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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
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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
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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
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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)
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Land-Use Allocation Framework
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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
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( )∑=
−−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
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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
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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
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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)
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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
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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
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Results: Performance of Regression Technique
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Units: % of grid cell area
Results: Performance of Regression Technique
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Spatial Characteristics of Explanatory Variables
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Setup for Model Validation
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Historical Land-Use Data Aggregation
• Nine regions based on PET model
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Results from Model Validation
Units: % of grid cell area
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Model Estimated Net transitions: 1900-2005
Units: km2/yr
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Determining Land-Use Transitions
Meiyappan and Jain (2012)
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Carbon Emissions from ISAM – Initial testing
LEGENDS:
DOWNSCALED HYDE RF HOUGHTON
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How does a proportional downscaling method perform historically
( )∑=
−−2
1
21lglglg
l
tt YYQMinimize
( )2lglglgtt SYR −Eliminate
( ) ( )∑=
−−+−2
1
21lglglg
2lglglg
l
tttt YYQSYRMinimize
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How does a proportional downscaling method perform historically
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How does a proportional downscaling method perform historically
Net transitions: 1900-2005
Units: % of grid cell area
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Applications from our Validation Experiment
Spatial determinants of existing land-use patterns
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Applications from our Validation Experiment
How different driving factors change with the scale of analysis?
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Applications from our Validation Experiment
How different driving factors contributed to the 20th century land-use patterns?
Units: % of grid cell area
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Explaining the causes of historical land-use change patterns (cont.)
Units: % of grid cell area
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DiscussionMethodological Advantages
• Suited for long-term projections
• Continuous field approach
• State of the art elastic-net for multicollinearity
• Handles land-use competition consistently
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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
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The Big Picture: Coupled Modeling Framework
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[email protected]/~meiyapp2
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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]
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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