Experimental physical modeling Experimental physical modeling of tidal creek networksof tidal creek networks

Brigitte VlaswinkelBrigitte VlaswinkelAugust 2004August 2004

Marine Geology and Geophysics DivisionRosenstiel School of Marine and Atmospheric ScienceUniversity of Miami

This week’s goal…This week’s goal…

Build a tidal drainage network from scratch:Build a tidal drainage network from scratch:

Bidirectional flowBidirectional flow Very low gradient (6Very low gradient (6..1010-4-4))

Conform to the Conform to the Reality??Reality??

Study LocationsStudy Locations

Miami

Andros Island

South Florida

Digitized on IKONOS data and orthophoto Digitized on IKONOS data and orthophoto quadsquads

Analyzed in GISAnalyzed in GIS

Tidal Creek NetworksTidal Creek Networks

2000 m 500 m

B

© SpaceImaging

5 km

Andros South Florida

2 km

• muddy carbonates• microtidal, low energy• shallow creeks• juvenile mangrove

• mixed carbonate / organics• mesotidal• deep creeks (3-6 m), more straight• mature mangrove forests

Andros IslandBahamas

Big Sable CreekSouthwest Florida

1 km

Stabilizednetworks

Active networks

1

2

3

4

Horton (1945)Horton (1945) stream numbering – fluvial stream numbering – fluvial

channel segmentschannel segments

Order 3Order 2

Order 1

11

2

3

2

Tidal Creek SegmentsTidal Creek SegmentsSegment length by network – geographic context

Exponential distribution

Andros

0.010

0.100

1.000

0 200 400 600 800 1000

Length (m)E

xcee

dan

ce P

rob

abili

ty

0.010

0.100

1.000

0 200 400 600 800 1000

Length (m)

Exc

eed

ance

Pro

bab

ility

Segment length by network – geographic context

South Florida

Exponential distributions

(North)(South)

Tidal Creek Segments–InterpretationTidal Creek Segments–Interpretation

Greater length of inflection = more shorter creeks

Exponential distribution: consistent with stochastic processes

Inflection: change in probability distribution structure, change in processes??

• Geographical influence..

• Change systematically from north to south

• more abundant short creeks to south (probabilistically)

• more later….

0

100

200

300

400

500

600

1 2 3 4

network

leng

th o

f in

flec

tion

(m

)

southward

Andros

Tidal Creek Network StructureTidal Creek Network Structure

n

i

n

jijij rr

1 1sys )log(*E

Entropy: measure of network disorder

rij = probability of transition from a stream of order i into one of order j.

E = 0 indicates a perfectly ordered system (streams of order i flow only into streams of order i+1).

E = 0 E > 0

E = 0 means perfectly ordered system

E > 0 means disorder!

Creek networks are less ordered towards

the south…

0.4

0.65

0.9

1.15

1.4

1 2 3 4

Network

Sys

tem

En

trop

y

southward

Andros

Network Structure & Segment LengthNetwork Structure & Segment Length

Entropy (disorder)

correlates with

Abundance of short creeks

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

200 400 600

inflection in E.P.

syst

em

entr

opy

More shorter streams

Les

s o

rder

southward

R2 = 0.94

Andros

Composition Configuration

ConclusionsConclusions

Different settings, but many statistical similarities exist between two tidal networks in terms of scaling, patterns Different settings, but many statistical similarities exist between two tidal networks in terms of scaling, patterns and the and the exponentialexponential length-frequency distributions length-frequency distributions

Creek network metrics are consistentCreek network metrics are consistent among networks within each area among networks within each area

Bottom line: both composition and configuration of creek networks are Bottom line: both composition and configuration of creek networks are predictable (stochastically)predictable (stochastically)

ObjectivesObjectives

Create a tidal creek network with exponential length frequency Create a tidal creek network with exponential length frequency distributions similar to drainage systems found along distributions similar to drainage systems found along carbonate dominated shorelinescarbonate dominated shorelines

Observe and quantify (composition & configuration) the spatial Observe and quantify (composition & configuration) the spatial and temporal development of the tidal creek networksand temporal development of the tidal creek networks

Observe and quantify the similarities and differences that occur Observe and quantify the similarities and differences that occur during network elaboration using different scenarios of a tidal during network elaboration using different scenarios of a tidal regime (e.g. tidal range, asymmetry)regime (e.g. tidal range, asymmetry)

Compare and contrast the results with morphometric studies Compare and contrast the results with morphometric studies carried out in South Florida and Bahamascarried out in South Florida and Bahamas

HypothesesHypotheses

Glock, 1931

Tidal networks evolve differently though time than river networks…

HypothesesHypotheses

Tidal rangeTidal range Rel. # of 1Rel. # of 1stst order creeks order creeks

Vegetation density Vegetation density Width/depth ratioWidth/depth ratio

Max. channel depthMax. channel depth

A break in the probability distribution structure of creek lengths reflects A break in the probability distribution structure of creek lengths reflects an an abruptabrupt change in processes change in processes

Similar morphometric patterns, even with different hydrology, substrate Similar morphometric patterns, even with different hydrology, substrate and vegetation density, suggest the influence of more universal and vegetation density, suggest the influence of more universal processes and responses in the formation and evolution of tidal creek processes and responses in the formation and evolution of tidal creek networks.networks.

ReferencesReferences

Rankey, E.C., 2002. Spatial patterns of sediment accumulation on a Rankey, E.C., 2002. Spatial patterns of sediment accumulation on a Holocene carbonate tidal flat, northwest Andros Island, Bahamas. Holocene carbonate tidal flat, northwest Andros Island, Bahamas. Journal of Sedimentary Research, 51, p. 591-601.Journal of Sedimentary Research, 51, p. 591-601.

Rankey, E and Vlaswinkel, B., 2002. Morphometrics of carbonate tidal Rankey, E and Vlaswinkel, B., 2002. Morphometrics of carbonate tidal creek systems, Bahamas and Florida: Implications for tidal flat creek systems, Bahamas and Florida: Implications for tidal flat response to sea-level rise. Abstract and presentation at Geological response to sea-level rise. Abstract and presentation at Geological Society of America Conference, Denver, Co, October 2002. Society of America Conference, Denver, Co, October 2002.

My question to youMy question to you

With limitedWith limited and and

what would be the most useful dataset to collect ? what would be the most useful dataset to collect ?

Width/depthWidth/depth Hydrology Hydrology GradientsGradients