Spatial Modeling of Agricultural Land-Use Change at Global Scale

Prasanth MeiyappanPhD Candidate

University of Illinois at Urbana-Champaign

With contributions from

Michael Dalton (NOAA), Brian O’Neill (NCAR) & Atul Jain (U of I)

NCAR IAM Group Annual Meeting, 19 Aug 2013

Acknowledgement: NASA LCLUC Program

Why model land use at global scale

• Several key drivers of land use and its impacts have no regional boundaries and substantial feedbacks exist between them.

• Regions across the world are interconnected through global markets and trade that can shift the land requirements between regions.

Two key motivations

Structure of IAMs

Land-Use/Land-Cover Spatial Allocation

Biophysical Process Models

Demographic, Markets, And Development

Behavior

Coarse resolution: world split into 9-24 regions

Requires land information on uniform geographic grids:

typically: 0.5° x 0.5 ° lat/lon

Downscaling

ObjectivesDevelop a new land-use downscaling technique, with the following attributes (version 1)

• Address the mismatch between the scales at which land-use decisions are made and the scale at which global scale models are applied

• Account for variability in nature of driving factor• Suitable for long-term projections• Validated• Can handle land-use competition• Land-use representation using continuous field approach

Meiyappan et al. (in prep)

Land-Use Allocation Framework

Econometric Framework for Land-Use Allocation

( ) ( )∑=

−−2

1

2lglglglglg

l

tttt YRYWPMaximize

( ) ( )∑=

−−2

1

2lglglg

l

tt SYRMaximize

0lg ≥tY ∑

=≤

2

1lg

lg

t AY

Underlying Economic Motivation: Profit maximization of individual landowners at each grid cell – thereby reflecting small scale decisions at larger scales

Mathematical Formulation

Component 1: Static Profit Maximization Function

'' lgtY

Equation 1

Equation 2

Grid cell level constraints

Notations

''l

''t

'' g

( ) ttt YWP lglglg −

( ) ''2

lglgtYR−

'''' lglglgttt WPS −α

land-use type (1=crop, 2=pasture, 3= unmanaged land)

time (year)

grid cell

area of land use

net profit

non-linear cost term

( )∑=

−−2

1

21lglglg

l

tt YYQMinimize

( ) ( )∑=

−−+−2

1

21lglglg

2lglglg

l

tttt YYQSYRMinimize

regionaggregatethewithinltypelandfordemandareatotalYN

g

t ''1

lg∑=

=

Econometric Framework for Land-Use Allocation (Cont.)

Component 2: Dynamic Adjustment Cost Model

'' lgQ

Notations

Constant (adjustment cost per unit area)

Overall Objective Function: Component 1 + Component 2

Equation 3

0lg ≥tY ∑

=≤

2

1lg

lg

t AY

3 Constraints imposed

2 grid cell level constraints

1 regional level constraint

Regression Technique for Land Suitability

10 lg ≤≤F ∑=

=3

1lg 1

lF

∑=

+

+= 3

1

lgg0

lg0

k

X

X

kTkk

lT

l

e

eFββ

ββ

• World split into 325 distinct geopolitical regions; separate equations are derived for each region.

• Multicollinearity – dealt using elastic-net regularization• Spatial Autocoorelation - Autocovariate terms• FMNL and Elastic-net merged using coordinate descent algorithm

• Fractional Multinomial Logistic Regression (FMNL)• Allows fractional outcomes• More than two dependent variables can be modeled simultaneously

Notations

''l

''t

land-use type (1=crop, 2=pasture, 3= unmanaged land)

time (notation suppressed) '' lgtF

'' g grid cell

Fraction of grid cell area

tg

t FAS lglg =

'' gA Area of grid cell'' lgX Vector of driving factors

Determining Local Land SuitabilityBroad Category Explanatory Factor Unit

Climate

Seasonally averaged temperature K

Seasonally averaged precipitation mm/day

Seasonally averaged Potential Evapotranspiration (PET) mm/day

Squared seasonally averaged temperature K2

Squared seasonally averaged precipitation mm2/day2

Squared seasonally averaged PET mm2/day2

Seasonal Temperature Humidity Index (THI) °C

Climate Variability

Seasonal Palmer Drought Severity Index (PDSI) [-]

Heat wave duration index No of days

Simple daily precipitation intensity index mm/day

Soil Characteristics

Rooting Conditions and Nutrient Retention Capacity

[-]

Nutrient AvailabilityOxygen Availability

Chemical Composition (indicates toxicities, salinity and sodicity)

Workability (indicates texture, clay mineralogy and soil bulk-density)

Terrain Characteristics Elevation, Altitude and Slope Combined

Socio-economic

Built-up/urban land areaFraction of grid area

[m2/m2]

Urban population densityInhabitants/km2

Rural population density

Rate of change in rural population densityInhabitants/km2/yr

Rate of change in urban population density

Market Influence IndexInternational

dollars/person

Spatial AutocorrelationCropland Autocovariate Fraction of grid area

[m2/m2]Pastureland Autocovariate

Historical Data for Explanatory Factors: 1900-2005

Category Data Variable Description/Units

Spatial Characteris

ticsPeriod of Availability Source

Climate

Temperature (Ta)oC

0.5 degrees(lat/lon)

1901-2009(monthly)

Climatic Research Unit (CRU) TS 3.1 (updated estimates based on Mitchell and

Jones, 2005)

Daily Average Maximum Temperature (Tmax)

Potential Evapotranspiration Millimeters

Precipitation CRU TS 3.10.01#

Wet Day Frequency days 1901-2006(monthly) CRU TS 3.0&

Palmer Drought Severity Index (PDSI) No units2.5

degrees@

(lat/lon)

1870-2010(monthly) Dai et al. (2011a,b)

Soil Constraints

Rooting Conditions and Nutrient Retention Capacity Categorical

Data classified into

7 gradient classes of

land suitability for

agriculture5 minutes^

(lat/lon) Constant with time

FAO/IIASA, 2010. Global Agro-ecological Zones (GAEZ v3.0). FAO, Rome, Italy and

IIASA, Laxenburg, Austria. http://www.fao.org/nr/gaez/en/

Nutrient Availability Oxygen Availability

Chemical Composition (indicates toxicities, Salinity and Sodicity)

Workability (indicates texture, clay mineralogy and soil bulk-density)

Terrain Constraints

Elevation, Slope andInclination Combined

Categorical Data

classified into 9 gradient

classes

Socio-Economic

Factors

Urban/built-up land % of grid-cell area 5 minutes^

(lat/lon)10,000 BC – 2005 AD

(decadal)% Goldewijk et al. (2010)Urban Population Inhabitants/k

m2Rural Population

Gross Domestic Product (GDP) per capita

Constant 1990

international (Geary-Khamis)

dollars/person

National level

1 AD-2010(annually between 1800-2010)$

Bolt and Van Zanden (2013)(The Maddison Project -

http://www.ggdc.net/maddison/maddison-project/home.htm)

Market Accessibility No units 1 km^

(lat/lon) ~2005 Verburg et al. (2011)

Historical Land-Use Data: 1900-2005

• Existing data sets are based on data-model fusion

• Klein Goldewijk et al. (2011) HYDE reconstruction

• Ramankutty and Foley (1999) - 300 years of cropland data set

• Ramankutty et al., (2008) - crop and pasture, circa 2000

• Ramankutty (2012) updated data set – version II

Regression Technique for Land Suitability

10 lg ≤≤F ∑=

=3

1lg 1

lF

∑=

+

+= 3

1

lgg0

lg0

k

X

X

kTkk

lT

l

e

eFββ

ββ

• World split into 325 distinct geopolitical regions; separate equations are derived for each region.

• Multicollinearity – dealt using elastic-net regularization• Spatial Autocoorelation - Autocovariate terms• FMNL and Elastic-net merged using coordinate descent algorithm• Regression coefficients were standardized for comparison• 2003-05 data used for fitting the FMNL regression

• Fractional Multinomial Logistic Regression (FMNL)• Allows fractional outcomes• More than two dependent variables can be modeled simultaneously

Notations

''l

''t

land-use type (1=crop, 2=pasture, 3= unmanaged land)

time (notation suppressed) '' lgtF

'' g grid cell

Fraction of grid cell area

tg

t FAS lglg = '' gA Area of grid cell

Results: Performance of Regression Technique

Units: % of grid cell area

Results: Performance of Regression Technique

Spatial Characteristics of Explanatory Variables

Setup for Model Validation

Historical Land-Use Data Aggregation

• Nine regions based on PET model

Results from Model Validation

Units: % of grid cell area

Model Estimated Net transitions: 1900-2005

Units: km2/yr

Determining Land-Use Transitions

Meiyappan and Jain (2012)

Carbon Emissions from ISAM – Initial testing

LEGENDS:

DOWNSCALED HYDE RF HOUGHTON

How does a proportional downscaling method perform historically

( )∑=

−−2

1

21lglglg

l

tt YYQMinimize

( )2lglglgtt SYR −Eliminate

( ) ( )∑=

−−+−2

1

21lglglg

2lglglg

l

tttt YYQSYRMinimize

How does a proportional downscaling method perform historically

How does a proportional downscaling method perform historically

Net transitions: 1900-2005

Units: % of grid cell area

Applications from our Validation Experiment

Spatial determinants of existing land-use patterns

Applications from our Validation Experiment

How different driving factors change with the scale of analysis?

Applications from our Validation Experiment

How different driving factors contributed to the 20th century land-use patterns?

Units: % of grid cell area

Explaining the causes of historical land-use change patterns (cont.)

Units: % of grid cell area

DiscussionMethodological Advantages

• Suited for long-term projections

• Continuous field approach

• State of the art elastic-net for multicollinearity

• Handles land-use competition consistently

DiscussionKnown Issues/Limitations

• Irrigation not included due to data limitations

• Crude method to calibrate the relative weighing between static profit maximization function and the dynamic cost adjustment term

• Further room available for methodological improvements

• Land-Use Intensification

The Big Picture: Coupled Modeling Framework

meiyapp2@illinois.eduwww.atmos.illinois.edu/~meiyapp2

Downscaling in Current Approaches• IMAGE, MagPie, MIT-EPPA – follows the approach of

traditional geographic models; empirical rules based on current land use are assumed to hold true for the future (up to 2100)

• GLOBIO3, iESM-GLM – land use demands allocated as close as possible to existing land-use patterns

• In common • The downscaling algorithms have not been validated in the time scales at

which they are applied for [van Asselen & Verburg, 2013]• Land-use competition handled implicitly or not at all considered

[Heistermann et al., 2006]

Land cover/use representation in IAMs

van Asselen & Verburg (2013); Verburg et al. (2012)

Typically 0.5° or coarser

IMAGE

MagPie

GLOBIOM

Nexus land-use model

LandSHIFT - 5 minIMAGE - 5 min

IMAGE