**Appendix A**

Based on the proposed model, the indicator of energy improvement potential can be defined as the ratio of the difference between the actual value and the target value to the actual value, i.e.:

$$PE\_i = \frac{TE\_i - XE\_i}{XE\_i} \tag{A1}$$

Generally speaking, the infrastructures of the URT system are difficult to adjust further in the short term once they have been constructed. Therefore, we aim to investigate the improvement potentials for train, energy, passenger transport volume, revenue passenger kilometers, and CO2 emissions. Similarly, the targets of train, passenger transport volume, revenue passenger kilometers, and CO2 emissions are expressed as follows:

$$TT\_{\bar{i}} = \sum\_{\bar{j}=1}^{n} \lambda\_{\bar{j}} X T\_{\bar{j}} \tag{A2}$$

$$TP\_{\hat{\imath}} = \sum\_{\hat{\jmath}=1}^{n} \lambda\_{\hat{\jmath}} Y P\_{\hat{\jmath}} \tag{A3}$$

$$TR\_i = \sum\_{j=1}^{n} \lambda\_j \mathcal{Y} \mathcal{R}\_j \tag{A4}$$

$$T\mathbf{C}\_{\bar{i}} = \sum\_{\bar{j}=1}^{n} \lambda\_{\bar{j}} Y \mathbf{C}\_{\bar{j}} \tag{A5}$$

Likewise, the improvement potentials of train, passenger transport volume, revenue passenger kilometers, and CO2 emissions can be formulated as follows:

$$PT\_i = \frac{TT\_i - XT\_i}{XT\_i} \tag{A6}$$

$$PP\_{\bar{i}} = \frac{TP\_{\bar{i}} - \Upsilon P\_{\bar{i}}}{\Upsilon P\_{\bar{i}}} \tag{A7}$$

$$PR\_i = \frac{TR\_i - \mathcal{Y}R\_i}{\mathcal{Y}R\_i} \tag{A8}$$

$$PC\_i = \frac{TC\_i - \mathcal{YC}\_i}{\mathcal{YC}\_i} \tag{A9}$$
