Ecosystem feedbacks arising from wind transport in drylands: Results
from field experiments and modeling
Gregory S. Okin, U. California Los Angeles
David Rachal, Debra Peters, Finn PillsburyNew Mexico State University
Vegetation Community Change in DesertsShrub Encroachment
Note: These transformations have been ABRUPT and IRREVERSIBLE
The Teeter Totter/Islands of Fertility Model
Grasslands Shrublands
FEEDBACKS
Transport in Shrub EncroachmentThe Role of Connected Pathways
YesD
urin
g dr
ough
t
Fire fuel pathways
Vegetation cover
Vegetation cover
Climatic aridification
Mesic climate
Transport Pathways
Heterogeneouslydistributed
Low averagebiomassWoody
growth
Decreasedfire frequency
Increasedfire frequency
Woody mortality
Introduction ofexotic grasses Is cover dominated
by annuals orshort-lived perennials?
Homogenouslydistributed
High averagebiomass
Drought sensitivity
High P/PElow variability
Low intensityprecipitation
Low windspeeds
Low P/PEHigh variability
High intensityprecipitation
High windspeeds
Decreased transportDecreased runoff
Increased infiltration
Increased transportIncreased runoff
Decreased infiltration
Overgrazing, agriculture,other land use(fuelwood, ORV’s, etc.)
Shorter Longer
Longer Shorter
LOCOP: Length of Connected Pathways
Conceptual Cusp Catastrophe Models
Aeolian Processes: Basic Physics
• Saltation Flux – Efficient Saltators: 70 – 100 μm – Majority of momentum and mass
horizontal flux – Abrasion – Pedestaling – Burial (coppice dunes)
• Suspension Flux – Dust emission – Winnowing of soil – Removal of fines – Downwind deposition of fines
Verti
cal f
lux
Impacts of Saltation FluxAbrasion
Impacts of Saltation FluxPedestaling
Impacts of Saltation FluxBurial (coppice duning)
Effects of SuspensionDust Emission
• Emitted dust is generally < 50 μm • Particles < 50 μm are generally responsible for
– Most of the surface area of a soil – Most of the cation exchange capacity of a soil – Most of the water holding capacity of a soil – Most of the soil organic matter of a soil – Most of the available soil nutrients of a soil
• Losing these particles means degrading the ability of the soil to sustain plants, particularly during the germination and establishment phase
Testing the impact of dust emission on ecosystems
25m 25m 50
m
50m
Prevailing wind direction
10m meteorological tower
upwind
downwind
T4
100%
T3
75%
T2
50%
T1
25%
C
0%
Vegetation Removal
Aeolian sediment collectors (BSNEs)
25m
50m
Prevailing wind direction
50m
Upwind vegetation removed
Downwind no vegetation removed
25m
50m
Prevailing wind direction
50m
Upwind vegetation removed
Downwind no vegetation removed
line intercept transects
25m
50m
Prevailing wind direction
50m
Upwind vegetation removed
Downwind no vegetation removed
10m 10m
5m
10m
10m
5m
10m
10m 5m
10m
10m
5m
5x10m soil plots
25m
50m
Prevailing wind direction
50m
Upwind vegetation removed
Downwind no vegetation removed
10m
20m 10x20m veg plots
Changing Upwind BiogeochemistryMagnitude
Changing Upwind BiogeochemistryDistribution
0
0.5
1
1.5
2
2.5
Mar. 04 Jul. 04 Jul. 05
ratio
of C
.V. (
T4/C
)
TOCTN
Changing Upwind BiogeochemistryVariability - Geostatistics
γ(
h ) =
1
2nVt −Vt+
h ( )2
t
∑
Changing Upwind BiogeochemistryVariability - Geostatistics
0.0
0.5
1.0
1.5
2.0
2.5
T4 Mar. 04 T4 Jul. 04 C Mar. 04 C Jul. 04
0.00
0.05
0.10
0.15
0.20
0.25
T4 Mar. 04 T4 Jul. 04 C Mar. 04 C Jul. 04 0.00
0.02
0.04
0.06
0.08
0.10
0.12
T4 Mar. 04 T4 Jul. 04 C Mar. 04 C Jul. 04
TOC TN
Ran
ge (m
) V
aria
nce
(CO+
C)
0.0
0.5
1.0
1.5
2.0
2.5
T4 Mar. 04 T4 Jul. 04 C Mar. 04 C Jul. 04
Treatment Control Treatment Control
Treatment Control Treatment Control
Changing Upwind BiogeochemistrySoil Texture
Grain size category (D, µm)D>500 [250,500] [125,250] [50,125] D< 50
Mas
s pe
rcen
t
0
10
20
30
40
50
2004 2006
Changing Upwind Seed Bank
0
5
10
15
20
25
30
C T1 T2 T3 T4
Number of sprouts
Changing Downwind Biogeochemistry
0
1
2
3
4
5
6
7
2004 2006
CV
Dow
nwin
d/C
V C
ontr
ol
Navail
Na+
0
0.5
1
1.5
2
2.5
2004 2006
Con
c. D
ownw
ind/
Con
c. C
ontr
ol
Navail
Na+
Changing Downwind Communities
Feedbacks
Impact of aeolian processes on drylands
• Physical impact on plants – Abrasion, Pedestaling, Burial
• Biogeochemical impacts on soils – Soil texture and nutrient changes – Change in spatial distribution of nutrients
• Community composition changes – Changes to seedbank – Grass reduction and shrub increase
• Conceptual and mathematical models to integrate these effects
The ConMod Experiment
Wind Erodible SiteBasin Floor
Net
Sed
imen
t Flu
x (Δ
q z)
(g m
-2 d
-1)
-45
-30
-15
0
15
30
45N
et S
edim
ent F
lux
(Δq z)
(g m
-2 d
-1)
-10
-5
0
5
10
Net
Sed
imen
t Flu
x (Δ
q z)
(g m
-2 d
-1)
-20
-10
0
10
20N
et S
edim
ent F
lux
(Δq z
)(g
m-2
d-1
)
-10
-5
0
5
10
Non-WindErodible Site
Bajada
ConMods
• ConMods are effective at reducing the connectivity of degrading plots and changing them from deflationary to depositional
• Fallout Radionuclide work shows concentration of short-lived isotopes in ConMods and scouring from between them (with seasonal washing back into interspaces)
• A potential mechanism for rehabilitation?
A Simplistic Model for the Emergence of Bistability
• A bistable system is strongly suggested by – Presence of strong feedbacks – Abrupt and Irreversible transition
dG
dt= αG 1−
G
CG
⎛
⎝ ⎜
⎞
⎠ ⎟ − kGG
CG = f G( )
dS
dt= βS 1−
G + S( )CS
⎛
⎝ ⎜
⎞
⎠ ⎟ − kSG
G = Grass biomass S = Shrub biomass Ci=Carrying Capacity α, β, kG, kS = constants
The less grass there is, the lower the carrying capacity due to physical and biogeochemical factors
Grass growthdecreased
Grass growth Increased
threshold
ABRUPT
IRREVERSIBLE
A Bistable System
G: Grass Biomass α:Grass growth constant kG: Grass biomass decay rate
Grass and shrub states
Only shrub state
Threshold
More mesic climate, less grazing More arid climate, more grazing
The (very) Basics of Wind Erosion
• Wind erosion is threshold-controlled• Nonlinear above the threshold• Dust produced by sand blasting
Q∝u*−u*t( )a>1
for u*> u*t
0 for u*≤ u*t
⎧ ⎨ ⎪
⎩ ⎪ F = kQ
Total Horizontal Mass Flux(Mostly saltation)
Vertical Flux(Dust Emission)
36
Non-Erodible Elements
Viking Lander
Atriplex polycarpa
Spatially-Explicit Wind Erosion Model (SWEMO) (with vegetation)
QTot =ρg
u* u*2 − u*tv
2( )ΔTu*
∑ Shao & Raupach, 1993
F = QTotKGillette et al. 1997
U(z) =u*
kln
z − d
zo
⎛
⎝ ⎜
⎞
⎠ ⎟
zo =0.479λ − 0.001( )hc for λ ≤ 0.11
0.005hc for λ > 0.11
⎧ ⎨ ⎩
Marticorena et al. 1997
u*tv = u*t 1−mσλ( ) 1+ mβλ( )Raupach et al. 1993
u*tv = u*t (1−mC) 1+ mβCAp
AB
⎛
⎝ ⎜
⎞
⎠ ⎟
⎛
⎝ ⎜
⎞
⎠ ⎟
12
Okin and Gillette, 2004
Lateral Cover
• An index of how much profile area the wind encounters as it passes over a surface
• λ=N Ap (for a cylinder Ap= d h )
TextureSandy Loam
Loamy Sand
Clay LoamGravelly
Sand
u*t (cm/s) 29 34 68 28
Log (Fa/Qtot (cm-1
)) -3.7 -4.5 -5.7 -5.7
A 1.0 1.0 1.0 1.0
Vegetation Type
Grass Mesquite Creosote Tarbush SnakeweedOther Shrubs
Bare
Fractional Cover
0.25 0.21 0.17 0.12 0.29 0.17 0.001
Basal Area
(cm2)
900 5100 10800 13200 100 8500 0.001
Profile Area
(cm2)
1000 18500 9200 13800 100 8000 0.001
β 100 100 100 100 100 100 1
zo (cm) 3.8 4.1 8.2 4.6 1.8 5.6 0.04
Soil
Veg
etat
ion
Win
d
Okin and Gillette, 2004Okin and Gillette, 2004
Model Parameters
U*t (cm/s) U*tv (cm/s)
Okin and Gillette, 2004
Vegetation Type Grassland Mesquite Creosote Tarbush Playa Bare
Average -1.1 0.0 -1.0 -1.0 -0.8 1.5
Minimum -3.0 -0.6 -3.0 -2.3 -1.9 0.7
Maximum -0.3 0.9 -0.2 -0.4 -0.3 2.3
Log (QTot (g/cm/day))
Summary of measured values of QTot for different vegetation types in the Jornada Basin for the period July 24, 1998 to April 19, 2001. (Gillette, unpublished data)
Okin and Gillette, 2004
• Spatial– Soil and vegetation maps typically do not represent real
environmental variability– Variability in soil and vegetation parameters at scale smaller
than grid cell– Land use will be an important determinant of variability– Spatial organization in vegetation may exist
• Streets - elongated vegetation-free areas
• Temporal– Vegetation cover changes throughout the year
• Green and NPV BOTH have sheltering effect
– Land cover change & land use has a temporal signature
Sub-Grid Cell Heterogeneity
Modeling Spatial Variability
• Start with 2-D model
• Assume that u*t, C, β, Ap/AB are variable at a scale smaller than the grid cell (30 m)– (Modified) normal distribution characterized by
mean and coefficient of variation
• Parameterized bootstrap (Monte Carlo) estimation of the distribution of u*tv
• Calculate horiz. and vert. mass flux
QTot =ρg
u* u*2 − u*tv
2( )ΔTu*
∑ u*tv = u*t (1−C) 1+ βCAp
AB
⎛
⎝ ⎜
⎞
⎠ ⎟
⎛
⎝ ⎜
⎞
⎠ ⎟
12
QTot = Q(u*,u*tv )p(u*,u*tv )∑
Spatial Variability & Threshold
Okin, 2005
N=500,000
Spatial Variability and Wind Erosion
Okin, 2005
Variability is as important as mean values
Okin, 2005
Field Measurements
λ ~ 0.05
λ = 0
λ > 0.3
Conclusions so far….
• Wind erosion is not scale-independent• Variability at a scale smaller than the scale
of modeling is a key component of the observed fluxes
• Variability explains plumes– Can understand why they might happen, but
not where
…But, • The Raupach et al. (1993) model predicts NO flux at
relatively high lateral covers
• Even if we use the stochastic version
Some Results from the Field • Significant flux even at high lateral cover• No threshold behavior
-5
-4
-3
-2
-1
0
1
0 0.05 0.1 0.15 0.2 0.25Lateral Cover
Log
Flux
(g m
-2 s
-1)
3/27/961/26/9612/18/9511/30/951/2/961/22/96
Gillette and Pitchford, 2004
λgrama~0.3
Lancaster and Baas, 1998
u*tv ~ 6 -8 times u*ts
10
100
1000
0 200 400 600 800Average Gap Size (cm)
Horiz
onta
l Flu
x (g
m-1 d
-1)
Spring 05Summer 05
Okin et al, Journal of Arid Environments, 2006
Unpublished Data
λ~0.45
• Unvegetated Gap Size Seems to Matter
A closer look at the Raupach et al. (1993) model…
u*tv = u*ts 1−mσλ( ) 1+ mβλ( )
• u*tv is the threshold shear velocity in the presence of vegetation
• u*ts is the threshold shear velocity in the absence of vegetation
• σ is related to the shape of the plant (AB/AP)• β is the drag coefficient ratio
Decreased due to less affective areaIncreased due to drag on vegetation
The m Parameter
• Fits to experimental data gave m values from 0.13 to 0.58 (and not near 1 as Raupach suggested)
′ ′ τ s(λ) = ′ τ s(mλ)
Maximum surface shear stress Average surface shear stress
The Telephone Pole Problem
Lateral Cover = (Total Profile Area)/(Total Ground Area)
A
Raupach et al. (1993) model
• In the wake zone (A), the shear velocity is zero
Shear velocity is not everywhere zero in the wake zone
Bowker et al, Env. Fluid Mech, v6, 359-384, 2006 Bradley and Mulhearn, 1983
Problems with the existing model • In the field, flux is observed even at relatively high
lateral cover• In the model, saltation begins at every point in the
landscape at the same wind speed. In reality there are hotspots (Gillette, 1999)
• Scale unclear (Telephone Pole Problem)
• Wakes aren t on/off• m is a fudge factor:
– Literature Values:• m ~ 0.5, 1.0 (Raupach et al. 1993)• m = 0.16 (Wyatt and Nickling, 1997)• m = 0.53 - 0.58 (Crawley and Nicking, 2003)
Oblique Aerial PhotoWest TexasGillette (1999)
Mental Picture
PLA
NT
Shear Velocitylow high
Saltation Fluxlow high
• The landscape is made of areas that are more or less protected• Wakes are essentially 2-dimensions• The more protected areas are activated at higher u* and exhibit less flux than the less protected areas• For plant-erosion feedbacks, we need to have a grip on very local transport• At this point, the model doesn t presuppose any plant distribution
Wind
QTot = Pdqx∫ dx
All we need to know….
• The probability of any point being a certain distance from the closest upwind nonerodible element, Pd
• – Pg = gap size probability distribution – Pd = probability of being x from upwind shrub
• Can assume statistical distribution for Pg or Pd
• Can measure Pg by line-intercept transects, Pacing method
• Can measure Pd using Spatial Connectivity (McGlynn and Okin, RSE, 2006)
Pg (x)∝ xPd (x)
Gap size vs. lateral cover
• AP = Profile Area• AB = Basal Area• W = Average Plant Width along a transect = π/4*diameter for circular plants• L = Average Gap Width
λ =APW
AB L + W ( )0
0.1
0.2
0.3
0.4
0 10 20 30 40 50Average Gap Size/Average Plant Height
Late
ral C
over
In the new model, gap size (normalized by canopy height) is the controlling variable, not lateral cover
Mathematical Description of Model
QTot = Pdqx∫ dx Raupach and Lu (2004)
Shao & Raupach, 1993
x = distance from upwind plant
qx =ρg
u*x u*x2 − u*ts
2( )
Bradley and Mulhearn, 1983
Raupach et al (1993) modelu*x = u*
u*s
u*
10
100
1000
0 5 10 15 20Average Gap Size/Canopy Height
Horiz
onta
l Flu
x (g
m-1 d
-1)
Spring 05Summer 05
Solid: New Model Dashed: Old ModelHeavy: Real Wind Record Light: Constant u*
-5
-4
-3
-2
-1
0
1
0 0.05 0.1 0.15 0.2 0.25Lateral Cover
Log
Flux
(g m
-2 s
-1)
3/27/961/26/9612/18/9511/30/951/2/961/22/96
Lancaster and Baas, 1998
log
(hor
izon
tal fl
ux +
1 (
g cm
-1 d
-1))
λ~0.45
Shear Stress Ratio
SSR =′ τ s (vegetated)
′ τ s (unvegetated)
How can we reconcile the new model with the old model?
Qnew > Qold
Qnew < Qold
Symbols: Constant u*, Constant Gap SizeLight:Constant u*, Gamma Distribution for Gap SizeBold: Variable u, Gamma Distribution for Gap Size
Advantages of this model
• Explains observations of saltation even at high lateral cover• Explains hot spots , and where they occur (in streets )
• Explains variability in m• Allows calculation of flux at any place
– This is important for understanding plant-wind erosion feedbacks in desertification
• Its easier to measure gap size distribution than λ