Multivariate geostatistical analysis of fallout radionuclides activity measured by in-situ gamma-ray spectrometry

Abstract

Cs-137 and other fallout radionuclides (FRNs) have been used worldwide for more than four decades as powerful techniques to assess the magnitude and spatial pattern of soil redistribution. Cs-137, ²¹⁰Pb_ex, and ⁷Be have successfully been used as tracers of soil redistribution. Their coincident use can frequently provide worthwhile information for different time scales of soil redistribution. These radionuclides can either be measured in the laboratory or in-situ. In the present study in-situ measurements using a portable HPGe detector were carried out in two loessial paired sub-catchments with fairly similar characteristics in northeast Iran. Spatial sampling design based on a minimax approach was used to determine that 60 sites were sufficient for both areas of interest. Geostatistical analysis and the linear model of co-regionalization (LMC) were applied in this study for radionuclides. The spherical model for Sample and Testifier sub-catchments with ranges of 750 m and 500 m respectively was selected as the most suitable model. The highest and the lowest non-captured variability belonged to ²¹⁰Pb_ex and ⁷Be for both studied areas. The patterns of spatial variation of ⁷Be and Cs-137 for Sample and the patterns of spatial variation of ⁷Be and ²¹⁰Pb_ex for Testifier sub-catchment were very similar. For Cs-137, global uncertainty for both sub-catchments was nearly the same, but different for other radionuclides. The distribution of local uncertainty for all radionuclides in the Testifier sub-catchment was the same. The means of spatial distance between the grid cells with the highest and the lowest uncertainty for ⁷Be, Cs-137, and ²¹⁰Pb_ex, are 0.4, 1, and 7 km, respectively.

Introduction

Cs-137, excess or unsupported lead-210 (²¹⁰Pb_ex), and beryllium-7 (⁷Be) are non-exchangeable radionuclides. They have been used world-widely for more than four decades, and their use has proved to be a powerful technique to assess the magnitude and spatial pattern of soil erosion and sedimentation (Ritchie and Ritchie, 2008). They are rapidly and strongly fixed by the surface soil or small sediment particles. For these reasons, they have successfully been used as tracers of soil redistribution (Wallbrink and Murray, 1993, Walling and He, 1999, Matisoff et al., 2002, Zapata, 2002, Walling et al., 2003, Zhang et al., 2003, Mabit et al., 2008, An et al., 2014).

Due to different history and half-life of these radionuclides (Zapata, 2002), their simultaneous use can frequently provide worthwhile information for different temporal scales of soil erosion and sedimentation (Mabit et al., 2008).

Not only soil redistribution data over different temporal scales can be obtained using a single soil sampling, thereby avoiding time consuming and costly installations (Mabit et al., 2008), but also, the resulting FRNs measurements can provide appropriate spatial data. These data integrates the effects of all processes leading to soil redistribution that frequently cannot be achieved using conventional soil erosion and sedimentation models (Mabit et al., 2008).

Radionuclides can either be measured in the laboratory and in-situ. The advantages and disadvantages have already been discussed in detail (He and Walling, 2000, Mabit et al., 2008). Field measurements using a high purity germanium (HPGe) detector have shown to provide spatially representative estimates of environmental radioactivity across a range of landscapes (Tyler et al., 1996). Thus, it was used in this research. This measurement technique for Cs-137, ⁷Be, and ²¹⁰Pb_ex has been previously employed (Blake et al., 1999, Tyler and Copplestone, 2007). Apart from agricultural practices, overland flow (van der Perk et al., 2002) and changes in altitude (Porto et al., 2009) are the main drivers of the redistribution of Cs-137, ⁷Be, and ²¹⁰Pb_ex. Erosion investigations using Cs-137, however, often assume that Cs-137 is relatively homogeneously distributed from field to a small catchment scale (Walling and Quine, 1991, Wu and Tiessen, 2002, Schuller et al., 2004, Heckrath et al., 2005), and for a small catchment, a homogeneous rainfall pattern can be assumed as well (Schaub et al., 2010). Meanwhile, as ²¹⁰Pb_ex and Cs-137 both behave similarly and are absorbed strongly by soil clays, their spatial patterns are similar (Zhang et al., 2006). This particular behaviour of the atmospherically derived radionuclides allows the prediction of soil redistribution rates under water erosion (Stefano et al., 2005, Mabit and Bernard, 2007, Mabit et al., 2008).

Based on published results, only a few authors have used geostatistics to characterize the spatial variability of soil redistribution from Cs-137 data (Chappell, 1998, van der Perk et al., 2002, Chappell and Warren, 2003, Mabit and Bernard, 2007, Navas et al., 2011). Variograms are suitable tools to model the spatial distribution of variables and if they are done with proper care, kriging provides the best possible prediction from data (Goovaerts, 1997, Gong et al., 2014). Their associated uncertainty is of great importance (Goovaerts, 2001), however rarely assessed.

Multivariate geostatistical methods (co-simulation and co-kriging) have been used to analyse the spatial co-variation of soil properties (Goovaerts, 1997), but to the best of our knowledge, no published papers have paid attention to multivariate geostatistical methods and uncertainty in radionuclide measurements to capture soil redistribution. So, in this study radionuclides activity were taken into consideration.

In the case where spatially distributed information is needed, local and global uncertainties of maps should be known in advance. One of the common techniques that can be used for this is geostatistical stochastic simulation (Goovaerts, 1997, Deutsch and Journel, 1998). Geostatistical stochastic simulation is also designed to overcome the smoothing effect of the kriging estimator (Deutsch and Journel, 1998), especially when extreme spatial discontinuities have to be mapped or when interpolation errors need to be reproduced through a non-linear model.

As aforementioned, in the case of radionuclides in soil redistribution, local and global uncertainties are ignored, and the impact of agricultural activities on soil redistribution should be assessed in large scales of sub-basin or micro-watershed. To address this issue, loessial paired sub-catchments with fairly similar characteristics in northeast Iran was selected to reach the following objectives: 1) to use geostatistical stochastic simulation of radionuclide activities and assess their local and global uncertainties, 2) to upscale the area studied of ⁷Be from plot and field to micro watershed scale and sub-basin, 3) to use other radionuclides as co-variables to reduce prediction error (co-simulate radionuclides activities on different time scales).