*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

2

“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

Constructal River Basins

6

Few Large and Many Small

7

Few Large and Many Small

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

10

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%.

FRACTION OF FRESHWATER

WITHDRAWAL

FOR AGRICULTURE

UNEP/GRID, 2002

YEAR 2000

14

15

16

17

18

19

A. Bejan and S. Lorente, Design with Constructal Theory, Wiley, 2008

www.constructal.org

20

21

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.