# A Perfect Decomposition Model for Analyzing Transportation Energy Consumption in China
## 2 Methodology
### Transportation Energy Consumption Decomposition Model  
Transportation energy consumption is connected with transportation turnover volume (the product of transportation volume and average distance), transportation structure (the transport structure usually refers to the transport volume structure. In a certain period, within the scope of a country or region, the proportion of various transport modes in the total passenger and freight transport volume or total turnover. It reflects the status and role of modes of transportation in the whole transportation system. Transportation volume share of mode \(i\) among all modes) and transportation energy intensity. The perfect complete decomposition model for explaining the change of transportation energy consumption can be written as follows.  
\[E=\sum_{i}E_{i}^{t}=\sum_{i}\frac{E_{i}^{t}}{D_{i}^{t}}\times D_{i}^{t}=\sum _{i}\frac{E_{i}^{t}}{D_{i}^{t}}\times\frac{D_{i}^{t}}{D^{t}}\times D^{t}=\sum_ {i}l_{i}^{t}\times S_{i}^{t}\times D^{t} \tag{21}\]  
where \(i=1,2,3,4,5\) presents five transportation modes, namely, highway, railway, aviation, water transportation, pipeline, respectively; \(E\) is total energy consumption of the five transportation modes; \(E_{i}^{t}\) is energy consumption transportation mode \(i\) in year \(t\); \(D_{i}^{t}\) is transportation turnover volume of mode \(i\) in year \(t\); \(I_{i}^{t}=E_{i}^{t}/D_{i}^{t}\) is transportation energy intensity of mode \(i\) in year \(t\); \(S_{i}^{t}=D_{i}^{t}/D^{t}\) is transportation structure share of mode \(i\) in year \(t\).  
It can be seen from Equation (21), transportation energy consumption can be decomposed into the common effect of three factors: transportation turnover volume, transportation structure and transportation energy consumption intensity. The impact of each factor on transportation energy consumption not only has a close relationship with the changes of the factors, but is also connected with the initial and final value of the other two factors.  
The contribution of each influence factor to transportation energy consumption change can be seen as the product of five \"three factors\". Transportation energy consumption factor decomposition model can be constructed. \(D_{i}^{0}=D_{i}^{0}+\Delta D_{i}\), \(S_{i}^{t}=S_{i}^{0}+\Delta S_{i}\), \(I_{i}^{t}=I_{i}^{0}+\Delta I_{i}\), according to the three-factor decomposition model, the change of transportation energy consumption in the base year 0 and target year \(t\), \(\Delta E\) can be calculated as Equations (22) and (23).  
\[\Delta E=E^{t}-E^{o}=\sum_{i}l_{i}^{t}\times S_{i}^{t}\times D^{t}-\sum_{i}l_ {i}^{0}\times S_{i}^{0}\times D^{0} \tag{22}\]  
\[\Delta E=\Delta E_{t}-\Delta E_{0}=\Delta E_{D}+\Delta E_{I}+\Delta E_{S} \tag{23}\]  
where \(\Delta E_{I}\), \(\Delta E_{S}\) and \(\Delta E_{D}\) are the contributions of transportation energy consumption intensity, transportation structure, and transport turnover volume, respectively.  
Based on the perfect decomposition model, three influence factors of transportation energy consumption changing direction can be divided into two cases.