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

Riccardo Rigon

Objectives

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Riccardo Rigon

Objectives

2

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



Riccardo Rigon

Objectives

2


•To apply some simple hydrological balances at slope scale



Riccardo Rigon

Objectives

2



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



Riccardo Rigon

Objectives

2



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

•To define the concept of a digital catchment



Riccardo Rigon

The Discretisation of the Terrain

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http://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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The Primary Topographic Attributes:

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- Altitude

- Slope

- Curvature



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Altitude

z = f(x, y)

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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

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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

)



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Gradient

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Gradient

fy =∂z

∂yfx =

∂z

∂x∇z = (fx, fy)Gradients

9



Riccardo Rigon

Gradient

fy =∂z

∂yfx =

∂z


9

γ = arctan�

f2x + f2

y

Slope

Slope



Riccardo Rigon

Gradient

fy =∂z

∂yfx =

∂z


9

γ = arctan�

f2x + f2

y

Slope

Slope

Aspect

α = arctanfy

fxAspect



Riccardo Rigon

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Gradient



Riccardo Rigon

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

curve is.

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CURVATURE:



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curve is.

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A line segment has null curvature.

CURVATURE:



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curve is.

CURVATURE:



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curve is.

CURVATURE:



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CURVATURE : once some curves have been

identified on a surface their curvature can be

defined.

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Riccardo Rigon

Curves along the flowlines are defined by Longitudinal Curvature.

Curves along the contour lines are defined by Transversal Curvature.

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TC 16

CURVATUREThe composition of the curvatures produces 9 main

topographic forms



Riccardo Rigon

The main derived quantities are:

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•Drainage Directions

•Contributing Areas



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It’s easy to say Drainage Directions



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DrainDir20

It’s easy to say Drainage Directions

Orl

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et a

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00

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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



Riccardo Rigon

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Drainage Directions



Riccardo Rigon

The Hydrographic Network: where do the Channels begin?

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Mon

tgom

ery

and

Die

tric

h, W

RR

, 19

92




Riccardo Rigon

Ab29




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How

ard

, WR

R, 1

99

4




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Hydrographic Catchments after SCHUMM

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Riccardo Rigon

Hydrographic Catchments

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Riccardo Rigon

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From

Arc

Hyd

ro

Hydrographic Catchments in digital


What is Geomorphometry? A Brief Introduction - I

Silvia Franceschi

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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



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



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



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



Silvia Franceschi

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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



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



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.

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Digital Watershed



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.

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Digital Watershed



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Riccardo Rigon

Strahler Numbering

and

Horton’s Laws

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• The “extracted” hydrographic network is, mathematically

speaking, an oriented graph.

•The elements of such a graph have a tree topology.



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Strahler Numbering and Horton’s Laws



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The “sources” are

marked in yellow



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49



marked in yellow

The sources have

S t r a h l e r s t r e a m

order 1



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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



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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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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




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



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

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



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

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Rig

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, 19

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Silvia Franceschi

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Numbering in JGrass

MAIN TRIBUTARIES:second-level even numbers

third-level channel

MODIFIED PFAFSTETTER SYSTEM

MAIN CHANNEL:first-level odd numbers



Silvia Franceschi

Network level 5

Network level 4

Network level 3

Network level 2

Network level 1

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Numbering in JGrass



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Network level 4

Network level 3

Network level 2

Network level 1

Numbering in JGrass



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Network level 3

Network level 2

Network level 1

Numbering in JGrass



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Network level 2

Network level 1

Numbering in JGrass



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Network level 1

Numbering in JGrass



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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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Riccardo Rigon

What happens on the slopes?

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Riccardo Rigon

Idrologia stazionaria dei versanti : T ∇z b + u d b = q a


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Am

pli

tud

e Fu

nct

ion



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



Riccardo Rigon

Q ∝ Ab

V ∝ Ac

w ∝ Ad

d ∝ Af

Q = V × w × d =⇒ c + d + f = b71



Questa tabella e’ immagine - non e’ modificabile con LaTeX



Riccardo Rigon

Q ∝ Ab

V ∝ Ac

w ∝ Ad

d ∝ Af

Q = V × w × d =⇒ c + d + f = bAvisio, after Rigon et al. 2006 72





Riccardo Rigon

P [A > a] = a−βf(a/AT )

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Riccardo Rigon

Area - Slope Relationship

After Montgomery & Dietrich

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Immagine non modificabile



Riccardo Rigon


Hydrologic Flows within the Slopes


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



Riccardo Rigon



Stationary Hydrology of the Slopes:

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.



Riccardo Rigon




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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Riccardo Rigon

The Topographic Index


It = log A/log (b ∇z)

T /q ∇z = A/b

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Th

e T

op

ogra

ph

ic

Ind

ex



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The Topographic Index

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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



Riccardo Rigon

Thank You for Your Attention.

84

G. U

lric

i -


2 hydro-geomorphology

Education

Transcript of 2 hydro-geomorphology