Virtual Water Trade Networks and Sustainability of the Food System

Water-controlled wealth of nations: Using Water Footprints to Estimate Nations

Carrying Capacities and Demographic

Sustainability

Samir Suweis, Andrea Rinaldo, �

Amos Maritan and Paolo D'Odorico �

Welcome to Amos Maritan Lab

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ABOUT!US NEWS

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PNAS, Vol. 110 no. 11 4230-4233 (2013)

SouthSudan

Libya

2012Proportion of total population undernourished, 2010-12 The map shows the prevalence of undernourishment in the total population as of 2010 – 2012. The indicator is an

estimate of the percentage of the population having access to an amount of energy from food insufficient to maintain a healthy life. Further information is available at www.fao.org/publications/sofi/en/

Source: FAO, IFAD and WFP. 2012. The State of Food Insecurity in the World 2012: Economic growth is necessary but not sufficient to accelerate reduction of hunger and malnutrition. Rome.

© 2012 World Food Programme

The designations employed and the presentation of material in the maps do not imply the expression of any opinion whatsoever on the part of WFP concerning the legal or constitutional status of any country, territory or sea area, or concerning the delimitation of frontiers.

* The Line of Control in Jammu and Kashmir agreed on by India and Pakistan is represented approximately by a dotted line. The final status of Jammu and Kashmir has not yet been agreed on by the parties.

** A dispute exists between the governments of Argentina and the United Kingdom of Great Britain and Northern Ireland concerning sovereignty over the Falkland Islands (Malvinas).

*** Final boundary between the Republic of Sudan and the Republic of South Sudan has not yet been determined.

It costs on average just US 25 cents a day to feed a hungry child and change her life forever.

While food is the most basic of human

needs required for survival, on average, 1 in 8 people

go to bed hungry each night.

Hunger kills, maims, reduces IQ,

lowers wages, reduces school attendance andundermines economic

growth.

(U.K.)

***

No dataVery low

undernourishment

<5%

Moderately low undernourishment

5-14%

Moderately high undernourishment

15-24%

High undernourishment

25-34%

Very high undernourishment

35% and over

Missing or insufficient

comparative data

***

State of Palestine

Food Security: physical, social and economic access to sufficient, safe and nutritious food to meet dietary needs for a productive and healthy life (World Food Summit of 1996).

FOOD SECURITY

Figure  .  Annual  water  use  per  capita  (data  from  Falkenmark  et  al.,  2004).  

"Over  the  coming  decades,  feeding  a  growing  global  population  and  ensuring  food  and  nutrition  security  for  all  will  depend  on  increasing  food  production.  This,  in  turn,  means  ensuring   the   sustainable   use   of   our   most   critical   <inite   source   -­‐   water”        

Ban  Ki-­moon,  World  Water  Day,  15  march  2012  

The Water footprints or Virtual Water concept

•   WF  determined  using  bottom-­‐up  hydrological  modeling  at  5  by  5  arc  spatial  resolution.  • Average  values  are  calculated  over  10  years  periods.  • Calibration:  AQUASTAT  and  UN  statistical  division  database  (FAO,  2010b,  UNSD,  2010°).    

The Local Carrying Capacities of Nations

MekonnenMM,  Hoekstra  AY  (2011)  

Schema8c  diagram  of  water  withdrawals  in  the  H08  model  [Hanasaki  et  al.,  2008]  

TFM  =trade  food  matrix  

TFMy   (i,j)   =   volume   of  commodity   y   traded  from  i  and  nation  j.  

The Virtual Carrying Capacities of Nations

€

aijy =Θ[TFMy(i, j)]

€

wijy = TFMy(i, j)⋅ VWy(i)

Suweis  et  al.,  GRL  2011  

€

VWE(i) = wijy

j=1

N∑

y∑

€

KVi = Kloc

i +VWI (i) −VWE (i)

Wci

Water Wealth of Nations

€

dxidt

= α ixi 1−xiKi

⎛

⎝ ⎜

⎞

⎠ ⎟

€

K →Kloc or KV

γ i =1xi(t)

[xi(t + Δt) − xi(t)]Δt

→α i

€

xi(t) =Kix0,ie

α i t

Ki + x0,ieα i t − x0,i

Countries Demographic Dynamics

€

x <<Kloc; Kloc > x > KV ; x ≈ Kloc; x > KV

4.1 107

Argentina9.6 107

Brazil

3.1108

USA

7.8 107

Germany

1990 2010 2030 2050 2070

6 107Italy

1.1 108Mexico

5.6 107

UK

year [t]

x(t)

x(t)

x(t)

x(t)

x(t)

x(t)

x(t)

1970

1990 2010 2030 2050 2070year [t]

1970

1990 2010 2030 2050 2070year [t]

1970

1990 2010 2030 2050 2070year [t]

1970

1990 2010 2030 2050 2070year [t]

1970

1990 2010 2030 2050 2070year [t]

1970

1990 2010 2030 2050 2070year [t]

1970

€

K = KV

€

K = Kloc

Water Global Unbalance

€

DataWater  Rich  

Virtual  Water  Dependent  

20 40 60 80 100

4.1 107

Argentina

20 40 60 80 100

2.2107

Australia

20 40 60 80 100

105

Belize

20 40 60 80 100

9.6 107

2. 108

Brazil

20 40 60 80 100

3.4 107

Canada

20 40 60 80 100

1.8 106

5. 106CostaRica

20 40 60 80 100

6.0 106

1.4 107

Ecuador

20 40 60 80 100

8.7 106

2.4 107

Ghana

20 40 60 80 100

5.4106

1.4107Guatemala

20 40 60 80 100

6. 105

2. 106

GuineaBissau

20 40 60 80 100

5.2 106

2.2 107

IvoryCoast

20 40 60 80 100

1.1 107

Cuba

20 40 60 80 100

1.2 108

2.3108

Indonesia

20 40 60 80 100

1.1 107

2.8 107

Malaysia

20 40 60 80 100

2.6 107

5.0 107

Myanmar

20 40 60 80 100

4. 106

NewZealand

20 40 60 80 100

2.4106

6. 106

Nicaragua

20 40 60 80 100

5.6 107

1.6 108Nigeria

20 40 60 80 100

2.5 106

6. 106

Paraguay

20 40 60 80 100

3.7 107

6.8 107

Thailand

20 40 60 80 100

9.4 106

3.4 107Uganda

20 40 60 80 100

3. 106

Uruguay

20 40 60 80 100

3.1108

USA

20 40 60 80 100

4.3 107

8.9 107

Vietnam

€

K = KV

€

K = Kloc

€

Data

Popu

la8o

n  

Years  aIer  1970  

20 40 60 80 100

7.5 106

Austria

20 40 60 80 1002.2 105

8. 105

Bahrain

20 40 60 80 100

9.6 106

Belgium

20 40 60 80 100

1.7 107Chile

20 40 60 80 100

5.3 106

Finland

20 40 60 80 100

1.8 106Gambia

20 40 60 80 100

7.8 107

Germany

20 40 60 80 100

5.3 107

Italy

20 40 60 80 100

6.5 106Libya

20 40 60 80 100

1.1 108Mexico

20 40 60 80 100

3.9106

Norway

20 40 60 80 100

6.9 106PapuaNewGuine

20 40 60 80 100

2.9 107Peru

20 40 60 80 100

1.5 106Qatar

20 40 60 80 100

1.3107Senegal

20 40 60 80 100

5.8106SierraLeone

20 40 60 80 100

5.3 106

Slovakia

20 40 60 80 100

4.5 107Spain

20 40 60 80 100

1.2 106

Swaziland

20 40 60 80 100

8.1 106

Sweden

20 40 60 80 100

9.7 105

Trinidad Tobago

20 40 60 80 100

5.6 107

UK

20 40 60 80 100

4.7 106UnitedArabEmirates

20 40 60 80 100

2.4 107

Yemen

20 40 60 80 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100

20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100

100

8. 105

Cyprus5.2 10

6 Eritrea6.4 107

France

7.5 107

Iran

1.6 107

Netherlands2.9 106

Oman1.1 107

Portugal7. 6 106

Switzerland

€

K = KV

€

K = Kloc

€

Data

Popu

la8o

n  

Years  aIer  1970  

Modelling Sustenability of VW Dependent Countries Population

dx

i

dt

= ↵

i

x

i

✓1� x

i

K

i

loc

◆for i=Rich Water

dx

j

dt

= ↵

j

x

j

0

@1� x

i

K

j

loc

+

PRichi

aji

di(K

i

loc

� x

i

)

VWiVWj

1

Afor i=VW dependent

⇢ System  of  coupled  differential  equations  

j  

Diets!  

Water  Rich  Virtual  Water  Dependent  

€

aijGraph  Topology  

Results & Effect of Network Topology

Posi8ve  feedback  between  demographic  growth  and  technological  innova8ons    

Sta8c  

4.5 108

5.0 108

5.5 108

6.0 108

2020 2040 2060 2080 21002000Times [years]

X vwd

! = 0.08! = 0.04! = 0

4.5 108

5.0 108

5.5 108

6.0 108

6.5 108

7.0 108

2020 2040 2060 2080 21002000

X vwd

Years

Random  graph    

Small  world  network  

Scale-­‐free  network    

Topological  properties  similar  to  those  observed  in  the  real  global  VW  trade  network  

Kloc(t)=Kloc(1+ε(t))  and  decreasing  Wc(t)    

Rockström,  J.,  et  al.  GRL  39.15  (2012).  

β =  cooperative  strength  

No e!ect of trade

Net Importers

Net Exporters

Food Scarce

Using Food Trade Data - Temporal Networks

Temporal Food Trade Patterns and Stability, in preparation

Group A Group B Group C Group D

1995 2000 2005 2010

0

10000

20000

30000

40000

50000

Years @y D

RTHyL-

CHyL@calD

1995 2000 2005 20100.6

0.8

1.0

1.2

1.4

Years @y D

CV@K TDêCV

@K LD

Out[479]=

Group A Group B Group C Group D

5 10 15 20 25

2400

2600

2800

3000

Years @t D

Group

Diet@c

alD

Balance  

Fluctua8on  of  the  avaliable  resources  

Diet  

Does globalization Increases stability?

-0.2 -0.1 0.0 0.10

5

10

15

20

25

Re@lD

PDF

y=1991 y=1997 y=2003 y=2009

x mode

1995 2000 2005Year

0.0090.0100.0110.0120.0130.014

»x Mode» A

B

1995 2000 2005

4

6

8

10

12

14

16

Year

Re@lD>0

Stability of the Food trade Network

If  Re(λi  >  0)                  xi(t)  is  very  sensitive  to  external  perturbations  

Effect  of  the  network  

• Side-­‐effects  of  the  globalization  of  resources  

• Unbalance   between   the   rate   of   growth   in   water   rich   countries   and   the  water  resources  exported  to  virtual  water  dependent  countries  

• Decreasing  stability  in  time  of  the  food-­‐demographic  coupled  system    

Conclusions & Perspectives

1990 1995 2000 2005 2010Years @t D

2¥ 107

4¥ 107

6¥ 107

8¥ 107Pop@t D Egypt

1990 1995 2000 2005 2010Years @t D

5.0¥ 106

1.0¥ 107

1.5¥ 107

2.0¥ 107

Pop@t D Australia

Conclusions & Perspectives

• Is  there  any  optimal  network  topology  in  terms  of  water  saving?  

• How  to  quantify  waste  or  detrimental  links  in  the  virtual  water  trade  networks?  

• Robustness  to  perturbations  and  fragility  of  the  network  

• Estimate  the  uncertainity  of  VW  footprint  calculations  

• Create  public  and  shared  databases  so  to  work  with  the  same  data  

• Data  on  Food  Stock,  Food  Waste,…  

MODELLING    

DATA  ANALYSIS  

Thanks for your attention!

Full reference: PNAS, Vol. 110 no. 11 4230-4233 (2013)

Contacts  

SamirSuweis   Questions?