## 2 Materials and Methods
### Methodology of NORMALYSA  
NORMALYSA is a software designed to simulate radionuclide transport from a source, such as a radiocatively contaminated land, to relevant receptors in the environment (e.g., residential areas, agricultural areas, and water bodies) and calculate radiation exposure doses to humans [27]. NORMALYSA was developed in Sweden by Facilia AB with support from the IAEA. It has been tested and benchmarked against other similar software tools as part of the IAEA-Modeling and Data for Radiological Impact Assessments project Work Group 3 (NORM and Radioactively Contaminated LegaCY Sites) activities. It is summarized into four modeling steps of estimating the radiological dose from different pathways. The NORMALYSA modeling steps are shown in Table 2.  
Figure 3 summarizes the four main libraries of NORMALYSA. The \"Sources\" library includes modules for calculating radionuclide releases (source term) from uranium mill and other radioactively contaminated lands. The \"Transports\" library includes modules for calculating radionuclide transport from the contaminated source to different receptors through atmospheric, groundwater, or surface runoff. The \"Receptors\" library includes modules for calculating radionuclide transfer and redistribution processes in different receptor environments. The doses are calculated for various relevant exposure pathways (e.g., external irradiation, inhalation, and ingestion) and can be summed into a total annual effective dose in Sv/year. NORMALYSA uses the previously recommended and documented environmental transport and exposure assessment models that are relatively simple. In particular, NORMALYSA uses models used in the Swedish Nuclear Fuel and Waste Management Company's safety assessment of radioactive waste disposal facilities and generic models recommended by the IAEA (e.g., from the IAEA SRS-19 report). In this study, we used the contaminated land module, which simulates contaminated land where individuals can be exposed through external irradiation, inhalation, and inadvertent ingestion of contaminated soil, although the ingestion pathway was not considered. The mathematical models used are as follows: \begin{table}
\begin{tabular}{c c} \hline \hline
**Modelling Steps** & **Description** \\ \hline Context model options & To define model structure \\ Time series parameters & To specify parameters models \\ Simulation & To carry out calculation \\ Charts, tables, and reports & To analyze and report results \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Modeling Steps in NORM and LegacY Site Assessment code. Figure 3: Main libraries in NORM and LegacY Site Assessment. Mass balance equation for soil media is given by the following equation:  
\[ \begin{split} dSoil\_RZ/dt=& Dep+Irr+Soil\_(DZ)\times Erosion\_(DZ)+ Soil\_(DZ)\times bioT\_(DZ)\\ -& Soil\_(RZ)\times Leach\_(RZ)-Soil\_(RZ)\times Erosion\_(RZ)- Soil\_(RZ)\times bioT\_(RZ)\\ -&\lambda\times Soil\_(RZ)\ +\sum\_(p\in P)Br\_(p)\times\lambda\times Soil\_ RZp\\ &\text{where}\\ & Dep=\text{total deposition of radionuclides from the atmosphere to the receptor area (Bq/year);}\\ & Irr=\text{transfer of radionuclides to the receptor area with irrigation water (Bq/year);}\\ & Soil\_(DZ)=\text{ radionuclide inventory in the deep zone of soil (Bq);}\\ & Erosion\_(DZ)=\text{transfer coefficient of radionuclide from deep soil zone to rooting zone to compensate for erosion losses from the rooting zone (1/year);}\\ & bioT\_(DZ)=\text{transfer coefficient of radionuclide from the deep soil to the rooting zone due to bioturbation (1/year);}\\ & Leach\_(RZ)=\text{transfer coefficient of radionuclides from the root zone to the deep zone by leaching (1/year);}\\ & Erosion\_(RZ)=\text{transfer coefficient of radionuclides from the rooting zone due to the erosion process (1/year);}\\ & bioT\_(RZ)=\text{transfer coefficient of radionuclide from the rooting soil to the deep zone due to bioturbation (1/year).}\\ \end{split}