Patterned Landscapes Ecohydrology Fall 2011

Self-organized patterning © 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) 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

Recent Example – Patterned Peatlands Striking spatial surface patterning has been a subject of study for 30 years. – 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) 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) 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 Flow06.7 Drained04.2 Conserved Conserved Transition Transition Impounded013.9 ENP

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) velocities  Wavelength governed by local velocity dynamics Nutrient redistribution (Ross et al., 2006; Cheng et al., 2011)  Requires unobserved hydraulic gradients in groundwater  Wavelength 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 accretion  Critically, 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 Northern WCA3AS Central WCA3AS 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 IMPOUNDEDCONSERVEDDRAINED 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 Length:WidthEccentricity 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