Carbonate coasts as complex systems: A Case Study from Andros Island, Bahamas Gene Rankey and Brigitte Vlaswinkel University of Miami Thanks to sponsors: NASA, National Science Foundation, Petroleum Research Fund, Contributors to the Comparative Sedimentology Lab Center for Southeastern Tropical Advanced Remote Sensing (CSTARS) 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 morphometrics to provide insights on sedimentary system

Outline Background Geomorphology of the tidal flat Systemic facies patterns Network structure Implications

Study Locations Miami Andros Island

Tidal Flat Subenvironments carbonate microtidal humid Readily discernable on remote sensing data 1 km TM bands 4,2,1

Tidal Flat Subenvironments Algal marsh Mangrove pond Beach ridge Channel

Outline Background Geomorphology of the tidal flat Systemic facies patterns  Subfacies size Network structure Implications

Remote Sensing Data Analysis 1 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 maps field observations

Composition - Patch Size Exceedance probability (E.P.) is the cumulative probability (P [Y ≥ x]) of a given patch of area Y having an area > x Rank/(n+1)

Composition - Patch Size Exceedance 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 size For 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 Stabilized networks

Horton (1945) stream numbering – fluvial channel segments Tidal Creek Networks Order 3 Order 2 Order 1

Tidal Creek Segments Segment length by network – exponential Suggests stochastic processes, change in ‘rules’ at a certain length scale

Tidal Creek Network Structure Entropy: measure of network disorder r ij = 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 E inactive = All active networks are more disordered than inactive Presence of divergence through time …chaos (?)…

Historical Changes 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-linearity Geomorphic evidence? Shoreline jumps Stratigraphic 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