Carbonate coasts as complex systems: A Case Study from Andros Island, Bahamas

Gene Rankey and Brigitte VlaswinkelUniversity of Miami

Thanks to sponsors:NASA, National Science Foundation, Petroleum Research Fund,

Contributors to the Comparative Sedimentology LabCenter for Southeastern Tropical Advanced Remote Sensing (CSTARS)

ROSENSTIEL SCHOOL

RSMAS

OF MARINE & ATMOSPHERIC SCIENCE

U N IV E R S IT Y O F

Coastal Sediments ‘03

Purposes• Quantify and describe spatial patterns on a

modern carbonate tidal flat

• Explore for the presence of chaos

• Highlight potential implications for interpretation of modern and ancient Earth surface systems

Focus of talk: Using quantitative morphometricsto provide insights on sedimentary system

Outline

• Background

• Geomorphology of the tidal flat

• Systemic facies patterns • Network structure

• Implications

Study Locations

Miami

AndrosIsland

Tidal Flat Subenvironments

• carbonate• microtidal

• humid

• Readily discernable on remote sensing

data

1 km

TM bands 4,2,1

Tidal Flat SubenvironmentsAlgal marsh

Mangrove pondBeach ridge

Channel

Outline

• Background

• Geomorphology of the tidal flat

• Systemic facies patterns Subfacies size

• Network structure

• Implications

Remote Sensing Data Analysis1 km

TM bands 4,2,1

1 km

Thematic Map‘Spectral Lithotopes’

Similar spectral signatures, NOT necessarily similar facies

Interpretation

1 km

Thematic Map‘Spectral Lithotopes’

…more than

‘just a pretty picture’

Calibration: Ikonos data

existing mapsfield observations

Composition - Patch SizeExceedance probability (E.P.) is the cumulative probability (P [Y ≥ x]) of a given patch of area Y having an area > x

Data3.61122.50039.45840.86453.56454.837123.516165.075187.622242.459

Data (raw)53.56454.83739.458123.51622.50040.864187.622242.4593.611

165.075

E.P.91%82%73%64%55%45%36%27%18%9%

Rank10987654321

Rank/(n+1)

Composition - Patch SizeExceedance probability (E.P.) is the cumulative probability (P [Y ≥ x]) of a given patch of area Y having an area > x

Exceedance probability has a power-law dependence on

the size of patch

Data is scale invariant or statistically self-similar

Spatial configuration (lacunarity) also scales

w/power-law

Composition - Patch sizeFor all intertidal facies:

• Data are statistically described by power laws

• Patch sizes have fractal distribution

Inflection suggests 2 different geomorphic processes

‘the spectrometer is not a geomorphologist’

Outline

• Background

• Geomorphology of Bahamian tidal flat

• Facies patterns

• Creek network structure Creek & network morphometrics Temporal character/evolution

• Implications

Tidal Creek Networks

• Creeks most dominant components wrt sediment distribution and overall morphology

Focus: Network attributes (composition & configuration) Temporal dynamics – compare active and inactive

networks - testing for divergence (chaos…maybe)

Distribution?

Tidal Creek Networks

Active networks

1 km

Stabilizednetworks

Horton (1945) stream numbering –

fluvial channel segments

Tidal Creek Networks

Order 3Order 2

Order 1

Tidal Creek SegmentsSegment length by network – exponential

Suggests stochastic processes, change in ‘rules’ at a certain length scale

Tidal Creek Network Structure

n

i

n

jijij rr

1 1sys )log(*E

Entropy: measure of network disorder

rij = probability of transition from a creek 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).

Tidal Creek Network Structure

E = 0 E > 0

Tidal Creek Network Structure

Entropy: measure of network disorder

Among active networks,entropy increases

exponentially from north to south

0.4

0.65

0.9

1.15

1.4

1 2 3 4

Network

Sys

tem

En

trop

y

southward

Einactive = 0.403

All active networks are more disordered than inactive

Presence of divergence through time…chaos (?)…

Historical Changes

1943 2001

• Creeks extending headwards, new creeks forming

…Observations consistent with predictions based on analysis

Tidal Creek Flow Structure

Data from UM/MIT field trip, March 2003

Flood tide; ‘predictable’

Summary

Nature of ‘Predictability’ varies depending on scale

• Subfacies size - power-law• Creek lengths - stochastic• Creek flow structure – ‘deterministic’ • Entropy of active networks > inactive networks: tidal creek networks more elaborate and diverge

Interpretation – Chaos?

Predicts non-linearityGeomorphic evidence?

Shoreline jumpsStratigraphic record? (TBA)

“Mix of randomness and order”

System Dynamics

Macro-scale:System

Meso-scale:Compartments

Micro-scale:Constituents

Fractal

Stochastic

Deterministic

Facies patterns

Tidal creeks

Grain transport

Important questions: Interfaces, characteristics, spatio-temporal domains

“Mix of randomness and order”

Take-Home Messages

• Nature and domains of co-existing order and disorder

• Divergent behavior (chaos)

• Implications for predictability