A Tutorial for the Management of. Digital Terrain ...... the flow with respect to the
real flow path actually followed by the water as it flows downhill, [Or- landini et al.
JGrass 2.0 A Tutorial for the Management of Digital Terrain Models Erica Ghesla & Riccardo Rigon
Trento, May 2006
ISBN 10: 88-8443-155-7 ISBN 13: 978-88-8443-155-4 Translation by Joseph E. Tomasi
Readme
This ebook was written by Erica Ghesla and Riccardo Rigon (University of Trento, Department of Civil and Environmental Engineering). It is distributed according to the CREATIVE COMMONS deed: Attribution-NoDerivs 2.5 According to this license type you are free to: • copy, distribute, display, and perform the work • to make commercial use of the work Under the following conditions: • Attribution. You must attribute the work in the manner speciied by the author or licensor. • No Derivative Works. You may not alter, transform, or build upon this work. • For any reuse or distribution, you must make clear to others the license terms of this work. Any of these conditions can be waived if you get permission from the copyright holder. Your fair use and other rights are in no way affected by the above. This is a human-readable summary of the Legal Code (the full license) that can be consulted at: http://creativecommons.org/licenses/by-nd/2.5/legalcode
Numbering convention used for the drainage directions, the red arrow indicates the direction really followed by a water particle passing through the pixel. . . . . . . . . .
2.13 h.draindir. Map of the contributing areas, calculated on the basis of the corrected drainage directions. The measurement units are pixels. The Flanginec Basin. . . . . 12 2.14 Map showing the real channel network of a catchment area in Veneto. . . . . . . . . 13 2.15 Map showing the channel network calculated on the basis of the DTM. . . . . . . . . 13 2.16 Map with the superimposition of the channel network calculated on the basis of the DTM (in red), and the real network (in blue). . . . . . . . . . . . . . . . . . . . . . . 14 2.17 r.correct. The r.correct graphic interface used to assign the drainage directions to a known channel network. The values equal to 1 represent the points of the ”real” network while the -9999 values represent points outside the network . . . . . . . . . . 15 iii
LIST OF FIGURES
2.18 r.correct. The r.correct graphic interface used to assign the drainage directions to a known channel network. The values equal to 1, which represent the network points, must be substituted with the corresponding drainage direction value. . . . . . . . . . . 16 2.19 Map of the drainage directions along the real hydrographic network. In correspondence of the network the values were manually input and they represent the drainage directions, outside the network the value is null. . . . . . . . . . . . . . . . . . . . . . 16 2.20 h.draindir. Graphic interface where the names of the input and output maps are specified. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.21 h.draindir. Drainage directions map calculated by imposing a known channel network. 18 2.22 Map with the channel network extracted on the basis of the modified drainage directions (in red) superimposed onto the real network (in blue). . . . . . . . . . . . . . . 18 2.23 The h.markoutlets icon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.24 h.markoutlets. Graphic interface where the names of the input and output maps are specified. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.25 h.markoutlets. The drainage directions map where the outlets of the region have been marked. The Flanginec Basin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.26 The h.extractnetwork icon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.27 h.extractnetwork. Graphic interface where the names of the input and output maps are specified. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.28 h.extractnetwork. The channel network map obtained by imposing a threshold value on the total contributing areas. The points of the network are marked in red (the associated value is 2). The map represents an area in the Province of Trento. . . . . 23 2.29 The h.gradient icon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.30 h.gradient. Graphic interface where the names of the input and output maps are specified. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.31 h.gradient. Gradient map. The Flanginec Basin. . . . . . . . . . . . . . . . . . . . . 25 2.32 h.extractnetwork. Graphic interface where the names of the input and output maps are specified. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.33 h.extractnetwork. Channel network map obtained by imposing a threshold value on the product of the contributing area by the gradient. The Flanginec Basin. . . . . . . 27 2.34 The h.curvatures icon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.35 h.curvatures. Graphic interface requiring the names of the input and output maps. . 29 2.36 h.curvatures. Tangent curvature map (left), profile curvature map (right), and planar curvature map (bottom) of the Flanginec Basin. . . . . . . . . . . . . . . . . . . . . . 30 iv
LIST OF FIGURES
2.37 The subdivision of the pixels according to the curvature. . . . . . . . . . . . . . . . . 32 2.38 The h.tc icon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.39 h.tc. Graphic interface requesting the names of the input and output maps. . . . . . 33 2.40 h.tc. Map of the topological classes, classified according to 9 categories. . . . . . . . . 34 2.41 h.tc. Map of the topological classes, reclassified according to 3 categories. Concave sites are shown in yellow, convex sites are shown in red,, and planar sites are shown in blue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.42 h.extractnetwork. Graphic interface requesting the names of the input and output maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.43 h.extractnetwork. Map of the hydrographic network obtained by imposing a threshold value on the contributing areas. The Flanginec Catchment Area. . . . . . . . . . . . 36 3.1
h.wateroutlet. Graphic interface requiring the name of the input map and the coordinates of the closing section. The blue circle marks the area in which the closing section of the basin is selected. The red circle marks the value of the hydrographic network map in correspondence of the selected point (it is 2, therefore the point is effectively part of the network). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.116h.mean drop. The graphic interface where the names of the input and output maps are given. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.117h.mean drop. Map showing the average value of the elevation. The Flanginec Basin. 118 4.118The h.sumdownstream icon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 4.119r.mapclac. Dialog box where the expression to be calculated is given. . . . . . . . . . 120 4.120r.mapcalc. Map with a value of 1 in correspondence of the basin and a ”null value” outside of it. The Flanginec Basin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.121h.sumdowndream. The graphic interface where the names of the input and output maps are given. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.122h.sumdownstream. Map of the contributing areas calculated with the aid of the r.mapcalc command. The Flanginec Basin. . . . . . . . . . . . . . . . . . . . . . . . 121 4.123The h.cb icon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.124h.cb. The graphic interface where the names of the input and output maps are given. The number of intervals, and the first and last moments are also specified. . . . . . . 123 4.125h.cb. The graphic interface where the names of the input and output maps are given. 124 4.126d.simplechart. Graph of the mean rescaled distance for each subbasin. . . . . . . . . . 125 4.127d.simplechart. Popup menu where the graph properties can be selected. . . . . . . . . 125 4.128d.simplechart. The properties dialog box. . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.129d.simplechart. Graph of the mean rescaled distance for each subbasin. . . . . . . . . . 126 4.130h.cb. The graphic interface where the names of the input and output maps are given. 127 4.131d.simplechart. Graph of the standard amplitude function calculated using the map of the distances to the outlet calculated with h.D2O. . . . . . . . . . . . . . . . . . . . . 128 4.132h.cb. Graphic interface where the input and output maps are specified. . . . . . . . . 128 4.133d.simplechart. Graph of the rescaled amplitude function calculated using the distance to outlet map as calculated with h.rescaleddistance, r=100. . . . . . . . . . . . . . . . 129 4.134h.cb. Graphic interface where the input and output maps are specified. . . . . . . . . 129 4.135d.simplechart. Graph of the rescaled amplitude function, calculated using the distance to outlet map as calculated with h.rescaleddistance, r=20. . . . . . . . . . . . . . . . 130
x
1
Introduction In this tutorial, the JGrass commands for the geomorphological analysis of catchment areas will
be described. The description of each command will be accompanied by an example in which its application to the Flanginec catchment area, in Trentino, will be presented. The tutorial begins with the analysis of the imported map and concludes with the extraction of the catchment basin of interest and the assessment of its morphological parameters. The other JGrass Tutorials, [1], and The Horton Machine Manual, [2], are to be considered preliminary reading. The commands that allow us to calculate these parameters are contained in the Horton Machine package. They have been divided into 7 main categories: • DEM manipulation: commands for preliminary analyses of digital terrain models; – h.pitfiller – h.markoutlets – h.wateroutlet – h.splitsubbasin • Basic topographic attributes: commands for the calculation of certain topographic attributes such as slope, flow directions, and contributing areas; – h.flowdirections – h.draindir – h.tca – h.tca3D – h.gradient – h.slope – h.aspect – h.curvatures – h.nabla – h.multitca – h.Ab • Network related measures: commands for the definition of some channel network properties;
1. Introduction
– h.extractnetwork – h.D2O – h.D2O3D – h.DD – h.hacklength – h.hacklengths3D – h.hackstream – h.magnitudo – h.seol – h.strahler – h.netnumbering – h.netdif • Hillslope analyses: commands for the calculation of some slope characteristics and their classification according to their morphological properties; – h.h2cA – h.h2cD – h.h2cD 3D – h.tau – h.tc – h.gc • Hydro-geomorphic indexes and relations: commands for the definition of some indices regarding the catchment basin; – h.rescaleddistance – h.rescaleddistance3D – h.topindex • Basin related analyses: commands for the analyses of catchment basins; – h.diametres – h.dist euclidea 2
1. Introduction
– h.principal axes – h.mean drop • Statistics: commands for the statistical analyses of catchment basins; – h.sumdownstream – h.cb Only a brief description of these commands will be given in this manual, for further details and theoretical explanations please refer to the The Horton Machine, [2].
1.1
Preliminary Operations
Before you can work on a DEM it is necessary to create a workspace, import the map containing the digital terrain model, and set up the active working region. All the details for carrying out these operations are found in the JGrass Manual, [1].
1.2
Credits
This project has been financed by the COFINLAB 2001 and COFIN 2003 projects, TIDE (contract No. EVK3-CT-00064 within the field of the V framework programme), and AQUATERRA.
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1. Introduction
4
2
Data Preparation for the Extraction of the Catchment Basin Before proceeding with the extraction of the catchment basin of interest, some processing of
the initial digital terrain data is necessary. In particular, these operations include the filling of the depressions (Pitfiller ), the calculation of the flow directions (Flowdirections or Draindir ), and the extraction of the channel network (Extractnetwork ).
2.1
Pitfiller
The pitfiller tool allows you to eliminate possible points of depression from the DEM so as to be able to correctly calculate the flow directions. The execution command is h.pitfiller. In order to execute it, from the main menu select: HortonMachine ⇒ DEM manipulation ⇒ h.pitfiller as shown in figure 2.1. The command can also be launched by clicking the corresponding icon from the toolbar that appears by checking: HortonMachine ⇒ DEM manipulation as shown in figures 2.2 and 2.3.
Figure 2.1: Launching h.pitfiller.
2. Data Preparation for the Extraction of the Catchment Basin
Figure 2.2: Launching h.pitfiller.
Figure 2.3: The h.pitfiller icon.
In both cases the graphic interface appears on screen, the interface allows you to select the map to use for the calculations, and to indicate the name of the resulting output map. The icon to launch the command is shown in figure 2.3. The h.pitfiller command can also be launched from the console command line: h.pitfiller [–quiet] [–verbose] [–version] [–usage] –elevation –inmapset [– inputformat ] –pit –outmapset [–outputformat ] [–usegui].
Example The DEM which was imported earlier is required as input. In this specific case the file to import is DTM. The h.pitfiller command requires the initial, unadulterated, DEM as input. The output file (without pits) is pit.test. The @f lan test string which follows the map name refers to the working mapset. The DTM map, therefore, is found in the flan geotop mapset. 6
2. Data Preparation for the Extraction of the Catchment Basin
Figure 2.4: h.pitfiller. Graphic interface where the names of the input and output maps are specified.
By clicking ok the h.pitfiller command is launched (in order to facilitate map management it is recommended that the maps be named in reference to the command which generated them). At this point it is possible to view the output map, pit test. For details on how to view a map and create its legend refer to the JGrass Manual, [1]. The output map is shown in figure 2.5.
Figure 2.5: h.pitfiller. Depitted elevation map. The Flanginec Basin.
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2. Data Preparation for the Extraction of the Catchment Basin
2.2
FlowDirections
The next step is to determine how water moves along the surface in relation to the topography that characterizes the study region. Flowdirections allows you to calculate the drainage directions. The limit to the exact identification of the natural flow path is linked to the way in which the land surface is discretized, in other words, to the fact that there are only 8 possible directions in which to direct the flow. Flowdirections identifies the drainage direction by directing the flow along the line of maximum slope, according to the D8 scheme. The convention used for the numbering of the 8 possible drainage directions is represented in figure 2.6. The command to execute is h.flowdirections, from the main menu select: HortonMachine ⇒ Basic topographic attributes ⇒ h.flowdirections or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Basic topographic attributes. The toolbar with the h.flowdirections icon is shown in figure 2.7. The legend in figure 2.9 highlights the fact that only 8 drainage directions are possible.
Figure 2.6: Numbering convention used for the drainage directions, the red arrow indicates the direction really followed by a water particle passing through the pixel.
Figure 2.7: The h.flowdirections icon.
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2. Data Preparation for the Extraction of the Catchment Basin
The h.flowdirections command can also be launched from the console command line: h.flowdirections [–quiet] [–verbose] [–version] [–usage] –pit –pitmapset [–pitfor mat ] –flow –flowmapset [–flowformat ] [–usegui].
Example The depitted DEM, obtained with h.pitfiller (paragraph 2.1), is required as input. To launch the command no other options need to be set. Figure 2.8 shows the window where the input and output map names are given.
Figure 2.8: h.flowdirections. Graphic interface where the names of the input and output maps are specified.
Once the process has finished it is possible to view the generated map (figure 2.9):
Figure 2.9: h.flowdirections. Drainage directions map. The Flanginec Basin.
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2. Data Preparation for the Extraction of the Catchment Basin
2.3
DrainDir
The method used by Flowdirections to calculate the drainage directions causes a deviation of the flow with respect to the real flow path actually followed by the water as it flows downhill, [Orlandini et al., 2003]. The Draindir command allows you to recalculate the flow path by applying a correction to the deviation incurred. This command also calculates the contributing areas (TCA or Total Contributing Area) which represent the horizontal projection of the areas that contribute to a point of the catchment basin. This value is calculated by following the drainage directions from every point of the catchment area and cumulating the uphill area. For more details about the method used you can refer to The Horton Machine Manual [2] and the article by Orlandini et al. [2003] [3].
The execution command is h.draindir, from the main menu select: HortonMachine ⇒ Basic topographic attributes ⇒ h.draindir or else click on the icon of the toolbar that appears by checking: HortonMachine ⇒ Basic topographic attributes The toolbar with the h.draindir icon is shown in figure 2.10.
Figure 2.10: The h.draindir icon.
The command allows you to choose the calculation method to apply and to fix the hydrographic network if this is already known. The h.draindir can also be launched from the console command line: h.draindir [–quiet] [–verbose] [–version] [–usage] –pit –pitmapset [–pitformat ] –flow –flowmapset [–flowformat ] [–net fixed ] [–net fixedmapset ] [–net fixedformat ] –draindir –draindirmapset [–draindirformat ] [–tca ] [–tcamapset ] [–tcaformat ] –mode –netmode – lambda [–usegui]. 10
2. Data Preparation for the Extraction of the Catchment Basin
Example: Calculating the Drainage Directions with the ”Normal ” Method The graphic interface for the h.draindir command is shown in figure 2.11. As input the DEM map, generated with the h.pitfiller command, and the drainage directions map, generated with the h.flowdirection command are required. Also, you need to assign a value to the λ parameter, which assigns a weight to the corrections made to the drainage directions (its value must be between 0 and 1). You also need to choose the calculation method to apply (either LAD, that is Least Angular Deviation, which calculates the angular deviation of the flow with respect to the real direction, or LTD, that is Least Transversal Deviation, which calculates the transversal deviation).
Figure 2.11: h.draindir. Graphic interface where the names of the input and output maps are specified.
In the example, the drainage directions are calculated without fixing the hydrographic network beforehand (select normal at the top of the window), the LAD method is used, and the value of 1 is assigned to the λ parameter. As input, the depitted DEM map, generated with h.pitfiller, and the drainage directions map, calculated with h.flowdirection, are required. The resulting maps are shown in figure 2.12, the corrected drainage directions map, and in figure 2.13, the total contributing areas map.
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2. Data Preparation for the Extraction of the Catchment Basin
Figure 2.12: h.draindir. Map of the corrected drainage directions. The Flanginec Basin.
Figure 2.13: h.draindir. Map of the contributing areas, calculated on the basis of the corrected drainage directions. The measurement units are pixels. The Flanginec Basin.
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2. Data Preparation for the Extraction of the Catchment Basin
Example: Calculating the Drainage Directions with the ”Net Fixed ” Method In certain cases, for example in the plains areas or where there are manmade constructions, it can happen that the extracted channel network does not coincide with the real channel network. The fixed network method allows you to assign a known channel network and to then correct the drainage directions. An example will now be given. The real channel network of a catchment basin in Veneto is shown in figure 2.14, while the channel network extracted on the basis of the DEM is shown in figure 2.15 (how to extract a hydrographic network on the basis of the DEM will be explained in Paragraph 2.28). Figure 2.16 shows the superimposition of the two networks (the calculated network is shown in red while the real network is shown in blue). It is easy to notice that in the central part the two networks do not coincide and the extracted network does not follow the real path.
Figure 2.14: Map showing the real channel network of a catchment area in Veneto.
Figure 2.15: Map showing the channel network calculated on the basis of the DTM.
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2. Data Preparation for the Extraction of the Catchment Basin
Figure 2.16: Map with the superimposition of the channel network calculated on the basis of the DTM (in red), and the real network (in blue).
An important detail in understanding the problem is that the file corresponding to the blue network does not include the drainage directions, in other words, it does not tell us, between two adjacent pixels, which is the draining pixel and which is the drained one. Therefore, these drainage directions need to be reassigned manually. The program that allows this operation to be carried out works in the following way: as well as the depitted DTM and the drainage direction map, another input map is required which gives the drainage directions along the real channel network. By means of the r.correct command, the values of the matrix that represents the real hydrographic network (the value is 1 in correspondence of the network and ”null” in the other points) can be edited in order to create a new map which gives the drainage directions along the network. To do so you must view the map of the ”real” network and launch the r.correct command. Select the map of the ”real” channel network (the blue network in the figure) as the map to modify, in the example it is called netfixed3. You can then proceed and substitute the network values with the drainage direction values (you, the user, must decide where each successive pixel drains). In figure 2.17 the graphic interface of the r.correct command shows the pixel values of the map of the ”real” network (the pixels of the network have an assigned value of 1 while the points outside the network have the null value assigned, conventionally represented with -9999.0). Figure 2.18 shows the r.correct graphic interface once the values equal to 1 have been substituted with the drainage direction values. The closing section of the network must be represented with the value of 10 (basin outlet) in order to distinguish it from the other network points. Once you complete the modifications, click Accept Changes and a new map is created which gives the value of the drainage directions, input manually, along the network and the ”null” value for the other points of the catchment basin. The map of the drainage directions along the hydrographic network is shown 14
2. Data Preparation for the Extraction of the Catchment Basin
in figure 2.19. Figure 2.20 shows the h.draindir graphic interface where the names of the input and output maps are specified. To calculate the drainage directions according to an imposed hydrographic network you must select to use the net fixed method. The input required is, in order, the depitted DEM, generated with h.pitfiller, the drainage directions map, calculated with h.flowdirections, the map of the drainage directions along the channel network to be fixed, created manually with the r.correct command, and the value to assign to the λ parameter. As output, a map of the drainage directions is generated. The total contributing areas map is not calculated simultaneously by h.draindir in this case but must be calculated separately by launching the h.tca command.
Figure 2.17: r.correct. The r.correct graphic interface used to assign the drainage directions to a known channel network. The values equal to 1 represent the points of the ”real” network while the -9999 values represent points outside the network
15
2. Data Preparation for the Extraction of the Catchment Basin
Figure 2.18: r.correct. The r.correct graphic interface used to assign the drainage directions to a known channel network. The values equal to 1, which represent the network points, must be substituted with the corresponding drainage direction value.
Figure 2.19: Map of the drainage directions along the real hydrographic network. In correspondence of the network the values were manually input and they represent the drainage directions, outside the network the value is null.
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2. Data Preparation for the Extraction of the Catchment Basin
Figure 2.20: h.draindir. Graphic interface where the names of the input and output maps are specified.
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2. Data Preparation for the Extraction of the Catchment Basin
Figure 2.21 shows the drainage direction map calculated using the net fixed method and figure 2.22 shows the channel network that was extracted from this drainage directions map (in red) superimposed on the known hydrographic network (in blue). It immediately noticeable that the two networks coincide, except for some isolated points.
Figure 2.21: h.draindir. Drainage directions map calculated by imposing a known channel network.
Figure 2.22: Map with the channel network extracted on the basis of the modified drainage directions (in red) superimposed onto the real network (in blue).
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2. Data Preparation for the Extraction of the Catchment Basin
2.4
MarkOutlets
At this point it is necessary to mark all the outlets of the considered region on the drainage directions map. In fact, by following the drainage directions you do eventually reach the edge of the DEM. These points on the edge are each the closing section of a catchment basin. The MarkOutlets command identifies these points. A convention has been adopted by which the the preexisting drainage direction value of every outlet is changed with the value 10. This operation is of fundamental importance for the calculation of other quantities. In all of the following operations the drainage directions map considered is always the one with the marked outlets, even if this is not specifically stated. The command to launch is h.markoutlets. In order to launch it, from the main menu select: HortonMachine ⇒ DEM manipulation ⇒ h.markoutlets or else click on the icon of the toolbar that appears by checking: HortonMachine ⇒ DEM manipulation
Figure 2.23: The h.markoutlets icon.
The h.markoutlets command can also be launched from the console command line: h.markoutlets [–quiet] [–verbose] [–version] [–usage] –flow –inmapset [–input format ] –mflow –mflowmapset [–mflowformat ] [–usegui].
Example To run MarkOutlets you need to input the name of the drainage directions map on which the outlets of the active region are to be marked. The graphic interface of the command is shown in figure 2.24. The resulting output map is shown in figure 2.24.
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2. Data Preparation for the Extraction of the Catchment Basin
Figure 2.24: h.markoutlets. Graphic interface where the names of the input and output maps are specified.
Figure 2.25: h.markoutlets. The drainage directions map where the outlets of the region have been marked. The Flanginec Basin.
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2. Data Preparation for the Extraction of the Catchment Basin
2.5
ExtractNetwork
It is now possible to proceed to the extraction of the channel network using one of the three available methods. The first is based on the contributing areas, the second on the product of contributing area and gradient, and the third on the curvature. Depending on the method chosen, it is necessary to calculate different additional maps. In all cases, the output map will have the value of 2 in correspondence of the network and the ”null value” in all other points. The command to launch is h.extractnetwork, in order to launch it from the main menu select: HortonMachine ⇒ Network related measures ⇒ h.extractnetwork or else click on the icon of the toolbar that appears by checking: HortonMachine ⇒ Network related measures Figure 2.26 shows the toolbar with the h.extractnetwork icon.
Figure 2.26: The h.extractnetwork icon.
The h.extractnetwork command can also be launched from the console command line: h.extractnetwork [–quiet] [–verbose] [–version] [–usage] –prof curv –prof curvmapset [–prof curvformat ] –tang curv –tang curvmapset [–tang curvformat ]–cp3map –cp3mapmapset [–cp3mapformat ] –cp9map –cp9mapmapset [–cp9mapformat ] –th prof
–th tan
[–usegui]. There follow some examples of execution of the command using the three available methods.
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2. Data Preparation for the Extraction of the Catchment Basin
2.5.1
Extracting the Network Using the Contributing Areas (or Magnitudo)
The calculation is carried out by fixing a threshold value on the contributing areas, or magnitudo. This method assumes that all pixels with a total contributing area value greater than the threshold value are channel pixels. The choice of the threshold value is made in relation to the territorial characteristics and the map resolution (pixel size). In the case of uncertainty it is advisable to try using different values of the threshold value and then compare the resulting map with an orthophoto of the catchment basin.
Figure 2.27: h.extractnetwork. Graphic interface where the names of the input and output maps are specified.
Example The calculation method is chosen by selecting the respective option in the lower part of the window, as shown in figure 2.27. The required input, in order, is: the drainage directions map 22
2. Data Preparation for the Extraction of the Catchment Basin
(with marked outlets), the map on which the threshold will be imposed, and the threshold value. In the example the contributing areas map generated with h.draindir is used and the threshold value is set to 150 pixels, the map resolution is 10m. the resulting map is shown in figure 2.28.
Figure 2.28: h.extractnetwork. The channel network map obtained by imposing a threshold value on the total contributing areas. The points of the network are marked in red (the associated value is 2). The map represents an area in the Province of Trento.
It is noteworthy that in the network map various groups of channel networks have been extracted, each one of which corresponds to a small catchment area, as will be seen.
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2. Data Preparation for the Extraction of the Catchment Basin
2.5.2
Extracting the Network Using the Contributing Areas and the Slopes
In this second case the network is calculated by imposing a threshold value on the product of two quantities, for example the contributing area and the slope. A preliminary operation is therefore the generation of the slope map, this operation is carried out with the h.gradient command.
Gradient To calculate the gradient in each point of the map, the command to execute is h.gradient. From the main menu select: HortonMachine ⇒ Basic topographic attributes ⇒ h.gradient or else click on the icon of the toolbar that appears by checking: HortonMachine ⇒ Basic topographic attributes The toolbar with the h.gradient icon is shown in figure 2.29.
Figure 2.29: The h.gradient icon.
The h.gradient command can also be launched from the console command line: h.gradient [–quiet] [–verbose] [–version] [–usage] –pit –pitmapset [–pitformat ] –gradient –gradientmapset [–gradientputformat ] [–usegui]
Example The first thing to do is calculate the gradient map, to launch the command click the icon shown in figure 2.29. The depitted elevation map, generated with h.pitfiller, is required as input. The graphic interface of the h.gradient command, where the names of the input and output maps are specified, is shown in figure 2.30. The resulting map is shown in figure 2.31. 24
2. Data Preparation for the Extraction of the Catchment Basin
Figure 2.30: h.gradient. Graphic interface where the names of the input and output maps are specified.
The resulting map is shown in figure 2.31.
Figure 2.31: h.gradient. Gradient map. The Flanginec Basin.
25
2. Data Preparation for the Extraction of the Catchment Basin
Calculation of the Network It is now possible to calculate the hydrographic network by fixing a threshold value to the product of the contributing area by the gradient. Click the h.extractnetwork icon and the graphic interface appears; select the second extraction method in the lower part of the window and input the information necessary for the calculation. The information required, in order, is: the drainage directions map, the contributing areas map, the slopes map, calculated with h.gradient, and the fixed threshold value. Even in this case the threshold value is chosen on the basis of the map resolution and the land surface being analyzed. Figure 2.32 shows the graphic interface where the names of the input map and the output map, which will be generated by the program, are given. The map resulting from the network extraction is shown in figure 2.33.
Figure 2.32: h.extractnetwork. Graphic interface where the names of the input and output maps are specified.
26
2. Data Preparation for the Extraction of the Catchment Basin
Figure 2.33: h.extractnetwork. Channel network map obtained by imposing a threshold value on the product of the contributing area by the gradient. The Flanginec Basin.
27
2. Data Preparation for the Extraction of the Catchment Basin
2.5.3
Extracting the Network Using the Curvature
The hydrographic network is extracted by considering only concave points as being part of the channel network. As in the first case, a threshold value is imposed on a map. In order to identify the concave points it is necessary to calculate the curvatures (tangent, profile, and planar) and then execute the Topological classes command in order to distinguish between points that are concave, planar, and convex.
Curvatures This program calculates the planar, profile, and planar curvatures of an area. The curvature represents the deviation of the gradient vector per unit length (in radians) along particular curves that are plotted on the surface under study. For more details refer to the The Horton Machine Manual [2]. The command to execute is h.curvatures, from the main menu select: HortonMachine ⇒ Basic topographic attributes ⇒ h.curvatures or else click the icon of the toolbar that appears by checking: HortonMachine ⇒ Basic topographic attributes The toolbar with the h.curvatures icon is shown in figure 2.34. The h.curvatures command can also be executed from the console command line: h.curvatures [–quiet] [–verbose] [–version] [–usage] –pit –pitmapset [–pitformat ] –prof curv –prof curvmapset [–prof curvformat ] –plan curv –plan curvmapset [–plan curv format ] –tang curv –tang curvmapset [–tang curvformat ] [–usegui]
Figure 2.34: The h.curvatures icon.
Example The first thing to do is calculate the curvatures. The depitted elevation map, calculated with h.pitfiller is required as input. Figure 2.35 shows the graphic interface where the names of the input 28
2. Data Preparation for the Extraction of the Catchment Basin
and output maps are given, figure 2.36 shows the maps obtained from the calculation process.
Figure 2.35: h.curvatures. Graphic interface requiring the names of the input and output maps.
29
2. Data Preparation for the Extraction of the Catchment Basin
Figure 2.36: h.curvatures. Tangent curvature map (left), profile curvature map (right), and planar curvature map (bottom) of the Flanginec Basin.
30
2. Data Preparation for the Extraction of the Catchment Basin
Tc Topological Classes classifies a land area, dividing it into 9 topological classes according to the value of the planar and profile curvatures [see The Horton Machine [2]]. On the basis of this classification the program then reclassifies the map by grouping these classes into the 3 categories of convex, conclave, and planar sites. The program requires a threshold value for the profile curvature and the planar one, in order to define the planarity (the sites with an absolute curvature value that is less then the threshold are considered planar). Normally, in order to determine this threshold value, experiments are carried out in each specific catchment basin in order to take into account the local topography. The conventions adopted to describe the topological classes are: • 10 → planar sites - parallel; • 20 → convex sites - parallel; • 30 → concave sites - parallel; • 40 → planar sites - divergent; • 50 → convex sites - divergent; • 60 → concave sites - divergent; • 70 → planar sites - convergent; • 80 → convex sites - convergent; • 90 → concave sites - convergent. in the map in which the 9 classes are grouped into 3 fundamental categories, the conventions adopted are the following: • 15 → concave sites (classes 30, 70, 90); • 25 → planar sites (class 10); • 35 → convex sites (classes 20, 40, 50, 60, 80).
31
2. Data Preparation for the Extraction of the Catchment Basin
Figure 2.37 shows the subdivision of the map pixels according to the adopted convention.
Figure 2.37: The subdivision of the pixels according to the curvature.
The command to execute is h.tc. From the main menu select:
HortonMachine ⇒ Hillslope analyses ⇒ h.tc or else click on the icon of the toolbar that appears by checking:
HortonMachine ⇒ Hillslope analyses Figure 2.38 shows the toolbar with the h.tc icon.
Figure 2.38: The h.tc icon.
32
2. Data Preparation for the Extraction of the Catchment Basin
The h.tc command can also be launched from the console command line: h.tc [–quiet] [–verbose] [–version] [–usage] –prof curv –prof curvmapset [–prof curvformat ] –tang curv –tang curvmap set [–tang curvformat ] –cp3map –cp3mapmap set [–cp3mapformat ] –cp9map –cp9mapmapset [–cp9mapformat ] –th prof
–th tan
[– usegui].
Example The execution of the command requires as input the curvature maps, generated with h.curvatures. Figure 2.39 shows the dialog window where the names of the input maps and those of the maps which will be generated are given. Figures 2.40 and 2.41 show the maps obtained from the calculations.
Figure 2.39: h.tc. Graphic interface requesting the names of the input and output maps.
33
2. Data Preparation for the Extraction of the Catchment Basin
Figure 2.40: h.tc. Map of the topological classes, classified according to 9 categories.
Figure 2.41: h.tc. Map of the topological classes, reclassified according to 3 categories. Concave sites are shown in yellow, convex sites are shown in red,, and planar sites are shown in blue.
34
2. Data Preparation for the Extraction of the Catchment Basin
Extraction of the Hydrographic Network Once the concave, convex, and planar sites have been identified, the channel network can be extracted using the third available method. Even in this case a threshold value is imposed on a map, in the specific example a threshold value was imposed on the contributing areas, but the map of the ratio of area to slope could have been chosen for example (this ratio map can be easily generated using the r.mapcalc command, for a description of this command you can refer to the JGrass Manual [1]).
Figure 2.42: h.extractnetwork. Graphic interface requesting the names of the input and output maps.
The map resulting from the choices made is shown in figure 2.43.
35
2. Data Preparation for the Extraction of the Catchment Basin
Figure 2.43: h.extractnetwork. Map of the hydrographic network obtained by imposing a threshold value on the contributing areas. The Flanginec Catchment Area.
36
3
Extraction of the Basin of Interest
3.1
WaterOutlets
Once the channel network has been identified, using one of the methods described earlier, it is possible to extract the subbasin of interest (which represents only a part of the area analyzed up to this point) and proceed to its geomorphological analyses. The program requires that the subbasin closing section be indicated. This point must necessarily be part of the channel network extracted in precedence. The command to execute is h.wateroutlet. From the main menu select: HortonMachine ⇒ DEM manipulation ⇒ h.wateroutlet or else click on the icon of the toolbar that appears by checking: HortonMachine ⇒ DEM manipulation.
Figure 3.1: The h.wateroutlet icon.
The command can also be executed from the console command line: h.wateroutlet [–quiet] [–verbose] [–version] [–usage] –drainage –basin –northing –easting [–extractmap ] [–usegui]
Example To execute the command, click the h.wateroutlet icon, the command’s graphic interface is so dispalyed. The drainage directions map and the coordinates of the desired closing section are required as input. The first operation is the identification of the closing section of the basin to extract. If you already know the coordinates, you only need to input them in the appropriate boxes. If you do not know the coordinates you will have to view the channel network before proceeding with the h.wateroutlet command. Input the name of the channel network map in the dialog window,
3. Extraction of the Basin of Interest
as shown in figure 3.2 (in the example the network map is net.test). The program allows you to click on the map and then view the maps value in the selected point. The closing section of the basin must necessarily be part of the network, make sure that the value of the selected point is 2 (convention adopted to distinguish between channel pixels and slope pixels). The dialog box is shown in figure 3.2. The WaterOutlets program generates two output files, one containing a mask of the extracted basin (that is a raster map with values equal to 1 in correspondence of the basin and null values outside of the basin), and the other containing a map trimmed along the mask boundary. It is possible to choose the map to trim, from the entire group of maps generated in precedence, by inputting the name in the appropriate box (beside the string the map to extract). In this example the extracted map is the depitted DEM, generated with the h.pitfiller command. The program will assign this trimmed map a composite name, made up of the original name and the name of the mask, in the example the new map is called pit.test.m. Figure 3.3 show the Flanginec Basin mask superimposed on the network map, while figure 3.4 shows the depitted DEM cut along the mask boundary.
Figure 3.2: h.wateroutlet. Graphic interface requiring the name of the input map and the coordinates of the closing section. The blue circle marks the area in which the closing section of the basin is selected. The red circle marks the value of the hydrographic network map in correspondence of the selected point (it is 2, therefore the point is effectively part of the network).
38
3. Extraction of the Basin of Interest
Figure 3.3: h.wateroutlet. The basin mask superimposed on the hydrographic network. The Flanginec Basin.
Figure 3.4: h.wateroutlet. Map of the extracted subbasin. The Flanginec Basin.
39
3. Extraction of the Basin of Interest
40
4
Analysis of the Extracted Catchment Basin Once the catchment area of interest has been extracted, it is possible to proceed with its analyses.
The first thing to do is trim the maps calculated in precedence along the catchment area mask: the drainage directions map, the slope map, the curvature map, and the network map. This operation is carried out by using the r.mapcalc command. To launch the r.mapcalc command select: Raster ⇒ Operations on raster maps ⇒ r.mapcalc To carry out the required calculations you need to input an expression of the type: new map = if(condition satisfied, then assign null value, else assign value from map) to trim the drainage directions map the expression to input is: dir.test.m = if($m$ == null, null, dir.test) in this way a map is created, called dir.test.m in the example, which has been assigned a ”null value” in correspondence of ”null values ” of the map called m (mask, see chapter 3), which correspond to points outside the catchment, and the value of the drainage directions map in all other points, which correspond to points within the catchment area. Figure 4.1 shows the graphic interface of the r.mapcalc command, while figure 4.2 shows the resulting map.
Figure 4.1: r.mapclac. Dialog box where the expression to be calculated is input.
Once the drainage directions map of the extracted catchment has been prepared, you need to mark the catchment outlet by using the h.markoutlets command. To trim the other maps you need only repeat the operations that have just been described.
4. Analysis of the Extracted Catchment Basin
Figure 4.2: h.draindir. Map of the corrected drainage directions for the extracted catchment basin. The Flanginec Basin.
Once the maps have been trimmed to correspond to the basin you will move on to the commands that have not yet been described which allow you to calculate a series of parameters which describe the catchment area. There follow the maps that were calculated earlier but which have been recalculated in correspondence of the extracted catchment area.
42
4. Analysis of the Extracted Catchment Basin
Figure 4.3: h.draindir. Contributing areas map of the extracted catchment. The Flanginec Basin.
Figure 4.4: h.extractnetwork. Map of the hydrographic network. The Flanginec Basin.
43
4. Analysis of the Extracted Catchment Basin
Figure 4.5: h.gradient. Gradient map of the extracted catchment. The Flanginec Basin.
Figure 4.6: h.curvatures. Map of the planar curvature of the extracted catchment. The Flanginec Basin.
44
4. Analysis of the Extracted Catchment Basin
Figure 4.7: h.curvatures. Map of the profile curvature of the extracted catchment. The Flanginec Basin.
Figure 4.8: h.gradient. Map of the tangent curvature of the extracted catchment. The Flanginec Basin.
45
4. Analysis of the Extracted Catchment Basin
Figure 4.9: h.tc. Map of the Parson classes of the extracted catchment, 9 classes. The Flanginec Basin.
Figure 4.10: h.tc. Map of the Parson classes of the extracted catchment, 3 classes. The Flanginec Basin.
46
4. Analysis of the Extracted Catchment Basin
For a complete understanding of the commands described below you should refer to The Horton Machine Manual [2] where the command algorithms are explained and the bibliographic references are given.
4.1 4.1.1
Basic Topographic Attributes Ab
For every point of the catchment basin, the Ab command allows you to calculate the draining area per unit length (A/b) and the length of the contour line, b, passing through the point to which corresponds a contributing area equal to A. The calculation of the draining contour is linked to the value of the planar curvature in every point of the catchment area. To launch the command select:
or else by clicking on the icon of the toolbar that appears by checking:
HortonMachine ⇒ Basic topographic attributes
The toolbar with the h.ab icon is shown in figure 4.11.
Figure 4.11: The h.ab icon.
The h.ab command can also be executed from the console command line: h.ab [–quiet] [–verbose] [–version] [–usage] –plan curv –plan curvmapset [–plan curvformat ] –tca –tcamapset [–tcaformat ] –alung –alungmapset –alungformat –b –bmapset [–bformat ] [–usegui] 47
4. Analysis of the Extracted Catchment Basin
Example By clicking on the icon the graphic interface, shown in figure 4.12, appears. The required input maps are the planar curvature map, calculated with the h.curvatures command, and the contributing areas map, calculated either with the h.tca or h.draindir commands. Plots of the resulting maps are shown in figures 4.13 and 4.14.
Figure 4.12: h.ab. Graphic interface requiring the names of the input and output maps.
Figure 4.13: h.ab. Map of the area per unit length. The Flanginec Basin.
48
4. Analysis of the Extracted Catchment Basin
Figure 4.14: h.ab. Map of the draining contour line. The Flanginec Basin.
4.1.2
Aspect
The aspect command allows you to calculate the aspect, which is defined as the inclination angle of the gradient, expressed in degrees. The command to to launch is h.aspect. From the main menu select:
or else click the icon from the toolbar that appears by checking:
HortonMachine ⇒ Basic topographic attributes
The toolbar with the h.aspect icon is shown in figure 4.15.
Figure 4.15: The h.aspect command icon.
49
4. Analysis of the Extracted Catchment Basin
The h.aspect command can also be executed from the console command line: h.aspect [–quiet] [–verbose] [–version] [–usage] –pit –pit –pitmapset [–pitformat ] –aspect –outmapset [–outputformat ] [–usegui]
Example Figure 4.16 shows the dialog window requiring the input and output details. The resulting map is shown in figure 4.17.
Figure 4.16: h.aspect. Graphic interface requiring the names of the input and output maps.
Figure 4.17: h.aspect. The aspect map. The Flanginec Basin
50
4. Analysis of the Extracted Catchment Basin
4.1.3
Multitca
The multitca command calculates the contributing areas, distinguishing between convex and concave areas. For convex areas the flow from the pixel is subdivided over all lower adjacent pixels, while for the concave areas only one drainage direction is used. To launch the command select: HortonMachine ⇒ Basic topographic attributes ⇒ h.multitca or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Basic topographic attributes Figure 4.18 shows the toolbar with the h.multitca icon.
Figure 4.18: The h.multitca icon.
The command can also be executed from the console command line. h.multitca [–quiet] [–verbose] [–version] [–usage] –pit –pitmapset 0, and planar sites |∇2 z| < , having imposed a threshold value, , to the Laplacian. For further details about the method refer to The Horton Machine Manual [2]. The command to execute is h.nabla. From the main menu select: HortonMachine ⇒ Basic topographic attributes ⇒ h.nabla or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Basic topographic attributes The toolbar with the h.nabla icon is shown in figure 4.21.
Figure 4.21: The h.nabla icon.
The command can also be executed from the console command line. h.nabla [–quiet] [–verbose] [–version] [–usage] –pit –pitmapset [–pitformat ] –nabla –nablamapset [–nablaformat ] –mode –th nabla
[–usegui]
Example To launch the command you need to input the name of the depitted DEM, calculated with the h.pitfiller command. To calculate the value of the Laplacian in every point of the catchment area of interest you must check the ”REAL VALUES” option in the dialog window, as shown in figure 4.22.
53
4. Analysis of the Extracted Catchment Basin
Figure 4.22: h.nabla. Graphic interface requiring the names of the input and output maps.
To obtain a classification in classes, the command has to be executed having checked the ”CLASSES” option. The distinction between concave, convex, and planar sites is made on the basis of the value of , set to 0.001 in the specific case. The value assigned is to be chosen in relation to the topography and land surface being analyzed. The graphic interface requiring the input and output map is shown in figure 4.23.
Figure 4.23: h.nabla. Graphic interface requiring the names of the input and output maps.
Figures 4.24 and 4.25 show the resulting maps of the two cases described.
54
4. Analysis of the Extracted Catchment Basin
Figure 4.24: h.nabla. Map of the Laplacian calculated in every point of the catchment area. The Flanginec Basin.
Figure 4.25: h.nabla. Map of the Laplacian, which distinguishes between concave, convex, and planar zones. The Flanginec Basin.
55
4. Analysis of the Extracted Catchment Basin
4.1.5
Slope
The h.slope command calculates the slopes along the drainage directions (which are different from those calculated with h.gradient, as specified in The Horton Machine Manual [2]). The command to execute is h.slope. From the main menu select: HortonMachine ⇒ Basic topographic attributes ⇒ h.slope or else click on the icon from the toolbar that appears by checking: HortonMachine ⇒ Basic topographic attributes The toolbar with the h.slope icon is shown in figure 4.26.
Figure 4.26: The h.slope icon.
The h.slope command can also be executed from the console command line: h.slope [–quiet] [–ver>bose] [–version] [–usage] –pit –pitmapset [–pitformat ] –flow –flowmapset [–flowformat ] –slope [–slopemapset ] [–slopeformat ] [–usegui]
Example The execution of the command requires the depitted DEM, calculated with the h.pitfiller command, as input. The dialog window requiring the names of the input and output maps is shown in figure 4.27. A plot of the resulting map is shown in figure 4.28.
56
4. Analysis of the Extracted Catchment Basin
Figure 4.27: h.slope. Graphic interface requiring the names of the input and output maps.
Figure 4.28: h.slope. Map of the slopes calculated along the drainage directions. The Flanginec Basin.
57
4. Analysis of the Extracted Catchment Basin
4.1.6
Total Contributing Area
This command returns the contributing area in every point of the basin. The total contributing area represents the planar projection of the areas that contribute to a point of the catchment basin. Once the drainage directions have been identified, it is possible to calculate the total draining area contributing to a point, known as TCA (Total Contributing Area), for every point of the basin. The command to execute is h.tca. From the main menu select: HortonMachine ⇒ Basic topographic attributes ⇒ h.tca or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Basic topographic attributes The toolbar with the h.tca icon is shown in figure 4.29.
Figure 4.29: The h.tca icon.
The h.tca command can also be executed from the console command line: h.tca [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [–flowformat ] –tca –tcamapset [–tcaformat ] [–usegui]
Example The execution of the command requires as input the drainage direction map, calculated either with h.flowdirection or h.draindir. Figure 4.30 shows the graphic interface requiring input and output map names. A plot of the resulting map is shown in figure 4.31.
58
4. Analysis of the Extracted Catchment Basin
Figure 4.30: h.tca. Graphic interface requiring the names of the input and output maps.
Figure 4.31: h.tca. Total contributing areas map. The Flanginec Basin.
59
4. Analysis of the Extracted Catchment Basin
4.1.7
Total Contributing Area 3D
This command allows you to calculate the real contributing area of the 3D surface in every point of the catchement basin, taking account of the varying elevation of the local topography. The command to execute is h.tca3D. From the main menu select: HortonMachine ⇒ Basic topographic attributes ⇒ h.tca3D or else click the icon of the toolbar that appears by checking: HortonMachine ⇒ Basic topographic attributes The toolbar with the h.tca3D icon is shown in figure 4.32.
Figure 4.32: The h.tca3D icon.
The command can also be executed from the console command line: h.tca3D [–quiet] [–verbose] [–version] [–usage] –pit –pitmapset [–pitformat ] –flow –flowmapset [–flowformat ] –tca3D –tca3Dmapset [–tca3Dformat ] [–usegui]
Example The execution of the command requires the drainage directions map, calculated either with h.flowdirection or h.draindir, and the elevation map, resulting from the h.elevation command. The graphic interface requiring input and output maps is shown in figure 4.33. A plot of the resulting output map is shown in figure 4.34.
60
4. Analysis of the Extracted Catchment Basin
Figure 4.33: h.tca3D. Graphic interface requiring names of the input and output maps.
Figure 4.34: h.tca3D. Real contributing areas map. The Flanginec Basin.
61
4. Analysis of the Extracted Catchment Basin
4.2 4.2.1
Network Related Measures Distance to Outlets
This command allows you to determine the projection onto the plane of the distance of every pixel of the catchment basin from the outlet, calculated along the drainage directions (so as to calculate the magnitude function). The command allows you to choose whether to calculate the distance in metres or in pixels. The command to execute is h.D2O. To execute the command, from the main menu select: HortonMachine ⇒ Network related measures ⇒ h.D2O or else click on the icon of the toolbar that appears by selecting: HortonMachine ⇒ Network related measures The toolbar with the h.D2O icon is shown in figure 4.35.
Figure 4.35: The h.D2O icon.
The command can also be executed from the console command line: h.D2O [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [–flowformat ] –dist2outlet –dist2outletmapset [–dist2outlet format ] –mode [–usegui]
Example To execute the command, and calculate the number of pixels that separates every point from the outlet, you must select the option topological distance. The graphic interface which requires the input and output map names is shown in figure 4.36, the map with the distances to the outlet are shown in figure 4.37. 62
4. Analysis of the Extracted Catchment Basin
Figure 4.36: h.D2O. Graphic interface requiring the names of the input and output maps.
Figure 4.37: h.D2O. Map of the distance of every point from the basin outlet. The Flanginec Basin.
In order to calculate the distance that separates every point of the map from the closing section of the basin in metres, you must check the simple distance option, as shown in figure 4.38.
63
4. Analysis of the Extracted Catchment Basin
Figure 4.38: h.D2O. Graphic interface requiring the names of the input and output maps.
64
4. Analysis of the Extracted Catchment Basin
4.2.2
Distance to Outlet 3D
The distance to outlet 3D command allows you to calculate the distance of every pixel to the basin outlet taking account of the varying elevation of the local topography. The command to execute is h.D2O3D. To execute the command from the main menu select: HortonMachine ⇒ Network related measures ⇒ h.D2O3D or else click the icon of the toolbar that appears by checking: HortonMachine ⇒ Network related measures The toolbar with the h.D2O3D icon is shown in figure 4.39.
Figure 4.39: The h.D2O3D icon.
The command can also be executed from the console command line: h.D2O3D [–quiet] [–verbose] [–version] [–usage] –pit –pitmapset [–pitformat ] –flow –flowmapset [–flowformat ] –D2O3D –D2O3Dmapset [–D2O3Dformat ] [–usegui]
Example To execution of the command requires as input the the depitted elevation map, calculated with h.pitfiller, and the drainage directions map, calculated either with h.flowdirection or h.draindir. The graphic interface requiring the input and output map names is shown in figure 4.40. The resulting output map is shown in figure 4.41.
65
4. Analysis of the Extracted Catchment Basin
Figure 4.40: h.D2O3D. Graphic interface requiring the names of the input and output maps.
Figure 4.41: h.D2O3D. Map of the distance of every point from the basin outlet. The Flanginec Basin. Graphically, it is similar to the ordinary distance to outlet map, the difference lies in the values assigned.
66
4. Analysis of the Extracted Catchment Basin
4.2.3
Drainage density
This command allows you to calculate the drainage density for every point of the basin, defined as the ratio of the length of the network at the point (that is to say, the length of the channel network upstream from the point), to the cumulated upstream area in the same point: Dd =
L A
(4.1)
where L represents the length of the channel network and A is the contributing area. Dimensionally, this parameter is the inverse of a length. To execute the command from the main menu select: HortonMachine ⇒ Network related measures ⇒ h.DD or else click the icon of the toolbar that appears by checking: HortonMachine ⇒ Network related measures The toolbar with the h.DD icon is shown in figure 4.42.
Figure 4.42: The h.DD command icon.
The h.DD command can also be executed from the console command line: h.DD [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [–flowmformat ] –tca –tcamapset [–tcaformat ] –net – netmapset [–netformat ] –dd
–ddmapset [–ddformat ] [–usegui]
67
4. Analysis of the Extracted Catchment Basin
Example The execution of the command requires as input the drainage directions map, calculated either with h.flowdirection or h.draindir, the contributing areas map, calculated either with draindir or h.tca, and the channel network map, calculated with h.extractnetwork. The graphic interface of the command, requiring the names of the input and output maps, is shown in figure in figura 4.43. The resulting output map showing the drainage density is shown in figure 4.44.
Figure 4.43: h.DD. Graphic interface requiring the names of the input and output maps.
Figure 4.44: h.DD. Drainage density map. The Flanginec Basin.
68
4. Analysis of the Extracted Catchment Basin
4.2.4
Hacklength
The Hack length is the distance that separates every point of the basin from the watershed, calculated along the channel network. The calculation is carried out in an upstream direction, starting from an arbitrary point of the basin. At every fork of the network, the network branch with the larger contributing area is followed. If two confluent branches have the same contributing areas then one of the two or more directions is chosen casually. In this way the length of the main channel of the basin passing through the point is calculated. This distance represents the distance, projected onto the horizontal plane, to the watershed. To calculate this distance you must execute the h.hacklength command, from the main menu select: HortonMachine ⇒ Network related measures ⇒ h. hacklength or else click the icon of the toolbar that appears by checking: HortonMachine ⇒ Network related measures The toolbar with the h.hacklength icon is shown in figure 4.45.
Figure 4.45: The h.hacklength icon.
the command can also be executed from the console command line: h.hacklength [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [– flowformat ] –tca –tcamapset [–tcaformat ] –hack –outmapset [–outputformat ] [–usegui]
69
4. Analysis of the Extracted Catchment Basin
Example The execution of the command requires as input the drainage directions map, calculated either with h.flowdirection or h.draindir. The graphic interface of the command, where the input and output maps are specified, is shown in figure 4.46. A plot of the resulting output map is shown in figure 4.47.
Figure 4.46: h.hacklength. Graphic interface requiring the names of the input and output maps.
Figure 4.47: h.hacklength. Map of the distances to the watershed. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
4.2.5
Hacklength 3D
The h. hacklength command calculates the distance from the watershed as a projection onto the horizontal plane, the hacklength 3D command, on the other hand, calculates this distance taking into account the varying elevation of the local topography. To calculate this distance, the command to execute is h.hacklengths3D, from the main menu select: HortonMachine ⇒ Network related measures ⇒ h.hacklengths3D or else click on the icon of the toolbar that appears by checking: HortonMachine ⇒ Network related measures The toolbar with the h.hacklengths3D icon is shown in figure 4.48.
Figure 4.48: The h.hacklength3D icon.
The h. hacklengths3D command can also be executed from the console command line: h.hacklengths3D [–quiet] [–verbose] [–version] [–usage] –pit –pitmapset [–pitfor mat ] –flow –flowmapset [–flowformat ] –tca –tcamapset [–tcaformat ] –hackl3D –hackl3Dmapset [–hackl3Dformat ] [–usegui]
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4. Analysis of the Extracted Catchment Basin
Example The execution of the command requires as input the depitted elevation map, calculated with h.pitfiller, and the drainage directions map, calculated with the h.flowdirection or h.draindir. The graphic interface for the input of the input and output maps is shown in figure 4.49. A plot of the resulting output map is shown in figure 4.50.
Figure 4.49: h. hacklength3D. Graphic interface requiring the input of the names of the input and output maps.
Figure 4.50: h.hacklengths3D. Map of the distance from the watershed. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
4.2.6
Hackstream
The HackStream command gives the channel numeration of the hydrographic network according to Hack’s numeration. The main channel of the network is assigned the value of 1, the channels that flow into it are assigned the value of 2, and the branches that flow in to channels of order 2 are assigned the value of 3 and so on. To calculate this numeration the command to execute is h.hackstream, from the main menu select: HortonMachine ⇒ Network related measures ⇒ h.hackstream or else click on the icon of the toolbar that appears by checking: HortonMachine ⇒ Network related measures The toolbar with the h.hackstream icon is shown in figure 4.51.
Figure 4.51: The h.hackstream icon.
The h.hackstream command can also be executed from the console command line: h.hackstream [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [– flowformat ] –tca –tcamapset [–tcaformat ] –hacklength –hacklengthmapset [–hacklengthformat ] –net –netmapset [–netformat ] –hackstream –hackstreamapset [–hackstreamformat ] [–usegui]
Example The execution of the command requires, as input, the drainage directions map, calculated with either h.flowdirection or h.draindir, the contributing areas map, obtained with either h.draindir or h.tca, the Hack length map, calculated with h.hacklength, and the map of the channel network, obtained with the h.extractnetwork command. The new map generated will contain the channel 73
4. Analysis of the Extracted Catchment Basin
network with its channels numbered according to their Hack order. The graphic interface for requiring the names of the input and output maps is shown in figure 4.52. A plot of the resulting output map is shown in figure 4.53.
Figure 4.52: h.hackstream. Graphic interface requiring the names of the input and output maps.
Figure 4.53: h.hackstream. Map of the channels numbered according to Hack’s numeration order. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
4.2.7
Magnitudo
Magnitudo calculates the magnitude of a catchment area, defined as the number of sources upstream from every point. If the fluvial network is trifurcated (one node with two channels entering and one exiting), then there is a bijective mapping between the number of sources and the number of channels: hc = 2ns − 1
(4.2)
where hc is the number of channels and ns is the number of sources; the magnitude is therefore also an indicator of the contributing area. The command to execute is h.magnitudo, from the main menu select: HortonMachine ⇒ Network related measures ⇒ h.magnitudo or else click the icon of the toolbar that appears by checking: HortonMachine ⇒ Network related measures The toolbar with the h.magnitudo icon is shown in figure 4.54.
Figure 4.54: The h.magnitudo icon.
The h.magnitudo command can also be executed from the console command line: h.magnitudo [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [– flowmformat ] –magnitudo –magnitudomapset [–magnitudoformat ] [–usegui]
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4. Analysis of the Extracted Catchment Basin
Example The execution of the command requires, as input, the drainage directions map, calculated with either h.flowdirection or h.draindir. The graphic interface, where the input and output maps are specified, is shown in figure 4.55. A plot of the resulting map is shown in figure 4.56.
Figure 4.55: h.magnitudo. Graphic interface where the names of the input and output maps are specified.
Figure 4.56: h.magnitudo. Map of the number of sources upstream from every point, considering the network to be formed by every point of the catchment basin. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
4.2.8
Seol
The seol command allows you to identify the nodes of the channel network. You are given the choice to select a map, form the ones generated previously, and assign to the channel nodes the value that the selected map assumes in these points. For example, by choosing the elevation map the result is the altimetric value of the DEM in correspondence of the nodes. The command to execute is h.seol, from the main menu select: HortonMachine ⇒ Network related measures ⇒ h.seol or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Network related measures The toolbar with the h.seol icon is shown in figure 4.57.
Figure 4.57: The h.seol icon.
The h.seol command can also be launched from the console command line: h.seol [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [–flowformat ] –quantity –quantitymapset [–quantityformat ] –net –netmapset [–netformat ] –seol –seolmapset [–seolformat ] [–usegui]
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4. Analysis of the Extracted Catchment Basin
Example To execute the command you need to input the drainage directions map, calculated either with h.flowdirection or h.draindir, the map of the quantity you want to extract, and the map of the channel network, obtained with h.extractnetwork. The graphic interface where the input and output maps are specified is shown in figure 4.58.
Figure 4.58: h.seol. Graphic interface where the names of the input and output maps are specified.
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4. Analysis of the Extracted Catchment Basin
4.2.9
Strahler
The Strahler command allows you to number the channel network channels according to Strahler. This numeration assigns order 1 to the source, when two branches of the same order, n, meet they form a channel of a greater order, n + 1. When two branches of different order, n and m with n > m, meet the order of the channel they form is that of the greater of the two, n. The command to execute is h.strahler. From the main menu select: HortonMachine ⇒ Network related measures ⇒ h.strahler or else click the icon of the toolbar that appears by checking: HortonMachine ⇒ Network related measures The toolbar with the h.strahler icon is shown in figure 4.59.
Figure 4.59: The h.strahler icon.
The h.strahler command can also be executed from the console command line: h.strahler [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [–flow format ] [–net ] [–netmapset ] [–netformat ] –mode –strahler –strahlermapset [–strahlerformat ] [–usegui]
Example The numeration can be carried out considering either the entire basin or only the channel network. In the first case, the execution of the command requires, as input, the drainage directions map, calculated either with h.flowdirection or h.draindir. The graphic interface where the input and output maps are specified is shown in figure 4.60. A plot of the resulting output map is shown in figure 4.61. 79
4. Analysis of the Extracted Catchment Basin
Figure 4.60: h.strahler. Graphic interface where the names of the input and output maps are specified.
Figure 4.61: h.strahler. Map of the basin numbered according to Strahler. The Flanginec Basin.
In the second case, the drainage directions map, calculated either with h.flowdirection or h.draindir, and the map of the hydrographic network, calculated with h.extractnetwork, are required as input. The graphic interface where the input and output maps are specified is shown in figure 4.62. The resulting output map is plotted in figure 4.63.
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4. Analysis of the Extracted Catchment Basin
Figure 4.62: h.strahler. Graphic interface where the names of the input and output maps are specified.
Figure 4.63: h.strahler. Map of the channel network numbered according to Strahler’s order. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
4.2.10
Netnumbering
The Netnumbering command allows you to number the channels of the channel network obtained earlier and to identify the basins that contribute to each one. Firstly, the program identifies the sources of the channels (the term source of the channel refers to the first point upstream from the channel), which are numbered in growing order. It then follows the network assigning to each pixel of the channel the value of its source until it reaches a confluence. If the new branch, which is formed downstream, is not yet processed, this is numbered and the program continues downstream until it reaches another confluence or the outlet. Once the network has been numbered the basins that drain into each single branch of the network are extrapolated. The command to execute is h.netnumbering, from the main menu select: HortonMachine ⇒ Network related measures ⇒ h.netnumbering or else click the icon of the toolbar that appears by checking: HortonMachine ⇒ Network related measures The toolbar with the h.netnumbering icon is shown in figure 4.64.
Figure 4.64: The h.netnumbering command icon.
The h.netnumbering command can also be executed from the console command line: h.netnumbering [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [–flowformat ] –net –netmapset [–netformat ] – netnumber –netnumbermapset [–netnumberformat ] –basin –basinmapset [–basinformat ] [–usegui]
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4. Analysis of the Extracted Catchment Basin
Example Before proceeding with the execution of the command, it is recommended that you recalculate the hydrographic network, inputting a threshold value which is not too low. In this way a hydrographic network is obtained which is not too dense, and the subbasins that will be extracted will not be too many (in this example a threshold value of 1000 pixels was set to the tca map). Each extracted subbasin is assigned a value equal to the number that identifies the corresponding channel. The execution of the command requires as input the drainage directions map, calculated either with h.flowdirection or h.draindir, and the hydrographic network map, obtained with h.extractnetwork. The graphic interface where the input and output maps are specified is shown in figure 4.65. Figure 4.66 shows the network map with its numbered branches and 4.67 shows the map of the extracted subbasins.
Figure 4.65: h.netnumbering. Graphic interface where the names of the input and output maps are specified.
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4. Analysis of the Extracted Catchment Basin
Figure 4.66: h.netnumbering. Map of the numbered hydrographic network. The Flanginec Basin.
Figure 4.67: h.netnumbering. Map of the extracted subbasins. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
4.2.11
NetDif
Netdif allows you to calculate the difference between two successive nodes of the network of some prefixed quantity, for example the elevation. By inputting, for example, the map of the numbered channels obtained with h.netnumbering (but other choices are possible, for example, you could use the map of the channels numbered according to Strahler), a map of the differences in elevation calculated along the network between two successive nodes. In the new map, every point of the same channel will be assigned a value equal to the difference in elevation calculated. To execute h.netdif, from the main menu select: HortonMachine ⇒ Network related measures ⇒ h.netdif or else click on the icon of the toolbar that appears by checking: HortonMachine ⇒ Network related measures The toolbar with the h.netdif icon is shown in figure 4.68.
Figure 4.68: The h.netdif icon.
The h.netdif command can also be executed from the console command line: h.netdif [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [–flowformat ] –stream –streammapset [–streamformat ] –mapdiff –mapdiffmapset [–mapdiffformat ] –diff –diffmapset [–diffformat ] [–usegui]
Example To execute the command you need to input the drainage directions map, calculated either with h.flowdirection or h.draindir, the map of where to calculate the differences (a classification of the hydrographic network is necessary), in the specific example the map generated with h.netnumbering 85
4. Analysis of the Extracted Catchment Basin
is used, and the map of the quantities to be used to calculate the differences, in the example the depitted elevation map obtained with h.pitfiller is used. In this way, a map of the channel network is obtained in which the channels are assigned the value of the difference in elevation between the nodes at the beginning and end of the channel branch. The graphic interface where the input and output maps are specified is shown in figure 4.69. The resulting output map is plotted in figure 4.70.
Figure 4.69: h.netdif. Graphic interface where the names of the input and output maps are specified.
Figure 4.70: h.netdif. Output map. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
The netdif command allows you to calculate the lengths of the single branches of the channel network by using the map of the distances of every point from the outlet, calculated with h.D2O, and the numbered network map, calculated with h.netnumbering, as input maps. The graphic interface where the input and output maps are specified is shown in figure 4.71. The resulting output map is plotted in figure 4.72.
Figure 4.71: h.netdif. Graphic interface for the input of the names of the input and output maps.
Figure 4.72: h.netdif. Map specifying the length of each channel of the network. The Flanginec Basin.
To obtain statistical information about the lengths, refer to paragraph 4.7.2. 87
4. Analysis of the Extracted Catchment Basin
4.3 4.3.1
DEM Manipulation SplitSubbasin
This command extracts the catchment subbasins of a the i-th order according to the hackstream numeration, [2]. Furthermore, it generates a new map of the channel network, where the channels are numbered according to their corresponding subbasins. The program allows you to decide which subbasins to extract in relation to the channel numbering obtained with h.hackstream. If, for example, you choose a hackstream order of two, then the program will extract subbasins of order 1 and 2. The program also requires a limit on the value of the contributing area so as to exclude subbasins which are smaller than the threshold value (subbasins that are not considered significant). The command to execute is h.splitsubbasin. To execute it, from the main menu select: HortonMachine ⇒ DEM Manipulation ⇒ h.splitsubbasin or else click the icon of the toolbar that appears by selecting: HortonMachine ⇒ DEM Manipulation
Figure 4.73: The h.splitsubbasin icon.
The h.splitsubbasin command can also be executed from the console command line: h.splitsubbasin [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [– flowformat ] –hackstream –hackstreammapset [–hackstreamformat ] –tca –tcamapset [–tcaformat ] –threshold –number –netnumber –netnumbermapset [–netnumberformat ] –subbasin –subbasinmap set [–subbasinformat ] [–usegui]
Example The execution of the command requires as input the drainage directions map, calculated with either h.flowdirection or h.draindir, the hackstream map, obtained with h.hackstream, and the 88
4. Analysis of the Extracted Catchment Basin
contributing areas map, obtained either with h.draindir or h.tca. In this example, a threshold value of 150 pixels is assigned to the contributing area, and the hackstream order is set to 2. Figure 4.74 shows the graphic interface where the input and output maps are specified. The resulting output map is plotted in figure 4.75.
Figure 4.74: h.splitsubbasin. Graphic interface where the names of the input and output maps are specified.
Figure 4.75: h.splitsubbasin. Map of the subbasins. The Flanginec Basin.
Once the map of the subbasins has been produced, it is possible, by means of the r.mapcalc command, to produce maps of the single subbasins and then proceed with their analysis. To carry out the calculation, you need to give r.mapcalc an expression of the type: 89
4. Analysis of the Extracted Catchment Basin
new map = if(condition satisfied, then assign the value from the map, else assign the null value) to extract basin no.46, for example, the expression to input is: basin46DTM = if($subbasin.test.m$ == 46, $DTM$, null) in this way a map called basin46DTM is generated in which the value from the DTM map is assigned to all those points with a value of 46 in the map of the subbasins (that is to say, within subbasin no.46), while the null value is assigned to all other points (that is to say, outside subbasin no.46). Figure 4.76 shows the r.mapcalc dialog box, figure 4.77 shows the resulting map. The value corresponding to the required subbasin can be obtained by querying the map of figure 4.75,(in this specific example the map is subbasin.test.m), by using the d.what.rast command, found in the Raster ⇒ Query raster maps menu.
Figure 4.76: r.mapclac. Dialog box where the expression to calculate is given.
There now follow other examples of subbasin extraction. Figure 4.79 shows the results obtained by imposing a threshold value of 150 pixels on the contributing area and a hackstream order of 3. Figure 4.78 shows the result obtained by increasing the contributing area threshold value to 1000 pixels and setting the hackstream order to 2.
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4. Analysis of the Extracted Catchment Basin
Figure 4.77: r.mapcalc. Map of the extracted subbasin, superimposed onto the aspect map, the channel network is also shown. The Flanginec Basin.
Figure 4.78: h.splitsubbasin. Map of the subbasins obtained by setting the tca threshold to 150 pixels and the hackstream order to 3.
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4. Analysis of the Extracted Catchment Basin
Figure 4.79: h.splitsubbasin. Map of the subbasins obtained by setting the tca threshold to 1000 pixels and the hackstream order to 2.
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4. Analysis of the Extracted Catchment Basin
4.4 4.4.1
Hillslope Analyses Hillslope to Channel Attribute
The Hillslope to channel attribute algorithm calculates, for every pixel, labeled P, which is not part of the channel network, the value of the attribute of the channel pixel, labeled Q, into which pixel P drains. In this way it is possible to assign to every basin slope the value of the channel branch into which it drains. To execute the command, from the main menu select: HortonMachine ⇒ Hillslope analyses ⇒ h.h2cA or else click the icon of the toolbar that appears by checking: HortonMachine ⇒ Hillslope analyses Figure 4.82 shows the toolbar with the h.h2cA icon.
Figure 4.80: The h.h2cA icon.
The h.h2cA command can also be executed from the console command line: h.h2cA [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [–flow format ] –net –netmapset [–netformat ] –attribute –attmapset [–attformat ] –h2c attribute – h2c attributemapset [–h2c attributeformat ] [–usegui]
Example In this example, it has been decided to assign to each slope the value of the gradient in correspondence of the channel into which the slope drains. To execute the command you need to input the drainage directions map, calculated either with h.flowdirection or h.draindir, and the channel network map, obtained with h.extactmetwork. The graphic interface, where the names of the input 93
4. Analysis of the Extracted Catchment Basin
and output maps are given, is shown in figure 4.81. The resulting output map is plotted in figure 4.82.
Figure 4.81: h.h2cA. Graphic interface where the names of the input and output maps are specified.
Figure 4.82: h.h2cA. Map obtained using the gradient map as the attribute. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
4.4.2
Hillslope to Channel Distance
The Hillslope to channel distance command calculates the projection onto the horizontal of the distance of each point of the basin not belonging to the channel network to the network itself. The calculation is carried out following the drainage directions. The command gives the choice of calculating the distance either in metres or in pixels. To execute the h.h2cD command, from the main menu select: HortonMachine ⇒ Hillsloe analyses ⇒ h.h2cD or else click the icon of the toolbar that appears by checking: HortonMachine ⇒ Hillslope analyses Figure 4.85 shows the toolbar with the h.h2cD icon.
Figure 4.83: The h.h2cD icon.
The h.h2cD command can also be executed from the console command line: h.h2cD [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [–flow format ] –net –netmapset [–netformat ] –h2c dist –h2c distmapset [–h2c distformat ] –mode [–usegui]
Example The execution of the command requires the input of the drainage directions map, calculated either with h.flowdirection or h.draindir, and the channel network map, obtained with h.extactnetwork. The graphic interface of the command, requiring the names of the input and output maps, is shown in figure 4.84. The resulting output map is shown in figure 4.85.
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4. Analysis of the Extracted Catchment Basin
Figure 4.84: h.h2cD. Graphic interface where the names of the input and output maps are specified.
Figure 4.85: h.h2cD. Hillslope to channel distance map. The Flanginec Basin.
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4.4.3
Hillslope to Channel Distance 3D
This command allows you to calculate the distance to the network taking account of the varying elevation of the local topography. The command to execute is h.h2cD3D, from the main menu select: HortonMachine ⇒ Hillslope analyses ⇒ h.h2cD3D or else click the icon of the toolbar that appears by checking: HortonMachine ⇒ Hillslope analyses Figure 4.88 shows the toolbar with the h.h2cD3D command icon.
Figure 4.86: The h.h2cD3D icon.
The h.h2cD3D command can also be executed from the console command line: h.h2cD 3D [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [– flowmformat ] –net –netmapset [–netformat ] –pit –pitmapset [–pitformat ] –h2c distmapset [–h2c distformat ] [–usegui]
Example The execution of the command requires the elevation map, calculated with h.pitfiller, the drainage directions map, calculated either with h.flowdirection or h.draindir, and the channel network map, obtained with h.extactmetwork. Figure 4.87 shows the graphic interface of the command where the names of the input and output maps are given. In figure 4.88 the resulting output map is plotted.
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4. Analysis of the Extracted Catchment Basin
Figure 4.87: h.h2cD3D. Graphic interface where the names of the input and output maps are specified.
Figure 4.88: h.h2cD3D. Hillslope to channel distance map. The Flanginec Basin.
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4.4.4
Tau
The Tau command calculates the bed shear stress due to surface runoff in every point of the basin, according to the following relation: τb =
g 2 kρ3 8ν c
!1 3
A ∗ S ∗ q − TS b 2 3
2+c 3
where: g is the acceleration due to gravity, k and c are parameters linked to the resistance coefficient, ρ is the density of water, ν is the kinematic viscosity of water, S is the local slope, q is rainfall per unit area, A is the contributing area, b is the drainage distance, and T is the transmissivity. The command to execute is h.tau, from the main menu select: HortonMachine ⇒ Hillslope analyses ⇒ h.tau or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Hillslope analyses Figure 4.89 shows the toolbar with the h.tau icon.
Figure 4.89: The h.tau icon.
The h.tau command can also be executed from the console command line: h.tau [–quiet] [–verbose] [–version] [–usage] –slope –slopemapset [–slope format ] –Ab –Abmapset [–Abformat critical value). A second map is generated which contains an aggregation of the eleven classes into four fundamental ones, indexed as follows: • 15 → non-channel valley sites (classes 70, 90, 30 ); • 25 → planar sites (class 10); • 35 → channel sites (class 100); • 45 → hillslope sites (classes 20, 40, 50, 60, 80); • 55 → ravine sites (class 110). The command to execute is h.gc, from the main menu select: HortonMachine ⇒ Hillslope analyses ⇒ h.gc or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Hillslope analyses Figure 4.92 shows the toolbar with the h.gc icon.
Figure 4.92: The h.gc icon.
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4. Analysis of the Extracted Catchment Basin
The command can also be executed from the console command line: h.gc [–quiet] [–verbose] [–version] [–usage] –slope –slopemapset [–slope format ] –net –netmapset [–netformat ] –cp9map –cp9mapmapset [–cp9mapformat ] –classes –classesmapset [–classesformat ] –aggclass –aggclassmapset [–aggclassformat ] –th grad
[–usegui]
Example The execution of the command requires the input of the slope map, calculated with the h.gradient command, the channel network map, obtained with h.extactmetwork, and the map of the nine Parson classes, calculated with the h.tc command. Furthermore, a threshold value to apply to the slope is required in order to identify the eleventh class. Figure 4.93 shows the graphic interface where the input and output maps are specified. Figures 4.94 and 4.95 show the resulting output maps.
Figure 4.93: h.gc. The graphic interface where the names of the input and output maps are given.
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4. Analysis of the Extracted Catchment Basin
Figure 4.94: h.gc. Map of the eleven classes. The Flanginec Basin.
Figure 4.95: h.gc. Map of the four classes. The Flanginec Basin.
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4.5 4.5.1
Hydro-Geomorphic Indexes and Relations Rescaled Distance
This command allows you to determine the rescaled distance of each pixel from the basin outlet. This distance can be defined by the following relation:
x0 = xc + rxh
(4.3)
where x0 is the rescaled distance of a point P . The rescaled distance is made up of two parts: a distance xh from the point, P , to the channel measured along the drainage directions, and a distance from the channel point to the outlet. r is a weight, generally > 1, assigned to the distance on the slopes. This weight parameter can be thought of as the ratio of the water velocity in the channels and on the slopes. The command to execute is h.rescaleddistance, from the main menu select: HortonMachine ⇒ Hydro-Geomorphic Indexes and Relations ⇒ h.rescaleddistance or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Hydro-Geomorphic Indexes and Relations Figure 4.96 shows the toolbar with the h.rescaleddistance icon.
Figure 4.96: The h.rescaleddistance icon.
The h.rescaleddistance command can also be executed from the console command line: h.rescaleddistance [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [–flowmformat ] –net –netmapset [–netformat ] –rescaledistance –rescdistmapset –rescdistformat –r [–usegui] 104
4. Analysis of the Extracted Catchment Basin
Example The execution of the command requires the input of the drainage directions map, calculated using the h.flowdirection or h.draindir commands, and the hydrographic network map, obtained with the h.extactmetwork command. Figure 4.97 shows the graphic interface where the input and output maps are specified. The resulting output map is plotted in figure 4.98.
Figure 4.97: h.rescaleddistance. The graphic interface where the names of the input and output maps are given.
Figure 4.98: h.rescaleddistance. Rescaled distance map. The Flanginec Basin
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4.5.2
Rescaleddistance 3D
This command calculates the rescaled distance of every point of the basin from the outlet, taking into account the varying elevation, as documented by the DEM. The command to execute is h.rescaleddistance3D, from the main menu select: HortonMachine ⇒ Hydro-Geomorphic Indexes and Relations ⇒ h.rescaleddistance3D or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Hydro-Geomorphic Indexes and Relations Figure 4.99 shows the toolbar with the h.rescaleddistance3D icon.
Figure 4.99: The h.rescaleddistance3D icon.
The h.rescaleddistance3D command can also be executed from the console command line: h.rescaleddistance3D [–quiet] [–verbose] [–version] [–usage] –pit –pitmapset [– pitformat ] –flow –flowmapset [–flowmformat ] –net –netmapset [–netformat ] –rescaledistance3D –rescdist3Dmapset –rescdist3Dformat –r [–usegui]
Example The execution of the command requires the input of the elevation map, calculated with h.pitfiller, the drainage directions map, calculated with the h.flowdirection or h.draindir commands, and the channel network map, obtained with the h.extactmetwork command. Figure 4.100 shows the graphic interface where the input and output maps are specified. The resulting output map is plotted in figure 4.101.
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Figure 4.100: h.rescaleddistance3D. The graphic interface where the names of the input and output maps are given.
Figure 4.101: h.rescaleddistance3D. The rescaled distance map. The Flanginec Basin
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4.5.3
Topindex
Topindex allows you to calculate the topographic index of a basin. This is defined as:
log(A/s) − µ where: A is the contributing area in a point, s is the slope, and µ =
(4.4) 1 N
P
i log(Ai /si )
is the average
value of the logarithm over the entire basin (N is the number of pixels in the basin). This index allows you to identify the points that generate dunnian surface runoff in a similar way. Points with a higher topographic index saturate before points with lower topographic index values. The command to execute is h.topindex, from the main menu select: HortonMachine ⇒ Hydro-Geomorphic Indexes and Relations ⇒ h.topindex or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Hydro-Geomorphic Indexes and Relations Figure 4.102 shows the toolbar with the h.topindex icon.
Figure 4.102: The h.topindex icon.
The h.topindex command can also be executed from the console command line: h.topindex [–quiet] [–verbose] [–version] [–usage] –tca –tcamapset [–tcaformat ] –slope –slopemapset [–slopeformat ] –topindex –topindexmapset –topindexformat [–usegui]
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4. Analysis of the Extracted Catchment Basin
Example The execution of the command requires the input of the contributing areas map, calculated with h.draindir or with h.tca, and the slope map, obtained with h.gradient. Figure 4.103 shows the graphic interface where the input and output maps are specified. The resulting output map is plotted in figure 4.104.
Figure 4.103: h.topindex. The graphic interface where the names of the input and output maps are given.
Figure 4.104: h.topindex. Map of the topographic index. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
4.6 4.6.1
Basin Related Analyses Diameters
Diameters calculates the diameter of a catchment basin. The term diameter refers to the distance between the outlet and the furthest point from it. The calculation is repeated considering every point as the outlet. The command to execute is h.diameters, from the main menu select: HortonMachine ⇒ Basin related analyses ⇒ h.diameters or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Basin related analyses Figure 4.105 shows the toolbar with the h.diameters icon.
Figure 4.105: The h.diameters icon.
The h.diameters command can also be executed from the console command line: h.diameters [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [– flowmformat ] –diameters –diametersmapset [– diametersformat ] –mode [–usegui]
Example The execution of the command requires the input of the drainage directions map, calculated with either h.flowdirection or h.draindir. The command calculates the distance either in the source points or in all the points of the basin. In the following example, the latter case is shown. Figure 4.106 shows the graphic interface where the input and output maps are specified. The resulting output map is plotted in figure 4.107.
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4. Analysis of the Extracted Catchment Basin
Figure 4.106: h.diameters. The graphic interface where the names of the input and output maps are given.
Figure 4.107: h.diameters. Resulting map. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
4.6.2
Euclidean Distance
This command calculates the euclidean distance of each point of the basin from the outlet. This distance is an elementary application of Pythagoras’ Theorem. The command to execute is h.dist euclidea, from the main menu select: HortonMachine ⇒ Basin related analyses ⇒ h.dist euclidea or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Basin related analyses Figure 4.108 shows the toolbar with the h.dist euclidea icon.
Figure 4.108: The h.dist euclidea icon.
The h.dist euclidea command can also be executed from the console command line: h.dist euclidea [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [– flowmformat ] –dist euclidea –dist euclideamapset [–dist euclideaformat ] [–usegui]
Example The execution of the command requires the input of the drainage directions map, calculated either with h.flowdirection or h.draindir. Figure 4.109 shows the graphic interface where the input and output maps are specified. The resulting output map is plotted in figure 4.110.
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4. Analysis of the Extracted Catchment Basin
Figure 4.109: h.dist euclidea. The graphic interface where the names of the input and output maps are given.
Figure 4.110: h.dist euclidea. Euclidean distance map. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
4.6.3
Principal axes
Principal axes calculates the moment of inertia of the hydrographic basin. This moment is calculated with respect to the principal axes of the basin, considering the basin as a two-dimensional body of uniform mass. The program calculates two maps, one with the maximum moment of inertia and the other with the minimum moment of inertia. To execute h.principal axes, from the main menu select: HortonMachine ⇒ Basin related analyses ⇒ h.principal axes or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Basin related analyses Figure 4.111 shows the toolbar with the h.principal axes icon.
Figure 4.111: The h.principal axes icon.
The h.principal axes command can also be executed from the console command line: h.principal axes [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [–flowmformat ] –tca –tcamapset [–tcaformat ] – principal axes1 –principal axesmapset1 [–principal axes format1 ] –principal axes2 –principal axesmapset2 [–principal axesformat2 ] [–usegui]
Example The execution of the command requires the input of the drainage directions map, calculated with either h.flowdirection or h.draindir, and the contributing area map, obtained with either h.draindir or h.tca. Figure 4.112 shows the graphic interface where the input and output maps are specified. Figure 4.113 and figure 4.114 show the resulting maps. 114
4. Analysis of the Extracted Catchment Basin
Figure 4.112: h.principal axes. The graphic interface where the names of the input and output maps are given.
Figure 4.113: h.principal axes. Map of the maximum moment. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
Figure 4.114: h.principal axes. Map of the minimum moment. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
4.6.4
Mean drop
Mean drop calculates the average value of a chosen quantity, this value is calculated in every point of the basin, going from upstream to downstream. The calculation is made using the following relation: X
Bj = (
Bi )j /Aj − Bj
(4.5)
i
B represents the value of which to calculate the average in the j-th point, Aj is the contributing area in the point. The summation in i varies in all the points upstream of the point j. The command to execute is h.mean drop, from the main menu select: HortonMachine ⇒ Basin related analyses ⇒ h.mean drop or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Basin related analyses Figure 4.115 shows the toolbar with the h.mean drop icon.
Figure 4.115: The h.mean drop icon.
The h.mean drop command can also be executed from the console command line: h.mean drop [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [– flowmformat ] –tca –tcamapset [–tcaformat ] – summ –summmapset [–summformat ] –mean drop –mean dropmapset [–mean dropformat ] [–usegui]
Example To execute the command you will need to input the drainage directions map, calculated either with h.flowdirection or h.draindir, the contributing areas map, obtained with either h.draindir or h.tca, and the map of the quantity from which to calculate the average, in the example, the DEM 117
4. Analysis of the Extracted Catchment Basin
map obtained with the h.pitfiller command is used. Figure 4.116 shows the graphic interface where the input and output maps are specified. Figure 4.117 shows the resulting map.
Figure 4.116: h.mean drop. The graphic interface where the names of the input and output maps are given.
Figure 4.117: h.mean drop. Map showing the average value of the elevation. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
4.7 4.7.1
Statistics Sumdownstream
Sumdownstream calculates the sum of the values of a specified quantity from every point to the outlet, during the calculation the drainage directions are followed. The final result is therefore a matrix of values containing the sum of the input quantity in all upstream points:
S=
X
Aj
(4.6)
ij
where i is the point of interest and the j index varies on all the points upstream of the point of interest. The command to execute is h.sumdownstream. To execute the command, from the main menu select: HortonMachine ⇒ Statistics ⇒ h.sumdownstream or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Statistics
Figure 4.118: The h.sumdownstream icon.
The h.sumdownstream command can also be executed from the console command line: h.sumdownstream [–quiet] [–verbose] [–version] [–usage] –flow –flowmapset [–flowformat ] –summap –summapset [–sumformat ] –output –outputmapset [–outputformat ] [– usegui]
Example To execute the command it is necessary to input the drainage directions map, calculated with either h.flowdirection or h.draindir, and the map of the quantity to sum. With this command it is possible, for example, to obtain the contributing areas map. This is possible by using a map 119
4. Analysis of the Extracted Catchment Basin
with a value of 1 over the entire area of the basin, such a map can be created with the r.mapcalc command. It is sufficient to input an expression of the following format: new map = if(condition satisfied, then assign null value, else assign value equal to 1)
in the specific example, the expression to give is: map1 = if($pit.test.m$ == null, null, 1) in this way a map, map1, is created with a ”null value” in correspondence of a ”null value” in the pit.test.m map (and therefore outside the basin), and 1 in all other points (and therefore inside the basin). Figure 4.119 shows the r.mapcalc command dialog box, figure 4.120 shows the resulting map.
Figure 4.119: r.mapclac. Dialog box where the expression to be calculated is given.
Figure 4.120: r.mapcalc. Map with a value of 1 in correspondence of the basin and a ”null value” outside of it. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
Figure 4.121 shows the graphic interface of the h.sumdowndream command, here the input and output maps are specified. Figure 4.122 shows the resulting map.
Figure 4.121: h.sumdowndream. The graphic interface where the names of the input and output maps are given.
Figure 4.122: h.sumdownstream. Map of the contributing areas calculated with the aid of the r.mapcalc command. The Flanginec Basin.
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4. Analysis of the Extracted Catchment Basin
4.7.2
Coupledfieldmoments
This command calculates a scatter plot of the data set contained in one raster with respect to the data set contained in another raster. Basically, an R → R map is created from an R2 → R2 correspondence in which every point of a two-dimensional set is mapped onto a second twodimensional set according to position (two quantities in the same position in two different rasters are made correspond, so producing, usually in an x,y diagram, a cloud of points variably scattered). The data of the first set, which are considered the ”independent variable”, are then grouped by value into a set number of intervals. The average of this (first) variable is then calculated for each interval. To each interval there corresponds a certain number of values of the second set, of which the average can be calculated, as well as a set number of moments, these moments can be centred if the mode of binning is ”Histogram”, or non-centred in ”Moment” mode. If, for example, the assigned number of intervals is less than 1, the data are subdivided into data classes having the exact same abscissa (a fact that can produce a very large number of elements). The program generates a text file subdivided in columns (the number of which is equal to the moment order + 2), containing the following information: 1) the number of elements in each interval (of the first quantity); 2) the average value of the abscissa data (of the second quantity); 3) the average value of the ordinate data; n+2) the n-th moment of the ordinate data. The file is created in the working mapset, in the hortonmachine directory. The program also produces a second file which contains columns 2) and 1) from the first file. This second file has a *.hdsc extension and can be viewed with the command d.simplechart. The command to execute is h.cb. To execute it, from the main menu select: HortonMachine ⇒ Statistics ⇒ h.cb or else click the icon from the toolbar that appears by checking: HortonMachine ⇒ Statistics The h.cb command can also be executed from the console command line: h.cb [–quiet] [–verbose] [–version] [–usage] –map1 –map1mapset [–map1 format ] –map2 –map2mapset [–map2format ] –coupled –bins –firstmoment –secondmoment –bintype –binmode –base [–usegui]
Figure 4.123: The h.cb icon.
Example The execution of the command requires the input of the map of the independent variable, the map of the dependent variable, the number of intervals, and the first and last moment to calculate. Figure 4.124 shows the graphic interface where the input and output maps, the number of intervals, and the first and last moments are specified.
Figure 4.124: h.cb. The graphic interface where the names of the input and output maps are given. The number of intervals, and the first and last moments are also specified.
For example, you could calculate the mean rescaled distance of every subbasin as calculated with h.splitsubbasin.
In this case the independent variable is represented by the map of the
subbasins, while the dependent variable is the map of the rescaled distances, as calculated with 123
4. Analysis of the Extracted Catchment Basin
h.rescaleddistance. The number of intervals in which to divide the independent variable has been set to 65, this is the number of subbasins that were extracted, the value is known as the map generated by splitsubbasin was analyzed earlier. In this way the program calculates the mean rescaled value for each subbasin.
Figure 4.125: h.cb. The graphic interface where the names of the input and output maps are given.
At this point it is possible to view the results produced in graph format, just select the command d.simplechart from the Extra menu, and choose to open the file in the hortonmachine directory, in the example given it is numresc.hdsc. The graph shown in figure 4.126 appears. The properties of the graph can be modified by right-clicking on the graph and selecting Properties from the popup menu that appears. Figure 4.127 shows the popup menu while figure 4.128 shows the properties dialog box. Finally, figure 4.129 shows the resulting graph after having modified the properties.
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4. Analysis of the Extracted Catchment Basin
Figure 4.126: d.simplechart. Graph of the mean rescaled distance for each subbasin.
Figure 4.127: d.simplechart. Popup menu where the graph properties can be selected.
Figure 4.128: d.simplechart. The properties dialog box.
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4. Analysis of the Extracted Catchment Basin
Figure 4.129: d.simplechart. Graph of the mean rescaled distance for each subbasin.
126
4. Analysis of the Extracted Catchment Basin
With the h.cb command it is possible to calculate many other relationships, for example, the amplitude function, which represents the number of pixels of the hydrographic basin which find themselves at the same distance from the outlet. This quantity can be calculated with the distance to outlet data, calculated with h.D2O, and hypothesizing that the speed of the water flow on the slopes and in the network is the same, or else the quantity can be calculated with the rescaled distance data, calculated with h.rescaleddistance and considering different speeds for the channels and the slopes. To calculate the ”standard” amplitude function, you only need to input the distance map, as calculated with h.D2O, both as the independent variable and the dependent variable. In this way the mean distance is calculated in each interval. Figure 4.130 shows the h.cb command dialog box, the graph obtained, by using the d.simplechart command, is shown in figure figure 4.131.
Figure 4.130: h.cb. The graphic interface where the names of the input and output maps are given.
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4. Analysis of the Extracted Catchment Basin
Figure 4.131: d.simplechart. Graph of the standard amplitude function calculated using the map of the distances to the outlet calculated with h.D2O.
In order to calculate the rescaled amplitude function you must input the rescaled distance map, calculated with h.rescaleddistance, both as the independent variable and the dependent variable. Two examples now follow, in the first the ratio between network velocity and slope velocity,(r ), was set at 100, in the second example it was set at 20. Figure 4.132 shows the h.cb command dialog box, the rescaled distance is being used and r=100. Figure 4.133 shows the resulting graph obtained with the d.simplechart command.
Figure 4.132: h.cb. Graphic interface where the input and output maps are specified.
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4. Analysis of the Extracted Catchment Basin
Figure 4.133: d.simplechart. Graph of the rescaled amplitude function calculated using the distance to outlet map as calculated with h.rescaleddistance, r=100.
Figure 4.134 shows the h.cb dialog box, the rescaled distance is again used but r=20, the resulting graph, obtained with d.simplechart, is shown in figure 4.135.
Figure 4.134: h.cb. Graphic interface where the input and output maps are specified.
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4. Analysis of the Extracted Catchment Basin
Figure 4.135: d.simplechart. Graph of the rescaled amplitude function, calculated using the distance to outlet map as calculated with h.rescaleddistance, r=20.
130
Bibliography [1] A. Antonello, S. Franceschi, R. Rigon: JGrass 2.0 Manuale Utente, Gennaio 2006. [2] R. Rigon, E. Ghesla, C. Tiso, A. Cozzini: The Horton Machine: a system for DEM analysis, Dipartimento Ingegneria Civile ed Ambientale, 1999 - 2005. [3] Orlandini S., Moretti G., Franchini M.: Path-based methods for the determination of non dispersive drainage directions in grid-based elevation models., Water Resources Research, Vol. 39, NO. 6, 1144, doi:10.1029/2002WR001639, 2003.
