Download - Dynamics of sand dunes stabilization
Dynamics of sand dunes stabilization Or:
What can nonlinear dynamics tell us about ecology?
Shai KinastThe Negev Physics Fete
March 15, 2013
Sand dunesA pattern-forming system
MoroccoNamibia
Kasuy wadi, Israel Mars
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
Sand dunes stabilization
active stabilized
why is it important?
people live on sand
Sand dunes stabilizationpsammophilic flora and fauna
Change in dune mobility change in biodiversity
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
Israel Egypt
Fixed dunes Active dunes
Israel-Egypt Border (NW Negev)annual precipitation ~ 100mm/year
Stabilization by biogenic crust
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…
Model assumptions
crust vegetation
precipitationInfluence index:
Positive
Negative
precipitation
grow
th ra
tes
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)
Model assumptions
crust vegetation
precipitation
Influence index:
Positive
Negative
wind – indirect and direct
competition
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
bvs 1
A. Dune cover vs. precipitation
bare sand fraction:
compare with field observations
(a) p = 40 (b) p = 80
(d) p = 400(c) p = 150
A. Dune cover vs. precipitation
steady state depends on initial conditionsBistability
A. Dune cover vs. precipitation
ecosystem may not recover after droughtHysteresis
A. Dune cover vs. precipitation
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
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
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
on-site removal of plants and crusts more than 15 years ago!
100m
bistability?
B. Dune cover vs. precipitation and wind
C. Desertification vs. rehabilitation
B = crust-dominated duneV = plants-dominated dune
arrows represent possible disturbances
(BV) (VB)
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
Thank you!
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
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