## 2 Data Sources and Research Methodology
### Research Methodology  
By considering each section of emissions of greenhouse gases in carbon equivalent (CE), the TCF in the agricultural sector was estimated over 1995-2016, which was caused by 10 main inputs of chemical fertilizers, pesticides, plastic film, raw coal, gasoline, diesel, and electricity. The TCF for agricultural production mainly consists of two parts, i.e., (1) indirect emissions of greenhouse gases from the manufacture of chemical fertilizers, pesticides, and plastic film and (2) direct emissions of greenhouse gases from the raw coal, gasoline, diesel, and electricity used by agricultural activities. Based on the published data [27], the annual emission coefficient for electricity use was estimated, which ranged from 0.23 to 0.18 kg C/kWh over 1995-2016. The coefficient for N\({}_{2}\)O emissions from chemical fertilizer-N application in Qinghai province was based on the regional mean value of 0.0056 kg N\({}_{2}\)O-N/kg N fertilizer in northwestern China [28], which was lower than the mean of the whole country [29]. The direct N\({}_{2}\)O emissions from chemical fertilizer-N application in agricultural lands should be taken into account, because it was one of the major contributors to the TCF [8].  
The CF of individual emission source input for agricultural production was estimated based on Equation (1):  
\[CF=ES\times EC, \tag{1}\]  
where \(CF\) is the carbon footprint in carbon equivalent (CE) for CO\({}_{2}\) emissions caused by individual emission source input; \(ES\) is the amount of individual emission source input; and \(EC\) is the individual emission coefficient. Table 1 lists the individual emission source and coefficient in the agricultural sector in Qinghai province.  
The CF for N\({}_{2}\)O emissions caused by chemical N fertilizer use was estimated based on Equation (2):  
\[CF=127.21\times 0.0056N, \tag{2}\]  
where \(CF\) is the carbon footprint in carbon equivalent for N\({}_{2}\)O emissions caused by N fertilizer use; \(N\) is the amount of N fertilizer used; 0.0056 is the emission coefficient for N\({}_{2}\)O emissions caused by N fertilizer application in the study area; and 127.21 is the conversion coefficient [8; 32].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Emission Source** & **Emission Coefficient (kg C/kg)** & **Reference** \\ \hline  & Nitrogen & 1.74 & [30] \\  & Phosphorus & 0.20 & [10] \\ Agrochemicals & Potassium & 0.15 & [10] \\  & Pesticles & 6.00 & [10] \\  & Plastic film & 2.58 & [9] \\ \hline  & Raw coal & 0.52 & [29; 31] \\ Energy & Gasoline & 0.80 & [29; 31] \\  & Diesel & 0.84 & [29; 31] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main emission sources and emission coefficients in the agricultural sector in Qinghai province.  
The TCF caused by agrochemical and energy inputs was calculated based on Equation (3):  
\[TCF=\sum_{i=1}^{10}ES_{i}EC_{i}, \tag{3}\]  
where _TCF_ is the total carbon footprint, \(ES_{i}\) is the input amount of the emission source \(i\); \(EC_{i}\) is the emission coefficient of emission source \(i\); and \(i\) means the main type of emission source, which ranges between 1 and 10.  
Two types of carbon intensities were selected to describe the economic benefits and related environmental issues caused by CO\({}_{2}\) emissions for agricultural production [10]. Carbon intensity in output value (CV) means the total carbon footprint per unit of agricultural output value. Carbon efficiency can be used to directly reflect the benefit of agricultural production at the expense of agricultural CO\({}_{2}\) emissions, which is the reciprocal of CV. Carbon intensity in area (CA) means the total carbon footprint per unit of agricultural land area, which can be used to reflect the potential environmental problems.  
In order to reflect the relative carbon efficiency and potential environmental problems in Qinghai province, comparative analysis of the changing trends of TCF, CV, and CA was used between the study area and the whole country.