# Exploring a Moderate Fallow Scale of Cultivated Land in China from the Perspective of Food Security
## 3 Materials and Methods
### Methods  
#### 3.2.1 Estimation of the Reserved and Lost GPP Caused by Cultivated Land Use Change  
The GPP of cultivated land to be excavated included recoverable cultivated land production potential and unrecoverable cultivated land production potential loss. The formula was as follows:  
\[CLPP=CLPP_{1}-CLPP_{2} \tag{1}\]  
where \(CLPP\) is the \(GPP\) of cultivated land to be excavated, \(CLPP_{1}\) is the recoverable \(GPP\) of cultivated land, and \(CLPP_{2}\) is the loss of unrecoverable cultivated land grain potential. (1) GPP of Cultivated Land That Can Be Recovered  
The production potential of cultivated land that can be recovered included the GPP due to a decline in grain yield per unit, an MCI reduction, and agricultural structure adjustment. The formula was as follows:  
\[CLPP_{1}=\sum_{j=1}^{31}\bigl{(}Q_{j1}+Q_{j2}+Q_{\beta}\bigr{)} \tag{2}\]  
where \(CLPP_{1}\) is the recoverable \(GPP\) of cultivated land; \(Q_{j1}\) is the \(GPP\) due to the yield per unit area reduction in the \(j^{th}\) province, \(j=1\), \(2\),..., \(31\); \(Q_{j2}\) is the \(GPP\) due to MCI reduction in the \(j^{th}\) province; and \(Q_{j3}\) is the \(GPP\) due to agricultural structure adjustment in the \(j^{th}\) province. First, the reserved GPP due to a yield per unit area reduction referred to the maximum per unit area yield of grain in history achieved by using agricultural technology to increase the grain yield. Part of the increase in grain production was the reserved potential for a reduction in yield per unit area. This potential size was estimated by multiplying the yield reduction per unit area by the sown area of grain in 2016. The formula was as follows:  
\[Q_{j1}=(Y_{max}-Y_{2017})\cdot S_{2017} \tag{3}\]  
where \(Q_{j1}\) is the GPP due to a yield per unit area reduction in the \(j^{th}\) province, \(Y_{max}\) is the average of the maximum yield per unit area for two years from 1990 to 2017, \(Y_{2017}\) is the grain yield per unit area in 2017, and \(S_{2017}\) is the grain sowing area in 2017. Second, the reserved GPP due to MCI reduction refers to a decrease in grain production because of a decline in the MCI. To avoid large differences in the results due to different data sources, cultivated land data published by the Ministry of Natural Resources of China were used to calculate the reserved GPP. The calculation period was 2006 to 2017 for this part of the GPP because data were available starting in 2006. The reserved GPP of the decline in MCI was obtained by multiplying the amount of multiple cropping index decrease, grain sown area, and grain yield per unit area. Considering thatlocation is the main factor affecting crop ripening, the cultivated land area in 2006 was used to calculate the change in MCI. The formula was as follows:  
\[Q_{j2}=(MCI_{max}-MCI_{2017})\cdot A_{2006}\cdot Y_{2006} \tag{4}\]  
where \(Q_{j2}\) is the \(GPP\) in province \(j\) due to a decline in MCI; \(MCI_{max}\) is the maximum MCI value of grain from 2006 to 2017, which is expressed by the ratio of grain sown area to cultivated land area in province \(j\) in that year; \(MCI_{2017}\) is the MCI of grain in 2017; \(A_{2006}\) is the cultivated area in 2006; and \(Y_{2006}\) is the grain yield per unit area in 2006. Third, the reserved GPP due to agricultural structure adjustment included the potential in economic crop land and the potential in orchards and fishponds. The potential in economic crop land was estimated by the reduction in the proportion of grain sown area. The potential in orchards and fishponds was estimated by analysing land use change in 1990 and 2015, and the area of cultivated land that was converted to other gardens and fishponds was extracted. Considering that the grain yield may decrease to a certain extent after the reclamation of garden land and fishpond water surfaces, this part of the potential value was estimated by the average grain yield of cultivated land in 1990.