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

Riccardo Rigon

Objectives

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

Riccardo Rigon

Objectives

•To apply some simple hydrological balances at slope scale

Riccardo Rigon

Objectives

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

Riccardo Rigon

Objectives

•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

Riccardo Rigon

A grid is a geographical space of equidistant cells.

Each cell contains a value, for example, of altitude.

Riccardo Rigon

The Primary Topographic Attributes:

- Altitude

- Slope

- Curvature

Riccardo Rigon

Altitude

z = f(x, y)

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

Riccardo Rigon

Statistical Properties: DISTRIBUTION CURVES

1200 1400 1600 1800 2000 2200 2400h m

P H > h

CoupledFieldsMoments8

no, IT

Riccardo Rigon

Gradient

Riccardo Rigon

Gradient

fy =∂z

∂yfx =

∂x∇z = (fx, fy)Gradients

Riccardo Rigon

Gradient

fy =∂z

∂yfx =

γ = arctan�

f2x + f2

Riccardo Rigon

Gradient

fy =∂z

∂yfx =

γ = arctan�

f2x + f2

Aspect

α = arctanfy

fxAspect

Riccardo Rigon

Gradient

Riccardo Rigon

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

curve is.

CURVATURE:

Riccardo Rigon

curve is.

A line segment has null curvature.

CURVATURE:

Riccardo Rigon

curve is.

CURVATURE:

Riccardo Rigon

curve is.

CURVATURE:

Riccardo Rigon

curve is.

CURVATURE:

Riccardo Rigon

curve is.

CURVATURE:

Riccardo Rigon

CURVATURE : once some curves have been

identified on a surface their curvature can be

defined.

Riccardo Rigon

Curves along the flowlines are defined by Longitudinal Curvature.

Curves along the contour lines are defined by Transversal Curvature.

Riccardo Rigon

CURVATUREThe composition of the curvatures produces 9 main

topographic forms

Riccardo Rigon

The main derived quantities are:

•Drainage Directions

•Contributing Areas

Riccardo Rigon

It’s easy to say Drainage Directions

Riccardo Rigon

DrainDir20

It’s easy to say Drainage Directions

Riccardo Rigon

Drainage Directions

Riccardo Rigon

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

Drainage Directions

Riccardo Rigon

The Hydrographic Network: where do the Channels begin?

Riccardo Rigon

Hydrographic Catchments after SCHUMM

Riccardo Rigon

Hydrographic Catchments

Riccardo Rigon

Hydrographic Catchments in digital

What is Geomorphometry? A Brief Introduction - I

Silvia Franceschi

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

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

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

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

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

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.

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.

Digital Watershed

Riccardo Rigon

Strahler Numbering

Horton’s Laws

• The “extracted” hydrographic network is, mathematically

speaking, an oriented graph.

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

Riccardo Rigon

Strahler Numbering and Horton’s Laws

Riccardo Rigon

The “sources” are

marked in yellow

Riccardo Rigon

marked in yellow

The sources have

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

order 1

Riccardo Rigon

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

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

Riccardo Rigon

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

Riccardo Rigon

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

Riccardo Rigon

1 10 100 1000Area

<L̂n>ê<L̂Hn-1L>

1 10 100 1000

h = 0.54

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

<L̂n>ê<L̂Hn-1L>

1 10 100 1000

h = 0.54

Silvia Franceschi

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

Numbering in JGrass

Silvia Franceschi

Network level 4

Network level 3

Network level 2

Network level 1

Numbering in JGrass

Silvia Franceschi

Network level 3

Network level 2

Network level 1

Numbering in JGrass

Silvia Franceschi

Network level 2

Network level 1

Numbering in JGrass

Silvia Franceschi

Network level 1

Numbering in JGrass

Riccardo Rigon

Drainage Density

Riccardo Rigon

Drainage Density

Riccardo Rigon

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

Riccardo Rigon

What happens on the slopes?

Riccardo Rigon

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

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 )

Riccardo Rigon

Area - Slope Relationship

After Montgomery & Dietrich

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

Riccardo Rigon

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

Riccardo Rigon

The Topographic Index

It = log A/log (b ∇z)

T /q ∇z = A/b

Riccardo Rigon

The Topographic Index

Riccardo Rigon

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

∇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.

2 hydro-geomorphology

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