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This introduces the basin delineation and analysis with a GIS
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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
Riccardo Rigon
Objectives
2
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Objectives
2
•To introduce the concepts correlated with the delineation of a hydrographic catchment
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Objectives
2
•To introduce the concepts correlated with the delineation of a hydrographic catchment
•To apply some simple hydrological balances at slope scale
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Objectives
2
•To introduce the concepts correlated with the delineation of a hydrographic catchment
•To apply some simple hydrological balances at slope scale
•To lay a theoretical base for the successive lectures on JGrass
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Objectives
2
•To introduce the concepts correlated with the delineation of a hydrographic catchment
•To apply some simple hydrological balances at slope scale
•To lay a theoretical base for the successive lectures on JGrass
•To define the concept of a digital catchment
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
The Discretisation of the Terrain
3
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Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
A grid is a geographical space of equidistant cells.
Each cell contains a value, for example, of altitude.
4
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Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
The Primary Topographic Attributes:
5
- Altitude
- Slope
- Curvature
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Altitude
z = f(x, y)
6
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
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
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Statistical Properties: DISTRIBUTION CURVES
1200 1400 1600 1800 2000 2200 2400h m
0.2
0.4
0.6
0.8
1
P H > h
CoupledFieldsMoments8
Torr
ent
Lon
go (
Tre
nti
no, IT
ALY
)
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Gradient
9
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Gradient
fy =∂z
∂yfx =
∂z
∂x∇z = (fx, fy)Gradients
9
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Gradient
fy =∂z
∂yfx =
∂z
∂x∇z = (fx, fy)Gradients
9
γ = arctan�
f2x + f2
y
Slope
Slope
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Gradient
fy =∂z
∂yfx =
∂z
∂x∇z = (fx, fy)Gradients
9
γ = arctan�
f2x + f2
y
Slope
Slope
Aspect
α = arctanfy
fxAspect
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
10
Gradient
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
as the word itself says, an indication of how “curvy” a
curve is.
11
CURVATURE:
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
as the word itself says, an indication of how “curvy” a
curve is.
11
A line segment has null curvature.
CURVATURE:
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
12
as the word itself says, an indication of how “curvy” a
curve is.
CURVATURE:
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
12
as the word itself says, an indication of how “curvy” a
curve is.
CURVATURE:
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
13
as the word itself says, an indication of how “curvy” a
curve is.
CURVATURE:
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
13
as the word itself says, an indication of how “curvy” a
curve is.
CURVATURE:
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
CURVATURE : once some curves have been
identified on a surface their curvature can be
defined.
14
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Curves along the flowlines are defined by Longitudinal Curvature.
Curves along the contour lines are defined by Transversal Curvature.
15
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
TC 16
CURVATUREThe composition of the curvatures produces 9 main
topographic forms
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
The main derived quantities are:
17
•Drainage Directions
•Contributing Areas
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
18
It’s easy to say Drainage Directions
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
19
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Delineation of the Hydrographic Catchment
Riccardo Rigon
DrainDir20
It’s easy to say Drainage Directions
Orl
and
ini
et a
l., 2
00
3
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
21
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
22
Drainage Directions
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
23
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
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
24
Drainage Directions
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
The Hydrographic Network: where do the Channels begin?
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25
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
26
The Hydrographic Network: where do the Channels begin?
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Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
27
The Hydrographic Network: where do the Channels begin?
from
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Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
28
Mon
tgom
ery
and
Die
tric
h, W
RR
, 19
92
The Hydrographic Network: where do the Channels begin?
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Ab29
The Hydrographic Network: where do the Channels begin?
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
30
The Hydrographic Network: where do the Channels begin?
from
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Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
31
How
ard
, WR
R, 1
99
4
The Hydrographic Network: where do the Channels begin?
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Hydrographic Catchments after SCHUMM
32
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Hydrographic Catchments
33
from
Fou
fula
e P
aola
: ww
w.c
uah
si.o
rg
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
34
From
Arc
Hyd
ro
Hydrographic Catchments in digital
Friday, September 10, 2010
What is Geomorphometry? A Brief Introduction - I
Silvia Franceschi
35
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.
Digital Watershed
Friday, September 10, 2010
What is Geomorphometry? A Brief Introduction - I
Silvia Franceschi
DIGITAL EARTHAl Gore 1998
virtual 3D representation of the
Earth
spatially georeferenced
connected to digital archives all over the world
scientific, natural, and cultural information
describe and understand the Earth, its environment and human activity 36
Digital Watershed
Friday, September 10, 2010
What is Geomorphometry? A Brief Introduction - I
Silvia Franceschi
37
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
Digital Watershed
Friday, September 10, 2010
What is Geomorphometry? A Brief Introduction - I
Silvia Franceschi
38
The following information is considered: Geographic Background Natural Resources Ecological Environment Population Distribution Social and Economic Conditions at Watershed Scale
Digital Watershed - beyond Hydrology
Friday, September 10, 2010
What is Geomorphometry? A Brief Introduction - I
Silvia Franceschi
39
In order to:build a visual digital platformfurnish specific applications to administrative bodies
in various fieldsdevelop a global decision making system that will
optimise watershed management
Digital Watershed - beyond Hydrology
Friday, September 10, 2010
What is Geomorphometry? A Brief Introduction - I
Silvia Franceschi
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
Digital Watershed
Friday, September 10, 2010
What is Geomorphometry? A Brief Introduction - I
Silvia Franceschi
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
Digital Watershed
Friday, September 10, 2010
What is Geomorphometry? A Brief Introduction - I
Silvia Franceschi
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
Digital Watershed
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
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Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
44
from
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Delineation of the Hydrographic Catchment
Riccardo Rigon
45
from
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ahsi
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Delineation of the Hydrographic Catchment
Riccardo Rigon
46
from
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Delineation of the Hydrographic Catchment
Riccardo Rigon
47
from
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Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Strahler Numbering
and
Horton’s Laws
48
• The “extracted” hydrographic network is, mathematically
speaking, an oriented graph.
•The elements of such a graph have a tree topology.
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
49
Strahler Numbering and Horton’s Laws
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
49
Strahler Numbering and Horton’s Laws
The “sources” are
marked in yellow
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
49
Strahler Numbering and Horton’s Laws
The “sources” are
marked in yellow
The sources have
S t r a h l e r s t r e a m
order 1
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
49
Strahler Numbering and Horton’s Laws
The “sources” are
marked in yellow
The sources have
S t r a h l e r s t r e a m
order 1
Two sources meet and
form a branch with
Strahler stream order 2
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
50
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
Strahler Numbering and Horton’s Laws
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
51
I n t h i s w a y a
hierarchical network,
w i t h s t r e a m s o f
different orders, is
formed. With this it is
possible to:
-count the number
-evaluate the average
length
-evaluate the average
contributing area
Strahler Numbering and Horton’s Laws
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
52
Strahler Numbering and Horton’s Laws
from
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Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
53
from
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ahsi
.org
Strahler Numbering and Horton’s Laws
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
54
from
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ahsi
.org
Strahler Numbering and Horton’s Laws
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
55
from
Tar
boto
n: w
ww
.cu
ahsi
.org
Strahler Numbering and Horton’s Laws
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
56
The distance of every point of a catchment from the divide. Hack’s Law
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
1 10 100 1000Area
0.01
0.1
1
10
100
<L̂n>ê<L̂Hn-1L>
1 10 100 1000
0.001
0.01
0.1
1
10
100
h = 0.54
Rig
on
et
al.,
19
96
57
The distance of every point of a catchment from the divide. Hack’s Law
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Fractal River Networks:Chance and Self-Organization
1 10 100 1000Area
0.01
0.1
1
10
100
<L̂n>ê<L̂Hn-1L>
1 10 100 1000
0.001
0.01
0.1
1
10
100
h = 0.54
Rod
rigu
ez-I
turb
e e
Rin
ald
o, 1
99
7
Rin
ald
o, R
od
rigu
ez-I
turb
e e
Rig
on
, 19
98
58
Friday, September 10, 2010
What is Geomorphometry? A Brief Introduction - I
Silvia Franceschi
59
Numbering in JGrass
MAIN TRIBUTARIES:second-level even numbers
third-level channel
MODIFIED PFAFSTETTER SYSTEM
MAIN CHANNEL:first-level odd numbers
Friday, September 10, 2010
What is Geomorphometry? A Brief Introduction - I
Silvia Franceschi
Network level 5
Network level 4
Network level 3
Network level 2
Network level 1
60
Numbering in JGrass
Friday, September 10, 2010
What is Geomorphometry? A Brief Introduction - I
Silvia Franceschi
61
Network level 4
Network level 3
Network level 2
Network level 1
Numbering in JGrass
Friday, September 10, 2010
What is Geomorphometry? A Brief Introduction - I
Silvia Franceschi
62
Network level 3
Network level 2
Network level 1
Numbering in JGrass
Friday, September 10, 2010
What is Geomorphometry? A Brief Introduction - I
Silvia Franceschi
63
Network level 2
Network level 1
Numbering in JGrass
Friday, September 10, 2010
What is Geomorphometry? A Brief Introduction - I
Silvia Franceschi
64
Network level 1
Numbering in JGrass
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Drainage Density
65
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Delineation of the Hydrographic Catchment
Riccardo Rigon
66
Drainage Density
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
The Distance of the Points on the Slopes from the Hydrographic Network
67
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
What happens on the slopes?
68
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Idrologia stazionaria dei versanti : T ∇z b + u d b = q a
Idrologia stazionaria dei versanti : T ∇z b + u d b = q a
69
Am
pli
tud
e Fu
nct
ion
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Leopold & Maddock 1953:
Relationships between Areas and Discharge
d ∝ Af
V ∝ Am
w ∝ Ab
Q ∝ Ac
Q = V × w × d =⇒ m + b + f = c70
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Q ∝ Ab
V ∝ Ac
w ∝ Ad
d ∝ Af
Q = V × w × d =⇒ c + d + f = b71
Leopold & Maddock 1953:
Relationships between Areas and Discharge
Questa tabella e’ immagine - non e’ modificabile con LaTeX
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Q ∝ Ab
V ∝ Ac
w ∝ Ad
d ∝ Af
Q = V × w × d =⇒ c + d + f = bAvisio, after Rigon et al. 2006 72
Leopold & Maddock 1953:
Relationships between Areas and Discharge
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
P [A > a] = a−βf(a/AT )
73
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Area - Slope Relationship
After Montgomery & Dietrich
74
Immagine non modificabile
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Idrologia stazionaria dei versanti : T ∇z b + u d b = q a
Hydrologic Flows within the Slopes
Idrologia stazionaria dei versanti : T ∇z b + u d b = q a
Stationary Hydrology of the Slopes:T ∇z b + u d b = q a 75
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Idrologia stazionaria dei versanti : T ∇z b + u d b = q a
Idrologia stazionaria dei versanti : T ∇z b + u d b = q a
Stationary Hydrology of the Slopes:
T ∇z b + u d b = q A
T ∇z b = q A
T /q ∇z = A/b
76
Hydrologic Flows within the Slopes
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
77
Area - Slope Relationship
After Montgomery & Dietrich
Immagine non modificabile.
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Idrologia stazionaria dei versanti : T ∇z b + u d b = q a
Idrologia stazionaria dei versanti : T ∇z b + u d b = q a
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
Hydrologic Flows within the Slopes
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
79
Area - Slope Relationship
After Montgomery & Dietrich
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
The Topographic Index
Stationary Hydrology of the Slopes:
It = log A/log (b ∇z)
T /q ∇z = A/b
80
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
81
Th
e T
op
ogra
ph
ic
Ind
ex
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
The Topographic Index
82
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
83
List of SymbolsSymbol 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
Friday, September 10, 2010
Delineation of the Hydrographic Catchment
Riccardo Rigon
Thank You for Your Attention.
84
G. U
lric
i -
Friday, September 10, 2010