2.3. LCA computations
The LCA computational framework by Heijungs and Suh (2002)
was implemented in Matlab to automate the LCA computation for
the GWP evaluation in the eco-sphere. The required LCA computation
was simplified by scoping the LCA to the evaluation of carbon
footprint. The simplified computations are represented by Eqs. (1)–
(3). The inventory of the cropping system was arranged into two
matrices A and B. Rows (i1) of matrix A presents n1 = 5 economic
flows of wheat, fuel and N, P, k fertilizers. Rows (i2) of matrix B presents
n2 = 4 environmental interventions of CO2 and N2O flows in
addition to the yield of biomass residues and land use. The columns
of both matrices (j) present the n1 = 5 production/consumption
processes of wheat, fertilizers and fuel. The demand vector f
was set to the base of the functional unit, i.e., per ha. In other
words, the emissions per production unit of agricultural inputs
are scaled according to the amounts used to cultivate one hectare.
Eq. (1) determined a scale vector s. Eq. (2) determined the vector g
of the total interventions. A characterization vector Q was used to
evaluate CO2e, e.g. 298 kg CO2e/kg N2O (IPCC, 2007).
s ¼ A1
f ð1Þ
g ¼ Bs ð2Þ
GWP ¼ Qg ð3Þ
Contribution analyses were performed by the elemental operations
in Eq. (4) to determine the contribution of each process and
intervention to the GWP.