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 SelfOrganization
Rinaldo, RodriguezIturbe e Rigon, 1998
1 10 100 1000
RodriguezIturbe 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:
firstlevel odd numbers
thirdlevel channel
MAIN TRIBUTARIES:
secondlevel 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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