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*A. Bejan and S. Lorente, Design with Constructal Theory (Wiley, 2008)
www.constructal.org
Adrian Bejan
Duke University
USA
The Constructal Law of Design in Nature
Thanks:
Sylvie Lorente
Miguel Medina
Amilcare Porporato
“Design” and “evolution” is a physics phenomenon,
summarized by the constructal law (1996):
“For a flow system to persist in time (to live) it must evolve
such that it provides greater access to its currents”.
The time direction of design evolution:
3
Time
Distribution of river sizes
3/ 70 1
3/ 71 2
2
D / D 2
D / D 2
Fully turbulent, P ~ m
4 /70 1
2 / 71 2
D / D 2
D / D 2
a bΔZ ΔZ = 1.964
4
4 /70 1
2 / 71 2
3/ 72 3
D / D 2
D / D 2
D / D 2
a bΔZ ΔZ = 0.815
5/ 70 1
2 / 71 2
2 / 72 3
2 / 73 4
D / D 2
D / D 2
D / D (2 /3)
D / D (3/ 4)
5
ET(s)
SOIL MOISTURE
STOCHASTIC
RAINFALL
FORCING
LQ (s)
I(s) R(t)
ECOHYDROLOGY OF MANAGED ECOSYSTEMS
Modeling the continuum
from
rainfed agriculture
to traditional irrigation
EVAPOTRANSPIRATION IRRIGATION
RUNOFF
AND PERCOLATION
RUNOFF
AND PERCOLATION
LQ (s)
Modeling the continuum
from
rainfed agriculture
to traditional irrigation
PHOTO: USGS
PHOTO: USDA
Different irrigation schemes/methods
Traditional (Impulsive: flood,
sprinkler)
Micro-irrigation (continuous)
Rain-fed vs stress- avoidance
irrigation
The population of the countries in the
Arabian Peninsula is expected to double in
fifty years (to 600 million), and only
through desalination will the fresh-water
resource increase. They are already
withdrawing over 75% of their Total
Renewable Water Resources.
Potential Conflict: Turkey has
been building dams on the Tigris
and Euphrates rivers that will
reduce flows downstream into
Syria and Iraq by 80%.
A. Bejan and S. Lorente, Design with Constructal Theory, Wiley, 2008
www.constructal.org
20
Amilcare Porporato
Giulia Vico
H32B - Ecohydrology within the context of global change II
AGU Fall Meeting 2009
AN ECO-HYDROLOGICAL APPROACH
TO SUSTAINABLE IRRIGATION
OF MANAGED ECOSYSTEMS
Lessons from ecohydrology…
• Soil-plant system is rather complex (beyond just
being complicated)
• Two essential elements of complex systems:
– Nonlinearity
– Large number of degrees of freedom (calls for a stochastic
approach)
• With suitable simplifications can be described
quantitatively:
– soil moisture probabilistic structure,
– plant water stress, productivity & photosynthesis,
– soil nutrient cycling,…
Abiotic processes Abiotic processes (water and energy cycles)
Biotic processes (nutrient cycles CNP, microbial and vegetation biomass)
2-way interaction
~60-90% of rainfall is used as transpiration by
vegetation while doing photosynthesis (also for
agricultural areas!)
Rule of thumb: 1 kg of bread requires 1 m3 of water
Society ?
(managed ecosystems-agricultural use)
1920 1940 1960 1980 2000
1000
2000
3000
4000
5000
World water use (km3)
agricultural use
After: Postel, Nature 1992
Fragile system sustainable use
of soil and water resources ? • Dust Bowl
• In the 1930s, following drought and agricultural malpractice crops were destroyed by insect infestations and dust storms which impacted the entire US Great Plains (immortalized in the novel ‘The Grapes of Wrath’ by J. Steinbeck)
• The resulting agricultural depression contributed to the Great Depression’s bank closures, business losses; millions of people migrated from the drought areas.
• Effects on wildlife and plant life were also enormous
Buried machinery in barn lot, Dallas, South Dakota, May 1936
Dust storm approaching Stratford, Texas, April 18 1935
Vico and Porporato, in prep.
FROM RAINFED AGRICULTURE TO TRADITIONAL
IRRIGATION
Onset of stress s*
Days
So
il m
ois
ture
Rainfed agriculture
Traditional irrigation
Micro-irrigation Continuous supply of water to keep
soil moisture at the intervention
point
No irrigation applied
Impulsive application of water when
the intervention point is reached to
bring soil moisture back to a fixed
target level
Wilting point sw
Target level s ̂
Intervention
point s ~
Vic
o a
nd
Po
rpo
rato
, in
pre
par
atio
n
Traditional irrigation
Micro-irrigation
Rainfed agriculture
Tar
get
so
il m
ois
ture
s
^
Intervention point s Soil moisture triggering
irrigation application
~ s* sw
Wilting point Onset of stress
sfc
s*
s fc
OVER IRRIGATION
FROM RAINFED AGRICULTURE TO
TRADITIONAL IRRIGATION
Vico and Porporato, WRR, in press
1) Soil water balance
2) Evolution of soil moisture
3) Analytic solution
(statistical steady state)
nZr =R(t)+I(s)-ET(s)-LQ(s) ds(t) dt
= - ∂J(s,t)
∂s ∂p(s,t)
∂t
p(s)
J(s)=-ρ(s)p(s,t)+λ∫e-γ(s-u)p(u,t)du s
rainfall pattern
irrigation parameters
plant water requirements
soil features
PROBABILISTIC APPROACH
4) Irrigation requirements (soil moisture crossing properties)
Vic
o a
nd
Po
rpo
rato
, in
pre
p.
Target level s
Onset of stress level s*
Intervention
point s
Days
Soil
mo
istu
re
STEADY STATE PDF OF SOIL MOISTURE
Soil moisture
p(s
)
^ ~
800 mm
200 mm
Total rainfall over
the growing season
Ra
infa
ll fr
eq
ue
ncy (
da
y-1
)
Rainfall event depth (mm)
0.12 m
0.08 m
0.04 m
0.02 m
Vico and Porporato, WRR, in press
Differences in irrigation requirements
between traditional and micro
irrigation for a 180-day growing
season as a function of rainfall
amount and frequency
as a function of rainfall, soil, and crop parameters…
IRRIGATION VOLUMES
Assessing irrigation schemes for different targets
Water requirement
Crop yield
Net income
SUSTAINABILITY
FOOD SECURITY
PROFITABILITY
OPTIMAL IRRIGATION SCHEME
Water availability
Salinization
Pollution
Eutrophication
Vico and Porporato, in prep.
CROP YIELD
a function of
seasonal
transpiration
ECONOMIC RETURN • Fixed irrigation costs, function of
irrigation method
Transpiration (mm season-1) Cro
p y
ield
(to
n h
a-1)
Zea mays
(Corn)
North Platte, NE
(Payero et al. 2006,2008,2009)
Ruaha River, Tanzania
(Igbadun et al., 2007)
• Water related costs, proportional
to irrigation volumes
• Price paid for crop, fixed by the market
• Other fixed costs, independent of irrigation s ^
s ~
Increasing fixed irrigation
costs
0.4
Vico and Porporato, in preparation
IRRIGATION VOLUMES (m season-1)
Intervention point
Intervention point
Intervention point
CROP YIELD (ton ha-1)
ECONOMIC RETURN ($ ha-1)
10
5
600
200
-200
0.2
Tar
get
so
il m
ois
ture
s
^
Zea mays
RAINFALL INTERANNUAL VARIABILITY
Porporato et al., GRL, 2006
Manhattan, KS
MEAN EVENT DEPTH
MEAN STORM FREQUENCY
TOTAL RAINFALL
DRY WET
Crop Yield (ton ha-1) p(Y
ield
) Irrigation volume (m season-1)
p(V
olu
me)
• Larger volumes are needed for minimal interannual yield variability.
• Irrigation may become unfeasible during extremely dry years.
Vic
o a
nd
Po
rpo
rato
, in
pre
par
atio
n
Deficit traditional
irrig.
Rainfed
Stress avoidance
traditional irrigation
Rainfall interannual variability is
included by randomly choosing rainfall
parameters
Probability density functions of
required irrigation volumes and crop
yields
Increasing intervention
point
Conclusions
• Analytical approach which includes explicitly the rainfall unpredictability
• Gives irrigation requirements as a function of crop, soil, rainfall (climate) characteristics
• Continuum between rain-fed and stress-avoidance (traditional and micro) irrigation
• Suitable to be coupled to nutrient cycling (NP) as well as to analyze salinization risk by irrigation
Arabian Peninsula:
Bahrain, Kuwait, Oman,
Qatar, Saudi Arabia,
United Arab Emirates,
Yemen.
Annual average precipitation is 62
mm in Oman, the driest country in
the Arabian Peninsula.
Agricultural withdrawal accounts for
more than 85 percent of the total
water withdrawal in Oman.
Freshwater withdrawal in Oman represents 91 percent of
renewable water resources.