Land-use change modeling is performed as follows. Firstly, the availability of suitable land for agricultural uses is defined. A land structure is defined, based on the disaggregation of suitable available agricultural land in hierarchical levels. Based on this land structure, an allocation procedure is defined to distribute land among competing agricultural land-uses. In a second step, the approach to model land supply for agricultural uses is defined based on the possibility to expand agricultural (managed) land into unmanaged lands. Finally, the approach to estimate land-use changes from soybean production and its allocation to biodiesel is described, incorporating the additional drivers of soybean production.
Land-use change modeling is based on the following basic assumptions: § Total suitable agricultural is fixed for each managed land-use type. § Managed land is a mobile and heterogeneous production factor.
§ Cropland and managed land allocation depends on relative net returns per unit of land (unit profit) between competing managed land-uses.
§ Managed land supply for each managed land-use type depends on the aggregated land unit profit.
MODELING FRAMEWORK
§ Managed land expansion is allocated between unmanaged land-uses based on constant exogenous shares for each unmanaged land-use type in each soybean supply region. § Land-use changes are allocated to biodiesel based on the share of soybean for
biodiesel on soybean land supply.
4.5.1.
Total suitable agricultural land and land productivity
Land is a primary production factor and probably the most important one in the production function of agricultural products. Total suitable agricultural land (qlandT) is defined as the quantity of land at the country level that can hold agricultural land-uses with a minimum productivity level (Eq. 4-40).
) ( x X x x T land L q =
å
m s.t. mx ³m Eq. 4-40The approach used by van Meijl et al. (2006) is followed to estimate total suitable agricultural land for each managed land-use type. The advantage of this approach is that land suitability is estimated based on geo-referenced land productivity data. Consequently, the estimation of land suitable to hold agricultural land-uses accounts for biophysical constraints limiting the expansion possibilities of agricultural land.
Total suitable agricultural land is determined by dividing the national territory in equal square parcels (L ). Each parcel x x has a land productivity index m which indicates the percentage x
difference between the parcel yield and the maximum obtainable yield at the country level. The suitability threshold m defines the maximal acceptable percentage difference between yields and represents the minimum acceptable productivity level.
The parcel productivity is calculated based on the aggregated productivity of a set of selected land-uses. Parcels are sorted by decreasing productivity, so that the land productivity index of the last parcel added to qlandTequals the maximum threshold.
Total suitable agricultural land depends on the productivity of land. The minimum productivity threshold however differs among managed land-use types. Indeed, higher productivities are generally required to obtain acceptable returns to cropland than to pastureland. In order to account for this effect, total suitable agricultural land for each managed land-use type is estimated based on specific land productivity curve (Figure 4-3). Land productivity curves take the exponential form and depend on the maximum land suitability potential (qlandcrop-suit, qlandpast-suit) and the land productivity index. The quantity of land suitable for cropland is lower than the quantity of land suitable for pasture (INDEC 2002). Consequently, it is assumed that less land is available for cropland than for pasture. This implies that land productivity decreases more smoothly for pastureland than for cropland, given the shape of the respective curves.
pcrop Qland crop-suit Qlandpast-suit ppast Alandsuit μx
Figure 4-3. Land productivity curve by managed land type.
4.5.2.
Land structure
Land is modeled assuming a hierarchical structure consisting in different levels. As studies by Conforti and Londero (2001) and Golub et al. (2006) have reported, land is disaggregated to account for heterogeneity and imperfect mobility of land among a set of selected land-uses. Land heterogeneity is assumed to derive from different land productivities among land-uses (Baltzer and Kløverpris 2008). Imperfect land mobility is assumed to derive among other factors, from differences in costs of land conversion, managerial inertia and un-measured benefits from crop rotation (Golub et al. 2006).
This conventional approach is adopted by assuming 12 final land-uses, aggregated in a three- level nesting structure (Figure 4-4). Each level aggregates the quantity of land available in each final land-use type, as follows:
§ Crop (n): Land occupied with a specific crop. Includes soybean and corn land, with n=soy, corn.
§ Managed land (
l
): Land under economic use. Aggregates cropland and pasture land, with l=crop, past.§ Unmanaged land ( k ): Land not under economic use (nature land). Aggregates forest, grassland, mixedland, savannas, shrubland and degraded land, with k=for, grass, mix, sav, shrub, deg.
Suitable land for cropland can generally hold a large variety of crops. In the Argentinean case 60% of cropland is occupied by soybean and corn, accounting also for the two main competing crops (INDEC 2002). Therefore, in the first level, cropland is represented by two competing crops n, namely soybean (soy) and corn (corn).
Managed lands typically account for cropland, pastureland and managed forests (Taheripour et al. 2008). In Argentina, cattle production is done partly on cropland and partly on unmanaged natural land (INDEC 2002). So, a fraction of grasslands and savannas is allocated
MODELING FRAMEWORK
to pastureland for cattle production37. For simplicity, managed forest land is assumed to be natural forestland, as it only accounts for 3% of total forest land (INDEC 2002). In the second level therefore, cropland (crop) and pasture (past) uses are aggregated into managed land, where each managed land type is denoted as l.
Figure 4-4. Land supply structure.
Finally, in the third level, managed and unmanaged lands are aggregated into the total available suitable agricultural land. This level defines the total suitable agricultural land to allocate managed land-uses, and consequently the possibility of expansion of managed into unmanaged land.
Unmanaged land is aggregated in a single nesting structure, summing up the total quantity of available unmanaged land. The unmanaged land nesting structure includes several unmanaged land-use types, denoted as k. Following the ICF model (ICF 2009), six different unmanaged land-uses are assumed, including forest (for), grassland (grass), mixed land (mix), savannas (sav), shrubland (shrub) and degraded land (deg).
4.5.3.
Managed land allocation
An allocation procedure is then defined to distribute land among competing land-uses in the same hierarchical level. Land allocation among competing managed land-uses is modeled based on a modified version of the constant elasticity of transformation (CET) function, to account for physical units in land conversions. Physical units are required to estimate GHG emissions from LUC. The CET function accounts for imperfect mobility among competing land-uses.
37 Cattle rising are done on natural grasslands. Cattle breeding is partially done on managed pastures (cropland)
and dairy farms are located in croplands Rearte, D. (2007). Distribucion territorial de la ganaderia vacuna. Programa National de Carnes, . Balcarce, BA, Argentina, Estación Experimental Agropecuaria Balcarce -
The CET function is specified as a three-level nesting structure, following land disaggregation in Figure 4-4. Denoting s and n s as the elasticity of transformation for competing crops and l managed lands, respectively, the nested CET function respects that sn ³ , based on the sl assumption that rationally it is easier to convert land among crops than among cropland and pasture, and similarly, among managed lands than among managed and unmanaged lands. In the first level, the CET function allocates land between crop types based on the net return to soybean (n1) respect to corn (n2) per unit land. (
n land
g ). The land allocation function for soybean land is then given by:
n s n land n land sp land sp land
q
÷÷
ø
ö
çç
è
æ
×
=
2 1g
g
l
Eq. 4-41 s.t. landl n n land q q =å
Eq. 4-42where s is the elasticity of transformation between competing crop n1 and n2 and n sp land
l a parameter representing the initial quantity of soybean land at the national level. In order to account for biophysical limits in land availability, the land allocation function for competing crops respects that the total land allocated among crops should equal the total land available under cropland. Therefore a constraint is added in Eq. 4-42 to land supply for soybean production.
Analogously, land conversion among managed lands is modeled as a CET function depending on relative land unit profits so that qlandl1 =q
(
llandl1,glandl1,glandl2,sl)
, where glandl1 is the aggregated cropland unit profit and glandl2 is the pastureland unit profit. Initial conditions and the transformation elasticity between managed land-uses l are given by parameters llandl1 andl
s , respectively. The elasticity parameter defines the easiness of conversion between cropland and pasture. Analogously to Eq. 4-42, this procedure considers that the sum of the quantity of land allocated to each managed land-use l should be equal to the total managed land, so that
M land l l land q q =
å
.4.5.4.
Managed land supply
The supply of land for managed land-uses depends on the possibility of expansion of the agricultural frontier. The modeling framework therefore allows for managed land to increase, representing the expansion possibility of cropland and pastures into natural land. Two major issues are being considered in modeling managed land supply, namely:
§ The quantity of managed (agricultural) land that expands into unmanaged (natural) land.
§ The type of converted unmanaged land-uses.
Land supply for each managed land-use type is modeled following (van der Mensbrugghe 2005). In this approach the quantity of managed land that expands into unmanaged land
MODELING FRAMEWORK
depends on the aggregated net return to each managed land-use type. Land unit profits of managed lands are used due to the absence of a land value for unmanaged lands and the lack of detailed geo-referenced data. A land supply function is then defined for cropland and pastureland depending on their own aggregated unit profit.
For each managed land-use type a constant elasticity function is specified (Eq. 4-43).Analogously to Eq. 4-42, this procedure considers that the sum of the quantity of land supplied to each managed land-use l should equal the total available agricultural land. Additionally the quantity of land supplied to each managed land-use l should be equal or lower than the maximum suitable available land for each managed land-use type (Eq. 4-44). Formally managed land supply for each managed land-use type is given by:
( )
l el land l land l landq
=l
×
g
Eq. 4-43 s.t. landM l l land q q =å
qlandl £qlandl-suit
Eq. 4-44
where glandl is the aggregated unit profit of managed land l and llandl and e are parameters l representing initial conditions and the land supply elasticity, respectively.
Different land supply elasticities (e ) are assumed for cropland and pasture land supply given l the different land productivity thresholds and other factors affecting land conversion decisions for each managed land-use type. Parameter e is a constant that was calibrated to fit historical l
land expansion patterns for cropland and pasture land in each region.
Cropland average unit profit is estimated as the weighted sum of soybean and corn land unit profits. Pastureland revenue depends on the beef price, the pasture land yield and the unit production costs. Soybean and corn revenues depend on the crop price, yield and unit production cost. Crops and pasture yield are partially determined by land productivity that in turn affects the expected land unit profit from cultivation in new lands. Considering that managed lands are assumed to expand into less productive lands, yields and consequently land revenues are assumed to decrease as managed lands increases.
Finally, the quantity of managed land that expands into unmanaged land is allocated among unmanaged land-use types following the approach used by Searchinger et al. (2008). This approach assumes future land-use changes will follow the same historical land-use conversion patterns. To this end, the shares of unmanaged land-uses on managed land expansion are exogenously introduced, considering historical trends in each soybean supply region.
4.5.5.
Direct land-use change from soybean production for biodiesel
Direct land-use change (dLUC) from soybean production for biodiesel is estimated based on the following procedure. Firstly, the quantity of cropland expansion into managed and unmanaged lands is estimated. Then, dLUC from cropland expansion is allocated to soybean production for biodiesel.
For modeling purposes, soybean production is assumed to be located in four different supply regions sr. Land-use patterns in each region determine the share of unmanaged land-uses k on managed land-use l expansion (al ,ksr). Therefore, for each region sr, the expansion rate of managed land l (cropland) into each unmanaged land-use k (ql,k) depends on the quantity of land supplied to each managed land l and the historical share of land-use conversion from each managed land l into each unmanaged land k. Cropland (l) expansion into each unmanaged land-use k is then given by:
l land sr k l k l q q, =a , × Eq. 4-45
A similar formulation is specified for pastureland expansion into unmanaged lands.
In this modeling framework, cropland and pasture compete for managed lands. In order to estimate dLUC from cropland expansion, the rate of cropland expansion into pasture land is specified. This rate depends on the supply of cropland (qlandl) and the share of cropland on pasture expansion (al ,lsr). l land sr l l l l q q, =a , × Eq. 4-46
In Eq. 4-46, al ,lsr is estimated based on the land supply CET function that allocates land between cropland and pasture.
Direct land-use change (dLUC) induced by cropland expansion is then estimated based on Eq. 4-46 and Eq. 4-47 as:
å
+ = k k l l l l q q dluc , , Eq. 4-47In the Argentinean case, the soybean producer decision on the quantity of land diverted to soybean is independent of the market destination of the product. Moreover, there is no tradability system that allows identifying the location from where soybean for biodiesel is supplied. An allocation procedure is then proposed based on assigned dLUC from soybean expansion to the biodiesel.
The allocation of dLUC from soybean production to the biodiesel is then performed based on direct land-use estimated through Eq. 4-47, the shares of soybean in cropland supply (asoycrop) and the share of soybean for biodiesel on soybean production (asoybio), so that,
bio soy crop soy crop bio soy dluc dluc = ×
a
×a
Eq. 4-48The share of soybean in cropland supply is given by the ratio between land supply for soybean production and the aggregated land supply for cropland: Similarly, the share of soybean for biodiesel on soybean production depends on the quantity of biodiesel production and the quantity of soybean production. This allocation procedure allows assigning land-use change GHG emissions to biodiesel; provided that other drivers, such as soybean, oil and meal
MODELING FRAMEWORK
international demand also underpin land supply for soybean production. The allocation of emissions to biodiesel exports is finally assigned based on the share of biodiesel production diverted to the export market (bbioexp).