1. Patterned Landscapes
Ecohydrology
Fall 2017

2. Self-organized patterning
Ocean: reefs
Sub-surface flow wetlands:
© Compics International Inc.
Arid lands: Tiger Sahel
Surface flow wetlands:
Landscape patterns have been observed in a variety of landscapes, from ocean reefs (upper left; Great Barrier Reef in Australia) to arid lands (Tiger Sahel in Mali, West Africa). These patterns are made up of either scale-invariant (power-law) or regular patches that are the result of multiple-scale interactions arising from an unusual control of biota on landform (ecosystem engineering). The pattern formation is important for local and landscape processes, where the patterning lends increased stability and primary productivity to the landscape. For this talk, we will focus on the processes that create landscape patterns in wetlands. These patterned wetlands occur it peatlands, and have been observed in subsurface flow peatlands (upper right; boreal peatlands) and surface flow wetlands (lower left; central Everglades).

3. 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

4. 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

5. Patterned Landscapes and Regime Shifts
Rietkerk et al. (2009)
Science

6. Engineering the Planet (Gaia)+
Photosynthetic
Plants
Atmospheric
Oxygen - - +
Heterotrophy

7. 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

8. 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
Rietkerk and Van De Koppel (2008)
TREE

9. 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 and Van De Koppel (2008)
TREE

10. Reaction – Diffusion Simulations
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”

11. Recent Example – Patterned Peatlands
Striking spatial surface patterning has been a subject of study for 30 years.
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

12. Diagnostic Properties of Patterned Landscapes
Evidence of bi-stability
Evidence of scale dependent feedbacks
Eppinga et al. (2008)
Ecosystems
Rietkerk and van de Koppel (2008)
TREE

13. Evapotranspiration mechanism
Precipitation ET
ET needs to be high enough that it can create head differences from lower areas to higher areas in order to preferentially accumulate P in higher-elevation patches, so that higher ET rates cause water to flow from patches with lower ET rates (i.e., lower production, lower elevation patches) to patches with higher ET rates (i.e., higher production, higher elevation patches). As high-density patches pull water from the soil and release it to the atmosphere (transpiration), ground water must flow from the lower-density patches to the higher-density patches. Essentially, this mines nutrients from the landscape to preferentially accumulate in higher-density patches as solutes flow with water, which feeds back to control the rate of higher ET, higher nutrient patch expansion. This mechanism is predicated on ET-generated movement of water being higher than drainage-generated movement of water, because gravity will move water from higher to lower elevations in the absence of a hydrologic pumping mechanism altering the gradient (i.e., drainage would occur), particularly in high-porosity peat. Therefor this condition is going to be more likely to be met when ET:P ratios are higher.
Peat
Nutrients (TP)
Nutrients (TP)
ground water flow:
ET pump
Hollow
Hummock

14. 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

15. Tidal Mud Flats Origins of ephemeral tidal mudflat patterns
Top-down control of pattern loss

16. Regular Pattern on Mud Flats
Hummock and hollow morphology
Regular, Transient
Hummocks contain large biomass of diatoms
EPS cohesion of sediments
Hollows have low biomass
Weak cohesion
Biogeomorphic pattern

17. Models of Pattern
Bifurcation (alternative stable states) in response to erosion rates and photosynthesis

18. Measurements of Pattern
Significant negative spatial autocorrelation at pattern “wavelength”
Orientation matters

19. Impacts of Pattern
Pattern mudflats are more productive than homogenous mudflats
Trophic impacts
Patterned mudflats hold the sediment more effectively than homogeneous mudflats
Water quality impacts

20. Trophic Interactions
Loss of pattern over the summer

21. Sediment Processes Impacted by Grazers
Increase in benthic invertebrate grazers over summer leads to loss of diatoms
Loss of diatoms leads to loss of pattern
Observations over Time
Experimental Manipulation

22. Persistence and Loss of Pattern in the Everglades

23. What Drives Local Variation in “States”?
Watts et al. (2010)

24. 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

25. 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
6.7
Drained
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
13.9
ENP
16.9
14.2

26. Scale-Dependent Feedbacks are Present, Anisotropic, and can Degrade

27. What Are the Mechanisms?
Discriminating amongst causes and consequences is hard (correlation ≠ causation)
So how to proceed?

28. Model Experiments – Turn On and Turn Off Mechanisms

29. Rich Pattern Variety

30. 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?

31. 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)

32. 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
Soil TP
Hydroperiod
Lago et al., 2010
Larsen et al., 2011
Cheng et al., 2011
Acharya et al., 2015

33. 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)

34. 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

35. Evidence of Scale-Dependent Feedbacks in Regular Patterns
DeBlauw et al. 2007

36. 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)

37. Ridge-Slough Pattern
Northern
WCA3AS
Central
WCA3AS
WCA3AN
No periodicity (i.e., no characteristic wavelength)
Patterning is scale-free (global not distal feedback)
Casey et al. 2016

38. 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
CONSERVED
DRAINED
Yuan et al. 2017

39. 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. 2016

40. Scale Dependent Pattern Features: Elongation and Orientation
Length:Width
Eccentricity
Orientation
Solidity
Casey et al. 2016

41. 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

42. 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

43. 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

44. 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

45. 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

46. 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

47. 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

48. Next Time…
Humid Land Ecohydrology