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- 1. What is Geomorphometry? A Brief Introduction - I Riccardo Rigon, with numerous contributions “stolen” from D. Tarboton Friday, September 10, 2010
- 2. Delineation of the Hydrographic Catchment Objectives 2 Riccardo Rigon Friday, September 10, 2010
- 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. 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. 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. 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. Delineation of the Hydrographic Catchment The Discretisation of the Terrain from Tarboton: www.cuahsi.org 3 Riccardo Rigon Friday, September 10, 2010
- 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. Delineation of the Hydrographic Catchment The Primary Topographic Attributes: - Altitude - Slope - Curvature 5 Riccardo Rigon Friday, September 10, 2010
- 10. Delineation of the Hydrographic Catchment Altitude z = f (x, y) 6 Riccardo Rigon Friday, September 10, 2010
- 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. 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. Delineation of the Hydrographic Catchment Gradient 9 Riccardo Rigon Friday, September 10, 2010
- 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. 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. 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. Delineation of the Hydrographic Catchment Gradient 10 Riccardo Rigon Friday, September 10, 2010
- 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. 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. 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. 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. 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. 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. 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. 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. 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. Delineation of the Hydrographic Catchment The main derived quantities are: •Drainage Directions •Contributing Areas 17 Riccardo Rigon Friday, September 10, 2010
- 28. Delineation of the Hydrographic Catchment It’s easy to say Drainage Directions 18 Riccardo Rigon Friday, September 10, 2010
- 29. Delineation of the Hydrographic Catchment from Tarboton: www.cuahsi.org 19 Riccardo Rigon Friday, September 10, 2010
- 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. Delineation of the Hydrographic Catchment 21 Riccardo Rigon Friday, September 10, 2010
- 32. Delineation of the Hydrographic Catchment Drainage Directions 22 Riccardo Rigon Friday, September 10, 2010
- 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. Delineation of the Hydrographic Catchment Drainage Directions 24 Riccardo Rigon Friday, September 10, 2010
- 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. 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. 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. 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. Delineation of the Hydrographic Catchment The Hydrographic Network: where do the Channels begin? Ab 29 Riccardo Rigon Friday, September 10, 2010
- 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. Delineation of the Hydrographic Catchment The Hydrographic Network: where do the Channels begin? Howard, WRR, 1994 31 Riccardo Rigon Friday, September 10, 2010
- 42. Delineation of the Hydrographic Catchment Hydrographic Catchments after SCHUMM 32 Riccardo Rigon Friday, September 10, 2010
- 43. Delineation of the Hydrographic Catchment Hydrographic Catchments from Foufula e Paola: www.cuahsi.org 33 Riccardo Rigon Friday, September 10, 2010
- 44. Delineation of the Hydrographic Catchment Hydrographic Catchments in digital From Arc Hydro 34 Riccardo Rigon Friday, September 10, 2010
- 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. 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. 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. 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. 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. 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. 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. 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. Delineation of the Hydrographic Catchment from Tarboton: www.cuahsi.org 43 Riccardo Rigon Friday, September 10, 2010
- 54. Delineation of the Hydrographic Catchment from Tarboton: www.cuahsi.org 44 Riccardo Rigon Friday, September 10, 2010
- 55. Delineation of the Hydrographic Catchment from Tarboton: www.cuahsi.org 45 Riccardo Rigon Friday, September 10, 2010
- 56. Delineation of the Hydrographic Catchment from Tarboton: www.cuahsi.org 46 Riccardo Rigon Friday, September 10, 2010
- 57. Delineation of the Hydrographic Catchment from Tarboton: www.cuahsi.org 47 Riccardo Rigon Friday, September 10, 2010
- 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. Delineation of the Hydrographic Catchment Strahler Numbering and Horton’s Laws 49 Riccardo Rigon Friday, September 10, 2010
- 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. 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. 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. 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. 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. Delineation of the Hydrographic Catchment Strahler Numbering and Horton’s Laws from Tarboton: www.cuahsi.org 52 Riccardo Rigon Friday, September 10, 2010
- 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. Delineation of the Hydrographic Catchment Strahler Numbering and Horton’s Laws from Tarboton: www.cuahsi.org 54 Riccardo Rigon Friday, September 10, 2010
- 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. 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. 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. 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. 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. 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. 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. 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. What is Geomorphometry? A Brief Introduction - I Numbering in JGrass Network level 2 Network level 1 63 Silvia Franceschi Friday, September 10, 2010
- 77. What is Geomorphometry? A Brief Introduction - I Numbering in JGrass Network level 1 64 Silvia Franceschi Friday, September 10, 2010
- 78. Delineation of the Hydrographic Catchment Drainage Density from Tarboton: www.cuahsi.org 65 Riccardo Rigon Friday, September 10, 2010
- 79. Delineation of the Hydrographic Catchment Drainage Density 66 Riccardo Rigon Friday, September 10, 2010
- 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. Delineation of the Hydrographic Catchment What happens on the slopes? 68 Riccardo Rigon Friday, September 10, 2010
- 82. Delineation of the Hydrographic Catchment Amplitude Function 69 Riccardo Rigon Friday, September 10, 2010 Idrologia stazionaria dei versanti : : Idrologia stazionaria dei versanti
- 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. 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. 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. Delineation of the Hydrographic Catchment P [A a] = a−β f (a/AT ) 73 Riccardo Rigon Friday, September 10, 2010
- 87. Delineation of the Hydrographic Catchment Area - Slope Relationship After Montgomery Dietrich Immagine non modificabile 74 Riccardo Rigon Friday, September 10, 2010
- 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. 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. Delineation of the Hydrographic Catchment Area - Slope Relationship After Montgomery Dietrich Immagine non modificabile. 77 Riccardo Rigon Friday, September 10, 2010
- 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. Delineation of the Hydrographic Catchment Area - Slope Relationship After Montgomery Dietrich 79 Riccardo Rigon Friday, September 10, 2010
- 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. Delineation of the Hydrographic Catchment The Topographic Index 81 Riccardo Rigon Friday, September 10, 2010
- 95. Delineation of the Hydrographic Catchment The Topographic Index 82 Riccardo Rigon Friday, September 10, 2010
- 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. Delineation of the Hydrographic Catchment Thank You for Your Attention. G. Ulrici - 84 Riccardo Rigon Friday, September 10, 2010

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