Soil carbon in dynamic land
use optimization models
Uwe A. Schneider
Research Unit Sustainability and Global Change
Hamburg University
Topics

I Land use models

II Linking biophysical and economic models

III Soil carbon in economic models

IV FASOM
I Land use models
Research Questions

Economic
Sustainability
– Food
– Energy
– Commodities

Policy analysis
– Economic potential
– Impacts

Environmental
Sustainability
– Air
– Water
– Soil
– Climate
– Ecosystems
Focus of land use models

Technologies (Species, Tillage, Planting,
Fertilizing, Protection, Harvesting)

Economics (Market Prices, Trade,
Income)

Environment (Resources, Emissions,
Sinks, Wildlife, Climate)
Land use estimation

Storylines

Statistics

Optimization
Optimization

Constrained welfare/profit maximization

Normative economics (positive economics
via calibration)

Application to structural change beyond
historical observations
Land use optimization

Find welfare maximizing land management
s.t.
resources
technologies
markets
policies
Linear Program
Max
∑c X
∑a X
j
j
ij
j
≤
bi
for all i
Xj
≥
0
for all j
j
s.t.
j
II Linking biophysical
and economic models
Why linkage?

Standalone biophysical models simulate
environmental impacts of land
management but don’t explain why a
certain land management is chosen

Standalone economic models explain land
management adoption but cannot
internalize environmental impacts
Challenges

Spatial resolution (field vs. globe)

Temporal resolution (days vs. decades)

Technological resolution

Environmental resolution
Types of Linkage (Problems)
A.
Economic model → Biophysical model
(no adaptation, no feedback)
B.
Biophysical model → Economic model
(curse of dimensionality)
C.
Iterative link (costly, ITR)
D.
Fully integrated model (computational
limits)
Economic model → Biophysical model
Determine land use trajectory with
economic model for different scenarios
 Simulate environmental impacts for each
scenario
 Adaptation of land management to
environmental policies ignored
 Feedback of changing environment on
adaptation ignored as well

Biophysical model → Economic model
Simulate environmental impacts for all
possible land use choices
 Enter environmental impacts in economic
model
 Set values for environmental impacts
(environmental policies)
 Find welfare maximizing levels

Curse of Dimensionality?
20 Crops
 5 Management options per crop
 100 Regions
 5 Soil Types per region

50,000 Land use alternatives
Curse of Dimensionality?
20 Crops
 5 Management options per crop
 100 Regions
 5 Soil Types per region
 20 Periods

5*E42 Trajectories
1*E94 Trajectories
(independent sites)
(dependent sites)
III Soil carbon in
economic models
Soil carbon and economics

Productivity impact of soil carbon (yields,
suitability)

Economic potential of carbon sinks for
climate change mitigation

Carbon sinks vs. bioenergy vs. biodiversity
vs. traditional markets
Soil Carbon Determinants
Crop Choice
 Tillage
 Irrigation
 Fertilization
 Residue Mgt
 Soil Carbon

Soil
Carbon
Change
Soil Organic Carbon (tC/ha/20cm)
45
40
35
Wheat-Lucerne 3/3
30
Wheat-Lucerne 6/3
25
20
No-till wheat-fallow
15
Tilled wheat-fallow
10
5
0
10
20
30
Time (years)
40
50
Simple Multi-Period Land Use Model
(
Max ∑ β t ⋅ ( v
t, r,i,u
s.t.
∑X
Market
t,r,i,u
t,r,i,u
+v
Environment
t,r,i,u
)⋅X
t,r,i,u
)
≤ l t,r,i
u
Indexes: t = time, r = region, i = soil type, u = management
Data: β = interest rate, v = net benefit, l=land endowment
Variables: X = land use
Explicit Land Use Trajectories
(
Max ∑ v
r,i, u d
s.t.
Market
r,i,u d
∑X
ud
r,i,u
+v
d
Environment
r,i,u d
)⋅X
r,i, u d
≤ L r,i,u d
Indexes: r = region, i = soil type, ud = management path
Implicit Land Use Trajectories

Assume that management history is
manifest in current soil carbon levels

Divide soil carbon range

Implement Markov Chain
Markov Process
Max
∑ (β ⋅ ( v
t
Market
t,r,i,u,o
+v
Environment
t,r,i,u,o
)⋅X
t,r,i,u ,o
t,r,i,u,o
s.t.
∑X
t,r,i,u, o
∑X
t,r,i,u,o
≤ l t,r,i
u, o
u
=
∑ (ρ
u, o

r,i,u,o,o
⋅ X t −1,r,i,u,o )
Indexes: t = time, r = region, i = soil type, u = management
o,ố = soil carbon state
ρ = transition probability from old state ố to new state o
)
Soil Carbon Transition Probabilities
SOC1 SOC2 SOC3 SOC4 SOC5 SOC6 SOC7 SOC8
SOC1 0.81 0.19
SOC2
1
SOC3
0.09 0.91
SOC4
0.31 0.69
SOC5
0.5
0.5
SOC6
0.74 0.26
SOC7
1
SOC8
0.04 0.96
No-till wheat-Fallow
Soil Organic Carbon (tC/ha/20cm)
45
40
Wheat-Lucerne 3/3
35
30
Wheat-Lucerne 6/3
25
20
No-till wheat-fallow
15
10
Tilled wheat-fallow
5
0
10
20
30
Time (years)
40
50
Curse of Dimensionality?
20 Crops
 5 Management options per crop
 100 Regions
 5 Soil Types per region
 20 Periods

5E42 Trajectories
1E94 Trajectories
(independent sites)
(dependent sites)
Curse of Dimensionality?
20 Crops
 5 Management options per crop
 100 Regions
 5 Soil Types per region
 20 Periods

1E6 Variables (No Soil Carbon)
1E7 Variables (Markov process with 10 states)
5E42..1E94 Variables (Explicit Path)
Extensions?

Markov chains are applicable to relatively
independent environmental qualities
(humus, salt, contamination)

Method not suitable for complex
environmental properties (climate)
IV Forest and Agricultural
Sector Optimization Model
FASOM
Overall Objective
Portray agricultural and forest commodity
markets and internalize all
land use externalities
Analyze Policies
Integrate Synergies, Trade-offs
Markets
Soil
Farmers
Land use
decisions
Wildlife
Water
Climate
Model Structure
Limits
Limits
Resources
Inputs
Supply
Functions
Land Use
Products
Markets
Processing
Technologies
Demand
Functions,
Trade
Technologies
Environmental
Impacts
Limits
Economic Surplus Maximization
Land Supply
Forest Inventory
Processing Demand
Water Supply
CS
Labor Supply
PS
Implicit Supply and Demand
Animal Supply
National Inputs
Domestic Demand
Import Supply
Feed Demand
Export Demand
Spatial Resolution
Soil texture
 Stone content
 Altitude levels
 Slopes
 Soil state

Political regions
 Ownership
(forests)
 Farm types
 Farm size

Many crop and tree species
 Tillage, planting irrigation,
fertilization harvest regime

Homogeneous
Response Units
Altitude:
1. < 300 m
2. 300-600 m
3. 600-1100 m
4. >1100 m
Texture:
1. Coarse
2. Medium
3. Medium-fine
4. Fine
5. Very fine
Stoniness:
1. Low content
2. Medium content
3. High content
Slope Class:
1. 0-3%
2. 3-6%
3. 6-10%
4. 10-15%
5. …
Soil Depth:
1. shallow
2. medium
3. deep
DE11
DE12
DE13
DE14
Climate Change Mitigation
Carbon price ($/tce)
500
Afforestation
400
300
CH4
N2O
Biofuel
offsets
Ag-Soil
sequestration
200
100
0
0
20
40
60
80
100
120
140
160
Emission reduction (mmtce)
180
200
Soil Carbon Potentials
Carbon price ($/tce)
500
400
Economic
Potential
300
Competitive
Economic
Potential
200
100
Technical
Potential
0
0
20
40
60
80
100
120
140
Soil carbon sequestration (mmtce)
160
Biofuel Potentials
500
Carbon price ($/tce)
Economic
Potential
400
300
Competitive
Economic
Potential
200
Technical
Potential
100
0
0
50
100
150
200
250
Emission reduction (mmtce)
300
350
Afforestation Potentials
Carbon price (Euro/tce)
500
400
300
Competitive
Economic
Potential
200
Economic
Potential
100
Technical Potential
0
0
50
100
150
200
Emission reduction (mmtce)
250
300