Quantifying geostatistical properties of 137Cs and 210Pbex at small scales for improving sampling design and soil erosion estimation

Knowledge of spatial structures of the radionuclides 137Cs and unsupported 210Pb (210Pbex) is vital for developing sound sampling designs that are crucial for deriving quantitative soil erosion estimates. The objectives are to characterize spatial structures of 137Cs and 210Pbex inventories at small spatial scales under different land uses, and to quantify the effects of core sizes on (1) estimated sample means and variances of the 137Cs and 210Pbex inventories and (2) sample numbers required for estimating the mean inventories at a given confidence level. Three different core sizes were used to take soil samples along three 10-m transects at 0.25-m or 0.5-m intervals for each land use. Land uses included cropland, grassland, forestland, and rangeland. 330 samples were analyzed for 137Cs and 210Pbex inventories. Semivariograms were obtained by plotting empirical semivariances with sample separation distances. The spatial correlation distances ranged from 0.2 to 0.75 m for most cases. The semivariances at the separation distances of >0.75 m were close to the variances of the fields for all four land uses, indicating that the spatial distributions of 137Cs and 210Pbex were nearly stationary and had little spatial dependence at scales between 0.75 and 5 m. The overall results suggested that samples taken at a separation distance of >0.75 m would be largely independent and could be composited to form a representative sample for the sampling location for most cases. Given the large spatial variability at such a small scale, quantitative soil erosion rates cannot be estimated for a single soil core, because remarkably different soil erosion rates can be estimated for soil cores taken within a meter. Core size variation between 38 mm and 86 mm has no apparent effect on estimating sample means and sample standard deviations of 137Cs and 210Pbex inventories, except for gravely soils. In general, 15-30 samples are needed to estimate 137Cs reference inventory on reference sites, but may be more for gravely soils. More samples are required for forest and cultivated sites than for uncultivated grassland sites. On measuring sites, it is strongly recommended that 5-15 samples be taken for a grid point and measured individually if feasible or as a combined sample to allow reliable estimation of the mean 137Cs inventory for the location for most soils and land uses. If samples are taken for each of uniformly eroded land form units, the same number of individual samples as on the reference site are recommended. This work will be useful to improving sampling designs and consequently the accuracy of soil erosion estimation of the 137Cs technique.