research and Technological Development, the Environment and Geo-Information (EGEO) Unit of JRCs Space Applications Institute (SAI) is aiming to construct such fundamental knowledge and information through the implementation of the EuroLandscape project. EuroLandscape (Geo-Information for Development and Environmental Monitoring) is aiming at assessing, mapping and monitoring the European Environment, with special emphasis on the sustainable management of natural resources, including forests, grasslands and water resources. The catchment, as a basic physical entity of the landscape, has gained increasing attention in this context. Most processes related to the movement and quality of water are best studied at the catchment or sub-catchment scale and many associated processes such as soil erosion, mass movements, sediment transport, or land cover changes are strongly linked to this spatial reference unit. The EEA, therefore, intends to set-up a comprehensive database of catchment boundaries and river networks for the whole pan-european territory. Such database should include information on the topology and ordering of both the catchments and river stretches in order to allow for a detailed analysis of data on water quality and quantity, which are collected through the EuroWaternet network of measurement stations. This network is established by the EEA with the support of the national water authorities. Eurostats sections for Geographic Information (GISCO) and for Water Statistics are additional customers for the use and dissemination of such information. Together with the planned physical and socio-economic characterisation of the mapped catchments, the information will also be useful for the hydrological, geomorphological and socio-economic modelling communities in order to put the results of a wide variety of models into a wider geographical context. Within EuroLandscape it is the Catchment Characterisation and Modelling (CCM) activity to implement the catchment related work. CCM aims at a comprehensive mapping and characterisation of catchments in Europe and at a subsequent modelling of key processes in a set of representative catchments. This work is implemented at SAI, in close collaboration with the EEA and with a network of experts in a variety of institutions throughout Europe. This report has been written as a preparation to the European-wide mapping of catchments and drainage networks. In parallel, different algorithms have been tested for selected regions in Europe. Ispra, April 2000 Jürgen Vogt EuroLandscape CCM Leader EuroLandscape CCM, April 2000

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Catchment Delineation and Characterisation 1 1. Introduction The Catchment Characterisation and Modelling (CCM) activity of the EuroLandscape project is aiming at a European-wide mapping of catchments and drainage networks. The derived catchments shall then be characterised and classified according to surface characteristics, land cover dynamics and run-off conditions. It is in this context that this report on the state-of-the-art in catchment mapping and characterisation has been prepared. In particular two aspects have been investigated: how to automatically extract and map catchments and drainage networks from digital elevation models (DEMs) and whether examples of catchment classifications at regional level have been described in the literature. The availability of a DEM with adequate spatial resolution and covering the whole area of interest is a basic requirement to achieve the goals of CCM. It is evident that the quality of the DEM is of high importance and that considerable attention has to be paid to the errors that are introduced by the terrain model itself. This is related to the problem of scale: does the geometric resolution of the DEM have any influence on the precision of catchment boundaries and drainage channels and which degree of error is introduced by using a given DEM? In connection to that, it is important to highlight that the final database of European catchments will be the core of a Geographic Information System (GIS). Since the propagation of errors plays a significant role in GIS analysis it is important to have a clear understanding of how to deal with them. Procedures have, therefore, to be implemented for evaluating the reliability of both the input data and the final results (Chapter 2). A further step relates to the available algorithms for delineating catchments and river networks. It is not only important to know how to analyse the DEM, but also to understand the limitations of each algorithm. The method that ideally fits the needs of the EuroLandscape project must be computationally robust and efficient, and must be able to cope with the most important problems that this kind of analysis presents: DEM inherent altitude errors and the difficulty to recognise the pathways of water in flat areas. Another interesting problem is the definition of the river source area; in fact there is an intrinsic difficulty to define where exactly water starts to form a river channel. Finally, there is a need for a theory to help in taking a decision on the minimum source area that can be mapped from medium resolution DEMs (Chapter 3). Some attention needs to be given to the fact that, at the end, a large database has to be managed. Within this database the geographic relationships between different river networks or different catchments must be defined through an adequate nomenclature or coding system. This nomenclature or coding system is necessary for analysing the associated information (e.g. water quality, water quantity, sensitivity to flooding) in a geographical context and for understanding the environmental implications of political decisions. A specific chapter, therefore, is EuroLandscape CCM, April 2000

2 Francesca Bertolo devoted to investigate existing coding systems and to understand if it is possible to implement a similar system at the European level (Chapter 4). Finally, the question of catchment characterisation and classification involves a problem of scale and of data availability. In this framework is important to understand which are the most important parameters that characterise the landscape, the hydrological response and the environmental behaviour of a catchment at different scales, since CCM aims to obtain a database through which it will be possible: a) to derive a catchment typology and to select a set of representative catchments; b) to aggregate catchments to identify homogeneous zones or groups of catchment units at the pan-european scale; c) to extrapolate model results from representative catchments to the entire pan- European region. Simultaneously, it is important to consider which data are available or can reasonably be derived for the whole European territory (Chapter 5). 2. Digital Elevation Models Raster DEMs can be derived directly from stereo-photos or from satellite imagery such as stereoscopic SPOT images, but are generally derived by interpolation of scattered point elevation data, of contour lines, or of Triangulated Irregular Networks (TIN). The main limitation of a regular gridded DEM appears to be the fixed grid cell size. Such a DEM cannot always accurately describe the topography, especially in landscapes with varying complexity. Errors are introduced by the interpolation procedure, whatever method is used and, in general, these errors are spatially autocorrelated. Moreover, in order to save memory, gridded elevation data are often rounded to the nearest meter. In regions with gentle slopes this creates flat areas with abrupt changes in altitude (similar to stairs). All of these errors produce artefacts, such as pits and hummocks, that do not correspond to real landscape features and they affect the derived quantities such as slope-gradient and slope-aspect. While slope-gradient has about the same degree of error as the original elevation data, slope-aspect errors are usually amplified during calculation (Isaacson and Ripple, 1990; Bolstard and Stowe, 1994; Giles and Franklin, 1996; Desmet, 1997). JRC SAI EGEO

Catchment Delineation and Characterisation 3 These drawbacks have a clear impact for the extraction of the channel network and for the catchment delineation, which are generally based on slope gradient and slope aspect. For most hydrological applications, the vertical resolution of a DEM is considered satisfactory if the ratio of the average drop per pixel and the vertical resolution is greater than unity. The average drop per pixel is defined as the elevation between a pixel and the next in steepest descent (Thieken et al., 1999, Walker and Willgoose, 1999). Scale and grid cell size influence the extraction of the channel network to a point where the same method produces different results for the same area. In general, the grid cell size dependency is introduced by the inability to accurately reproduce drainage features that are at the same scale as the spatial resolution of the DEM. For meandering channels, this results in shorter channel lengths and for networks with high drainage density, it leads to channel and drainage area aggregation. In these situations, the number of channels, the size of direct drainage areas and the network pattern may depart considerably from the initial reference values (Wang and Yin, 1998). Garbrecht and Martz (1994) presented a sensitivity analysis on drainage properties extracted from DEMs of increasing cell size and for several hypothetical network configurations. On the basis of these results they found that a DEM should have a grid cell area of less than 5% of the network reference area in order to reproduce important drainage features with an accuracy of about 10%. The network reference area is the mean area draining directly into the channel links of the network. The underlying data source used for deriving the DEM is a crucial factor. For this reason, the aggregation of an accurate DEM is considered better than using a DEM derived from maps at a lower scale (Thieken et al., 1999; Wolock and Price, 1994, Walker and Wilgoose 1999). Different studies highlighted that the importance of these issues is due to the fact that the extent of the stream network and the length of the overland flow path strongly influence hydrological modelling results (Wolock and Price, 1994; Zhang and Montgomery, 1994; White and Running, 1994; Thieken et al., 1999). Hussein and Schwartz (1997) presented a systematic strategy for improving the quality of a DEM by including additional digital information on the geometry of the stream network. The approach is based on a theory developed by Hutchinson (1988, 1989) for creating digital elevation models by combining point elevation data and/or contour lines with a stream network. A unique feature of Hutchinson s approach is an automatic drainage enforcement algorithm, which attempts to remove spurious sinks in order to create a depressionless DEM. In addition, the algorithm also modifies the elevation of grid points that conflict with a downstream decrease in stream elevation. Control over the removal of spurious sinks and conflicting elevation points is achieved using two tolerances: the first controls the maximum EuroLandscape CCM, April 2000

4 Francesca Bertolo difference between a sink considered for removal and the nearest pour point (i.e., the local topographic minimum controlling a basin area). The second tolerance controls the maximum allowable modification of grid points that conflict with the stream network. The method of Hutchinson is incorporated in Arc/Info (ESRI) as a function called Topogrid. To correct the errors derived from elevation round-off, Nelson and Jones (1994) proposed a smoothing filter. The weights of the filter matrix are determined using an inverse distance squared function, so that the elevations of cells nearest to the central cell will influence the result more than those of cells that are further away. A final constraint is placed on the calculated elevation so that it is not adjusted by more than one half the elevation resolution, to ensure that the terrain model is smoothed without any loss of the original accuracy. Only a few DEMs are available covering the whole pan-european area. One of them is the so-called GTOPO30. It is a global DEM that was released by the USGS EROS Data Center in 1996 (http://edcwww.cr.usgs.gov/landdaac/gtopo30/gtopo30.html). The elevation values in GTOPO30 are regularly spaced at 30-arc seconds, which corresponds to approximately one kilometre. They are derived from eight sources of elevation information, including both vector and raster data sets. For most of Eurasia the data source is the Digital Terrain Elevation Data (DTED) produced by the National Imagery and Mapping Agency (NIMA, formerly the Defense Mapping Agency), which is a raster topographic database with a horizontal grid spacing of 3- arc seconds (approximately 90 meters). The generalization of the high-resolution data to the 30-arc seconds horizontal grid spacing was conducted by calculating the median value of the 100 full resolution cells corresponding to each cell of the new DEM. For this reason the accuracy of the values obtained is the same as in the original data set. The full resolution 3-arc seconds DTED has a vertical accuracy of ± 30 meters linear error at the 90% confidence level, which correspond to a RMSE of 18 meters. To ensure that the DEM is able to reproduce the correct movement of water across its surface, the DEM is processed to remove elevation anomalies that can interfere with hydrologically correct flow (Verdin and Jenson, 1996). Another high resolution DEM of Europe is distributed by GAF mbh, Germany, according to a sales agreement with GEOSYS/MONA PRO Visual Media, France. The MONA PRO DEM covers 22 countries in Europe and is available with the grid cell sizes of 75 m, 100 m and 250 m. The altitude precision (according to GEOSYS) is about 3,5 5 m in relatively flat terrain, and 12 15 m in very steep mountains (GAF Products and Services, http://www.gaf.de/gaf04.htm). The X-SAR/SRTM Shuttle Radar Topography Mission flown on the Space Shuttle in February 2000 will result in another potentially interesting DEM. This joint mission of the US National Imagery and Mapping Agency (NIMA), the US National Aeronautics and Space Administration (NASA), the German Aerospace Centre (DLR) and the Italian Space Agency (ASI) had the objective to use C-band and X- band interferometric synthetic aperture radars (IFSARs) to acquire topographic data JRC SAI EGEO

Catchment Delineation and Characterisation 5 over 80% of Earth s land mass (between 60 degrees North and 56 degrees South) during the 11-day Shuttle mission. Within 18 months after the mission the data will be processed into digital topographic data with a 30 x 30 m spatial sampling rate. The expected accuracy of the resulting data is given as 16 m absolute vertical height accuracy, 10 m relative vertical height accuracy and 20 m absolute horizontal circular accuracy at a 90% confidence level. Worldwide data will be distributed at a spatial resolution of around 100 m. When available, the X-SAR/SRTM DEM will be the first continuous high-resolution product, which has not been mosaiced from data derived from differing sensors, formats and dates. (http://www.jpl.nasa.gov/srtm/; http://www.dlr.de/srtm/). Higher resolution DEMs could also be collected from national databases. Although these DEMs are generally of high quality they are usually very expensive. In addition, it is generally difficult to join adjacent DEMs that come from different sources and have been produced in different ways. Finally, with increasing spatial resolution there is an increasing need of storing capacity and of computational power. Clearly, these problems limit the use of such data within the CCM project. A homogeneous DEM, covering the whole area of interest should be the preferred option. 3. Catchment Delineation The last years saw a general recognition of the catchment or the drainage basin as the most significant surface unit in environmental studies. Traditionally catchment boundaries have been manually derived from topographic maps, a labour-intensive activity. This limitation has changed after the introduction of Digital Elevation Models (DEMs). Even though methods for delineating catchment boundaries and flow paths from contour lines (Moore and Grayson, 1991) and triangulated irregular networks (Jones et al., 1990; Palacios-Velez and Cuevas-Renaud, 1986) provide reliable results, they require extensive data storage and computation time. Grid cell elevation models have advantages for their computational efficiency and the availability of topographic databases (Sabbagh et al., 1994). Therefore, they have seen widespread application for analysing hydrological problems. There is only one method, which does not require a DEM; it is based on an automated river network overlay (Sekulin et al., 1992). This approach needs a welldefined river network database, in which the basic unit is a river stretch (link) defined as the river length between two nodes. Each cell of a grid is allocated to river stretches using a shortest distance algorithm. Boundaries of hydrometric areas, coastlines, and boundaries of the catchment area above the gauging stations can be used with a point-in-a-polygon algorithm to give added precision in the allocation phase. Grid cells are then accumulated upstream of river stretches using a EuroLandscape CCM, April 2000

6 Francesca Bertolo down-network travel technique. This procedure has been proposed in the ERICA (European Rivers and Catchments) project of the EEA (Flavin, 1998). The catchment delineation is a two-step procedure: drainage patterns have to be recognized before the boundaries between different catchments can be inferred. 3.1 Defining Drainage Networks From Raster Datasets Three main approaches to the automated recognition of valleys and drainage lines from raster DEM can be identified (Tribe, 1992): A. The recognition of individual DEM cells as valley cells, where a cell is classified as a valley if some of the cell s neighbours are higher; B. The assignment of drainage directions to each DEM cell and the use of this information for the derivation of a drainage network; C. Two-step methods based on a combination of approaches A and B. They will be described in the following sections. Finally, a few remarks concerning the scale properties and fractal geometry of drainage networks will be given in section D. A. The recognition of individual DEM cells as valley cells In the first approach individual DEM cells are identified as valley cells by comparing the heights of each neighbour of the cell in turn with that of the cell. The methods of comparison are based on different concepts: graphs constructed from the elevations of cell s neighbours (If the cell represents a valley cell this graph will conform to a particular configuration); the connectivity number and the coefficient of curvature are calculated from the cell s neighbours; comparison of the elevations of the neighbour cells in predefined directions (Peucker and Douglas, 1975). The methods described produce noise and valleys, which extend too far up-valley because they are based on the concept of higher than. Higher could be only 1 m, meaning that any cell representing a hardly discernible or a local depression can be classified as part of the valley network. Generally the network is discontinuous and some procedure is needed to connect the different valley segments and finally to derive the channel network by thinning. JRC SAI EGEO

Catchment Delineation and Characterisation 7 B. The assignment of drainage directions to each DEM cell. Mark (1984) and O Callaghan and Mark (1984) noted the discontinuities produced by the previous methods and proposed an algorithm to produce a continuous network. The algorithm, known as the D8 algorithm, is based on the flow of water over terrain along lines of steepest slope and is a computerized version of a manual method of catchment area measurement (Speight, 1968). Each cell is considered to drain to whichever of its eight neighbours has the steepest downslope from it. This is not always the lowest neighbour, since the height differences for the four diagonal half-neighbours of a point must be divided by the grid spacing multiplied by the square root of two. Initially, each cell may be considered to produce a unit quantity of runoff; this runoff is then carried downslope in accordance with drainage directions of the grid cells. Then, whenever the runoff in a cell exceeds some threshold, the cell is considered to be part of the drainage network. The principal limitation in the method is that each cell of the DEM has to have a drainage direction assigned to it. The D8 algorithm appears in many works, and in particular in Jenson and Domingue (1988) on which the ARC/Info tools for catchment delineation are based. The biggest drawback of this method is the fact that it represents only convergent flow. To overcome this limitation in flow direction assignment different approaches have been proposed. Fairfield and Leymarie (1991) proposed to introduce a stochastic rule in order to follow more closely the aspect of the slope to avoid the fact that in the D8 algorithm the flow is discretized to only one of eight directions, separated by 45º. The disadvantage of this new procedure is that the result is not exactly reproducible because of its randomness. Some authors have proposed that flow must be partitioned between different pixels. Freeman (1991) allocates flow to each lower neighbour in proportion to an exponent p of the slope. According to his results, a value of p = 1.1 is appropriate. These methods have the disadvantage that flow from a pixel is dispersed to all neighbouring pixels with lower elevation. Therefore the contributing area of a pixel does not include any full pixel but instead is composed of portions of different pixels and is discontinuous. Costa-Cabral and Burges (1994) oppose to most current models because of their point source representation of flow generation and the resulting one-dimensional representation of flow paths; as an alternative they presented an elaborate set of procedures which model downslope flow in two dimensions in well-defined flow tubes. Flow at one point is in the direction of maximal surface slope. For planar pixels, if the flow direction is parallel to the grid orientation, the exit portion of the boundary is a single full boundary segment. If the flow direction is not parallel to the grid orientation, the exit portion of the boundary consists of two full adjacent boundary segments. EuroLandscape CCM, April 2000

8 Francesca Bertolo Tarboton (1997) tries to reduce dispersion by dividing the flow between one or two downslope pixels. The flow direction is a continuous quantity between 0 and 2π that is determined in the direction of the steepest downwards slope on the eight triangular facets formed in a 3 x 3 pixel window centred on the pixel of interest. Where the direction does not follow one of the cardinal or diagonal directions, the upslope area is calculated by distributing the flow from a pixel between the two downslope pixels according to how close the flow angle is to the direction of the pixel centre. Unresolved flow directions, in flat areas or depressions, are resolved iteratively by making them flow toward a neighbour of equal elevation that has a flow direction resolved. A suite of programs for the Analysis of Digital Elevation Data (TARDEM) from David Tarboton is freely distributed (http://www.engineering.usu.edu/dtarb/). For all of those methods depressions (pits) cause serious problems, but also in flat areas the assignment of a flow direction is not obvious. While closed depressions and flat areas in a DEM may represent real landscape features, they are more often artefacts that arise from errors in the input data, interpolation procedures, and the limited horizontal and vertical resolution of the DEM (Mark, 1984; Jenson and Domingue, 1988; Tribe, 1992; Martz and Garbrecht, 1998; Zhang and Montgomery, 1994). The correction of spurious pits has been conducted principally with two strategies. The first strategy attempts to remove depressions by smoothing the DEM data (Mark, 1984). Objections to this method are threefold: It does not distinguish between natural and spurious pits. It fails to remove all spurious pits, in particular deeper ones. A loss of significant information is evident after smoothing. The second strategy is to fill depressions by increasing the values of cells in each depression to the value of the cell on the depression boundary with the lowest value (Jenson and Domingue, 1988). First, the algorithm finds the pit s outflow point: that cell on the pit s boundary where water would flow out of the pit if it were filled with water. Then the heights of all cells in the pit, lower than the outflow, are changed to the height of the outflow. This creates a flat area over which drainage directions can be assigned. Fairfield and Leymarie (1991), among others, suggested to treat the pits as if they were real depressions, and to find the lowest point, the pass, from which water could flow out of the pit basin. This is achieved changing the directions of flow on the path between the pass and the low point of the pit. Water is figuratively made to climb up the side of the basin, which is unrealistic, but the DEM is not changed. JRC SAI EGEO

Catchment Delineation and Characterisation 9 Martz and Garbrecht (1998), from the consideration that a pit can be produced also by elevation overestimation errors, proposed a breaching algorithm which simulates breaching of the outlet of closed depressions to eliminate or reduce those expected to have been produced by elevation overestimate. It evaluates the local outlet of each closed depression in a DEM to determine whether the elevation of one or two cells at the outlet could be lowered to eliminate or reduce the size of the depression without reversing the direction of overland flow across the outlet. C. Two-step methods Several researchers have developed two-step procedures for extracting channel networks. Start cells or disconnected valley segments are first identified using a method similar to, or based on the concept of higher than, and these are then grown, usually down the line of steepest slope, to give continuous drainage lines (Band, 1986; Riazanoff et al., 1992; Lammers and Band, 1990; Skidmore, 1990; Yoeli, 1984; Smith et al., 1990). Yoeli (1984) proposed a valley line finding algorithm that, first of all, finds elevation minima on the DEM using a spline curve. A continuous search for the next lower neighbour is then conducted in a sampling square of twice the grid interval around the current last point of the valley line. Valley lines start from the highest minimum which, at this stage does not lie in an existing valley line, and finish when one of three possible situations is reached: joining another valley line; flowing into a lake or sea; reaching the edge of the DEM. Band (1986) in a first step marks convex- and concave-upward points as ridge and stream points, respectively, then the procedure searches for segment ends; new pixels are added downstream to the segments using a maximum descent algorithm until another stream segment is encountered. The final result is obtained by thinning the image to single pixel-width lines. Band s stream network and sub-catchment extraction algorithms, along with the production of topological codes describing their structures have been released as part of GRASS, a US Army Corps of Engineers public domain GIS (http://www.geog.uni-hannover.de/grass/). Smith et al. (1990) describe a two-step method based on a procedure first proposed by Haralick (1983). A cubic surface is fitted to the neighbourhood of each pixel. A pixel is defined as a valley pixel if the first directional derivative has zero crossings in a direction in which the second-directional derivative has positive extreme values. In a second step the procedure applies knowledge about drainage networks to integrate these probable valley pixels into a network of single-pixel-width lines satisfying the constraints imposed by a binary tree model. Riazanoff et al. (1992) and Chorowicz et al. (1992) first identify saddles, points that divide two groups of pixels in a neighbourhood which have higher elevation than the saddle. In their method these researchers use two layers: one is the DEM and the EuroLandscape CCM, April 2000

10 Francesca Bertolo second is a virtual image of the network represented by segments. From each saddle, a segment is initialised in all the possible directions (generally not more than two); segments are grown in the virtual image in the direction of maximum slope, until another segment, or another saddle, or the border of the DEM is reached. The resulting network is very dense. Meisels et al. (1995) propose a two-stage algorithm of multilevel skeletonisation of a DEM, followed by a process of enumeration, mainly to eliminate loops in the extracted drainage network. Depressions are filled to the surrounding elevation level before the extraction of the drainage network. The main algorithm extracts pixels that lie on high curvature contours starting from pixels of maximal elevation, elevation-level by elevation-level; the selection is based on a condition for a large enough number of higher elevation pixels in the immediate neighbourhood of a pixel belonging to the elevation currently being processed. The second stage uses a complementary local condition of connectivity and connects all the pixels of the flow path. In general, these methods suffer from the same problems as the methods described in the first section; they are effective only when the drainage network is well defined by the local surface properties, which can be derived from the DEM. D. Scale properties and fractal geometry of channel networks In the context of the studies on scale properties of channel networks, several researchers have been interested in the fractal geometry of individual streams and channel networks as a whole (Hjelmfelt, 1988; Tarboton et al., 1988; LaBarbera and Rosso, 1989). The fractal nature of river networks manifests itself in two ways: on the one hand, the plane pattern of an individual watercourse has fractal geometry and, on the other hand, fractal properties are also characteristics of the branched pattern of river networks (Da Ros and Borga, 1997). As a conclusion from all these works, Roth et al. (1996) propose a global approach to the problem of drainage network identification. All empirical evidence and the theoretical description of the hydrodynamical and morphological conditions, which are expected to hold in the streams constituting the effective drainage network, can be expressed in the form: A Φ S = constant (1) Where A is the drainage area, S is the local slope and Φ is a constant ranging from 0.44 to 0.5. The practical application of this relation for the extraction of the channel network is often limited by the low accuracy of the elevation data; in particular the evaluation of the local slope is a critical issue. The resulting network is often formed of non-connected streams and therefore this approach is only used as a theoretical basis for the design of filtering procedures. JRC SAI EGEO

Catchment Delineation and Characterisation 11 Another approach, which LaBarbera and Roth propose, starts from the analysis of the altimetric properties of the area that contribute to a given site. Under the hypothesis of self-similarity of stream slopes, as described by the Hortonian slope ratio, the relation S l S a can be assumed between the local slope, S l, and the average slope in the subcatchment draining in the point being studied, S a. Introducing: H a = (1/ n )Σ i (H i -H s ) (2) as the relative elevation of the subcatchment draining in the selected point, we obtain that: S a H a /L (3) where n is the number of pixels in the subcatchment, H i is the elevation of a pixel in the subcatchment, H s is the elevation in the site studied and L is a linear measure of the subcatchment size. Introducing the fractal dimension of single rivers, d, a relation with the contributing area has been defined (Rosso et al., 1991): L A d/2 (4) H a A d/2 S l (5) Equation 5 provides a link between the relative elevation of the subcatchment at a given site, H a, the contributing area, A, the fractal dimension of single rivers, d, and the local slope, S l. Moreover, the structure on the right-hand side of this equation is the same as the general equation 1. The application of this approach leads to a wellconnected and coherent network; the spatial variation of the drainage density is well reproduced with a high drainage density in the mountain regions that tends to decrease towards the alluvial areas, characterized by low slope values, and a very low density in the plains. 3.2 The Problem of Flat Areas. In a DEM, there is a well-known difficulty to discriminate between flat areas drained by incised channels and truly flat areas that carry water as sheet flow. It is a general problem that follows from the horizontal resolution of the DEM: it is clear that when the size of a drainage feature is much smaller than the grid cell size of the DEM, the channels cannot be captured by the DEM. However assigning drainage directions to cells where there are two or more possible choices, and to flat areas, is a general problem for all the methods described previously. Generally, following Jenson and Domingue (1988), flat area cells adjacent to other cells with a defined flow direction are identified. These flat area cells are then assigned a flow direction, pointing to the nearest adjacent cell with a defined flow direction. This is repeated until all flat area cells are assigned a flow direction. This EuroLandscape CCM, April 2000

12 Francesca Bertolo kind of approach constrains the flow path to remain within the flat area and allows the possibility of multiple outlets. However it often produces unrealistic, parallel flow patterns. Other researchers proposed to infer flow paths in flat areas from the surrounding topography. Tribe (1992) suggests defining a main flow path through the flat area and directing other flow paths towards this main path. Unfortunately, because the main flow path is defined along the shortest path between the inflow and the nearest outlet, it is possible for the main flow path to pass through areas of higher elevation to reach the outlet. Garbrecht and Martz (1997) and Martz and Garbrecht (1998) describe an algorithm, which is a core component of the freely available TOPAZ (TOpographic PArameteriZation) landscape analysis tool (http://duke.usask.ca/~martzl/topaz/). The method is based on the recognition that in homogeneous natural landscapes the drainage is generally towards lower terrain while simultaneously being away from higher terrain. Such a drainage is achieved by imposing two gradients on the flat surface: one towards lower terrain which draws flow to the nearest downslope outlet, and a second which forces flow away from higher terrain. Mackay and Band (1998) recently proposed to first identify flat features (e.g. lakes and relatively flat areas) on the DEM for which slope tracking is likely to fail. Contiguous groups of flat areas are formed into labelled regions by using local region growing. The labelled regions are then classified into water bodies or land areas using supervised classification of remotely sensed imagery. Different cellbased algorithms can be associated with each class of flat feature: for lakes the goal is to deliver the total upslope area contributed to the lake and the lake itself to the lake outlet, for other flat areas it is necessary to optimise the slope threshold needed to define the flow path (Band, 1986). Since actual flow of water through a lake requires additional information, a lake boundary-following procedure is used: each grid cell along the boundary acts as a depression point for catchments that drain into it. The contributing area assigned to the lake outlet cell is the total area along the boundary plus the area of the unmarked cells in the interior of the lake; this retains the topology of the land-lake features, but eliminates cell-to-cell flow within the lake itself. 3.3 The Channel Source Definition. The delineation of catchments is an important aspect in hydrological modelling and is closely related to the definition of channel networks. Physically based hydrological models must distinguish between overland runoff and water that flows in channels. On the other hand a catchment outlet must be on a river course. It appears clearly that the correct delineation of a catchment is closely related to the correct extraction of its channel network. JRC SAI EGEO

Catchment Delineation and Characterisation 13 Hydro-physically, the channel network represents those points at which runoff is sufficiently concentrated for fluvial processes to dominate over slope processes (Mark, 1984). This mechanism is basically driven by the topography; therefore a different kind of information is needed to define the conditions of this transition, which introduces an indetermination in the methods available. The correct automatic derivation of the channel network is an unsolved problem. Field investigations showed that the source area above the channel head decreases with an increasing local valley gradient of the slopes, except in locations where bedrock properties control the channel head locations (Montgomery and Foufoula- Georgiou, 1993). Although steeper channel heads are, at least, partially controlled by slope instability, landslide instability alone is not sufficient for canalisation. Critical sheer stress is a dominant control factor on the extent of the channel network when saturation overland flow is significant, but it is difficult to quantify this in the field. The most common method of extracting channel networks from DEMs is to specify a critical support area that defines the minimum drainage area required to initiate a channel (Mark, 1984; Band, 1986; Jenson and Domingue, 1988). In practice, this threshold value is often selected on the basis of visual similarity between the extracted network and the blue lines depicted on topographic maps. Tarboton et al. (1989, 1992) propose a method to find the critical value of the contributing area from the scaling diagram of slope versus contributing area for individual grid cells within a catchment. An example is given in figure 1. 1.E+00 Contributing Area (m 2 ) 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10 1.E-01 Fluvial process (Channelized pixels are considered those with A > A t) Local slope (m/m) 1.E-02 Hillslope processes Fluvial scaling line S θ A θ - 0.5 1.E-03 A t = 5 Km 2 = 80 pixels 0.5 Dd A Figure 1: Diagram of local slope versus contributing area, derived for the Po catchment in northern Italy from a DEM with 250 m grid-cell size. EuroLandscape CCM, April 2000

14 Francesca Bertolo The theoretical argument for using an area-threshold is based on the hypothesis that the channel network extends up to the point where unstable fluvial sediment transport processes change to stable diffusive hill-slope processes. Several researchers showed that the change of dominance from hill-slope to fluvial processes is equivalent to a change in the slope versus contributing area diagram from a positive-gradient (ds/da > 0) at small values of the contributing area, to a negative-gradient (ds/da < 0) at larger values of the contributing area. Tarboton et al. (1989, 1992) propose to use the size of the contributing area that corresponds to the change in the scaling response, as the critical support area for finding the extension of the channel network. The break in slope-area scaling, however, seldom goes from a positive to a negative gradient as predicted by the theory, but appears instead as an inflection from a low to a high negative gradient in the slope-area diagram (see figure 1). Montgomery and Dietrich (1988, 1992) demonstrate that channel heads lie at a transition between channelled and unchannelled portions of the landscape but that for any given slope the size of the source area may vary by as much as an order of magnitude. In other words the threshold area is not constant in a basin but it is a function of the local valley slope (the slope immediately upstream of the channel source in the unchannelled valley). Their research has identified an empirical relationship (power law) between threshold area and slope: A th = CS -θ (6) where C and θ are constants empirically determined from field data and S is the local valley slope. Identification of an appropriate value for C is a major impediment for implementing this model, as this parameter should vary with both rainfall and critical shear stress of the ground surface, the latter reflecting both soil properties and the type and density of vegetation cover (Montgomery and Foufoula-Georgiou, 1993). Using a slope-dependent threshold, drainage density is greater in steeper portions of a catchment, which generally corresponds to the situation found in natural landscapes. For the case of a catchment with little spatial variability in slope, the constant threshold and the slope-dependent threshold methods converge and predict similar channel networks for the same mean source area. (Montgomery and Foufoula-Georgiou, 1993). However the area-threshold and the slope-area-threshold criteria need not to be conflicting and they may be even combined in a single framework, or be considered as a representation of processes over different geomorphic time scales (Ijjasz-Vasquez and Bras, 1995). The general conclusion of the majority of works on the source area location is that even limited field data collection on the drainage area-slope relation for channel heads, is the best method for determining appropriate values of parameters defining channel network extent (Montgomery and Foufoula-Georgiou, 1993; Helmlinger et al., 1993). JRC SAI EGEO

Catchment Delineation and Characterisation 15 All the analyses described above refer to DEMs of maximum 30 m grid cell size; it is stated several times in those works that the correct solution to the question of the channel initiation needs high resolution DEMs, able to depict the landscape in a consistent way. At lower resolution it is more appropriate to analyse the problem from another point of view. The fundamental assumption is that runoff is generated uniformly over the basin and that the geomorphologic or erosional response to that runoff is spatially homogeneous regarding channel initiation. Under these conditions the threshold contributing area can be used to represent the complex interaction of factors such as geology, vegetation, soils and topography, which control the initiation and maintenance of a channel network. At a regional level, where the conditions of uniformity may not be assumed, it is better, either to allow the threshold contributing area to vary between different geomorphic regions, or to include physical parameters that underlie the spatial variability of the geomorphology (Martz and Garbrecht, 1995). The importance of the selection of the threshold area is related to the high impact that this value has on the morphometric properties (such as drainage density, length of drainage paths, statistics of external and internal links) and scaling properties (such as Horton s ratios and fractal dimensions) of a channel network (Helmlinger et al., 1993; Moussa and Bocquillon, 1996; Da Ros and Borga, 1997). 3.4 About Errors. As stated frequently before, the final result of the automatic delineation of the catchments is influenced by many sources of errors. Selecting a DEM of good quality and paying attention to the algorithm used can minimize some of the possible errors a priori. Other errors need the definition of some criteria that help to limit their influences. Finally, some errors are inherent to all the procedures and need to be clearly evaluated and quantified. Generally, the evaluation of the results of catchment delineation and network extraction procedures is made by visual comparison with existing vectors. It is, however, difficult to quantitatively evaluate the results. Generally, quantitative comparisons are made on the total area included in the catchment boundaries. Miller and Morrice (1996) proposed to evaluate the reliability of the catchment boundaries using the rate of change of height and aspect in the neighbourhood of the borderlines. In order to assess the sensitivity of the boundary location to errors in the DEM, they proposed to add an error with normal distribution and fixed standard deviation to the elevation values and to quantify the areas that would be re-allocated between catchments. It is supposed that the sensitivity to DEM errors is best EuroLandscape CCM, April 2000

16 Francesca Bertolo represented by the area of land that is subject to re-allocation as a proportion of the catchment area. 4. River and Catchment Ordering. In order to construct a geographical database of all the catchments of Europe, a crucial point is to define a system for the codification of the catchments and related channel networks. This is a necessary step in order to maintain the topology of the hydrological system and is useful to facilitate the access to the database. A unique code that identifies each catchment and its river network is necessary for the structure of a database. But it is also important for describing the relationships that exist within a hydrological region, or between mainstreams and tributaries, or between headwaters, drainage system and outlet, etc. Each country has its own system of coding the national river network. Generally the network itself influences the coding system through characteristics such as the drainage density, the shape of the drainage system (i.e. coastal drainage or no sea outlet), or the mean drained area. It is difficult to find a method that fits to all the possible combinations that arise on a continent. Another relevant aspect is the number of digits (alphanumeric elements) that is necessary to completely describe a catchment: at a national level this is less important than at a continental scale where thousands of catchments have to be coded. In the United States the Water Resources Division of the US Geological Survey has its Hydrologic Units System (Seaber et al., 1987), which divides the Nation in 21 major geographic areas, or regions, composed of 222 sub-regions. A sub-region includes the area drained by a river system, a reach of a river and its tributaries in that reach, a closed basin, or a group of streams forming a coastal drainage area. The third level of classification subdivides many of the sub-regions into accounting units and, furthermore, the fourth level in cataloguing units, which are the smallest elements in the hierarchy of hydrologic units. An eight-digit code uniquely identifies each of the four levels of classification within four two-digit fields. The first two digits identify the region, the next two digits the sub-region, the next two digits the accounting unit and the last two digits the cataloguing unit. In France the Environment Ministry has defined a coding system in 1991, which is based on a code of eight digits. The first four digits indicate the hydrographic zone, which refers to a hydrological classification of the country in four levels: regions (1 st level), sectors, sub-sectors and zones. There are six regions that represent the most important river basins of the country. Each region is subdivided in not more than ten JRC SAI EGEO

Catchment Delineation and Characterisation 17 sectors, each sector in not more than ten sub-sectors that have not more than ten zones inside. The next three digits (5, 6, 7) refer to a single entity which can be one out of five different inland waters: river, tributary, artificial channel, lake, wetland, or coastline. The last digit refers to the class of inland water. An additional parameter, the kilometric point (pk), defines the position of a specific point along or in the border of an entity. It is used to concatenate each entity with the neighbouring entities and to describe changes in the entity, like different regulations for water use or for fishing, different fish species, or different owners, etc. A different approach is used in the Baltic Sea Region GIS, Maps and Statistical Database developed by United Nations Environmental Program - Global Resource Information Database (UNEP/GRID) Arendal (Norway) in collaboration with Institutes in Sweden (http://www.grida.no/prog/norbal/baltic/ welcome.htm). In this database there are only 81 sub-basins, in total forming the seven major catchments that define the Baltic Sea drainage area. The sub-basins all have an outlet to the sea or are coastal drainage areas; portions of the Baltic Sea are considered sub-basins. Therefore the sub-basins are numbered sequentially in clock-wise order beginning from the northern catchment (Bothnian Bay); jumping in the numbering scheme can occur when a portion of sea is encountered: a number ending by nine is always assigned to it. An additional parameter is linked to each sub-basin indicating the major catchment it belongs to. The Catchment Database for Sub-equatorial Africa (Verheust and Johnson, 1998) is another example of a regional database. The catchment delineation for subequatorial Africa was done in 1997 based on a digital elevation model and the river layer of the Digital Chart of the World. The database was developed for users who do not have access to high-end GIS packages and can be used as a standalone cellular database or in combination with simple mapping packages. The database holds 1157 catchment polygons; the ordering was done manually and names assigned using a map of Central and Southern Africa from J. Bartholomew & Sons LTD at a 1:5,000,000 scale (1988). At the same time, a parameter was added to each polygon, which identifies the next catchment downstream. With a repetitive linking of this parameter to the catchment identifier a downstream sequence is generated and stored in a related database. Based on the created downstream sequence an upstream sequence was also generated and stored in another related database. The first record of this sequence refers to the outlet (ocean, internal basin, or edge basin) and the second refers to the lowest catchment, which drains to the outlet. This lowest catchment is the outlet area of the principal river of the network, and gives the name to a megabasin. Two other parameters associated to each catchment complete the description of the topology of the drainage system in this database: the level, indicating the number of catchments that separate it from the outlet, and the megabasin name. Verdin and Verdin (1999) propose a reference system that at once uniquely identifies and indicates the spatial nature of a hydrographic basin, with the aim to have a simple and globally applicable method of coding. The system proposed is EuroLandscape CCM, April 2000