Lead in Plants and the Environment pp 15-32 | Cite as

# Environmental Distribution and Modelling of Radioactive Lead (210): A Monte Carlo Simulation Application

## Abstract

The abundance of lead element with an atomic number 82 is 1.03 × 10^{−8} % in the Solar System, 14 mg kg^{−1} in the Earth’s surface and 3 × 10^{−5} mg L^{−1} in the oceans. The most dangerous radioisotope of lead is the ^{210}Pb, which has a half-life of 22.26 years and gamma energy of 46.5 keV. Modelling is one of the most effective ways of appreciation about the distribution effects and transport of the elements to the earth. It has a wide range of content from pure differential equations to spatial analysis calculations. In this section, the modelling with Monte Carlo Simulation method of the environmental distribution of the lead can be found. The Monte Carlo Simulation method on ^{210}Pb data lead to concentrations for future times. In addition, models of auto regressive integrated average (ARIMA), generalized autoregressive conditional heteroscedastic (GARCH) and autoregressive conditional heteroscedastic (ARCH) are obtained to determine the environmental distribution characteristics of the lead. The proposed simulation methodologies can also be used successfully for other variables other than lead.

## Keywords

Lead 210 Monte Carlo simulation ARIMA Modelling Probability distribution GARCH Forecasting## References

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