## 2 Materials and Methods
### Methods
#### 2.3.2. ESV Accounting Methods
\[ES_{2}=V_{\rm C}+V_{\rm O}, \tag{7}\]  
\[V_{\rm C}=H\times\alpha\times N_{\rm C}\times P_{\rm C}, \tag{8}\]  
\[ES_{f}=M_{f}\times P_{f},\]0  
\[ES_{f}=M_{f}\times P_{f},\]1  
In Equation (7), \(ES_{2}\) is the value of carbon fixation and oxygen release from rice (RMB 10 k); \(V_{c}\) is the value of carbon fixed by rice (RMB 10 k) and \(V_{o}\) is the value of oxygen released from rice (RMB 10 k). In Equation (8), \(H\) is the amount of dry matter (t), \(\alpha\) is the amount of CO2 that can be fixed by producing 1 g of plant dry matter (1.63 g), and \(N_{c}\) is the proportion of C in CO2 (27.27%). \(P_{c}\) is the Swedish carbon tax rate [55] of USD 150/t carbon, equivalent to RMB 996.34/t. In Equation (9), \(\beta\) is the amount of O2 released from 1 g of plant dry matter, with a value of 1.2 g, and \(P_{o2}\) is the industrial oxygen production cost of RMB 400/t. In Equation (10), \(M_{f}\), \(M_{\rm s}\) and \(\gamma\) are rice yield, rice by-product (straw) yield and rice economic coefficient, respectively; \(\gamma\) was set to 0.5. II. Climate regulation  
The climate regulation effect of the PFE is to reduce the air temperature, reduce the range of temperature variation and increase air humidity through plant transpiration and water surface evaporation; thus, improving the comfort level of the human living environment. The energy consumed for cooling and humidification is used as the evaluation index of the climate regulation function, and its value is estimated using the alternative cost method:  
\[ES_{f}=M_{f}\times P_{f},\]2  
where, \(ES_{3}\) is the value of climate regulation (RMB 10 k); \(ET\) is the cumulative evapotranspiration (mm) from July to August; \(\xi\) is the heat consumed by evaporation of 1 mm of water in 1 hectare of paddy field, which is replaced by the combustion of 0.6114 t of standard coal [56]; \(P_{coal}\) is the coal price 340 (RMB/t) [37]. III. Groundwater recharge  
The rice inundation period in the study area was up to 140 days. In addition to satisfying the growth and evaporation of crops, part of the water in the field seeps into the underground to replenish the groundwater resources. The other water is returned to rivers and lakes through the irrigation system and drainage. In this study, only the ecological value of groundwater replenishment was considered, and the market value method was used for calculation as:  
\[ES_{f}=M_{f}\times P_{f},\]3  
where, \(ES_{4}\) is the value of groundwater conservation (RMB 10 k); \(IW\) is the amount of irrigation water (mm) during the rice growing period, which was set at 608, \(P_{r}\) is the accumulated precipitation (mm) during the rice growing period (May-August); \(ET_{growth}\) is the cumulative evapotranspiration (mm) in the rice growth period (May-August); \(P_{w}\) is the price of agricultural water (RMB/m\({}^{3}\)), which was set at 0.24 [57]. IV. Flood regulation  
A paddy field is a special type of artificial wetland which can divert and store rainwater and play a role in regulating and storing floods and reducing flood disasters [58]. This ecological value is calculated mainly using the shadow engineering method to estimate the construction and maintenance cost of the flood volume regulated and stored by a paddy field relative to a reservoir of the same capacity. The value of water storage and flood control is calculated according to the average height of a paddy field ridge, the daily average water depth in the field, the paddy field area and the construction and maintenance cost of flood control reservoirs with unit flood diversion capacity in the study area:  
\[ES_{f}=M_{f}\times P_{f},\]4  
where, \(ES_{5}\) is the value of flood regulation and storage (RMB 10 k); \(H_{r}\) is the average height of the paddy field ridge (m); \(D_{w}\) is the average water depth (m) during the paddy inundation period; \(C_{w}\) reservoir unit storage project cost and maintenance costs [50] (RMB/m\({}^{3}\)), and the value of 1.51 was taken in this study.