## 2 Materials and Methods
### Life Cycle Inventory (LCI)
#### 2.2.4 LCI Data  
The primary data for cassava cultivation were collected in Malaysia by a questionnaire in the years 2016/2017 and complemented with data from literature. Pesticide application was modelled based on data from [28]. Table 4 shows the emission models used in this study for calculation of direct emissions. In more detail, the following formulas were used for calculation of direct emissions (adapted from [27]). For ammonia (NH\({}_{3}\)) emissions to air, the following equation was used:  
\[\text{NH}_{3}=\frac{17}{14}\cdot\sum\
olimits_{1}^{m}((p\cdot EF_{am}+(1-p) \cdot EF_{bm}))\cdot N_{min}\cdot\text{Mm}-1), \tag{1}\]  
where NH\({}_{3}\) is ammonia emission after mineral fertilizer application (kg NH\({}_{3}\)), \(m\) is fertilizer type (\(M\) is number of fertilizer types), \(EF_{am}\) is emission factor on soils with pH \(\leq\) 7 (kg NH\({}_{3}\)-N/kg N), \(EF_{bm}\) is emission factor on soils with pH \(>\) 7 (kg NH\({}_{3}\)-N/kg N), \(p\) is fraction of soils with pH \(\leq\) 7 (%/100) and \(N_{min}\) is mineral fertiliser application (kg N/ha). The emissions of various nitrogen oxides (NO\({}_{\text{X}}\), NO, NO\({}_{2}\)) were calculated based on the remaining N after NH\({}_{3}\) emission. The emission factor for the application of all types of mineral and organic fertilizer is 0.012 kg NO\({}_{\text{X}}\)-N per kg of applied N based on [29]. For the calculation of nitrate (NO\({}_{3}\)) leaching to ground water, the SQCB-NO\({}_{3}\) model was used as reported in [31]:  
\[\text{NO}_{3}=21.37+\frac{P}{C\cdot L}\Big{(}0.0037\cdot N_{sup}+0.0000601 \cdot N_{org}-0.00362\cdot N_{up}\Big{)}, \tag{2}\]  
where NO\({}_{3}\) is leached NO\({}_{3}\)-N (kg N/(ha a)), \(P\) is precipitation and irrigation (mm/year), \(c\) is clay content (%), \(L\) is rooting depth (m), \(N_{sup}\) is nitrogen supply through fertilizer (kg N/ha), \(N_{org}\) is nitrogen in organic matter (kg N/ha) and \(N_{up}\) is nitrogen uptake by crop (kg N/ha). Nitrous oxide (N\({}_{2}\)O) from nitrification and denitrification processes are considered by the following equation:  
\[\text{N}_{2}\text{O }=\frac{44}{28}\cdot\Big{(}0.01\left(N_{tot}+N_{cr}+N_{ som}+\frac{14}{17}\cdot\text{NH}_{3}+\frac{14}{46}\cdot\text{NO}_{x}\right)+0.0075 \cdot\frac{14}{62}\cdot\text{NO}_{3}\Big{)}, \tag{3}\]  
where N\({}_{2}\)O is the emission of N\({}_{2}\)O (kg N\({}_{2}\)O/ha a), \(N_{tot}\) is total nitrogen in mineral and organic fertiliser (kg N/ha), \(N_{cr}\) is nitrogen contained in the crop residues (kg N/ha), \(N_{som}\) is nitrogen from the mineralization of soil organic matter (kg N/ha), NH\({}_{3}\) is the loss of nitrogen in the form of ammonia (kg NH\({}_{3}\)/ha), NO\({}_{\text{x}}\) is losses of nitrogen in the form of nitrogen oxides (kg NO\({}_{2}\)/ha) and NO\({}_{3}\) is the loss of nitrogen in the form of nitrate (kg NO\({}_{3}\)/ha). For urea application, in addition, CO\({}_{2}\) emission were also calculated at 1.57 kg CO\({}_{2}\) per kg of applied urea-N. \begin{table}
\begin{tabular}{c c} \hline \hline
**Emission** & **Emission Model** \\ \hline Ammonia (NH\({}_{3}\)) & EMEP Tier 2 [29] \\ Nitrogen oxides (NO\({}_{\text{X}}\), NO, NO\({}_{2}\)) & EMEP [29] \\ Nitrous oxide (N\({}_{2}\)O) & IPCC Tier1 [30] \\ Nitrate (NO\({}_{3}\)\({}^{-}\)) & SQCB [31] \\ Phosphorous (P, PO\({}_{4}\)\({}^{3-}\)) & SALCA-P [32] \\ Heavy metals (Cd, Cr, Cu, Hg, Ni, Pb, Zn) & Freiermuth [33] \\ Carbon dioxide (CO\({}_{2}\)) & IPCC [30] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Emission models used (adapted from [27]). Regarding phosphorus emissions to water, the following pathways have been differentiated according to [27; 32]: (i) leaching of PO4 to ground water, (ii) run-off of PO4 to surface water, and (iii) phosphorus emissions to surface water through soil particles transported by water erosion. Heavy metal emissions to soil, surface water and ground water were calculated for Cd, Cr, Cu, Pb, Hg, Ni, Zn according to the SALCA-heavy metal method, as described in [33].