Spatial Planning of Agricultural Production

under Environmental Risks and Uncertainties

G. Fischer, T. Ermolieva

International Institute for Applied Systems Analysis, Laxenburg, Austria

CwU 2007 December 10-12, 2007

IIASA, Laxenburg Austria

This research is under the umbrella of two EU-sponsored projects

CHINAGRO: Decision Support System for China's Agricultural Sustainable Development (EU-ICA4-CT-2001-10085), 2002-2005.

CATSEI: Chinese Agricultural Transition: Trade, Social and Environmental Impact (EU FP6 Project 44255), 2007-2009.

BackgroundBackground

Broad range of factors determining spatio-temporal heterogeneity of demand

and supply of agricultural products:

• Demographic change

• Urbanization

• Overall economic growth

• Availability of farmland; irrigated land

• Technological progress in agriculture

• Trade policies

• Conditions on international markets

Research questionResearch question

Growing demands for meat, intensification trends, concentration

of production according to “increasing returns” principle.

Main risks:

- environmental pollution (manure combined with chemical fertilizers) - livestock related diseases and epidemics - market risks - demand uncertainties and instabilities

A continuation of current intensification trend would bring in high risks for the future.

Risk perspective suggests rationales for spatial diversification

and co-existence of large- and small-scale producers.

Long-term planning needs to base on sustainability principles:

increasing returns in combination with enforced policies relying

on risk indicators.

Co-existence of heterogeneous producers:Co-existence of heterogeneous producers:a risk-hedging strategya risk-hedging strategy

Absence of risks: Two producers with production costs c1 < c2 < b

dxaxa 2211

Risk exposure: a1 and a2 are random variables (shocks to production)

2211 xcxc

dx *1 0*

2 x

dxx 21 01 x 02 x

2211 xcxc

},0max{)( 22112211 xaxadbExcxcxF

where bE max{0, d – a1x1 – a2x2} is the expected import cost if demand

exceeds the supply.

minimize

solution

minimize

minimize

Ermoliev, Y., Wets, R. (Eds.) Numerical Techniques for Stochastic Optimization.Computational Mathematics, Springer Verlag, Berlin, 1988.

of the distribution function describing

contingencies of the Producer 1, i.e., a1 , and the ratio c2 / b.

Optimal production share of Producer 2 is defined by the quantile

The cost efficient producer 1 is active if: c1 – bEa1 < 0

The less-efficient producer 2 stabilizes the aggregate production and the market in the presence of contingencies affecting the “most cost-effective” producer 1.

Market share of the Producer 2 (risk-free producer with higher production costs):

][),( 21222xxadbPcxxFx

0*2 x

bcxxadP /][ 2*2

*11

Take derivative

If Producer 1 is at risk: 0 < E a1 < 1, a2 = 1. Positive optimal decisions exist if:

0)0,0(1

xF 0)0,0(2

xF 11)0,0(1

bEacFx bcFx 2)0,0(2

i.e., less efficient producer 2 is active unconditionally: c2 – b < 0

Co-existence of heterogeneous producersCo-existence of heterogeneous producers

ChallengesChallenges of spatial livestock production of spatial livestock production planning under risks and uncertaintiesplanning under risks and uncertainties

Long horizons of problems related to production and risks. Spatially explicit framework: 2434 counties. Aggregate or insufficient data for estimation of spatially

“disperse” agricultural risks, indicators and constraints;

compound risks. Need for spatially-explicit stochastic LS production planning

model and data upscaling/downscaling, harmonization

procedures. Production allocation and intensification levels are projected from the base year for: - Pigs, poultry, sheep, goat, meat cattle, milk cows) and - Management system (grazing, industrial, specialized, traditional.

IIASA model for livestock production planning IIASA model for livestock production planning

Model structure and inputs

Base year distribution of production activities/resources at county level Alternative demographic projections and Economic scenarios Model derives estimates of:

- Demand for cereals and livestock products

- Spatial allocation and intensity levels of crop and livestock production;

- Environmental pressure from agricultural production

- Health and environmental risk indicators

Incorporates/compares:

Alternative production allocation criteria;

Procedures: Rebalancing/dowscaling & stochastic optimization

Livestock production allocation under Livestock production allocation under risks and uncertaintiesrisks and uncertainties

id is the expected national supply increase in the livestock product i

ijlx is the unknown portion of the supply increase i related to location j and

management system l In its simplest form, the problem is to find ijlx satisfying the following system

of equations:

ijlijl dx

,, (1)

0ijlx , (2)

jliijl bx , Ll :1 , nj :1 , mi :1 , (3)

where jlb is aggregate risk constraint restricting the expansion of production

in system l and location j .

Apart from jlb , there may be additional limits imposed on ijlx , ijlijl rx ,

which can be associated with legislation, for example, to restrict production i within a production “belt”, or to exclude from urban or protected areas, etc. Thresholds jlb and ijlr may either indicate that livestock in excess of these

values is strictly prohibited or it incurs measures such as taxes or premiums, for eradication of the risks, say, livestock diseases outbreaks or environmental pollution. In this sense, they are analogous to the risk constraints from the catastrophe and insurance theory. Values jlb and ijlr may be reasonably

treated in priors.

Sequential rebalancing procedure Sequential rebalancing procedure

iikik dqy 0- expected initial allocation of demand to location i and system k

i ikkk yb 00 /Derive relative imbalance and update000kikik yz

ki

byik

0But may not satisfy the constraint0iky

0ikz may not satisfy the constraint ik ik dz 0

k ikii zd 00 /Calculate and update 001iikik zy

siky i

kik

sik dqy can be represented as

jskik

skik

sik qqq 11 /

ik

ik dy

0ikyki

ik by

1k ikq - prior, reflects alternative “behavioral” allocation principles

Demand for product i; production in location k

Aggregate constraint on meat production at location k

by applying sequentially adjusted : , 1sikq

iskik

skik

sik qqq /1

The procedure can be viewed as a redistribution of required supply increase di

ikik qq 0e.g., by using a Bayesian type of rule for updating the prior distribution, .

The procedure converges to the optimal solution maximizing

the cross-entropy function ij

ijij q

yy ln

Fischer, G., Ermolieva, T., Ermoliev, Y., and van Velthuizen, H.,“Sequential downscaling methods for Estimation from Aggregate Data”In K. Marti, Y. Ermoliev, M. Makovskii, G. Pflug (Eds.)Coping with Uncertainty: Modeling and Policy Issue, Springer Verlag, Berlin, New York, 2006.

Bregman, L.M. “Proof of the Convergence of Sheleikhovskii’s Method for a Problem with Transportation Constraints”, Journal of Computational Mathematics and Mathematical Physics,Vol. 7, No. 1, pp191-204, 1967 (Zhournal Vychislitel’noi Matematiki, USSR, Leningrad, 1967).

For Hitchcock-Koopmans transportation model the proof is in:

For more general constraints and using duality theorem the proof is in:

Sequential rebalancing procedure Sequential rebalancing procedure

Alternative production allocation scenariosAlternative production allocation scenarios

2. Sustainable Scenario: trade-off between development and risks.

1. Demand Driven Scenario: Production increase in locations is proportional to demand potential (people, rural/urban, income)

Economic, social, environmental risk and sustainability indicators and constraints reflect location-specific conditions and limitations such as water and land scarcity, livestock density, urbanization level.

Allocation of livestock beyond specified constraints may lead to disastrous consequences related to water and air pollution, hazards of livestock disease outbreaks, threats to human health, which may incur high costs.

The indicators and constraints are treated within priors or as explicit constraints/goals. Individual “weights” of indicators/constraints reflect the critical trade- offs, limitations and goals in locations.

0 (%)

3-5 (%)

6-10 (%)

11-15 (%)

16-20 (%)

21-25 (%)

26-30 (%)

31-35 (%)

36-40 (%)

41-45 (%)

46-50 (%)

51-55 (%)

56-60 (%)

61-65 (%)

66-70 (%)

71-75 (%)

76-80 (%)

81-85 (%)

86-90 (%)

91-95 (%)

96-100 (%)

Resource Constraints: Resource Constraints: Intensity of cultivated and orchard land Intensity of cultivated and orchard land

(percent of total land in county) in 2000.(percent of total land in county) in 2000.

Population distributionPopulation distribution(persons per square kilometer)(persons per square kilometer)

Rural

Urban

0

20000

40000

60000

80000

100000

2000 2005 2010 2015 2020 2025 2030

1000

mt

Other meat

Pork

Poultry

0

20000

40000

60000

80000

100000

2000 2005 2010 2015 2020 2025 2030

10

00 m

t

0.0

0.2

0.4

0.6

0.8

1.0

1.2

6 7 8 9 10

log(Income)

Inco

me E

lasti

cit

yMeat demand by income

0

100

200

300

400

500

600

2000 2005 2010 2015 2020 2025 2030

Mil

lio

ns

Large

Spec

Trad

Pigs by type of production system Meat demand by type

Meat demand by sector

01-150151-300301-600601-10001001-1500>1500

01-150151-300301-600601-10001001-1500>1500

2030

Hot-spots of high intensity of confined livestock(livestock biomass in kg/ha cultivated land)

2000

0

1-25

26-50

51-100

101-150

>150

2000

a.

01-2526-5051-100101-150>150

44: Guandong

33: Zhejiang

0

1-25

26-50

51-100

101-150

>150

Hot-spots of manure nutrients from confined livestock, (kg nitrogen/ha cultivated land), year

2000:2030: a. Demand-drivingb. Risk-adjusted

01-5051-150151-250251-350351-500>500

01-5051-150151-250251-350351-500>500

Hot spots of fertilizer consumption (kg nitrogen/ha cultivated land)

2030

2000

Nutrient balance calculations.

County-specific nutrient balances compare nutrients from livestockmanure and fertilizers with the requirements and uptake capacities of crops.

Thus, calculated total nutrients losses include:

nutrient losses from livestock housing, from manure storage facilities as well as total liquid manure (largely unused),

losses stemming from non-effective manure and fertilizers,

losses due to over-supply of nutrients from fertilizers and manure to crops,

non-effective manure nutrients produced by pastoral livestock systems.

Nutrient (nitrogen) losses per unit Nutrient (nitrogen) losses per unit area, kg/haarea, kg/ha

0

1-25

26-50

51-100

101-150

151-250

>250

2000

0

1-25

26-50

51-100

101-150

151-250

>250

2030

A B

0

400

800

1200

1600

2000

2400

1-25 26-50 51-100 101-150 151-250 >250

Intensity of nitrogen losses per unit land (kg/ha)

Nu

mb

er o

f co

un

ties

0%

20%

40%

60%

80%

100%

Per

cen

tag

e o

f co

un

ties

Frequency distribution of:Frequency distribution of:a. Number of counties, anda. Number of counties, and

b. Population, with regard to the intensityb. Population, with regard to the intensityof nitrogen losses per unit of landof nitrogen losses per unit of land area. area.

0%

20%

40%

60%

80%

100%

1-25 26-50 51-100 101-150 151-250 >250

Intensity of nitrogen losses per unit land (kg/ha)

Per

cen

tag

e o

f p

op

ula

tio

n

0%

20%

40%

60%

80%

100%

Cu

mu

lati

ve p

erce

nta

ge

of

po

pu

lati

on

0.0 0.2 0.4 0.6 0.8 1.0

N

NE

E

C

S

SW

NW

0.0 0.2 0.4 0.6 0.8 1.0

N

NE

E

C

S

SW

NW

Figure 3. Relative distribution of population according to classes of severity of environmental pressure from livestock, 2030: (a) demand driven scenario, (b) environmentally friendly scenario.

Two scenarios are compared with respect to Two scenarios are compared with respect to number of people in China’s regions exposed to number of people in China’s regions exposed to

different categories of environmental risksdifferent categories of environmental risks