Patterned
Landscapes
Ecohydrology
Fall 2011
Self-organized patterning
Ocean: reefs
Sub-surface flow wetlands:
© Compics International Inc.
Arid lands: Tiger Sahel
http://www.atmos.albany.edu/student/gareth/amma.html
Surface flow wetlands:
What are patterned landscapes?
• The emergence of spatial pattern in
ecosystems from the action of local ecological
interactions (self-organization)
– Order emerges from disorder via the assembly of
small scale interactions (emergent property)
• Can occur at multiple scales
– Most striking at the ecosystem scale
Underlying Mechanisms
• Activator-inhibitor principle
– A system component “generates” itself via some
autocatalytic action (self-reinforcement)
– Acts at a local scale
– At the same time, this self-generation inhibits
growth at a larger scale
• Production of toxins, exhaustion of a critical resource,
competitive effects
Patterned Landscapes and Regime Shifts
Rietkerk et al. (2009)
Science
Engineering the Planet (Gaia)
+
Photosynthetic
Plants
Atmospheric
Oxygen
+
Heterotrophy
-
Activator-Inhibitor
• Activators catalyze
themselves
– Slow diffusion prevents rapid
expansion, but creates strong
local positive feedbacks
– Plants in the Gaia system
• Inhibitors result from that
action
– Rapid diffusion allows the
inhibitory effect to be felt at
distance
– Distal negative feedbacks
– Oxygen in the Gaia system
Rietkerk and van de Koppel (2008)
TREE
Scale Dependent Feedbacks
• Local positive
feedbacks catalyze
dispersal over short
distances
• Inhibition occurs over
longer range
– Autocorrelation as an
indicator
Rietkerk and van de Koppel (2008)
TREE
Simulating Scale-Dependent Feedbacks
• Random initial
conditions
• X-axis increases the
strength of the local
positive feedback
• Y-axis decreases the
scale of the distal
negative feedback
Rietkerk et al. (2009)
Science
Reaction – Diffusion Simulations
• http://www.aliensaint.com/uo/java/rd/
Recent Example – Patterned Peatlands
• Striking spatial surface
patterning has been a
subject of study for 30
years.
– 10-100 m2 patches of
hummocks (thicker peat)
and hollows (thinner
peat)
– Typically radial/maze on
flat ground, ribbons
orthogonal to flow on
sloped ground
Eppinga et al. (2008)
Ecosystems
Diagnostic Properties of Patterned Landscapes
• Evidence of bi-stability
Eppinga et al. (2008)
Ecosystems
• Evidence of scale
dependent feedbacks
Rietkerk and van de Koppel (2008)
TREE
Evapotranspiration mechanism
Precipitation
ET
Nutrients (TP)
Peat
Nutrients (TP)
Hollow
ground water flow:
ET pump
Hummock
Mechanism for Bog Patterning
• Nutrient accumulation in higher
ground driven by accelerated
evapotranspiration and higher
productivity
– Water flows towards hummocks
(either radially in flat landscapes
or along slopes in sloped
landscapes)
• “Mines” nutrients from distal
locations, making them less
productive, and therefore less
likely to maintain a positive
carbon balance at high
elevation
Persistence and Loss of Pattern in the
Everglades
What Drives Local Variation in “States”?
Watts et al. (2010)
Predictions
• Bi-modal distribution of
soil elevation
• Scale-dependent autocorrelation
– Anisotropic because the
landscape is patterned
in the direction of flow
• Changes with
hydrologic modification
Bi-Modality is a
Keystone Feature of
the Best Conserved
Parts of the
Landscape
(and the loss of this
feature PRECEDES
changes in vegetation!)
Bimodal (cm) A-priori (cm)
Stabilized Flow
0
6.7
Drained
0
4.2
Conserved 1
17.4
14.1
Conserved 2
20.2
19.1
Transition 1
24.7
24.1
Transition 2
26.1
12.2
Impounded
0
13.9
ENP
16.9
14.2
Scale-Dependent
Feedbacks are
Present,
Anisotropic, and
can Degrade
What Are the Mechanisms?
• Discriminating amongst causes and
consequences is hard (correlation ≠ causation)
• So how to proceed?
Model Experiments – Turn On and
Turn Off Mechanisms
Rich Pattern Variety
Everglades Ridge-Slough
Landscape
• Important features
–
–
–
–
Shallow regional slope (3 cm km-1)
Elevated ridges, lower sloughs (Δh ~ 25 cm)
Autogenic (i.e., not driven by limestone)
Patches elongated with historical flow, sloughs
are interconnected
– Ridges cover ca. 50% of area in conserved
– Hydroperiod – R ~ 90%, S ~ 100%
– Regular patterning?
Patterning/Pattern Loss in the Everglades
Historic Flow
Parallel ridges and
sloughs existed in an
organized pattern,
oriented parallel to the
flow direction, on a
slightly sloping peatland
Contemporary Flow
Compartmentalization
and water management
have led to degraded
landscape patterns 
detrimental ecological
effects (SCT, 2003)
Mechanisms Matter
• “Getting the water right” = understanding
mechanisms of pattern genesis
• Competing mechanisms all make predictions
that “look” similar (elongated patches)
• Alternative discriminant indicators?
Velocity & Sediment
Lago et al., 2010
Larsen et al., 2011
Soil TP
Cheng et al., 2011
Hydroperiod
Acharya et al., in prep
Hypotheses for Landscape Formation
• Sediment redistribution (Larsen et al., 2007; Larsen and Harvey,
2010, 2011)
Potentially
Requires unobserved
(and Indicators
unlikely) velocities
Useful
 Wavelength governed by local velocity dynamics
• Presence
and(Ross
magnitude
of
• Nutrient
redistribution
et al., 2006; Cheng et al., 2011)
 Requires
unobserved
hydraulic gradientswavelength
in groundwater
landscape
characteristic
 Wavelength controlled by lateral transport distances
•
Distribution
of
patch
sizes
(power
• “Self-Organizing Canal” Hypothesis (Cohen et al., 2011)
vs. exponential)
 Feedback
between pattern (as it relates to landscape flow
routing), hydroperiod and C accretion
 Critically, predicts the distal feedback is diffuse, acting
weakly at any location…no characteristic wavelength
Spectral Analysis Reveals Scale Dependent
Feedbacks in Regular Patterns
• 2D Fourier transform used to
extract spectral information
• Peaks in R-spectrum correspond to
dominant wavelengths
Evidence of Scale-Dependent
Feedbacks in Regular Patterns
DeBlauw et al. 2007
Theory: Fractal Patterning
• Local facilitation, growth impeded by global
constraints (e.g., finite water)
• Patch sizes are power functions with no
characteristic wavelength
Scanlon et al., 2007 (isotropic local contagion)
Ridge-Slough Pattern
WCA3AN
Northern
WCA3AS
Central
WCA3AS
• No periodicity (i.e., no characteristic wavelength)
• Patterning is scale-free (global not distal feedback)
Casey et al. in prep
Fractal Patch Size Distributions
• Regular patterns yields exponential functions
– Patch size truncated by distal feedbacks
• Fractal patterns produce power functions
– Local facilitation with diffuse constraints
IMPOUNDED
Yuan et al. in prep
CONSERVED
DRAINED
Simple Aperiodic Model
• Based on cellular automata
model (Scanlon et al. 2007)
• Scale-free (global) constraint
on ridge expansion
– Ridge prevalence controls
landscape discharge
competence
• Anisotropic local feedback
– Invoked in ALL ridge-slough
models
– Mechanism?
Casey et al. in prep
Scale Dependent Pattern Features:
Elongation and Orientation
Length:Width
Orientation
Casey et al. in prep
Eccentricity
Solidity
Summary:
Discriminating Mechanisms of Pattern Genesis
• The ridge-slough landscape exhibits fractal not
regular patterning
– No characteristic wavelength; power function
distribution of lengths, widths and areas
• Implies weak distal feedbacks inconsistent with
most proposed mechanisms
• Our scale-free model misses scale-dependencies
– Orientation & elongation increase with patch size
• Getting the water right for the ridge-slough
landscape means resolving the mechanisms
An Abiotic Example – Sorted Stones
•
•
•
Pattern emergence in polar
and high alpine
environments
Self-organized (or by the
Yeti)
Formed by freeze-thaw
cycles
– Activator = freezing is
preferential where stones
are sparse; freezing
displaces stones
– Inhibitor = ice moves
stones and concentrates
them
•
Shapes configured by the
orientation of the inhibitor
– Hillslopes = stripes
– Flat – labyrinth or circular
Kessler and Werner (2003)
Science
Underlying Mechanisms
• Frost heave expands soil
(horizontally and vertically)
• Stones creep towards “stone
domains” while soil creeps
towards “soil domain”
• Stones fall away from “stone
domain” centers (making stone
piles of standard size)
• Wider stone domains are pushed
more, and therefore get taller, and
therefore spread
– Stones can get pushed along a
stone domain if they are
constrained against radial
expansion
Simulation (Cellular Automata)
A.
Vary initial
stone density
(high to low)
B.
Vary lateral
slope (low to
high)
C.
Vary lateral
confinement
(low to high)
Confinement = do stones stay in a stone domain; high values increase lateral transport
along stone domains and lower radial diffusion
Time-Series
• Emergence of pattern
from random initial
conditions
• Scale 10 x 10 m
• High confinement,
low slope
– There are physical 6
parameters in their
model
Self-Organization of Sand Dunes
• Self-organized
morphology
– Activator = wind and
friction
– Inhibitor = height
increases gravitation loss,
and increases wind
velocity
• Star formation when
there are seasonally
adjusting winds
Self-Organization of River Channels
• Activator = water flow
and erosion; variable
deposition
• Inhibitor = sustained
differences in
erosion/deposition overbend the river, causing
catastrophic resetting
(ox-bows)
• Biota confer bank
stability which
constrains channel
movement
Next Time…
• Humid Land
Ecohydrology