## 5 Discussion on Relevant Issues
### Derivation of Calculation Formulas for Agricultural Production Potential on Roofs and Urban Spaces  
Based on the previous analysis and calculation process, the following four calculation formulas were derived. 1. The first step was to obtain the roof inventory area of a certain city or region, which can calculate the annual production of vegetables grown on the roof of that city or region. \[\text{P}_{\text{Annual yield of roof vegetables}}=\text{S}_{\text{Roof inventory area}}\times\text{A}\times\text{Q}\] \[=\text{0.847S Roof inventory areaQ}_{\text{Annual vegetable yield per unit area}}\] (1)  
P--Annual yield of vegetables grown on roofs of buildings in a certain city or region, unit kg; S--The roof area of a city or area that can be used for agricultural cultivation, unit m\({}^{2}\); A--Utilization rate of roof area, 84.7% (ratio of roof agricultural planting area to roof area); Q--Annual yield of vegetables per unit area, which can be selected according to cultivation methods: soil cultivation can choose 4.78 kg/m\({}^{2}\), facility cultivation can choose 15.04 kg/m\({}^{2}\), and the mixed method of soil cultivation and facility cultivation can choose 9.91 kg/m\({}^{2}\). 2. The inventory is a time-consuming and labor-intensive work. If the conservative value of 5.81 ha/km\({}^{2}\) (5.81%) obtained from the inventory of the Shibei District of Qingdao is taken as the calculation basis, the annual production of vegetables grown on the roof of a city or region can be derived by knowing the size of its land area. The calculation formula is as follows: \[\text{P}_{\text{Annual yield of roof vegetables}}=\text{S}_{1}\times\text{S}_{2} \times\text{A}\times\text{Q}\] \[=\text{6.1}\times\text{10}^{4}\text{S}_{\text{1 Urban land areaQ}_{\text{Annual vegetable yield per unit area}}}\] (2)  
P, A, and Q are the same as Formula (1); S--Land area of a certain city or region, unit km\({}^{2}\); S--Roof area per square kilometer; the conservative value of 7.2 ha/km\({}^{2}\) (7.2%), which is obtained from the inventory, is taken here. 3. According to the above derivation process of roof production potential, we can know the annual production of vegetable planting and the amount of the population that can be supplied by a certain type of space (not limited to the roof) in a city or region. The calculation formulas are as follows: \[\text{P}_{\text{Annual yield of vegetables}}=\text{S}\times\text{A}\times\text{Q}\] (3) \[\text{N}_{\text{The number of people that can supply the city}}=\text{(S}\times\text{A}\times\text{Q)/C}\] (4)  
Q can refer to Formula (1); P--The annual yield of vegetables that can be grown in a certain type of space in a city or region, unit kg; S--The area of a certain type of space that can be used for agricultural cultivation obtained from the inventory of a certain city or region, unit m\({}^{2}\); A--Utilization rate of a certain type of space area (the ratio of available agricultural planting area to a certain type of space area after considering the occupation of space by roads, management, and facilities); N--The number of urban population that can be supplied by the annual yield of a certain type of vegetables in a city or region, unit person; C--Annual per capita vegetable consumption (refer to the data obtained in this article, 140 kg/year). According to the China Statistical Yearbook 2022, the area of urban built-up areas in China is 62,420.5 square kilometers [30]. If calculated according to the usual ratio of 10-20% of the urban area, the usable roof area of urban built-up areas in China is 62,420-1,248,400 hectares. If the results of the roof inventory in the Shibei District of Qingdao are 7.2%, the available roof area in urban built-up areas in China is 449,400 hectares. Given the abundance of sloping roofs in Qingdao, the available roof area data are conservative. Based on the above, 624,200 hectares was selected as the available roof area in urban built-up areas.