What is Geomorphometry?
                                A Brief Introduction - I




             Riccardo Rigon, with num...
Delineation of the Hydrographic Catchment




                                             Objectives




                ...
Delineation of the Hydrographic Catchment




                                             Objectives

       •To   introd...
Delineation of the Hydrographic Catchment




                                             Objectives

       •To   introd...
Delineation of the Hydrographic Catchment




                                             Objectives

       •To   introd...
Delineation of the Hydrographic Catchment




                                             Objectives

       •To   introd...
Delineation of the Hydrographic Catchment




                                  The Discretisation of the Terrain
  from T...
Delineation of the Hydrographic Catchment




                                  A grid is a geographical space of equidist...
Delineation of the Hydrographic Catchment




                  The Primary Topographic Attributes:

            - Altitud...
Delineation of the Hydrographic Catchment




                                              Altitude

                    ...
Delineation of the Hydrographic Catchment




       Altitude: in Hydrological Modelling the height data is not
       eno...
Delineation of the Hydrographic Catchment




                      Statistical Properties: DISTRIBUTION CURVES


        ...
Delineation of the Hydrographic Catchment




                                             Gradient




                  ...
Delineation of the Hydrographic Catchment




                                             Gradient
                      ...
Delineation of the Hydrographic Catchment




                                             Gradient
                      ...
Delineation of the Hydrographic Catchment




                                              Gradient
                     ...
Delineation of the Hydrographic Catchment



                                             Gradient




                   ...
Delineation of the Hydrographic Catchment



                                             CURVATURE:

        as the word ...
Delineation of the Hydrographic Catchment



                                             CURVATURE:

        as the word ...
Delineation of the Hydrographic Catchment



                                             CURVATURE:

        as the word ...
Delineation of the Hydrographic Catchment



                                             CURVATURE:

        as the word ...
Delineation of the Hydrographic Catchment



                                             CURVATURE:

        as the word ...
Delineation of the Hydrographic Catchment



                                             CURVATURE:

        as the word ...
Delineation of the Hydrographic Catchment




              CURVATURE: once some curves have been
              identified...
Delineation of the Hydrographic Catchment




   Curves along the flowlines are defined by Longitudinal
   Curvature.

   ...
Delineation of the Hydrographic Catchment




                                        CURVATURE
                The compos...
Delineation of the Hydrographic Catchment




                        The main derived quantities are:

         •Drainage...
Delineation of the Hydrographic Catchment




                             It’s easy to say Drainage Directions




      ...
Delineation of the Hydrographic Catchment
  from Tarboton: www.cuahsi.org




                                            ...
Delineation of the Hydrographic Catchment




                                      It’s easy to say Drainage Directions
 ...
Delineation of the Hydrographic Catchment




                                             21

 Riccardo Rigon

Friday, Se...
Delineation of the Hydrographic Catchment



                                     Drainage Directions




                ...
Delineation of the Hydrographic Catchment




                 From DEM to Hydrographic Catchment

      Once the drainage...
Delineation of the Hydrographic Catchment



                                     Drainage Directions




                ...
Delineation of the Hydrographic Catchment



                                The Hydrographic Network: where do the
      ...
Delineation of the Hydrographic Catchment



                                The Hydrographic Network: where do the
      ...
Delineation of the Hydrographic Catchment



                                The Hydrographic Network: where do the
      ...
Delineation of the Hydrographic Catchment



                                       The Hydrographic Network: where do the...
Delineation of the Hydrographic Catchment



               The Hydrographic Network: where do the
                       ...
Delineation of the Hydrographic Catchment



                                The Hydrographic Network: where do the
      ...
Delineation of the Hydrographic Catchment



                       The Hydrographic Network: where do the
               ...
Delineation of the Hydrographic Catchment




             Hydrographic Catchments after SCHUMM




                      ...
Delineation of the Hydrographic Catchment




                                         Hydrographic Catchments
  from Fouf...
Delineation of the Hydrographic Catchment



                     Hydrographic Catchments in digital
 From Arc Hydro




 ...
What is Geomorphometry? A Brief Introduction - I




                                   Digital Watershed

        DEFINIT...
What is Geomorphometry? A Brief Introduction - I




                                   Digital Watershed
                ...
What is Geomorphometry? A Brief Introduction - I




                                   Digital Watershed

      System t...
What is Geomorphometry? A Brief Introduction - I




                 Digital Watershed - beyond Hydrology

     !
       ...
What is Geomorphometry? A Brief Introduction - I




                Digital Watershed - beyond Hydrology


        !
    ...
What is Geomorphometry? A Brief Introduction - I




                                   Digital Watershed

         !
    ...
What is Geomorphometry? A Brief Introduction - I




                                   Digital Watershed

      1.System ...
What is Geomorphometry? A Brief Introduction - I




                                   Digital Watershed


     2.Integra...
Delineation of the Hydrographic Catchment
  from Tarboton: www.cuahsi.org




                                            ...
Delineation of the Hydrographic Catchment
  from Tarboton: www.cuahsi.org




                                            ...
Delineation of the Hydrographic Catchment
  from Tarboton: www.cuahsi.org




                                            ...
Delineation of the Hydrographic Catchment
  from Tarboton: www.cuahsi.org




                                            ...
Delineation of the Hydrographic Catchment
  from Tarboton: www.cuahsi.org




                                            ...
Delineation of the Hydrographic Catchment




                                 Strahler Numbering
                        ...
Delineation of the Hydrographic Catchment




               Strahler Numbering and Horton’s Laws




                    ...
Delineation of the Hydrographic Catchment




               Strahler Numbering and Horton’s Laws

                       ...
Delineation of the Hydrographic Catchment




               Strahler Numbering and Horton’s Laws

                       ...
Delineation of the Hydrographic Catchment




               Strahler Numbering and Horton’s Laws

                       ...
Delineation of the Hydrographic Catchment




               Strahler Numbering and Horton’s Laws
                        ...
Delineation of the Hydrographic Catchment




               Strahler Numbering and Horton’s Laws
                        ...
Delineation of the Hydrographic Catchment




                                  Strahler Numbering and Horton’s Laws
  fro...
Delineation of the Hydrographic Catchment




                                  Strahler Numbering and Horton’s Laws
  fro...
Delineation of the Hydrographic Catchment




                                  Strahler Numbering and Horton’s Laws
  fro...
Delineation of the Hydrographic Catchment




                                  Strahler Numbering and Horton’s Laws
  fro...
Delineation of the Hydrographic Catchment




      The distance of every point of a catchment from
                  the ...
Delineation of the Hydrographic Catchment




                  The distance of every point of a catchment from
          ...
Delineation of the Hydrographic Catchment




                                                                            ...
What is Geomorphometry? A Brief Introduction - I




                                Numbering in JGrass


               ...
What is Geomorphometry? A Brief Introduction - I




                                 Numbering in JGrass

   Network     ...
What is Geomorphometry? A Brief Introduction - I




                                 Numbering in JGrass


   Network    ...
What is Geomorphometry? A Brief Introduction - I




                                Numbering in JGrass



   Network lev...
What is Geomorphometry? A Brief Introduction - I




                                Numbering in JGrass




   Network le...
What is Geomorphometry? A Brief Introduction - I




                                Numbering in JGrass




   Network le...
Delineation of the Hydrographic Catchment




                                   Drainage Density
  from Tarboton: www.cua...
Delineation of the Hydrographic Catchment




                                   Drainage Density




                    ...
Delineation of the Hydrographic Catchment




The Distance of the Points on the Slopes from the
             Hydrographic ...
Delineation of the Hydrographic Catchment




                             What happens on the slopes?




               ...
Delineation of the Hydrographic Catchment


     Amplitude Function




                                                  ...
Delineation of the Hydrographic Catchment




                       Leopold  Maddock 1953:
              Relationships be...
Delineation of the Hydrographic Catchment




                       Leopold  Maddock 1953:
              Relationships be...
Delineation of the Hydrographic Catchment




                       Leopold  Maddock 1953:
              Relationships be...
Delineation of the Hydrographic Catchment




                                             P [A  a] = a−β f (a/AT )




  ...
Delineation of the Hydrographic Catchment




                               Area - Slope Relationship
                   ...
Delineation of the Hydrographic Catchment




                        Hydrologic Flows within the Slopes




             ...
Delineation of the Hydrographic Catchment




                        Hydrologic Flows within the Slopes



              ...
Delineation of the Hydrographic Catchment




                               Area - Slope Relationship
                   ...
Delineation of the Hydrographic Catchment




                        Hydrologic Flows within the Slopes



              ...
Delineation of the Hydrographic Catchment




                               Area - Slope Relationship
                   ...
Delineation of the Hydrographic Catchment




                                The Topographic Index


                    ...
Delineation of the Hydrographic Catchment



       The Topographic
            Index




                                ...
Delineation of the Hydrographic Catchment




                                The Topographic Index




                  ...
Delineation of the Hydrographic Catchment




                                        List of Symbols
                Symb...
Delineation of the Hydrographic Catchment




                                 Thank You for Your Attention.



          ...
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2 hydro-geomorphology

  1. 1. What is Geomorphometry? A Brief Introduction - I Riccardo Rigon, with numerous contributions “stolen” from D. Tarboton Friday, September 10, 2010
  2. 2. Delineation of the Hydrographic Catchment Objectives 2 Riccardo Rigon Friday, September 10, 2010
  3. 3. Delineation of the Hydrographic Catchment Objectives •To introduce the concepts correlated with the delineation of a hydrographic catchment 2 Riccardo Rigon Friday, September 10, 2010
  4. 4. Delineation of the Hydrographic Catchment Objectives •To introduce the concepts correlated with the delineation of a hydrographic catchment •To apply some simple hydrological balances at slope scale 2 Riccardo Rigon Friday, September 10, 2010
  5. 5. Delineation of the Hydrographic Catchment Objectives •To introduce the concepts correlated with the delineation of a hydrographic catchment •To lay a theoretical base for the successive lectures on JGrass •To apply some simple hydrological balances at slope scale 2 Riccardo Rigon Friday, September 10, 2010
  6. 6. Delineation of the Hydrographic Catchment Objectives •To introduce the concepts correlated with the delineation of a hydrographic catchment •To define the concept of a digital catchment •To lay a theoretical base for the successive lectures on JGrass •To apply some simple hydrological balances at slope scale 2 Riccardo Rigon Friday, September 10, 2010
  7. 7. Delineation of the Hydrographic Catchment The Discretisation of the Terrain from Tarboton: www.cuahsi.org 3 Riccardo Rigon Friday, September 10, 2010
  8. 8. Delineation of the Hydrographic Catchment A grid is a geographical space of equidistant cells. Each cell contains a value, for example, of altitude. from Tarboton: www.cuahsi.org 4 Riccardo Rigon Friday, September 10, 2010
  9. 9. Delineation of the Hydrographic Catchment The Primary Topographic Attributes: - Altitude - Slope - Curvature 5 Riccardo Rigon Friday, September 10, 2010
  10. 10. Delineation of the Hydrographic Catchment Altitude z = f (x, y) 6 Riccardo Rigon Friday, September 10, 2010
  11. 11. Delineation of the Hydrographic Catchment Altitude: in Hydrological Modelling the height data is not enough. It is necessary to eliminate all the depressions that can form in the grid. PitFiller 7 Riccardo Rigon Friday, September 10, 2010
  12. 12. Delineation of the Hydrographic Catchment Statistical Properties: DISTRIBUTION CURVES PH>h Torrent Longo (Trentino, ITALY) 1 0.8 0.6 0.4 0.2 hm 1200 1400 1600 1800 2000 2200 2400 CoupledFieldsMoments 8 Riccardo Rigon Friday, September 10, 2010
  13. 13. Delineation of the Hydrographic Catchment Gradient 9 Riccardo Rigon Friday, September 10, 2010
  14. 14. Delineation of the Hydrographic Catchment Gradient ∂z ∂z Gradients fy = ∂y fx = ∇z = (fx , fy ) ∂x 9 Riccardo Rigon Friday, September 10, 2010
  15. 15. Delineation of the Hydrographic Catchment Gradient ∂z ∂z Gradients fy = ∂y fx = ∇z = (fx , fy ) ∂x Slope Slope γ = arctan fx + fy 2 2 9 Riccardo Rigon Friday, September 10, 2010
  16. 16. Delineation of the Hydrographic Catchment Gradient ∂z ∂z Gradients fy = ∂y fx = ∇z = (fx , fy ) ∂x Slope Slope γ = arctan fx + fy 2 2 Aspect fy Aspect α = arctan fx 9 Riccardo Rigon Friday, September 10, 2010
  17. 17. Delineation of the Hydrographic Catchment Gradient 10 Riccardo Rigon Friday, September 10, 2010
  18. 18. Delineation of the Hydrographic Catchment CURVATURE: as the word itself says, an indication of how “curvy” a curve is. 11 Riccardo Rigon Friday, September 10, 2010
  19. 19. Delineation of the Hydrographic Catchment CURVATURE: as the word itself says, an indication of how “curvy” a curve is. A line segment has null curvature. 11 Riccardo Rigon Friday, September 10, 2010
  20. 20. Delineation of the Hydrographic Catchment CURVATURE: as the word itself says, an indication of how “curvy” a curve is. 12 Riccardo Rigon Friday, September 10, 2010
  21. 21. Delineation of the Hydrographic Catchment CURVATURE: as the word itself says, an indication of how “curvy” a curve is. 12 Riccardo Rigon Friday, September 10, 2010
  22. 22. Delineation of the Hydrographic Catchment CURVATURE: as the word itself says, an indication of how “curvy” a curve is. 13 Riccardo Rigon Friday, September 10, 2010
  23. 23. Delineation of the Hydrographic Catchment CURVATURE: as the word itself says, an indication of how “curvy” a curve is. 13 Riccardo Rigon Friday, September 10, 2010
  24. 24. Delineation of the Hydrographic Catchment CURVATURE: once some curves have been identified on a surface their curvature can be defined. 14 Riccardo Rigon Friday, September 10, 2010
  25. 25. Delineation of the Hydrographic Catchment Curves along the flowlines are defined by Longitudinal Curvature. Curves along the contour lines are defined by Transversal Curvature. 15 Riccardo Rigon Friday, September 10, 2010
  26. 26. Delineation of the Hydrographic Catchment CURVATURE The composition of the curvatures produces 9 main topographic forms TC 16 Riccardo Rigon Friday, September 10, 2010
  27. 27. Delineation of the Hydrographic Catchment The main derived quantities are: •Drainage Directions •Contributing Areas 17 Riccardo Rigon Friday, September 10, 2010
  28. 28. Delineation of the Hydrographic Catchment It’s easy to say Drainage Directions 18 Riccardo Rigon Friday, September 10, 2010
  29. 29. Delineation of the Hydrographic Catchment from Tarboton: www.cuahsi.org 19 Riccardo Rigon Friday, September 10, 2010
  30. 30. Delineation of the Hydrographic Catchment It’s easy to say Drainage Directions Orlandini et al., 2003 DrainDir 20 Riccardo Rigon Friday, September 10, 2010
  31. 31. Delineation of the Hydrographic Catchment 21 Riccardo Rigon Friday, September 10, 2010
  32. 32. Delineation of the Hydrographic Catchment Drainage Directions 22 Riccardo Rigon Friday, September 10, 2010
  33. 33. Delineation of the Hydrographic Catchment From DEM to Hydrographic Catchment Once the drainage directions have been identified: •chosen a point (pixel) •the set of all points that “flow” to that point can be determined •this set constitutes the surface of a hydrographic catchment 23 Riccardo Rigon Friday, September 10, 2010
  34. 34. Delineation of the Hydrographic Catchment Drainage Directions 24 Riccardo Rigon Friday, September 10, 2010
  35. 35. Delineation of the Hydrographic Catchment The Hydrographic Network: where do the Channels begin? from Tarboton: www.cuahsi.org 25 Riccardo Rigon Friday, September 10, 2010
  36. 36. Delineation of the Hydrographic Catchment The Hydrographic Network: where do the Channels begin? from Tarboton: www.cuahsi.org 26 Riccardo Rigon Friday, September 10, 2010
  37. 37. Delineation of the Hydrographic Catchment The Hydrographic Network: where do the Channels begin? from Tarboton: www.cuahsi.org 27 Riccardo Rigon Friday, September 10, 2010
  38. 38. Delineation of the Hydrographic Catchment The Hydrographic Network: where do the Channels begin? Montgomery and Dietrich, WRR, 1992 28 Riccardo Rigon Friday, September 10, 2010
  39. 39. Delineation of the Hydrographic Catchment The Hydrographic Network: where do the Channels begin? Ab 29 Riccardo Rigon Friday, September 10, 2010
  40. 40. Delineation of the Hydrographic Catchment The Hydrographic Network: where do the Channels begin? from Tarboton: www.cuahsi.org 30 Riccardo Rigon Friday, September 10, 2010
  41. 41. Delineation of the Hydrographic Catchment The Hydrographic Network: where do the Channels begin? Howard, WRR, 1994 31 Riccardo Rigon Friday, September 10, 2010
  42. 42. Delineation of the Hydrographic Catchment Hydrographic Catchments after SCHUMM 32 Riccardo Rigon Friday, September 10, 2010
  43. 43. Delineation of the Hydrographic Catchment Hydrographic Catchments from Foufula e Paola: www.cuahsi.org 33 Riccardo Rigon Friday, September 10, 2010
  44. 44. Delineation of the Hydrographic Catchment Hydrographic Catchments in digital From Arc Hydro 34 Riccardo Rigon Friday, September 10, 2010
  45. 45. What is Geomorphometry? A Brief Introduction - I Digital Watershed DEFINITION: a set of digital tools with which to collect and organise data and models relative to a hydrographic watershed so that they can be easily queried for information necessary to planning by those bodies that manage watersheds. 35 Silvia Franceschi Friday, September 10, 2010
  46. 46. What is Geomorphometry? A Brief Introduction - I Digital Watershed DIGITAL EARTH Al Gore 1998 virtual 3D representation of the Earth spatially connected to digital scientific, natural, and georeferenced archives all over the world cultural information describe and understand the Earth, its environment and human activity 36 Silvia Franceschi Friday, September 10, 2010
  47. 47. What is Geomorphometry? A Brief Introduction - I Digital Watershed  System that uses the following technologies:  remote sensing (RS)‫‏‬  geographical information system (GIS)‫‏‬  global positioning system (GPS)‫‏‬  virtual reality (VR)‫‏‬  Database (DB)‫‏‬  internet and multimedia  to detect, store, manage, process and analyse information 37 Silvia Franceschi Friday, September 10, 2010
  48. 48. What is Geomorphometry? A Brief Introduction - I Digital Watershed - beyond Hydrology ! The following information is considered: ! Geographic Background ! Natural Resources ! Ecological Environment ! Population Distribution ! Social and Economic Conditions at Watershed Scale 38 Silvia Franceschi Friday, September 10, 2010
  49. 49. What is Geomorphometry? A Brief Introduction - I Digital Watershed - beyond Hydrology ! In order to: ! build a visual digital platform ! furnish specific applications to administrative bodies in various fields ! develop a global decision making system that will optimise watershed management 39 Silvia Franceschi Friday, September 10, 2010
  50. 50. What is Geomorphometry? A Brief Introduction - I Digital Watershed ! The digital watershed is made up of: 0.Visual digital platform: it is the base level for the building of a digital watershed. The digital platform has the job of collecting various types of information from within the watershed, build spatial and relational databases, and furnish a digital platform for the visualisation, analyses, and access to data based on a GIS. 40 Silvia Franceschi Friday, September 10, 2010
  51. 51. What is Geomorphometry? A Brief Introduction - I Digital Watershed 1.System of thematic applications: this constitutes the applicative pat of the system. Within a watershed, generally, there are various administrative bodies and professionals that act in different fields. Each one of these has different specifications for data management and decision support. Within the platform specific applications must be developed in order to furnish the various users with the data necessary for their activities. 41 Silvia Franceschi Friday, September 10, 2010
  52. 52. What is Geomorphometry? A Brief Introduction - I Digital Watershed 2.Integrated management and decision support system: this part of the system is used to analyse the watershed data present on the platform. The scope is to develop a a different method of analysis into one tool so as to integrate the information of the various disciplines. 42 Silvia Franceschi Friday, September 10, 2010
  53. 53. Delineation of the Hydrographic Catchment from Tarboton: www.cuahsi.org 43 Riccardo Rigon Friday, September 10, 2010
  54. 54. Delineation of the Hydrographic Catchment from Tarboton: www.cuahsi.org 44 Riccardo Rigon Friday, September 10, 2010
  55. 55. Delineation of the Hydrographic Catchment from Tarboton: www.cuahsi.org 45 Riccardo Rigon Friday, September 10, 2010
  56. 56. Delineation of the Hydrographic Catchment from Tarboton: www.cuahsi.org 46 Riccardo Rigon Friday, September 10, 2010
  57. 57. Delineation of the Hydrographic Catchment from Tarboton: www.cuahsi.org 47 Riccardo Rigon Friday, September 10, 2010
  58. 58. Delineation of the Hydrographic Catchment Strahler Numbering and Horton’s Laws • The “extracted” hydrographic network is, mathematically speaking, an oriented graph. •The elements of such a graph have a tree topology. 48 Riccardo Rigon Friday, September 10, 2010
  59. 59. Delineation of the Hydrographic Catchment Strahler Numbering and Horton’s Laws 49 Riccardo Rigon Friday, September 10, 2010
  60. 60. Delineation of the Hydrographic Catchment Strahler Numbering and Horton’s Laws The “sources” are marked in yellow 49 Riccardo Rigon Friday, September 10, 2010
  61. 61. Delineation of the Hydrographic Catchment Strahler Numbering and Horton’s Laws The “sources” are marked in yellow The sources have Strahler stream order 1 49 Riccardo Rigon Friday, September 10, 2010
  62. 62. Delineation of the Hydrographic Catchment Strahler Numbering and Horton’s Laws The “sources” are marked in yellow The sources have Strahler stream order 1 Two sources meet and form a branch with Strahler stream order 2 49 Riccardo Rigon Friday, September 10, 2010
  63. 63. Delineation of the Hydrographic Catchment Strahler Numbering and Horton’s Laws At every junction of two streams: if two branches of different order, m and n, meet, the resulting stream has order max(m,n)+1 50 Riccardo Rigon Friday, September 10, 2010
  64. 64. Delineation of the Hydrographic Catchment Strahler Numbering and Horton’s Laws In this way a hierarchical network, with streams of different orders, is formed. With this it is possible to: -count the number -evaluate the average length -evaluate the average contributing area 51 Riccardo Rigon Friday, September 10, 2010
  65. 65. Delineation of the Hydrographic Catchment Strahler Numbering and Horton’s Laws from Tarboton: www.cuahsi.org 52 Riccardo Rigon Friday, September 10, 2010
  66. 66. Delineation of the Hydrographic Catchment Strahler Numbering and Horton’s Laws from Tarboton: www.cuahsi.org 53 Riccardo Rigon Friday, September 10, 2010
  67. 67. Delineation of the Hydrographic Catchment Strahler Numbering and Horton’s Laws from Tarboton: www.cuahsi.org 54 Riccardo Rigon Friday, September 10, 2010
  68. 68. Delineation of the Hydrographic Catchment Strahler Numbering and Horton’s Laws from Tarboton: www.cuahsi.org 55 Riccardo Rigon Friday, September 10, 2010
  69. 69. Delineation of the Hydrographic Catchment The distance of every point of a catchment from the divide. Hack’s Law 56 Riccardo Rigon Friday, September 10, 2010
  70. 70. Delineation of the Hydrographic Catchment The distance of every point of a catchment from the divide. Hack’s Law 1 10 100 1000 100 100 h = 0.54 Rigon et al., 1996 10 10 L H 1 1 1 - n ê ^ L n ^ L 0.1 0.1 0.01 0.01 0.001 1 10 100 1000 Area 57 Riccardo Rigon Friday, September 10, 2010
  71. 71. Delineation of the Hydrographic Catchment Fractal River Networks: Chance and Self-Organization Rinaldo, Rodriguez-Iturbe e Rigon, 1998 1 10 100 1000 Rodriguez-Iturbe e Rinaldo, 1997 100 100 h = 0.54 10 10 L H 1 1 1 - n ê ^ L n ^ L 0.1 0.1 0.01 0.01 0.001 1 10 100 1000 Area 58 Riccardo Rigon Friday, September 10, 2010
  72. 72. What is Geomorphometry? A Brief Introduction - I Numbering in JGrass MAIN CHANNEL: first-level odd numbers third-level channel MAIN TRIBUTARIES: second-level even numbers MODIFIED PFAFSTETTER SYSTEM 59 Silvia Franceschi Friday, September 10, 2010
  73. 73. What is Geomorphometry? A Brief Introduction - I Numbering in JGrass Network level 5 Network level 4 Network level 3 Network level 2 Network level 1 60 Silvia Franceschi Friday, September 10, 2010
  74. 74. What is Geomorphometry? A Brief Introduction - I Numbering in JGrass Network level 4 Network level 3 Network level 2 Network level 1 61 Silvia Franceschi Friday, September 10, 2010
  75. 75. What is Geomorphometry? A Brief Introduction - I Numbering in JGrass Network level 3 Network level 2 Network level 1 62 Silvia Franceschi Friday, September 10, 2010
  76. 76. What is Geomorphometry? A Brief Introduction - I Numbering in JGrass Network level 2 Network level 1 63 Silvia Franceschi Friday, September 10, 2010
  77. 77. What is Geomorphometry? A Brief Introduction - I Numbering in JGrass Network level 1 64 Silvia Franceschi Friday, September 10, 2010
  78. 78. Delineation of the Hydrographic Catchment Drainage Density from Tarboton: www.cuahsi.org 65 Riccardo Rigon Friday, September 10, 2010
  79. 79. Delineation of the Hydrographic Catchment Drainage Density 66 Riccardo Rigon Friday, September 10, 2010
  80. 80. Delineation of the Hydrographic Catchment The Distance of the Points on the Slopes from the Hydrographic Network 67 Riccardo Rigon Friday, September 10, 2010
  81. 81. Delineation of the Hydrographic Catchment What happens on the slopes? 68 Riccardo Rigon Friday, September 10, 2010
  82. 82. Delineation of the Hydrographic Catchment Amplitude Function 69 Riccardo Rigon Friday, September 10, 2010 Idrologia stazionaria dei versanti : : Idrologia stazionaria dei versanti
  83. 83. Delineation of the Hydrographic Catchment Leopold Maddock 1953: Relationships between Areas and Discharge c Q∝A m V ∝A b w∝A f d∝A Q = V × w × d =⇒ m + b + f = c 70 Riccardo Rigon Friday, September 10, 2010
  84. 84. Delineation of the Hydrographic Catchment Leopold Maddock 1953: Relationships between Areas and Discharge Questa tabella e’ immagine - non e’ modificabile con LaTeX b Q∝A c V ∝A w ∝ Ad f d∝A Q = V × w × d =⇒ c + d + f = b 71 Riccardo Rigon Friday, September 10, 2010
  85. 85. Delineation of the Hydrographic Catchment Leopold Maddock 1953: Relationships between Areas and Discharge b Q∝A c V ∝A w ∝ Ad f d∝A Q = V × w × d =⇒ c + d + f = b Avisio, after Rigon et al. 2006 72 Riccardo Rigon Friday, September 10, 2010
  86. 86. Delineation of the Hydrographic Catchment P [A a] = a−β f (a/AT ) 73 Riccardo Rigon Friday, September 10, 2010
  87. 87. Delineation of the Hydrographic Catchment Area - Slope Relationship After Montgomery Dietrich Immagine non modificabile 74 Riccardo Rigon Friday, September 10, 2010
  88. 88. Delineation of the Hydrographic Catchment Hydrologic Flows within the Slopes Stationary Hydrology of the Slopes: T ∇z b + u d b = q a 75 Riccardo Rigon Friday, September 10, 2010 Idrologia stazionaria dei versanti : : Idrologia stazionaria dei versanti
  89. 89. Delineation of the Hydrographic Catchment Hydrologic Flows within the Slopes Stationary Hydrology of the Slopes: T ∇z b + u d b = q A T ∇z b = q A T /q ∇z = A/b 76 Riccardo Rigon Friday, September 10, 2010 Idrologia stazionaria dei versanti : : Idrologia stazionaria dei versanti
  90. 90. Delineation of the Hydrographic Catchment Area - Slope Relationship After Montgomery Dietrich Immagine non modificabile. 77 Riccardo Rigon Friday, September 10, 2010
  91. 91. Delineation of the Hydrographic Catchment Hydrologic Flows within the Slopes Stationary Hydrology of the Slopes: T ∇z b + u d b = q A T/q + u d/(q ∇z) = A/(b ∇z) T /q ∇z = A/b 78 Riccardo Rigon Friday, September 10, 2010 Idrologia stazionaria dei versanti : : Idrologia stazionaria dei versanti
  92. 92. Delineation of the Hydrographic Catchment Area - Slope Relationship After Montgomery Dietrich 79 Riccardo Rigon Friday, September 10, 2010
  93. 93. Delineation of the Hydrographic Catchment The Topographic Index Stationary Hydrology of the Slopes: It = log A/log (b ∇z) T /q ∇z = A/b 80 Riccardo Rigon Friday, September 10, 2010
  94. 94. Delineation of the Hydrographic Catchment The Topographic Index 81 Riccardo Rigon Friday, September 10, 2010
  95. 95. Delineation of the Hydrographic Catchment The Topographic Index 82 Riccardo Rigon Friday, September 10, 2010
  96. 96. Delineation of the Hydrographic Catchment List of Symbols Symbol Name Unit of Measure A Area L−2 Rb Bifurcation Ratio nd Ra Area Ratio nd RL Length Ratio nd Rs Slope Ratio nd h Hack’s Coefficient nd Dd Drainage Density L−1 V, u Mean Velocity of Water in the Channels L T−1 w Channel Width L d Mean Depth of a Channel Section L T Transmissivity L2 T−1 ∇z Slope nd b Boundary Length L d Surface Flow Depth L q Specific Discharge (per unit area) L T−1 83 Riccardo Rigon Friday, September 10, 2010
  97. 97. Delineation of the Hydrographic Catchment Thank You for Your Attention. G. Ulrici - 84 Riccardo Rigon Friday, September 10, 2010
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