Dynamics of sand dunes stabilization
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Transcript of Dynamics of sand dunes stabilization
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Dynamics of sand dunes stabilization Or:
What can nonlinear dynamics tell us about ecology?
Shai KinastThe Negev Physics Fete
March 15, 2013
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Sand dunesA pattern-forming system
MoroccoNamibia
Kasuy wadi, Israel Mars
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Distribution of sand dunes- Cover 6% of global surface area- Occur in two distinct habitats:
1. Along coasts of seas and rivers (3%)2. Deserts and arid regions (97%)
After Thomas (1997)
Approximated sand dunes map
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Sand dunes stabilization
active stabilized
why is it important?
people live on sand
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Sand dunes stabilizationpsammophilic flora and fauna
Change in dune mobility change in biodiversity
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mean annual precipitation (mm/year)40 100 150 400
a dcb
bare sand; active dunes
a
plants(no crusts); stabilized dunes
d
plants + crusts; stabilized dunes
c
plants + crusts; semi-stabilized dunes
b
Stabilization by biogenic crust and/or vegetation
a
b
c
d
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Israel Egypt
Fixed dunes Active dunes
Israel-Egypt Border (NW Negev)annual precipitation ~ 100mm/year
Stabilization by biogenic crust
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Model assumptions
crust vegetationcompetition
Influence index:
Positive
Negative
local competitionplants and crust compete for land
non local competitionplants and crust compete through:- distribution of water (“source-sink”)- toxic litter from plants
as simple as possible, yet not too simple…
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Model assumptions
crust vegetation
precipitationInfluence index:
Positive
Negative
precipitation
grow
th ra
tes
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Model assumptions
crust vegetation
wind – indirect and directInfluence index:
Positive
Negative
direct• increased evapotranspiration• branch cutting
indirectthrough sand transport:• root exposure• burial of crust and plants
Wind shield by vegetation (positive feed back)
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Model assumptions
crust vegetation
precipitation
Influence index:
Positive
Negative
wind – indirect and direct
competition
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vbvDPsvvvDPgsvpdtdv
vcvvv 3/2),())((
bvsbvvDPgsbpdtdb
bcbbb ),())((
10 bvv = vegetationb = biogenic crust
variables represent cover fraction
precipitation
precipitation
local competition
local competition
non local competition
non local competition
direct wind effect
indirect wind effect
indirect wind effect
Mathematical description
2/)1)(tanh()( cvvdvgwhere:
bvs 1
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bvs 1
A. Dune cover vs. precipitation
bare sand fraction:
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compare with field observations
(a) p = 40 (b) p = 80
(d) p = 400(c) p = 150
A. Dune cover vs. precipitation
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steady state depends on initial conditionsBistability
A. Dune cover vs. precipitation
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ecosystem may not recover after droughtHysteresis
A. Dune cover vs. precipitation
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cove
r fra
ctio
n
time
simulation of plants removaltime (yr)
cove
r fra
ctio
n
vegetation
crust
plants removal
B. Dune cover vs. precipitation and wind
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B. Dune cover vs. precipitation and windTwo types of bistability
Different mechanisms:
Type 1 - wind shield by vegetation
Type 2 - competition between crust and vegetation
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B. Dune cover vs. precipitation and windTwo types of bistability
Different ecological consequences:
Type 1 - bistability of vegetated dunes and bare dunes
Type 2 - bistability of vegetated dunes and crusted dunes
Yizhaq et al, PRL 2007
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on-site removal of plants and crusts more than 15 years ago!
100m
bistability?
B. Dune cover vs. precipitation and wind
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C. Desertification vs. rehabilitation
B = crust-dominated duneV = plants-dominated dune
arrows represent possible disturbances
(BV) (VB)
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SummaryA. Dune cover vs. precipitation
– Model vs. reality
B. Dune cover vs. precipitation and wind– Two types of bistability
C. Desertification vs. rehabilitation
Kinast et al, PRE 87 020701
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Thank you!
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amplitude of limit cycle
supercritical Hopf bifurcation
time (yr) time (yr)
cove
r fra
ctio
n
cove
r fra
ctio
n
d=9 d=13
D. Oscillations in dune cover
v
g
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cove
r fra
ctio
n
vegetation
crust
d=15
d
perio
d of
osc
illat
ions
time time time time
d=30 d=100 d=400
period saturates:yrTd 27.381
D. Oscillations in dune cover