Patterned Landscapes - PowerPoint Presentation

Slide1

Patterned Landscapes

EcohydrologyFall 2015Slide2

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: reefsSlide3

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

We’re interested in ecosystem scale

Math applies to attributes individual organisms (spots, fingerprints, eye-patterns), ecosystems, chemical reactions, interstellar reactions

https://

www.youtube.com/watch?v=u-mEjfBaYks Slide4

Underlying Mechanisms

Activator-inhibitor principleA system component “generates” itself via some autocatalytic action (self-reinforcement)Acts at a local scaleAt the same time, this self-generation inhibits growth at a larger scale

Production of toxins, exhaustion of a critical resource, competitive effectsSlide5

Patterned Landscapes and Regime Shifts

Rietkerk et al. (2009)

ScienceSlide6

Engineering the Planet (Gaia)

Photosynthetic

Plants

Atmospheric

Oxygen

+

-

Heterotrophy

+

-Slide7

Activator-Inhibitor

Activators catalyze themselvesSlow 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 feedbacksOxygen in the Gaia systemRietkerk and van de Koppel (2008)TREESlide8

Scale Dependent Feedbacks

Local positive feedbacks catalyze dispersal over short distancesInhibition occurs over longer rangeAutocorrelation as an indicator

Rietkerk and van de Koppel (2008)

TREESlide9

Simulating Scale-Dependent Feedbacks

Random initial conditionsX-axis increases the strength of the local positive feedbackY-axis decreases the scale of the distal negative feedbackSlide10

Reaction – Diffusion Simulations

http

://mrob.com/pub/comp/xmorphia/index.html

Two diffusing reagents (U and V) react in a control space (U + 2V → 3V and

V → P (inert)Parameters control:Diffusion (Du and Dv) rate (with concentration gradient)Replenishment of U and utilization of V via “F” and “k”Slide11

Recent Example – Patterned Peatlands

Striking spatial surface patterning has been a subject of study for 30 years.10-100 m

2

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)EcosystemsSlide12

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)

EcosystemsSlide13

Evapotranspiration mechanism

Nutrients (TP)

Nutrients (TP)

Hollow

Hummock

g

round water flow:

ET pump

Precipitation

ET

PeatSlide14

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 elevationSlide15

Tidal Mud Flats

Origins of ephemeral tidal mudflat patternsTop-down control of pattern lossSlide16

Regular Pattern on Mud Flats

Hummock and hollow morphologyRegular, Transient

Hummocks contain large biomass of diatoms

EPS cohesion of sediments

Hollows have low biomassWeak cohesion

Biogeomorphic patternSlide17

Models of Pattern

Bifurcation (alternative stable states) in response to erosion rates and photosynthesisSlide18

Measurements of Pattern

Significant negative spatial autocorrelation at pattern “wavelength”Orientation mattersSlide19

Impacts of Pattern

Pattern mudflats are more productive than homogenous mudflats

Trophic impacts

Patterned mudflats

hold the sediment more effectively than homogeneous mudflatsWater quality impactsSlide20

Trophic Interactions

Loss of pattern over the summerSlide21

Sediment Processes Impacted by Grazers

Increase in benthic invertebrate grazers over summer leads to loss of diatomsLoss of diatoms leads to loss of pattern

Observations over Time

Experimental ManipulationSlide22

Persistence and Loss of Pattern in the EvergladesSlide23

What Drives Local Variation in “States”?

Watts et al. (2010)Slide24

Predictions

Bi-modal distribution of soil elevationScale-dependent auto-correlationAnisotropic because the landscape is patterned in the direction of flow

Changes with hydrologic modificationSlide25

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 Flow06.7Drained0

4.2Conserved 117.4

14.1Conserved 220.219.1

Transition 1

24.724.1

Transition 226.1

12.2Impounded

013.9

ENP

16.9

14.2Slide26

Scale-Dependent Feedbacks are Present, Anisotropic, and can DegradeSlide27

What Are the Mechanisms?

Discriminating amongst causes and consequences is hard (correlation ≠ causation)So how to proceed?Slide28

Model Experiments – Turn On and Turn Off MechanismsSlide29

Rich Pattern VarietySlide30

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 interconnectedRidges cover ca. 50% of area in conservedHydroperiod – R ~ 90%, S ~ 100%Regular patterning?Slide31

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 FlowContemporary FlowSlide32

Mechanisms Matter

“Getting the water right” = understanding mechanisms of pattern genesisCompeting mechanisms all make predictions that “look” similar (elongated patches)

Alternative discriminant indicators?

Cheng et al., 2011

Lago

et al., 2010Larsen et al., 2011

Acharya et al., in prep

Velocity & Sediment

Soil TP

HydroperiodSlide33

Hypotheses for Landscape Formation

Sediment redistribution

(

Larsen et al., 2007; Larsen and Harvey, 2010,

2011

)Requires unobserved (and unlikely) velocitiesWavelength governed by local velocity dynamicsNutrient 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 IndicatorsPresence and magnitude of landscape characteristic wavelength

Distribution of patch sizes (power vs. exponential) Slide34

Spectral Analysis Reveals Scale Dependent Feedbacks in Regular Patterns

2D Fourier transform used to extract spectral information

Peaks in R-spectrum correspond to dominant wavelengthsSlide35

Evidence of Scale-Dependent Feedbacks in Regular

Patterns

DeBlauw

et al. 2007Slide36

Theory:

Fractal PatterningLocal facilitation, growth impeded by

global

constraints (e.g., finite water)

Patch sizes are power functions

with no characteristic wavelengthScanlon et al., 2007 (isotropic local contagion)Slide37

No periodicity (i.e.,

no characteristic wavelength)Patterning is scale-free (global not distal feedback)

Ridge-Slough Pattern

WCA3AN

Northern

WCA3AS

Central

WCA3ASCasey et al. in prepSlide38

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

IMPOUNDEDCONSERVEDDRAINEDYuan et al. in prepSlide39

Based on cellular automata model

(Scanlon et al. 2007)Scale-free (global) constraint on ridge expansionRidge prevalence controls landscape

discharge competence

Anisotropic local feedback

Invoked in ALL ridge-slough models

Mechanism? Simple Aperiodic ModelCasey et al. in prepSlide40

Scale Dependent Pattern Features: Elongation and Orientation

Length:Width

Eccentricity

Orientation

Solidity

Casey et al.

in prepSlide41

Summary:

Discriminating Mechanisms of Pattern GenesisThe ridge-slough landscape exhibits fractal

not

regular

patterningNo characteristic wavelength; power function distribution of lengths, widths and areasI

mplies weak distal feedbacks inconsistent with most proposed mechanismsOur scale-free model misses scale-dependenciesOrientation & elongation increase with patch sizeGetting the water right for the ridge-slough landscape means resolving the mechanismsSlide42

An Abiotic Example – Sorted Stones

Pattern emergence in polar and high alpine environmentsSelf-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 inhibitorHillslopes = stripesFlat – labyrinth or circularKessler and Werner (2003)ScienceSlide43

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 expansionSlide44

Simulation (Cellular Automata)

Vary initial stone density (high to low)

Vary lateral slope (low to high)

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 Slide45

Time-Series

Emergence of pattern from random initial conditionsScale 10 x 10 m

High confinement, low slope

There are physical 6 parameters in their modelSlide46

Self-Organization of Sand Dunes

Self-organized morphologyActivator = wind and friction

Inhibitor = height increases gravitation loss, and increases wind velocity

Star formation when there are seasonally adjusting windsSlide47

Self-Organization of River Channels

Activator = water flow and erosion; variable depositionInhibitor = sustained differences in erosion/deposition over-bend the river, causing catastrophic resetting (ox-bows)

Biota confer bank stability which constrains channel movementSlide48

Next Time…

Humid Land Ecohydrology