2 hydro-geomorphology

What is Geomorphometry?
A Brief Introduction - I

Riccardo Rigon, with numerous contributions “stolen” from D. Tarboton

Friday, September 10, 2010

Delineation of the Hydrographic Catchment

Objectives

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Riccardo Rigon



Objectives

•To introduce the concepts correlated with the
delineation of a hydrographic catchment

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Riccardo Rigon



Objectives


•To apply some simple hydrological balances at slope
scale

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Riccardo Rigon



Objectives


•To lay a theoretical base for the successive lectures on
JGrass
scale

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Riccardo Rigon



Objectives


•To define the concept of a digital catchment

•To lay a theoretical base for the successive lectures on
JGrass
scale

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The Discretisation of the Terrain
from Tarboton: www.cuahsi.org

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A grid is a geographical space of equidistant cells.
Each cell contains a value, for example, of altitude.

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Riccardo Rigon



The Primary Topographic Attributes:

- Altitude

- Slope

- Curvature

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Altitude

z = f (x, y)

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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

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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
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Gradient

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Gradient
∂z ∂z
Gradients fy =
∂y
fx = ∇z = (fx , fy )
∂x

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Riccardo Rigon



Gradient
∂z ∂z
Gradients fy =
∂y
fx = ∇z = (fx , fy )
∂x

Slope

Slope γ = arctan fx + fy
2 2

9

Riccardo Rigon



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



Gradient

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CURVATURE:

as the word itself says, an indication of how “curvy” a
curve is.

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CURVATURE:

curve is.

A line segment has null curvature.

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CURVATURE:

curve is.

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CURVATURE:

curve is.

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CURVATURE: once some curves have been
identified on a surface their curvature can be
defined.

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Curves along the flowlines are defined by Longitudinal
Curvature.

Curves along the contour lines are defined by Transversal
Curvature.

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CURVATURE
The composition of the curvatures produces 9 main
topographic forms

TC 16

Riccardo Rigon



The main derived quantities are:

•Drainage Directions

•Contributing Areas

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It’s easy to say Drainage Directions

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It’s easy to say Drainage Directions
Orlandini et al., 2003

DrainDir
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Drainage Directions

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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

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Drainage Directions

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The Hydrographic Network: where do the
Channels begin?

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Channels begin?

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Channels begin?

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Riccardo Rigon



Channels begin?
Montgomery and Dietrich, WRR, 1992

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Channels begin?

Ab
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Channels begin?

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Channels begin?
Howard, WRR, 1994

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Hydrographic Catchments after SCHUMM

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Hydrographic Catchments
from Foufula e Paola: www.cuahsi.org

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Riccardo Rigon



Hydrographic Catchments in digital
From Arc Hydro

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Riccardo Rigon


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



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



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



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



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



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



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



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



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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.

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Riccardo Rigon



Strahler Numbering and Horton’s Laws

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The “sources” are
marked in yellow

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Riccardo Rigon




marked in yellow

The sources have
Strahler stream
order 1

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Riccardo Rigon




marked in yellow

The sources have
Strahler stream
order 1

Two sources meet and
form a branch with
Strahler stream order 2

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Riccardo Rigon



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

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Riccardo Rigon



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
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The distance of every point of a catchment from
the divide. Hack’s Law

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Riccardo Rigon



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
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Riccardo Rigon



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

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Riccardo Rigon



Numbering in JGrass

MAIN CHANNEL:
first-level odd numbers
third-level channel

MAIN TRIBUTARIES:
second-level even numbers
MODIFIED PFAFSTETTER SYSTEM
59

Silvia Franceschi



Numbering in JGrass

Network level 5
Network level 4
Network level 3
Network level 2
Network level 1

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Silvia Franceschi



Numbering in JGrass

Network level 4
Network level 3
Network level 2
Network level 1

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Silvia Franceschi



Numbering in JGrass

Network level 3
Network level 2
Network level 1

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Silvia Franceschi



Numbering in JGrass

Network level 2
Network level 1

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Silvia Franceschi



Numbering in JGrass

Network level 1

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Silvia Franceschi



Drainage Density

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Drainage Density

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The Distance of the Points on the Slopes from the
Hydrographic Network

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What happens on the slopes?

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Amplitude Function

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Riccardo Rigon

Friday, September 10, 2010 Idrologia stazionaria dei versanti : :
Idrologia stazionaria dei versanti


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
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Riccardo Rigon




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




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



P [A a] = a−β f (a/AT )

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Area - Slope Relationship
After Montgomery Dietrich

Immagine non modificabile

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Hydrologic Flows within the Slopes

Stationary Hydrology of the Slopes:
T ∇z b + u d b = q a 75

Riccardo Rigon





T ∇z b + u d b = q A

T ∇z b = q A

T /q ∇z = A/b

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Immagine non modificabile.

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T ∇z b + u d b = q A

T/q + u d/(q ∇z) = A/(b ∇z)

T /q ∇z = A/b

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The Topographic Index


It = log A/log (b ∇z)

T /q ∇z = A/b

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The Topographic
Index

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The Topographic Index

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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

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Riccardo Rigon



Thank You for Your Attention.

G. Ulrici -

84

Riccardo Rigon


2 hydro-geomorphology

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