Patterned Landscapes Ecohydrology Fall 2011
Jan 15, 2016
Patterned Landscapes
EcohydrologyFall 2011
Self-organized patterning
http://www.atmos.albany.edu/student/gareth/amma.html
© Compics International Inc.
Arid lands: Tiger Sahel
Sub-surface flow wetlands:
Surface flow wetlands:
Ocean: reefs
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)
PhotosyntheticPlants
AtmosphericOxygen
+
-
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
• Evidence of scale dependent feedbacks
Rietkerk and van de Koppel (2008)TREE
Eppinga et al. (2008)Ecosystems
Evapotranspiration mechanism
Nutrients (TP)
Nutrients (TP)
Hollow Hummock
ground water flow:ET pump
Precipitation ET
Peat
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 auto-correlation– 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 6.7Drained 0 4.2Conserved 1 17.4 14.1Conserved 2 20.2 19.1Transition 1 24.7 24.1Transition 2 26.1 12.2Impounded 0 13.9ENP 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
Parallel ridges and sloughs existed in an organized pattern, oriented parallel to the flow direction, on a slightly sloping peatland
Compartmentalization and water management have led to degraded landscape patterns detrimental ecological effects (SCT, 2003)
Historic Flow
Contemporary Flow
Mechanisms Matter• “Getting the water right” = understanding
mechanisms of pattern genesis• Competing mechanisms all make predictions
that “look” similar (elongated patches)• Alternative discriminant indicators?
Cheng et al., 2011Lago et al., 2010 Larsen et al., 2011 Acharya et al., in prep
Velocity & Sediment Soil TP Hydroperiod
Hypotheses for Landscape Formation
• Sediment redistribution (Larsen et al., 2007; Larsen and Harvey, 2010, 2011)
Requires unobserved (and unlikely) velocitiesWavelength governed by local velocity dynamics
• Nutrient redistribution (Ross et al., 2006; Cheng et al., 2011)Requires unobserved hydraulic gradients in groundwaterWavelength controlled by lateral transport distances
• “Self-Organizing Canal” Hypothesis (Cohen et al., 2011) Feedback between pattern (as it relates to landscape flow
routing), hydroperiod and C accretionCritically, predicts the distal feedback is diffuse, acting
weakly at any location…no characteristic wavelength
Potentially Useful Indicators• Presence and magnitude of
landscape characteristic wavelength• Distribution of patch sizes (power
vs. exponential)
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)
• No periodicity (i.e., no characteristic wavelength)• Patterning is scale-free (global not distal feedback)
Ridge-Slough Pattern
WCA3AN NorthernWCA3AS
CentralWCA3AS
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 constraintsIMPOUNDED CONSERVED DRAINED
Yuan et al. in prep
• 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?
Simple Aperiodic Model
Casey et al. in prep
Scale Dependent Pattern Features: Elongation and Orientation
5 6 7 8 9 10 11 12 13 14 15-1.5
-1
-0.5
0
0.5
1
1.5
2log(L/W)
log(Patch Area)
log(
L/W
)
-0.34624+0.10126*X
r2 = 0.14019
5 6 7 8 9 10 11 12 13 14 15 1630
40
50
60
70
80
90
100Solidity
log(Patch Area)
Sol
idity
(pe
rcen
t)
5 6 7 8 9 10 11 12 13 14 15 16-100
-80
-60
-40
-20
0
20
40
60
80
100Patch Orientation
log(Patch Area)
Orie
ntat
ion
(deg
rees
)
5 6 7 8 9 10 11 12 13 14 15 16
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Patch Eccentricity
log(Patch Area)
Ecc
entr
icity
Length:Width Eccentricity
Orientation Solidity
Casey et al. in prep
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 over-bend the river, causing catastrophic resetting (ox-bows)
• Biota confer bank stability which constrains channel movement
Next Time…
• Humid Land Ecohydrology