## 2 Materials and Methods
### Methods
#### 2.3.2. ESV Accounting Methods  
According to Millennium Ecosystem Assessment [4], [PERSON] [38], [PERSON] [50] and [PERSON] [51], the ESV accounting framework of the PFE was divided into four categories of provisioning services, regulating services, cultural services, and negative regulating values, with 12 subcategories for monetization estimation. Due to data limitations, we did not include support services in the accounting framework. 1. Provisioning service value Among the provisioning service values, the primary products supply function is the most important contribution to human well-being and the primary service of PFE. In contrast, straw, as a renewable resource, can be used for fuel, feed, direct field return, and industrial processing. The market value approach was used to estimate the value of products. 1. The value of primary products was estimated as: \[ES_{1}=ES_{f}+ES_{s}-V_{cost},\] (1) \[ES_{f}=M_{f}\times P_{f},\] (2) \[M_{f}=\sum_{t=0}^{a}GPP_{t}\times F\times R\times HI\times r,\] (3) \[ES_{s}=M_{s}\times P_{s},\] (4) \[M_{s}=M_{f}\times K,\] (5)  
Figure 1: Map of the study area. Points of different shapes and colors in (**b**) are samples of remote sensing interpretation signs collected through field surveys. \[V_{cost}=M_{f}\times P_{cost}, \tag{6}\]  
In Equation (1), \(ES_{1}\) is the provisioning value (RMB 10 k); \(ES_{f}\) is the value of rice products (RMB 10 k); ES is the value of rice by-products (straw) (RMB 10 k); \(V_{cost}\) is the total cost of planting rice fields (RMB 10 k); in Equation (2), \(M_{f}\) is the rice yield (t). We improved the method of [PERSON] [52] to map the rice yield in our study area. \(P_{f}\) is the market price of rice (RMB/t) and, according to field research, the average price of rice in Tianjin in 2019 was RMB 3000/t. In Equation (3), \(GPP\) (kg\(\cdot\)C/m\({}^{2}\)) is the sum of GPP in each rice growing period; \(F\) is the conversion coefficient of carbon into rice biomass, which was set to 2.22; \(R\) is the proportion of above-ground rice biomass, which was taken as 0.90; \(HI\) is the rice harvest index, which was taken as 0.60; \(t\) ranges from 0 to \(a\), indicating the rice growing period, which is 1 May-31 August according to rice phenology observations in Tianjin; \(r\) is a constant with a value of 1.4. In Equation (4), \(M_{s}\) is the rice by-product (straw) yield (t); \(P_{s}\) is the rice by-product (straw) market price (RMB/t); according to market research, the straw price of Tianjin in 2019 was RMB 50/t; in Equation (5), \(K\) is the rice straw coefficient and was set to 1.33 [53]; in Equation (6), \(P_{cost}\) is the cost of paddy cultivation (RMB/t), which mainly includes the purchase of production materials (seeds, fertilizers, agriculture, etc. ), irrigation, tillage, and the cost of hired labor for agricultural production. Comparing the measured yield data of rice in field plots with the predicted yield of rice, Figure 2 shows high prediction accuracy of rice yield; the root mean square error (RMSE) is 0.60 t/ha. The accuracy rate reaches 93.97%. Therefore, we assumed that the method for predicting rice yield in this study is effective and feasible. (2) Regulation services value  
1. Carbon fixation and oxygen release  
Rice has the ability to absorb CO\({}_{2}\) and release O\({}_{2}\). According to the chemical reaction formula of photosynthesis, 1 g of plant dry matter can absorb 1.63 g of CO\({}_{2}\) and release 1.2 g of O\({}_{2}\). Referring to the calculation method of greenhouse gas inventory recommended by the IPCC [54], the ecological value of carbon sequestration and oxygen release is estimated by the carbon tax and industrial oxygen production methods. The calculation method is as follows:  
Figure 2: Comparison of predicted rice yield with measured rice yield.