Table 2 Indicators for depicting urban functional fragmentation.

Single-urban functional fragmentation depiction

Industrial/Public Edge Density (ED)

\(ED = \frac{{\mathop \sum \nolimits_{k = 1}^{m} e_{ik} }}{A}\)

\(e_{ik}\) indicates the total length of edge of a certain patch k belonging to the ith class. m indicates the total number of patches of the ith class. A refers to the total areas belonging to the ith urban functional class

As most of the anthropogenic emissions are generated from industrial and public lands, the shape complexities depicted by ED and LSI of industrial and public urban functional patches are considered. Higher values of ED and LSI indicate higher degree of edge density and complexity, respectively

Industrial/Public Landscape Shape Index (LSI)

\(LSI = \frac{{0.25\mathop \sum \nolimits_{k = 1}^{m} e_{ik} }}{\sqrt A }\)

Synthetical urban functional fragmentation depiction

Urban functional Aggregation Index (AI)

\(AI = \left[ {\mathop \sum \limits_{i = 1}^{m} \left( {\frac{{g_{ii} }}{{\max \left( {g_{ii} } \right)}}} \right)P_{i} } \right] \cdot \left( {100} \right)\)

\(g_{ii}\) represent the number of like adjacencies between pixels of the patches of the ith class. \(\max \left( {g_{ii} } \right)\) refers to the maximum number of \(g_{ii}\). \(P_{i}\) denotes the percentage of the ith urban functional class within each 3 km-radium area. N refers to the total number of urban functional patches within individual buffers

For all-type urban functions, higher values of NP represent large total number of urban functional patches and higher fragmentation degree within individual buffers. The AI values increase as the urban functional patches within buffers are increasingly aggregated

Urban functional Number of Patches (NP)

\(NP = N\)