Both intermediate use and final demand can be divided into three parts based on the proportion of local total output, domestic import, and foreign import [25�C27]. Therefore, local intermediate input, zL, can selleck chemicals Sorafenib be calculated aszijL=zij(xi(xi+xiF+xiD)),(1)where zij is the total intermediate input from Sector i to Sector j, xi is the total output of Sector i, xiF is the foreign imported economic flow of Sector i, and xiD is the domestic imported economic flow of Sector i. While final demand of Sector i from local output,fiL, is expressed asfiL=fi(xi(xi+xiF+xiD)),(2)where fi is the total final demand of Sector i.2.2. AlgorithmFrom the perspective of local decision makers, this study focuses only on carbon flows coming from the urban system without taking into account carbon flows coming from the international and domestic systems.

The embodied carbon flows for a typical sector in an urban economy based on local emissions can be described as Figure 1, including local and imported intra- and inter- sectoral carbon flows (��iL is the local embodied intensity of products from Sector i, zijL is the monetary value of local intermediate inputs from Sector i to Sector j, ��iM is the imported embodied intensity of products from Sector i, zijM is the monetary value of imported intermediate inputs from Sector i to Sector j, ��jL is the local embodied intensity of products from Sector j, and zjiL is the monetary value of local intermediate inputs from Sector j to Sector i), carbon flows embodied in final demand (fjL denotes the final demand of Sector j from local outputs), and net environmental inputs flows (cj is the amount of direct GHG emissions).

Figure 1Embodied GHG flows for a typical sector in an urban economy (carbon flows introduced by imported commodities from other domestic and foreign regions ��i=1n��iMzijM are not considered based on local emissions).Based on Figure 1, the sectoral biophysical Batimastat balance requires that��jLxj=��i=1n��iLzijL+��i=1n��iMzijM+cj,(3)where xj is the monetary value of total outputs of Sector j.To calculate local embodied emissions in this paper, emissions introduced by imported commodities from other domestic and foreign regions are not concerned. Then, rewrite the physical balance equation as��jLxj=��i=1n��iLzijL+cj.(4)Then an aggregate matrix equation can be induced as:ELX=ELZL+C,(5)in which EL = [��jL]1��n, ZL = [zijL]n��n, C = [cj]1��n, and X = [xij]n��n, where i, j (1,2,��, n), xij = xj(i = j), and xij = 0(i �� j).Therefore, with direct GHG emissions matrix C, local intermediate input matrix ZL, and total outputs matrix X properly given, the embodied GHG emissions intensity matrix EL can be calculated asEL=C(X?ZL)?1.