G. Belli

Modelling the chernobyl radioactive fallout (II): A multifractal approach in some European countries

This paper deals with the 137Cs cumulative soil deposition measured in some European Countries after the Chernobyl accident. We devised a multifractal model to aid in describing the spatial distribution of radioactivity. The model is based the Fractal Sum of Pulses theory, involving additive stochastic processes. We use, as input source of information, the available data of radioactive deposition measured in some European Countries. The results look promising, since realistic scenarios of environmental pollution are produced.

Fractal and multifractal approach to environmental pollution

A few case studies will be presented involving both radioactive and chemical pollution at small, medium, and large space-time scales. Reported are recent advances in the field of environmental pollution involving the use of fractals and multifractals. The mathematical tools proposed here may offer new perspectives for investigating many of the problems of nonlinear variability which commonly arise when dealing with pollutants, such as the presence of outliers and the sparseness of the sampling networks. They may also lead to a simplification of the models adopted for studying natural phenomena, thanks to a scaling approach. Finally, they may provide parameters whose values are directly related to the nonlinear dynamics involved in the pollutant distribution in the environment which, in turn, may be relevant for computer simulation and epidemiological or risk assessment purposes.

Multifractal objective analysis of seveso ground pollution

We analyse the Dioxin (TCDD) pollution of the Seveso (Milan, Italy) territory, seeking to statistically parametrize it in terms of Universal Multifractals. The data set contains the measurements collected from 1976 up to 1981. We apply the Double Trace Moment (DTM) technique in order to estimate both α (the degree of multifractality) and C 1 (the codimension of the mean field) and (with the help of spectral analysis) we also calculate H (the degree of non‐conservation of the process). We then discuss the effects introduced by statistical undersampling and network sparseness and provide a way to statistically correct for these effects. We conclude that the ground distribution of Dioxin shows clear multifractal features and can be classified as an unconditionally hard universal multifractal process.

An analysis of time-dependence for Chernobyl fallout in Italy

We present here an analysis of the airborne radioactivity measured in Italy after the Chernobyl accident. We provide some quality assurance, isolate suspicious data, and devise a mathematical model to aid in interpreting time-dependent fallout data. The model consists of an interpolating function whose parameters can be related to 1) the arrival time of the radioactive cloud; 2) the time of the maximum radioactive concentration; and 3) the decay-rate of airborne radioactivity as the pollutant cloud passes. Multiple arrivals of the radioactive cloud in a given site can also be considered. The parametrization can be used to estimate concentrations of 137Cs using measurements of (131)I, 103Ru, or 132Te. The interpolating function is fitted to the data collected in several Italian Provinces. We feel this model is an useful tool for interpreting time-dependent fallout data.

Modelling the Chernobyl radioactive fallout. (I): A fractal approach in Northern Italy

This paper deals with the 137Cs airborne radioactive concentration measured in Northern Italy after the Chernobyl accident. We devised a fractal model to aid in describing the space-time distribution of radioactivity. The model is based on the Fractal Sum of Pulses theory, involving additive stochastic processes. We use, as input source of information, the parametrization of the time trend of radioactive concentration in a few Italian Provinces we calculated in previous work. The results look promising, since realistic scenarios of environmental pollution are produced.

RISK ANALYSIS AND ASSESSMENT IN ENVIRONMENTAL SCIENCES : USE OF STATISTICAL METHODS TO HANDLE THE INFORMATION

Quite often, it is not the methodology of the risk assessment and the risk estimate that is lacking, but the level of confidence in the “indications”; about the actual measurements performed in emergency situations. In this paper we address the issue of finding a correct measure of the source term in risk estimate, and point out how crucial the correct understanding of the raw data may be. We apply a methodological approach to the case study of the TCDD ground pollution at Seveso (Milan, Italy), looking for biases and systematic errors in the available data with the purpose of assessing risk. We indicate how sham relationships and pseudoeffects may spoil the analysis and lead to wrong conclusions. Then, we show how to carry on a proper statistical analysis and how to correctly interpret the results, in view of their use for epidemiological purposes.