Applying the bootstrap technique for studying soil redistribution by caesium-137 measurements at basin scale

Abstract

The use of the bootstrap technique to estimate the reference level of¹³⁷ Cs in an uneroded site is tested. The analysis is developed using ¹³⁷Cs measurements made in a small experimental Sicilian basin. In the reference area the ¹³⁷Cs activity is normally distributed with a known sample mean value, m equal to 94.4 mBq cm^?2. The influence of¹³⁷ Cs reference site sampling was determined generating samples having a fixed size, N and six different values of the sample coefficient of variation, CV, by a Monte Carlo technique. Then, for each size N, the probability distribution of the mean μ of the sequences generated by Monte Carlo technique is defined. The soil redistribution is determined, both at morphological unit and basin scale, using the proportional method of Martz & de Jong for calculating the net soil loss. The analysis showed that the spatial distribution of the net soil loss E _i, and the basin value E _b are independent of the sample size, N, and the coefficient of variation, CV, of the samples drawn from the reference area, if the bootstrap technique is applied for estimating the mean μ(μ) to use as reference value. The soil redistribution is also examined using as reference value the quantiles μ2.5, μ25, μ75, μ97.5 corresponding to a frequency F(μ) equal to 2.5, 25, 75 and 97.5%, respectively. In conclusion, the analysis established that a robust estimate of the reference value can be obtained even in fields where a small number of samples was drawn (high CV of the ¹³⁷Cs activity of the field samples), using the bootstrap technique for generating sequences of reference values having known mean value m (the mean value of the ¹³⁷Cs activity of the drawn field samples) and large sample size (N = 50).