## 4 Methods
### BS-FMMS Carbon Emission Reduction Benefit Analysis Framework
#### 4.1.2 Calculation of Carbon Emission Reductions from Bikeshares  
Under the bottom-up carbon emission calculation idea of the Intergovernmental Panel on Climate Change (IPCC), this study adopts the calculation method based on the distance traveled to calculate the carbon emissions of each transport mode [6; 7; 26]. The carbon emission reduction of bikeshare can be quantified by comparing the carbon emissions generated by bikeshare with the carbon emissions generated by other transport modes for the same distance traveled. The travel chain of a bikeshare only contains the origin and destination locations, without specific paths or driving trajectories. The Manhattan distance, which is the sum of the distances moved along the horizontal and vertical directions between two points, is commonly used to estimate the distance between two locations in the urban road network [36] and is more applicable to the estimation of bikeshare cycling distance. Therefore, the Manhattan distance is used to approximate the estimation of the bikeshare transfer distance. Based on the literature [6], the following hypotheses are proposed by considering the potential transport modes that can be connected with bikeshare in daily travel in Shenzhen:(1) When the riding distance of bikeshare is less than 1 km, it is considered that bikeshare would substitute walking and other non-motorized transport modes (bikeshare, private bicycle, electric bicycle, etc.) during the feeder process and that this portion of the ride would not result in carbon reduction benefits. (2) When the riding distance of a bikeshare is more than 1 km, it is considered that bikeshare would substitute three transport modes (car, taxi, and bus) in the feeder process, and this portion of the ride would generate carbon emission reduction benefits. According to the Shenzhen 2020 travel survey report (see Table 1) [26], the ratio of mode share between the metro and other transport modes is evenly distributed among the three transport modes, cars, taxis, and buses, and it can be obtained that the ratio of mode share of these three transport modes is 61%, 13%, and 26%, respectively. To ensure randomness in the traveler's choice of travel mode, Python was used to simulate the travel chains with a connection distance greater than 1 km, and 61% of the bikeshare travel chains were randomly selected as alternatives to car trips, 13% as alternatives to taxi trips, and the rest as alternatives to bus trips. Fuel vehicles contribute directly to carbon emissions during the use phase. Electric vehicles do not cause carbon emissions during use, but the energy consumed in the operation of electric vehicles also causes emissions during production, so the use phase of electric vehicles also indirectly causes carbon emissions. Shenzhen has completed the electrification of all buses in 2017 and taxis in 2018. Among cars, electric vehicles occupy a certain share, and all of them should be taken into consideration when measuring the carbon emission reductions of bikeshare. Referring to existing studies [26], the carbon emission factors of cars, taxis, and buses in Shenzhen are 139.48 g/pkm, 155.00 g/pkm, and 79.62 g/pkm, respectively (see Table 2). Bikeshares often serve a single traveler, while cars, taxis, and buses can usually accommodate multiple travelers at the same time. Therefore, bikeshare has a passenger loading of 1, cars and taxis have an average passenger loading of 1.5, and buses have an average passenger loading of 17 [7]. In this study, it is considered that bikeshare does not consume energy (fuel, electricity, etc.) or cause carbon emissions in the use stage, so the carbon emissions caused by the transport modes replaced by bikeshare are taken as the carbon emission reduction of bikeshare. The equation for calculating the carbon emission reduction of bikeshare is as follows:  
\[\text{E}_{\text{i}}=\left\{