a new grass gis toolkit for hortonian analysis of drainage...

Computers & Geosciences ] (]]]]) ]]]–]]]

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Computers & Geosciences

0098-30

doi:10.1

n Corr

E-m

PleasGeos

journal homepage: www.elsevier.com/locate/cageo

A new GRASS GIS toolkit for Hortonian analysis of drainage networks

Jaros"aw Jasiewicz a,n, Markus Metz b

a Adam Mickiewicz University, Geoekology and Geoinformation Institute, Dziegielowa 27 60-081 Poznan, Polandb University of Ulm, Institute of Experimental Ecology, Allee 11, 89069 Ulm, Germany

a r t i c l e i n f o

Article history:

Received 8 March 2010

Received in revised form

24 February 2011

Accepted 2 March 2011

Keywords:

Drainage network

Multiple flow direction

Basin delineation

GRASS GIS

Network topology

Network extraction

Hortonian analysis

04/$ - see front matter & 2011 Elsevier Ltd. A

016/j.cageo.2011.03.003

esponding author.

ail address: [email protected] (J. Jasiewicz).

e cite this article as: Jasiewicz, J., Mciences (2011), doi:10.1016/j.cageo.

a b s t r a c t

The aim of this paper is to present a new GRASS GIS toolset designed for Hortonian analysis of drainage

networks. The r.stream toolset uses a multiple flow direction algorithm for stream network extraction

as well as for calculating other hydrogeomorphological features in the catchment’s area. As all GRASS

GIS toolsets, r.stream consists of several separate modules that can extract stream networks from a

spectrum of accumulation maps, order the extracted network using several ordering methods, do

advanced modeling of basin’s boundary, perform Hortonian statistics, calculate additional parameters

such as flow path distance to watershed elements, partition ordered and unordered networks into near-

straight-line sectors, and calculate sector directions. The package is free and open-source software,

available for GRASS version 6.4 and later.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Horton (1932, 1945) provided the theoretical basis for quantitativeanalysis of drainage network structures, and this framework rapidlyevolved into an important analytical tool, especially for geomorphol-ogists and geologists (Strahler, 1957; Scheidegger, 1961; Howard,1971; Shreve, 1974). Thanks to improvements in computationaltechnology, the 1980s saw routine use of digital elevation models(DEMs) for the extraction and the numerical analysis of drainagenetworks (O’Callaghan and Mark, 1984; Mark, 1984; Jenson, 1985;Jenson and Domingue, 1988; Hutchinson, 1989). In the early 1990s,limitations of the D8 algorithm (O’Callaghan and Mark, 1984) wereovercome with a number of more complex algorithms based onmultiple flow directions (MFD) (Freeman, 1991; Quinn et al., 1991,1995; Holmgren, 1994; Costa-Cabral and Burgess, 1994; Tarboton,1997; Lindsay, 2003), but until now these algorithms have not beenapplied to investigate a watershed’s structure. The improvement inpersonal computers at the end of the 20th century permittedincorporation of drainage network analysis into numerous specializedand general-purpose Geographic Information Systems packages(Hengl and Reuter, 2008). Today, quantitative analysis of drainagenetworks with commonly available software is utilized by numerousnatural-science researchers.

ll rights reserved.

etz, M., A new GRASS GIS to2011.03.003

There are, however, some limitations in existing modelingsoftware which make the obtained results deviate from expecta-tions, particularly in lowland areas:

�

olk

Modeling procedures require hydrological conditioning ofdigital elevation models, which is time consuming and mayproduce vast flat areas where streams flow in one of eightmain directions which result in unrealistic stream networks.
� Existing software for network tracing is often restricted to
Deterministic 8 (O’Callaghan and Mark, 1984), also calledsingle flow direction or D8-derivatives (TauDEM: Tarbotonand Ames, 2001; Orlandini et al., 2003). The use of differentaccumulation maps, especially those obtained with multipleflow directions, is either impossible or leads to nonnaturalresults, especially on areas such as flat valley bottoms orcoastal plains. One of the major constraints of the D8 methodis incorrect mapping of the drainage especially in the slopesubsystem (Tarboton, 1997). Therefore the reliance of thenetwork modeling process in existing software on a D8approach propagates these errors onto next steps of hydro-logical modeling like flow path distance calculation orwatershed delineation.
� Channel initiation methods included in existing software are
limited mainly to contributing area threshold (O’Callaghan andMark, 1984), slope, and contributing area threshold (Montgomeryand Dietrich, 1992) or an experimental solution such as contribut-ing area and stream length threshold (included in TauDEM). Therestriction of network definition modules to particular methodsleads to a situation where the testing of new solutions for drainage

it for Hortonian analysis of drainage networks. Computers &

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dx.doi.org/10.1016/j.cageo.2011.03.003

mailto:[email protected]

dx.doi.org/10.1016/j.cageo.2011.03.003

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J. Jasiewicz, M. Metz / Computers & Geosciences ] (]]]]) ]]]–]]]2

PG

network extraction requires the creation of dedicated softwareand is thus not available for nonprogrammers.
� Basin modeling requires exact indication of a basin’s outlet as
a pair of coordinates lying exactly on a stream course. There isno possibility of modeling the basin on the basis of only arough location of the outlet, and for natural objects such asshorelines or lakes.
�
Fig. 1. Location of the case study area. Stream networks, lakes, and basin

boundary comes from: Halina Czarnecka (Ed.), 2005. Atlas Podzia"u Hydrograficz-

nego Polski. Atlasy i Monografie IMGW Warszawa. Location of Figs. 3, 7, 8, and 10

marked with white rectangles.

While existing software offers fairly complete tools for thecalculation of basic parameters of drainage networks, studiesof stream flow direction, hypsometric relationships, andstream ordering methods (mostly Strahler and Shreve hier-archy), there is to our knowledge no existing software pre-pared to analyze extended geometry such as stream networkorientation, interstream angular relationships, and channelcurvature radius or sinuosity.

The aim of this paper is to present a new GRASS GIS softwaretoolkit, which overcomes the limitations described above. Thetoolkit has been prepared to work with drainage systems mod-eled with multiple flow direction algorithms (Freeman, 1991;Quinn et al., 1991, 1995; Holmgren, 1994). It includes a variety ofmethods for stream extraction including channel initiation meth-ods (O’Callaghan and Mark, 1984; Montgomery and Dietrich,1992; Dietrich et al., 1993), with modifications based on valleyrecognition (Molloy and Stepinski, 2007; Luo and Stepinski, 2008)and additional environmental information (Garbrecht and Martz,1997) where extraction is based on stream tube tracing to avoidangular and interstream artifacts (Turcotte et al., 2001; Orlandiniet al., 2003). The network modeling is based on accumulationmaps that are created internally or created with any external GISsoftware or created as the result of map algebra. Stream tracing isseparated from channel initiation calculations. It also includesseveral methods for stream ordering. Advanced basin delineationremoves the requirement of outlets precisely located on stream-lines as present in other modeling software and moves theextraction criteria to a map algebra system. It also offers calcula-tion of properties of channel and slope subsystems, elevation/distance relationships in a watershed, basic stream geometry, andHortonian statistic adapted to multiple flow direction approaches.

2. Case study area

The case study area lies in western Poland, and covers theK"odawka Basin of 321.078 km2 in size (Fig. 1) and its surround-ings, in total 1038.427 km2. The digital elevation model has beencreated by manual digitization of hypsometric maps with a gridresolution of 5�5 m2. However, the DEM used in this paper had agrid resolution of 15�15 m2 because the original 5 m DEM wastoo large for some external software. The area is a typical youngpostglacial surface formed during Vistulian between the Poznanand the Pomeranian stage (Galon, 1961; Kozarski, 1986). Its reliefvaries from 15 m a.s.l. in the pradolina up to 138 m a.s.l. in themorainic plateau with average 63 m a.s.l. The northern part of thearea is a waste outwash plain (sandur) with numerous dead-icedepressions, dissected by deep extraglacial channels poorly con-verted into river valleys (Galon, 1968). The middle-south part is amorainic undulated plateau of Gorzow Plain. The drainage systemof the morainic plateau is limited only to small valleys deeplydissecting its southern ledge. The southernmost part of the area isa flat valley bottom of Torun-Eberswalde Pradolina. This kind ofterrain is considered difficult in hydrological modeling, the reasonwhy this area was chosen as an example to show some of the newpossibilities of r.stream modeling algorithms addressed directlyto problematic areas.

lease cite this article as: Jasiewicz, J., Metz, M., A new GRASS GIS toeosciences (2011), doi:10.1016/j.cageo.2011.03.003

3. Software development

As a basis for developing the r.stream toolkit, GRASS GIS (GrassDevelopment Team, 2011) was chosen because it is a leadingopen-source GIS Software. Since version 4.0, GRASS GIS has beenan important environment for hydrological modeling and geo-morphological analysis, especially for erosion modeling (Mitasovaet al., 1995, 1996), sediment flux (Mitasova et al., 2004; Mitas andMitasowa, 1998; Mitasova and Mitas, 2001), and watershedmodeling (Weltz et al., 1987; McCool et al., 1987; Kinner et al.,2005). The well-known TOPMODEL simulation (Beven et al.,1995) and the TERRAFLOW project (Arge et al., 2001, 2003) havealso been included in GRASS since version 5.0. Regarding thisbackground, it is astonishing that GRASS GIS does not have anytools for topological analysis of drainage networks. The r.streamtoolkit attempts to fill this gap.

GRASS GIS offers a fairly complete analytical GIS environmentwith a large number of auxiliary tools, access to numerous datatypes via GDAL/OGR, and advanced map algebra (Shapiro andVestervelt, 1991). GRASS GIS integrates raster and vector dataprocessing techniques with access to several database systemsand with full SQL language support. GRASS GIS as a programmingenvironment has a very stable and mature application program-ming interface (API) and provides a spectrum of functions forhandling input/output subroutines and file management.

One of the major reasons for the choice of GRASS GIS was thepresence of the SEGMENT library, which allows one to makecalculations on very large raster maps that could not be per-formed all in memory. Since modern high-resolution DEMsderived from laser detection (LIDAR) and radar interferometry(IFSAR) can consist of hundreds of millions of grid cells, theproblem of data size limitation in existing software is becoming areal problem. The r.stream package is written in ANSI C usingthe GRASS API and provides two modes of calculation (identicalto the existing GRASS r.watershed module): the standard all-in-memory fast method of calculation suitable for smalland medium-sized datasets and the method utilizing theSEGMENT library, which is slower but with better managementof available system memory, suitable for calculations on verylarge DEMS.

olkit for Hortonian analysis of drainage networks. Computers &

dx.doi.org/10.1016/j.cageo.2011.03.003

Fig. 2. The structure of the r.stream toolset and data flow between particular modules and external software.

J. Jasiewicz, M. Metz / Computers & Geosciences ] (]]]]) ]]]–]]] 3

The package consists of several modules developed for hydro-geomorphological processing offering the following functionalities:

�

PG

extraction of stream networks from a DEM and any accumula-tion map, even those coming from any external software,according to various user-defined criteria (r.stream.extract);
� ordering of the extracted network and calculation of Hortonian
statistics (r.stream.order, r.stream.stats);
� advanced modeling of basins (r.stream.basins); � flow path relative distance/elevation calculation (r.stream.-
distance, r.stream.slope);
� some additional geometrical properties of ordered networks
(r.stream.segment, r.stream.channel);
� partitioning of stream segments into near-straight-line sectors
and calculation of sector directions (r.stream.segment);

The structure and the data flow between particular modulesare presented in Fig. 2.

4. Drainage network analysis procedures

The drainage network is analyzed here as a representation ofthe precipitation-surface runoff mechanism occurring in the basin(Rodriguez-Iturbe and Rinaldo, 1997) together with the hillslopeand channel systems (Horton, 1945). In order to avoid ambiguitywith real river networks (i.e., ‘‘blue lines’’) we use the term‘‘drainage network’’ for the whole basin system including thehillslope and channels, and the terms ‘‘channel’’ and ‘‘stream’’network to describe permanent relief features that are recogniz-able even in the absence of actual water flow (Montgomery andDietrich, 1988; Chorowicz et al., 1992).

The described package is designed to work on networks withstandard dendrite topology where a channel or stream network isa subset of a drainage network and can be idealized as a planartree. The root of the tree, or the point furthest downstream, iscalled the outlet. Points furthest upstream, or the initial points, arecalled sources. A point at which two or more upstream channelsjoin into one common downstream stream is called a junction.

4.1. Network extraction

Stream network extraction from raster grids can be dividedinto channel initiation (CI) methods, valley recognition (VR)methods, and a mixture of both (see, e.g., Lindsay and Creed,2005). Most CI methods were developed for D8-based approaches,assuming that flow dispersal is limited from each cell to only one


of eight principal directions separated by p/4 (451). To detect achannel, these methods use a defined threshold for surface flowaccumulation (O’Callaghan and Mark, 1984). If this threshold isreached or exceeded, grid cells are then defined as stream cells,and all grid cells with surface flow accumulation below thisthreshold are defined as nonstream cells. Montgomery andDietrich (1992) introduced an approach coupling flow accumula-tion (precisely: specific catchment area) with powered local slopefor slope-dependent channel initiation.

When applying these approaches to surface flow generated usingmultiple-flow-direction (MFD) algorithms, extracted streams can bewider than one cell, and the stream network must be skeletonized.This skeletonizing step can lead to numerous artifacts includingshort streams, short connections just above confluences (streamtriangles), or streams not properly centered in a broader streamtube. Broader stream tubes are, e.g., several grid cell broad riversthat can only be represented with MFD and not with D8 methods.These artifacts lead to improper stream ordering, basin delineation,and angular relations between streams. The valley recognitionmethods (Peuker and Douglas, 1975; Mark, 1984; Lindsay andCreed, 2005) do not create topologically correct drainage systemsthat can be utilized for further analysis. Therefore a differentapproach is required to discriminate between stream initiation(more precisely, detection of stream heads) and stream tracingand to avoid the need for postprocessing the drainage network toclean up artifacts.

From a geomorphological point of view, DEM-based approacheshave some limitations. The fit of geomorphological features to areal drainage network is difficult to obtain, especially on flat areaswhere D8-based flow tracing creates completely unrealistic drai-nage systems (Tribe, 1992; Liang and MacKay, 2000; Turcotte et al.,2001). Apart from preprocessing procedures for natural flat areas,depression filling tends to produce vast flat areas on filled lakesalong with filled natural or artificial depressions (Tribe, 1992;Turcotte et al., 2001). The stream burning algorithms (Hutchinson,1989), which may partially solve this problem, do not account forfirst- (and sometimes second- and third-) order channels (Horton,1945) that are recognizable in the field but are not marked asactive watercourses (i.e., ‘‘blue lines’’) on topographic maps(Helmlinger et al., 1993).

Tarboton (1997) introduced a mixed CI-VR method with amultiple-flow-direction approach to minimize dispersion (anartifact), assuming that flow accumulation and flow directionshould be modeled separately. Thus, the mixed CI-VR method is acompromise between D8 and multiple-flow directions (Orlandiniet al., 2003). The main limitation of Tarboton’s approach is that ituses accumulation maps only to determine the stream threshold


dx.doi.org/10.1016/j.cageo.2011.03.003


but still uses elevation to trace the stream. A different approachhas been used in SAGA GIS (Bohner et al., 2006, 2008). For thissystem, the initial channel cells are determined from an initiationmap, which can be a flow accumulation map or a map with pointsof channel initiation only. Channels are then started and tracedfrom these initial channel cells only if no neighboring cell wasalready identified as a final channel cell. SAGA GIS also uses anelevation-based D8 method to trace streams, but a flow directionmap can optionally be provided. The limitations of the SAGAchannel-extraction module are that short artificial channels arecreated within larger streams, that it requires DEM preprocessing,that it cannot use heuristic searching methods (which forbid anymodification of accumulation with map algebra), and that it doesnot allow the use of VR methods for network delineation.

The purpose of the r.stream.extract tool is to extract topolo-gically correct, dendritic stream networks, represented as a rasterwith one-cell-wide streams or vectorized with lines for streamsegments and points for stream heads, confluences, and outlets.Further on, drainage directions corresponding to the extractedstream networks are determined. This tool uses a digital elevationmodel and matching flow accumulation as input. Provided accu-mulation maps may be calculated with any algorithm (D8, FD8,DEMON, etc.). Currently GRASS GIS delivers only single (D8) andmultiple (FD8) flow direction accumulation maps but other typesof maps may be obtained with third party software. If noaccumulation map is provided, flow accumulation is calculatedinternally using the MFD method of Holmgren (1994).

The r.stream.extract module discriminates between streaminitiation and stream tracing. Streams are initiated according toa given threshold, but contrary to standard stream initiation,streams are initiated only if all grid cells contributing to the

Fig. 3. A comparison of results of network modeling made with different software and

(A) TauDEM, curvature based with modified D8/Dinf accumulation map (see Tarboton

TAS GIS (identical results) with D8 (SFD) accumulation map and with threshold 45

450,000 m2; (D) GRASS GIS r.watershed with FD8 (MFD) accumulation map with thre

with threshold 45,000 m2; (F) TauDEM/TAS GIS (identical results) Montgomery’s meth

map, slope exponent¼2 and accumulation threshold 10; (F) GRASS GIS r.stream.extract

accumulation threshold 50; (G) GRASS GIS r.stream.extract with FD8 (MFD) accumulatio

accumulation threshold 5.

Please cite this article as: Jasiewicz, J., Metz, M., A new GRASS GIS toGeosciences (2011), doi:10.1016/j.cageo.2011.03.003

current grid cell have surface flow accumulation below the giventhreshold and only if none of the neighboring grid cells has beenalready identified as a stream cell. This procedure attempts to findsources or stream heads only and does not attempt to find allchannel cells. It is well known (see, e.g., Rodriguez-Iturbe andRinaldo, 1997) that channel initiation is strongly influenced bythe local morphology and the spatial heterogeneity of the exposedlithology, vegetation cover, and dominating erosional mechanism.Therefore, an accumulation map can be modified with custommap algebra (e.g., it can be weighed according to slope, rainfall, orsoil moisture). The accumulation map may be also a very basicmap that merely indicates the location of stream heads and(optionally) the fragments of stream routes gathered during fieldor cartographic studies.

Stream tracing follows the main drainage direction. The maindrainage direction is determined using both flow accumulationand elevation because the traditional steepest slope approach isoften ambiguous since the steepest slope may be shared byseveral directions. In order to determine the main drainagedirection, grid cells are first sorted according to elevation with aleast-cost path search method as first implemented in ther.watershed module (Ehlschlaeger, 1989; Metz et al., 2011). Thereis no need to provide a hydrologically conditioned elevation mapbecause the search heuristic (Hart et al., 1968) used by r.strea-m.extract is very robust in handling depressions without the needto modify elevation values a priori. The main drainage direction isthen set for each cell toward the downstream cell with thehighest flow accumulation. The initially assigned drainage direc-tion is used as main drainage direction when several downstreamcells including the one pointed to by the initial direction share thesame highest flow accumulation. This approach is independent of

methods. Locations of artifacts noted in the text are marked with white rectangles.

and Ames, 2001, for details) with accumulation threshold 45,000 m2; (B) TauDEM/

0,000 m2; (C) SAGA GIS with FD8 (MFD) accumulation map and with threshold

shold 450,000 m2; (E) GRASS GIS r.watershed with FD8 (MFD) accumulation map

od (see Montgomery and Dietrich, 1992, for details) with D8 (SFD) accumulation

Montgomery’s method with FD8 (MFD) accumulation map, slope exponent¼1 and

n map masked with tangential curvature mask created with threshold 0.0027, and


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the method used to accumulate surface flow, and guarantees thata thin, one-cell-wide stream is extracted also for broader streamtubes as obtained with MFD methods. This flexibility makes itpossible to provide a channel initiation map that is only used toinitiate streams, and the elevation map can then be used to tracestreams if there is not sufficient information in the accumulationmap to unambiguously determine the predominant drainagedirection. The results are therefore independent of the methodused to accumulate surface flow. The main flow direction isindicated in D8 manner, and allows one to adjust calculation ofother hydrogeomorphological parameters.

Fig. 3 shows the comparison of different methods commonlyused in popular modeling software (TauDEM: Tarboton and Ames,2001; TAS GIS: Lindsay, 2005a,b, 2001b; SAGA GIS: Bohner et al.,2006, 2008) applied on testing area. The first four examples(Fig. 3A–D) show high threshold results of similar drainagedensity. The main shortcomings are too dense drainage networkson the sandur outwash plain and unresolved patterns of erosionaldissections in the southern ledge of the plateau. Some artifacts ofthe D8 approach (Fig. 3A and B) such as parallel adjacent flowlines (a) or lines flowing in one of main directions (a,b) and errorsin network mapping if a MFD map is applied to traditionalnetwork extraction methods (Fig. 3C) are also visible. The nextfour examples show solutions with good mapping of erosionaldissections in the ledge but with unnatural stream density in thesandur plain and valley bottom (Fig. 3E) or numerous spuriousstreams created with Montgomery’s method on inclined slopes(Fig. 3F and G). Also, Fig. 3G shows the result of coupling theoriginal Montgomery method with the new approach offered byr.stream.extract and Fig. 3H shows a stream network created from

Fig. 4. Different ordering systems included in r.stream.order and applied on the sam

(Hack 1957), and topological diameter (Marani et al., 1991).


a MFD accumulation map that has been transformed with a valleyrecognition mask based on a tangential (cross) curvature map(Molloy and Stepinski, 2007; Luo and Stepinski, 2008). Mixingdifferent methods in r.stream.extract is of course also possible.However, this case goes far beyond the scope of this paper andwill be discussed in detail elsewhere.

4.2. Network ordering, stream characteristics, and Horton statistics

There are several systems of stream ordering. Some of themhave been discussed in detail by Ranalli and Scheidegger (1968),Bukhari (2005), and Zhang et al. (2007). The r.stream.order toolallows one to order a network according to the followinghierarchy systems (Fig. 4): Strahler’s/Horton’s (1957), originalHorton’s (1945), Shreve’s-Scheidegger’s stream magnitude(Shreve, 1967; Scheidegger, 1965, 1966), normal stream hierarchyproposed by Gravelius (1914 cf. Horton 1945) also known asHack’s (1957) main streams (Antonello et al., 2006), and topolo-gical diameter (Marani et al., 1991). The theory of river networkhierarchy systems is broadly discussed in the literature (seeScheidegger, 1961; Zhang et al., 2007) as well as in programdocumentation and will not be presented here in detail.

All ordering routines do not require the network to be an idealbinary tree. All algorithms are presented in Listings 1, 2A, and 2Bin Appendix A. The main difference between Strahler’s methodand the original Horton ordering is that the order of any branch inHorton’s model remains unchanged from the source downstreamuntil it reaches the next order stream or the outlet of the networktree. The original Horton ordering requires Strahler’s order forevery channel, and an additional attribute to make a decision if at

e river network: (A) Strahler (1957), Horton (1954), Shreve (1967), Main Stream


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least two tributary branches are of the same Strahler order.Horton’s (1945) original approach to pick the branch with thelesser angle between the current and previous stream segment isnot a clear option (Ai, 2007). This approach is substituted by twoalternative attributes, flow accumulation or cumulative streamlength. Using accumulation instead of length leads to situationswhere the main channel is not always the longest one, but insteadrepresents the stream leading to the largest catchment area.

Gravelius’ (1914) normal hierarchy (or Hack’s main-streamordering) uses an algorithm similar to Horton’s ordering. The onlydifference is that it ascribes an order of 1 to the main channel andthen moves upstream until it reaches the source of the longestchannel in the tree (see Fig. 4E).

The supplementary r.stream.stats module calculates Horton’sstatistics for a derived drainage network, as well as for the wholearea. Statistics for Horton’s and Strahler’s ordering calculated bythe module are described in the software documentation. Thesecond additional module named r.stream.channel allows one tocalculate the changes of local properties like elevation difference,gradient, and curvature along ordered or unordered channelcourses.

4.3. Advanced basins modeling

The modules presented so far produce a pattern of overlandflow. The r.stream.basins module can be used to automaticallyderive upstream catchment areas and its subwatershed basins.Automatic basin delineation from digital elevation models wasintroduced in the ANSWERS code (Beasley and Huggins, 1978).Methods of catchment extraction have also been discussed byBand (1986), Douglas (1986), and Jenson and Domingue (1988).A similar tool is present in almost every package designed forhydrological modeling. However, its functionality is mostly lim-ited to a simple outlet definition by N and E coordinates or avector file with several outlets as a set of vector points.

The r.stream.basins module additionally introduces a newmethod of user-defined criteria. The method is based on an inputoutlets mask, which can be created with map algebra. An outletmask can store the following information:

�

PG

points representing outlets;
� stream segments with unique categories where the last cell is
used as an outlet;
� stream networks ordered according to one of the ordering
systems created by r.stream.order;
� raster areas representing possible outlet locations (stochastic
approach);
� raster areas representing natural objects like lakes or depres-
sions (see Fig. 8 for an example) including fragments of theshoreline of the lake with unique identifiers;
�
Fig. 5. Results of stochastic modeling of a basin boundary. The DEM was

iteratively changed using an autocorrelated error map modeled with r.random.

sufrace. Autocorrelation distance was set to 200 m and error range to 7 1.67 m

(vertical error for contour map 1:50,000).

any location represented by a single cell or a group of cellswith the same or unique identifiers, useful when outletscannot be precisely defined, for example, in stochasticsimulations.

Methods based only on outlet location suffer from one limita-tion: if the given outlet definitions lie outside the stream, then thebasin definition will produce a very small accidental basin nearthe appropriate stream. To avoid this, the module offers a methodof basin delineation that requires the original stream networkfiles and a custom list of categories for which basins will becreated. It allows one to automate stream extraction from a largenumber of outlets, for example, in stream gauges. Some additionaloptions for advanced modeling of complex watershed systems aredescribed in the toolset documentation. The routine of basindelineation uses a simple version of the one used in the


r.stream.distance module described in the next section andpresented in Listing 3.

4.3.1. Example: Stochastic modeling of watershed boundaries

On lowland areas watershed boundaries are difficult to deline-ate due to vaguely defined topographical divides between water-sheds. In such a situation, boundaries are rather fuzzy than sharplines. One of the most popular methods of stochastic modeling ofwatershed boundaries (Lindsay, 2008) uses iterative changes ofthe digital elevation model by random but autocorrelated values.However, changes in the DEM are reflected in changes of thestream network pattern. This means that the location of the outletcannot be predicted as a single cell but only as an area in whichthe outlet will be located. While r.stream.basins allows one to useany object (area) as an outlet definition, stochastic modeling ofcatchment boundaries requires only the definition of the outlet asan area and an iterative routine which will change the DEM andrepetitively extract the catchment boundary using an outletdefined in that way. Fig. 5 shows the result of stochastic simula-tion for K"odawka basin, with the outlet defined as a circle in thewatershed’s mouth.

4.3.2. Example: Pfafstetter’s basin topology coding system

The advanced application of r.stream.basins and r.stream.orderuses the coding system based on concepts first proposed byPfafstetter (1989); see also Danner et al. (2007). This system is basedon the topology of the hydrographic network. First, it is necessary todistinguish between the main stream and the tributaries. Because themain stream in Pfafstetter’s criterion is always taken as the water-course that drains the greater area, the main streams must bedelineated with an accumulation map instead of the internal max-imum length criterion used by r.stream.order.

Subdivision of the area drained by a main stream into codedbasins and interbasins first requires identification of the four largesttributaries, according to their drained area. These streams areassigned the numbers 2, 4, 6, and 8 (by creating reclassificationrules), in the order in which they are encountered upstream along the


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main stem (Fig. 6A). The interbasins are reclassified to the numbers 1,3, 5, 7, and 9 and are upstream from the outlet of the main stem.Interbasin 1 is the area drained by the main stem between the outletof basin 2 and the outlet of the whole catchment. The other basins aredefined similarly. Basins may be further subdivided by repeating thereclassification on the area within it (Fig. 6B). Depending on thedensity of the mapped stream network, any basin or interbasin can befurther subdivided (by adding reclassification rules) until tributariescan no longer be found. At the end, all remaining streams must bereclassified to a null value, and the reclassified stream map can thenbe used as a stream mask in the r.stream.basins module (Fig. 6).Because r.stream.basins is not limited by the number of catchments,the coding procedure may be done for more than one basinsimultaneously.

4.4. Flow path relative distance/elevation calculation

Overland flow distance to streams and outlets is an importanthydro- and geomorphological parameter (Horton, 1932) used inhydrological interpretations and erosional models. The r.stream.

Fig. 6. The Pfafstetter basin topology coding system applied to K"odawka

Fig. 7. A comparison of flow path distance modeling using single (A) and multiple (B) fl

was created with r.stream.distance. Note the differences in both stream network patte


distance module allows one to calculate distances to watershedfeatures (Martz and Garbrecht, 1993) along flow paths. Relativeelevation above a certain watershed element (i.e., the elevationdifference between the current cell and a selected outlet, junction,or stream cell) is also an important indicator used in erosionalmodels and in terrain classifications (MacMillan et al., 2000). Themost important novelty of r.stream.distance is that the modulelike the rest of the r.stream toolkit can use a multiple-flow-direction map as a base for distance/elevation calculation. Thedifference between the results of modeling with multiple andsingle flow direction approaches is shown in Fig. 7. The mostvisible difference is the more natural pattern of flow path distancein the MFD approach and the lack of artifacts like sharp bound-aries between microbasins and long straight flow lines in one ofthe main directions (Fig. 7A, upper-right corner).

The r.stream.distance module offers two modes of calculation:upstream and downstream. In upstream mode, the modulecalculates upstream distances along the flow path to the neareststream cell, outlet, or stream join in the river network (Beven andKirkby, 1979; Band et al., 1993). Based on the same algorithm as

catchment: (A) first level; (B) second level for the biggest subbasin.

ow direction algorithm. The SFD model was created with TAS GIS; the MFD model

rns and flow path distances.


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in r.stream.basins, r.stream.distance can also calculate flow pathdistances/elevation to objects like lakes, segments of the lakeshoreline swamps, or any user-defined natural or artificial areas(Fig. 8). In downstream mode, the module calculates distancesfrom divides to the nearest or farthest channel, depending on theused options.

Both r.stream.basins and r.stream.distance use the same algo-rithm, but r.stream.distance stores the upstream distance and

Fig. 8. An example of flow path distance to natural objects (lakes) calculated with

r.stream.distance.

Fig. 9. Explanation of the stream segmentation algorithm: (A) definition of parameters

points’’ cells; (C) second and third pass: finding the particular split points.


relative elevation values in the appropriate maps. In the first step,the module identifies and marks starting cells depending on theselected mode (either streams or outlets and junctions). In thenext step, it simultaneously calculates the upstream distance andelevation above every starting cell. Listings 4A and 4B show theroutine’s detail. The modules r.stream.basins and r.stream.ordercan be used before the distance/elevation calculation to prepro-cess the original network using map algebra and to limit it tospecific areas of interest in the watershed.

The toolkit offers also a supplementary module namedr.stream.slope, intended for calculating local properties such ascurvature, slope, or elevation change along the flow paths in theslope subsystem.

4.5. Stream network segmentation and orientation

The idea for these tasks comes from Horton (1932) andHoward (1971, 1990). The module is designed to calculate streamnetwork general orientation and additionally angle/gradient rela-tionships between tributaries and major streams (Howard, 1971,1990); however, the last feature is still experimental and will notbe analyzed here in detail. The main problem in calculatingdirectional parameters is that streams usually are not straightlines. Therefore, the first step of the procedure requires partition-ing of streams into near-straight-line segments.

The segmentation process uses a simplified method similar tothe one used by Wan and Ventura (1997) to detect corners and topartition curves into straight lines and gentle arcs. Because it isalmost impossible to create exactly straight sections withoutcreating many very short sectors, the division process requiressome approximation. The approximation is made based on threeparameters: the downstream/upstream search length, the thresh-old for skipping short segments, and the maximum angle betweenthe downstream/upstream segments for consideration as a straightline (Fig. 9A). To designate straight sections of the streams,the algorithm searches for the points where curves significantlychange their direction.

used in calculation; (B) first pass of the algorithm: selecting the ‘‘containing split


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Division of the curve into segments starts with a set of pointswhere the local differences between the upstream and the down-stream directions exceed a threshold value (3) defined by theuser. These directions are calculated as the difference of thedirection between the current point and the downstream/upstream points at a distance (1) globally defined by the user(Fig. 9B). If a point lies on a completely straight line along thesearch distance, then the difference is equal to 1801. The defaultthreshold value was determined experimentally at 1501. Thesecells are marked as ‘‘containing split points’’ (Fig. 9B).

In the next step, every group of marked cells is searched usinga similar method but with a shorter distance defining the pointwith the maximum difference between downstream/upstreamdirections (Fig. 9C). These points are marked as split points. Toavoid the creation of numerous short sections, the algorithm uses

Fig. 10. A comparison of stream directions using the segmentation process based

on different criteria for DEM resolution¼15 m/cell and Horton ordering model:

(A) search length, 15 cells; skip short segments, 5 cells; threshold 1501; (B) search

length, 25 cells; skip short segments, 10 cells; threshold 1501.


the third pass to search for split points closer than the distancedefined by parameter (2) and leaves only those with the highestdirection difference. In the last step, every stream is divided atsplit points into segments, and the other parameters for everysegment are calculated.

The definition of stream segments depends on the orderingmethod or the network may remain unordered. All junctions ofstreams to streams of higher order are always split points.However, for ordered networks, streams of higher order may bedivided into sections that ignore junctions with streams of lowerorder. In unordered networks, all junctions are always splitpoints. Fig. 10 shows the application of r.stream.segment tocompare differences in streamline patterns in different part ofthe K"odawka Basin.

The module also calculates the direction/orientation of amayor stream of the current segment (Howard, 1971) withinthe user-defined global search distance. To avoid local fluctua-tions, the tangent line is approximated as a secant line joining thedownstream and upstream points at a distance globally definedby the search length parameter (1). This definition of the anglebetween streams is not fully compatible with Horton’s originalcriterion (Horton, 1932; Howard, 1971). Horton’s criterion ofa ‘‘tributary with the same flow direction’’ remains unclear(Ai, 2007) for the same reasons as those in Horton’s orderingsystem. However, this functionality is added experimentally andwill be discussed elsewhere.

5. Conclusion and further work

The r.stream package applies a new approach to stream net-work analysis where flow direction is determined by tracing bothan accumulation map and an elevation model. The increasingnumber and availability of digital terrain representations illus-trate that hydrogeomorphological modeling remains an activebranch of natural science. In recent years, active development oftools related to digital terrain analysis has increased the need forspecialized tools that are currently not available in many popularGIS packages. The r.stream package is an integral toolkit forextended hydrogeomorphological analysis and has been preparedto work as a stand-alone GRASS GIS package or in cooperationwith other GRASS GIS tools and external software.

The main new feature offered by the r.stream toolset is a newapproach for modeling and extraction of stream networks based onaccumulation map created with any flow distribution method(D8, FD8, D-Inf, DEMON, etc.). The possibility of applying additionalnatural modifiers (e.g., geology, land cover, soil moisture, and directfield observations) during the modeling process is also a newquality, treating map algebra as a main tool to fine-tune channelinitiation and channel tracing. Researchers can now performadvanced network modeling without additional programmingeffort. When using MFD flow accumulation, the new approach canhandle a wide range of terrain, including low-relief and flat areasand is not affected by issues broadly discussed in the literature(Tribe, 1992; Liang and MacKay, 2000; Turcotte, 2001).

Other tools have been adapted to this new approach offeringbetter mapping of natural features than traditional software(Hengl and Reuter, 2008). Of course common tasks such asnetwork ordering, basin delineation, and calculation of relativedistance/position are not new. However, in combination with aMFD approach it allows one to achieve results that are notavailable in other programs. Easy basin modeling techniques fordifferent objects, such as lakes, coastlines, and areas of greatestprobability adopted here, are also a new quality in the modelingsoftware. The examples presented in the paper show that ther.stream toolset is also suitable for performing a complex analysis


dx.doi.org/10.1016/j.cageo.2011.03.003


such as modeling a hierarchical basin topology coding system(Pfafstetter, 1989).

The r.stream tools can be used for hydrogeomorphologicalresearch covering large spatial domains. The limitation by avail-able memory in data processing has been removed by using theSEGMENT library for the r.stream package.

Future work will focus on more methods for creating accumu-lation maps, as available in other GIS packages, implementingsupport of natural depressions. There is continuous effort toimplement a fully automated basin coding system based onmorphological and spatial criteria, to develop more accuratealgorithms for segment partitioning, and to implement moreadaptive criteria for segmentation and calculation of more geo-metrical properties of channels and slope subsystems.

Acknowledgments

We thank two anonymous reviewers for their comments andefforts in the evaluation of our publication. We also thank the GRASSGIS community for their support during the creation of the software.The digital elevation model used in the paper has been created byMiko"aj Strzelbicki and Anna Gierczyk, M.Sc. students of Prof. KarolRotnicki, to whom the authors sincerely thank for their work.

Appendix A. Pseudo-code listings

Listing 1

Algorithm for the calculation of Strahler and Shreve orderingsystems

FOR every_sources_in_mapIF all_tributuaries_have_order THEN

IF there_is_more_than_one segment_of_max_order thenorder¼orderþ1IF is_next_segmentGOTO next_segmentELSEstop_this_branch

ELSE//there are some tributaries without order

stop_this_branchGOTO next_sourceIF no_more_sourcesIF no_more_sources

PleaGeos

se ccie

itence

STOP

Listing 2

(A) Horton ordering algorithmFOR every_outlet_in_map

start_new_branchcurrent_Hortons_order¼current_Strahlers_orderadd_to_stackIF there_are_no_tributaries_with_same_order

GOTO tributary_with_higher_length/accumulationELSE

GOTO next_tributary_with_the_same_orderbranch_order¼current_Hortons_orderadd_to_stackIF no_tributaries OR all_assigned //source, go back

remove_from_stackstart_new_branchcurrent_Hortons_order¼current_Strahlers_order

this article as: Jasiewicz, J., Metz, M., A new GRASS GIS tos (2011), doi:10.1016/j.cageo.2011.03.003

add_to_stackIF stack_is_empty

GOTO next_outletIF no_more_outlets

olkit f
or
STOP(B) Main stream ordering algorithmFOR every_outlet_in_map

start_new_branchcurrent_order¼1add_to_stackGOTO tributary_with_higher_length/accumulationbranch_order¼current_orderadd_to_stackIF no_tributaries OR all_assigned //source, go back

remove_from_stackstart_new_branchcurrent_order¼current_orderþ1add_to_stack

IF nothing_on_stackGOTO next_outlet

IF no_more_outlets
STOP
Listing 4A

Algorithm used in r.stream.basins modules

mark_all_outlets_in_the_mapFOR every_outlet_in_map

add_outlet_to_queuecheck_if_contributing_cell_has_value

IF contributing_cell_has_valuedo_nothing //do not add cells to queue

ELSEadd_all_contributing_cells_to_queueassign_values_on_basins_map

GOTO next_cell_in_queueIF queue is empty //basins is filled


Hor

STOP

Listing 4B

Algorithm used in r.stream.distance modules

mark_all_outlets_streams_in_the_mapFOR every_outlet_in_map

add_outlet_to_queuecheck_if_contributing_cell_has_value

IF contributing_cell_has_valueIF outlet_modedo_nothing //do not add cells to queue

IF stream_modereset_distancereset_elevation

ELSEadd_all_contributing_cells_to_queueassign_values_on_distance_elevation_maps

GOTO next_cell_in_queueIF queue is empty


STOP

tonian analysis of drainage networks. Computers &

dx.doi.org/10.1016/j.cageo.2011.03.003


Appendix B. Supplementary material

Supplementary data associated with this article can be foundin the online version at doi:10.1016/j.cageo.2011.03.003.

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