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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
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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
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regionaggregatethewithinltypelandfordemandareatotalYN
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t ''1
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=
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
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∑=
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• 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
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tt YYQMinimize
( )2lglglgtt SYR −Eliminate
( ) ( )∑=
−−+−2
1
21lglglg
2lglglg
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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
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