## 2 Materials and Methods
### Estimation of the Urban Population, GDP, and Amount of Solid Waste  
Data on the population of Saudi Arabia were extracted from the United Nations [39], which estimated the population based on trends in the demographic components of population change including fertility, mortality, and migration. For projecting the future levels of fertility and mortality, the United Nations [39] used a probabilistic method taking into account the historical variability of uncertainty. In this paper, three projections, namely  
Figure 2: Composition of (**a**) municipal solid waste (MSW) [3] and (**b**) industrial waste [49] in Saudi Arabia. low, medium, and high variant projections were used, which is shown in Figure 3. In the high variant assumptions, 0.5 births above the total fertility of the medium variant were used, and in the low variant assumption, 0.5 births below the total fertility of the medium variant were used [39]. It should be noted in this regard that as a study area, the entire Saudi Arabia is considered for its urban population and generation of MSW. However, to examine the impact of urbanization on the CH\({}_{4}\) emission (Section 3.2.1), some major cities were considered. The gross domestic product of Saudi Arabia from 1970-2019 was collected from World Bank [38]. The future GDP of Saudi Arabia from 2020-2050 was estimated based on the GDP predicted at market exchange rate by price water Cooper [50], considering the growth in the labor force of working age, increase in human capital, growth in the physical capital stock, and the productivity. The GDP was used in the IPCC model to calculate the CH\({}_{4}\) generation from industrial waste. According to GAS [49], about 20.25 million tons of industrial waste was generated in 2017; the value was used to estimate the yearly industrial waste generation rate per GDP as 0.0294 Gg/Million $GDP/year. The per capita MSW generation in Saudi Arabia (Figure 4) between 2010 and 2017 ranged between 1.15 and 2.04 kg/capita/day [52], which is based on the total population of the country. The waste generation rate decreased in 2018 to 1.72 kg/capita/day, which is due to the encouragement of business owners by the government to recycle more and dump less [52]. However, due to the lack of published MSW generation data except 2010-2018, for the projection of total urban MSW generation, the value proposed by the IPCC [3] was used. The average MSW generation rate for Saudi Arabia proposed by IPCC [3] is 470 kg/capita/year (1.29 kg/capita/day). The total amount of MSW (Equation (6)) was calculated based on the estimated population (Figure 3) and the solid waste generation rate:  
\[Total\ amount\ of\ MSW_{T}=Per\ capita\ MSW_{T}\times Population\ projection \tag{10}\]  
Figure 3: Population and gross domestic product (GDP) projection of Saudi Arabia [50; 51]. Figure 4 shows the projected amount of total urban MSW for three population scenarios from 1990 to 2050. The yearly generated amount of MSW was used in the IPCC model for the calculation of CH\({}_{4}\) generation. Tables 2 and 3 summarize the parameters used along with their value, and input parameters for waste composition in the IPCC model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Assumptions/Value/Time Series** & **Data Source** \\ \hline Starting year & 1970 & \\ Urban population (in millions) & 1970–2050 & United Nations [39] \\ Total gross domestic product (GDP) (at & 1970–2019 & World Bank [38] \\ current USD) & 2020–2050 & Price Water Cooper [50] \\ Period of methane calculation & 1970–2050 & \\ Per capita waste generation & 470 kg/capita/year & [3; 53] \\ \hline \% MSW disposed to landfill & 96\% & \\ Fraction of methane in developed gas & 0.5 & \\ C to CH\({}_{4}\) conversion factor & 16/12 & \\ Oxidation factor & 0 (for managed landfill) & [3] \\ Methane correction factor & 0.6 & \\ Delay time & 6 months & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Assumptions and parameters used in calculating CH\({}_{4}\) emission in the IPCC [3] model.