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