Box 1.2 (continued)
Equation 10.1: Yield Factors Simple Calculation
YF
L
N ¼ Y
L
N =Y
L
W
Yield factor for a given country and land type ¼ yield for country and land
type/world average yield for given land type
Equation 10.2: Yield Factors Extended Calculation
YF
L
N ¼
P
A W =
P
A N , where A N ¼ P N /Y N and A W ¼ P N /Y W
Yield factor for a given country and land type ¼ sum (area required to produce
given product quantity using world average land)/sum (area harvested for a
given product quantity in given country), where
Area harvested for a given product quantity in a given country ¼ amount of
given product extracted, or waste generated in a country/national yield
for product extraction, and
Area required to produce a given product quantity using world average
land ¼ amount of given product extracted, or waste generated in country/world average yield for product extraction
Equation 10.3: Intertemporal Yield Factor Calculation
IYF W, j ¼ ∑ (P W, i, j /Y W, j, b )/ ∑ (P W, i, j /Y W, i, j )
World average intertemporal yield factor in year ¼ sum (world amount of
product harvested or CO 2 emitted for product i in year j/world productspecific yield for product i in the base year)/sum (world amount of product
harvested or CO 2 emitted for product i in year j/world product-specific
yield for product i in year j)
Source: Lin et al. (2019, Appendix A, pp. 63–66)
There are additional equations apparent in publications, as for example for the
carbon component of the Ecological Footprint (refined more recently by Mancini
et al. 2016):
carbon_EF ¼ (P C *S OCEAN )/Y W *EQF, with Y W ¼ AFCS/0.27 and AFCS ¼ NFP/AF,
where:
– P C is the world’s annual anthropogenic emissions of CO 2 measured in Mt
CO 2 ;
– S OCEAN is the fraction of anthropogenic CO 2 emission that is sequestered by
oceans in a given year. Data from Khatiwala et al. (2009) are currently used in
National Footprint Accounts and the oceanic uptake fraction for the year 2010,
for example, was 28% (Borucke et al. 2013);
– EQF is the equivalence factor used to weight forest land. (The GAEZ-based
method assigns forest land a value, indicating that a hectare of world-average
forest is that many times as productive as a world average hectare of land; see
Table 1.1);
– Y W is the annual rate of CO 2 sequestration per hectare of world average forest
land;
1.3 Conceptual Framework
9
Equation 10.1: Yield Factors Simple Calculation
YF
L
N ¼ Y
L
N =Y
L
W
Yield factor for a given country and land type ¼ yield for country and land
type/world average yield for given land type
Equation 10.2: Yield Factors Extended Calculation
YF
L
N ¼
P
A W =
P
A N , where A N ¼ P N /Y N and A W ¼ P N /Y W
Yield factor for a given country and land type ¼ sum (area required to produce
given product quantity using world average land)/sum (area harvested for a
given product quantity in given country), where
Area harvested for a given product quantity in a given country ¼ amount of
given product extracted, or waste generated in a country/national yield
for product extraction, and
Area required to produce a given product quantity using world average
land ¼ amount of given product extracted, or waste generated in country/world average yield for product extraction
Equation 10.3: Intertemporal Yield Factor Calculation
IYF W, j ¼ ∑ (P W, i, j /Y W, j, b )/ ∑ (P W, i, j /Y W, i, j )
World average intertemporal yield factor in year ¼ sum (world amount of
product harvested or CO 2 emitted for product i in year j/world productspecific yield for product i in the base year)/sum (world amount of product
harvested or CO 2 emitted for product i in year j/world product-specific
yield for product i in year j)
Source: Lin et al. (2019, Appendix A, pp. 63–66)
There are additional equations apparent in publications, as for example for the
carbon component of the Ecological Footprint (refined more recently by Mancini
et al. 2016):
carbon_EF ¼ (P C *S OCEAN )/Y W *EQF, with Y W ¼ AFCS/0.27 and AFCS ¼ NFP/AF,
where:
– P C is the world’s annual anthropogenic emissions of CO 2 measured in Mt
CO 2 ;
– S OCEAN is the fraction of anthropogenic CO 2 emission that is sequestered by
oceans in a given year. Data from Khatiwala et al. (2009) are currently used in
National Footprint Accounts and the oceanic uptake fraction for the year 2010,
for example, was 28% (Borucke et al. 2013);
– EQF is the equivalence factor used to weight forest land. (The GAEZ-based
method assigns forest land a value, indicating that a hectare of world-average
forest is that many times as productive as a world average hectare of land; see
Table 1.1);
– Y W is the annual rate of CO 2 sequestration per hectare of world average forest
land;
1.3 Conceptual Framework
9