HortonMachine is a software tool integrated with JGrass that provides quantitative and qualitative analysis of catchment morphology using hydro-geomorphological methods. It allows users to analyze erosion processes, network incision, and landslide potential in alpine catchments of various sizes. The tool calculates various topographic attributes, derives flow networks, and extracts channel networks to facilitate geomorphological analysis of catchment basins. It has evolved from standalone routines to being integrated within GRASS and now JGrass for improved interoperability and interface.

1. HortonMachine: application of hydro-geomorphological analysis integrated in JGrass Foss4G2008 – JGrass Workshop ing. Silvia Franceschi ing. Andrea Antonello prof. Riccardo Rigon HydroloGIS University of Trento

12. The topography is represented by a bivariate continuous function z = f(x,y) and with continuous derivative up to the second order almost everywhere. MORPHOLOGY

14. definition the working region pit detection definition of the drainage directions definition of the main network extraction of the interesting catchment D8 (maximum slope)‏ D8 with correction (correction on the direction of the gradient)‏ PRELIMINARY OPERATIONS import in JGrass the starting DEM which we want to analyse individuation of the existing sub basins

15. DERIVED ATTRIBUTES: Local slope (h.slope)‏ Local curvature (h.tapes o h.nabla)‏ Total contributing area (h.tca, h.multitca)‏ Catchment divide distance (h.hacklength)‏ Distance to outlet (h.distance2outlet)‏ ……… ..

16. FIRST STEP: DEPITTING THE DEM The first operation to do is to fill the depression points present within a DEM so that the drainage directions can be defined in each point. Observations on this topic demonstrate that this calculation addresses lesser than the 1% of the data and that usually this depressions are given by wrong calculation in the DEM creation phase and that in fact they are not real depressions. The command used to fill the depressions is: h.pitfiller based on the Tarboton algorithm.

17. h.pitfiller Fills the depressions following the Tarboton algorithm.

18. FLOW DIRECTIONS They define how water moves on the surface in relation to the topology of the study region. Flow directions allow you to calculate the drainage directions. Hypothesis: each DEM cell drains only in one of its 8 neighbours, either adjacent or diagonal in the direction of the steepest downward slope. only 8 possible direction in which direct the flux this is a limit of modelling the natural flow

19. h.flowdirections It calculates the flow direction in the direction of the steepest downward slope choosing for each DEM cell to one of its 8 neighbours. The flow directions convention numbers are from 1 to 8 where 1 is the east direction.

20. Map of the Flow Directions: In the map each colour represents one of the 8 drainage directions. The map contains the convention number of this directions.

21. Map of the Flow Directions:

22. A CORRECTION TO THE PURE D8 METHOD: h.draindir Using the “pure” D8 method for the drainage direction estimation cause an effect of deviation from the real direction identified by the gradients. This algorithm calculates the drainage direction minimizing the deviation of the flow from the real flux direction. The deviation is calculated beginning from the pixel at highest elevation and going downstream. The deviation is calculated with a triangular construction and can be expressed as angular deviation (method D8-LAD) or as transversal distance (method D8-LTD)‏ The lambda parameter is used to assign a weight to the correction made to the drainage directions. This method has been developed by S. Orlandini

23. h.draindir LAD method: angular deviation LTD method: transversal deviation The deviation is cumulated from higher pixels down-hill and the D8 drainage direction is redirected to the real direction when the value is larger than an assigned threshold. If λ = 0 the deviation counter has no memory and the pixels up-hill do not affect the choice.

24. THE NEW DRAINAGE DIRECTIONS AND THE NEW TCA STANDARD METHOD

25. THE NEW DRAINAGE DIRECTIONS AND THE NEW TCA STANDARD METHOD

26. THE NEW DRAINAGE DIRECTIONS AND THE NEW TCA STANDARD METHOD

27. THE NEW DRAINAGE DIRECTIONS AND THE NEW TCA STANDARD METHOD

28. h.dirdren Map obtained categorizing the resulting map of the command Map obtained personalizing the colours of the original map

29. THE NEW DRAINAGE DIRECTIONS AND THE NEW TCA STANDARD METHOD

30. h.dirdren NETWORK FIXED METHOD: in flat areas or where there are manmade constructions, it can happen that the extracted channel network does not coincide with the real channel network.

31. h.dirdren FLOW FIXED METHOD

32. h.dirdren FLOW FIXED METHOD

33. h.draindir

34. h.draindir

35. TOTAL CONTRIBUTING AREA: It represents the area that contributes to a particular point of the catchment basin. It is an extremely important quantity in the geomorphologic and hydrologic study of a river basin: it is strictly related to the discharge flowing through the different points of the system in uniform precipitation conditions. On this quantity most of the diffusive methods used to extract the stream network from the digital models are based.

38. RESULTS COMPARISON: In the figures are compared the total contributing areas calculated with the pure D8 method and with the corrected method (LAD-D8). In the second case the typical maximum steepest parallelisms are not present with a representation of the flow very near to reality. Log(TCA)‏ Log (LAD-TCA)‏

39. FLOW DIRECTIONS: Many applications to be correctly executed need a matrix of the flow directions that have a new class value. This new class (conventionally indicated in JGrass with 10) identifies the basin outlets, those are the pixels draining outside the analysed region. In other words this command marks the outlets: The command is:

40. MARKOUTLET

41. GRADIENTS: h.gradient The gradients are relevant because the main driving force of the flux is the gravity and the gradient identifies the flow directions of the water and contributes also to determinate its velocity. Let's observe that the gradient, contrarily to the slope, does not use the drainage directions. It calculates only the module of the gradient which in reality is a vectorial quantity oriented in the direction starting from the minimal up to the maximal potential.

42. We can see the deep network incision and the flat area near the basin outlet. The particular wrong calculation in the upper part of the basin is due to the union of the originally squared DEM. GRADIENTS: h.gradient

43. The gradient calculated whit this command is given as the tangent of the correspondent angle. Using the MAPCALCULATOR it is possible to obtain the map of the gradients in degrees: atan(gradient)*180/3.14 GRADIENTS: h.gradient

44. The gradient calculated whit this command is given as the tangent of the correspondent angle. Using the MAPCALCULATOR it is possible to obtain the map of the gradients in degrees: atan(gradient)*180/3.14 new_map = if (condition, then, else)‏ GRADIENTS: h.gradient

45. N.B. Convex sites (positive curvature) represent convergent flow, concave sites (negative curvature) represent divergent flow. THE CURVATURES: h.curvatures The mathematical definition is pretty complex. Longitudinal curvature Planar curvature it represents the deviation of the gradient along the flow (it is negative if the gradient increases)‏ it represents the deviation of the gradient along the transversal direction (along the contour lines)‏ it measure the convergence (+) or divergence (-) of the flow

46. CONTOUR LINES

47. THE CURVATURES: h.curvatures

48. THE CURVATURES: h.curvatures Longitudinal Curvature Planare Curvature The planar curvatures separate the concave parts from the convex ones The longitudinal curvatures highlight valleys

49. TOPOGRAPHIC CLASSIFICATION: h.tc It subdivides the sites of a basin in the 9 topographic classes identified by the longitudinal and transversal curvatures. The aggregation of the classes in the three fundamentals index: CONCAVE SITES CONVEX SITES PLANAR SITES

50. TOPOGRAPHIC CLASSIFICATION: h.tc The program asks as input the threshold values of the longitudinal and normal curvatures which define their planarity. THE VALUE IS STRICTLY RELATED TO THE TOPOLOGY

51. TOPOGRAPHIC CLASSIFICATION: h.tc h.tc 9 classes h.tc 3 classes

53. h.extractnetwork Threshold on the tca The threshold depends on: - dimensions of the pixels - topographical attributes 1°method

54. The threshold depends on: - pixels dimensions - topographical attributes 2°method h.extractnetwork The threshold is on the parameter: which is proportional to the stress tangential to the bottom.

55. Threshold on the tca of the concave sites. The threshold depends on: - pixel dimensions - topographical attributes 3°method h.extractnetwork

56. In the resulting raster map the network pixels have the 2 value and outside the network there are null values. 1°method: threshold on the tca h.extractnetwork

57. 2°method: threshold on the product between the tca and the gradient h.extractnetwork

58. 3°method: threshold on the tca in the concave pixels In this case there are various groups of stream networks, everyone of them corresponds to a catchment. h.extractnetwork

59. Example of a network extracted with a high threshold value. 1°method: threshold on the tca CHANNEL NETWORK EXTRACTION: h.extractnetwork

63. ESTRACTION OF THE WORKING BASIN: h.wateroutolet

66. BASIN ATTRIBUTES: h.ab It calculates the draining area per length unit (A/b), where A is the total upstream area and b is the length of the contour line which is assumed as drained by the A area. The contour length is here be estimated by a a novel method based on curvatures.

67. BASIN ATTRIBUTES: h.ab It calculates the draining area per length unit (A/b), where A is the total upstream area and b is the length of the contour line which is assumed as drained by the A area. The contour length is here be estimated by a a novel method based on curvatures.

69. h.ab

70. The higher values of A/b are registered near on the channel network. In fact those are the points in which the contributing area is the highest and the value of b is the lowest. THE RESULT OF A/B

71. THE RESULT OF A/B CHANGING THE COLORMAP

72. h.aspect Calculates for every point the aspect, defined as the inclination angle of the gradient. The considered reference system put the angle to zero when the gradient is orientated towards east and grows counter-clock-wise. The value is calculated in radiants. Mathematical formula:

73. N.B.angle is in radiants. h.aspect

74. It is defined as the area upstream that drains into the current point. A large part of DEM related literature analyses this parameter and its determination. Usually it is calculated taking into consideration the steepest slope, but a single flowdirection for every point is not enough to have an accurate description of the runoff. A solution to this problem is the use of an algorithm that introduces multiple draining directions on the hillslope and single ones for concave sites. THE TOTAL CONTRIBUTING AREA

76. h.multitca

77. TCA Multi TCA

78. N.B. Concave sites (positive curvature) represent converging flux, convex sites (negative curvature) represent diverging flux. Laplacian is a strict relative of the curvatures and gives a way to distinguish in a first iteration convex and concave sites of the catchment. Mathematical definition: FIRST APPROACH TO CURVATURES: LAPLACIAN

79. First approach to curvatures: h.nabla

80. h.nabla

81. convex element flat element concave element Positive curvature Negative curvature Null curvature DEFINITIONS FOR CURVATURES

82. h.nabla

83. h.nabla

84. h.curvatures

85. h.gc

86. THE DISTANCES BY HACK: It is given, assigned a point in the catchment, by the projection of the distance from the catchment divide along the network (until it exists), and then, proceeding upstream. For each network confluence, the direction of the tributary with maximal contributing area is chosen. If the tributaries have the same area, one of the two directions is chosen at random.

87. DISTANCE FROM THE CATCHMENT DIVIDE: h.hacklentgh

88. MAGNITUDO: h.magnitudo The magnitude is defined as the number of sources upstream to every point of the catchment. Also the mangitudo is an indicator of the contributing area.

89. SUBBASIN EXTRACTION: h.netnumbering The subbasins depend on the complexity of the network: a complex network has a large number of subbasins a simple network has a small number of subbasins

90. SUBBASIN EXTRACTION: h.netnumbering The subbasins depend on the complexity of the network: a complex network has a large number of subbasins a simple network has a small number of subbasins

92. h.hillslope2channel_distance Distance map for a simple channel network Distance map for a rather complex channel network

93. After the criterion of steepest slope every point of the basin is located at a known distance from the exit. The distribution of the fraction of pixels that are located at the same distance from the outlet is called “ width function ”. THE WIDTH FUNCTION

94. The assumption that the velocity is constant in the channels for events with the same rainfall recurrence interval is a concept supported by several experiments [e.g. Bathurst, 1993]. Defining that this is valid for every point, also of the hillslope makes it possible to transform every distance from the exit into a time information: where c is the celerity of the peak flow and t the time. THE WIDTH FUNCTION

95. h.distance2outlet With this option selected the distance is measured in meters

96. h.distance2outlet With this option the distance is calculated in pixel numbers With this option selected the distance is measured in meters

97. THE WIDTH FUNCTION Distance from the outlet: a constant celerity is assumed for the whole basin, without distinction between channel and hillslope

99. h.rescaleddistance

100. Distance from the outlet: a different speed is assumed for the whole basin, taking into account different velocities for channels and hillslopes RESCALED WIDTH FUNCTION

101. It calculates the histogram of a set of data contained in a matrix with respect to the set of data contained in another matrix. The data of the first set are then grouped in a prefixed number of intervals and the mean value of the independent variable for each interval is calculated. To every interval corresponds a certain set of values of the second set, of which the mean value is calculated, and a designate number of moments. STATISTIC: h.cb

102. STATISTIC: h.cb

107. THAKS FOR YOUR ATTENTION...