Accuracy and sensitivity of soil erosion estimation using 137Cs technology: A statistical perspective

Abstract

Random spatial variation of the 137Cs inventory is the principal contributor to uncertainty in soil erosion estimation using 137Cs technology. A statistically sound sampling design is imperative for obtaining reliable soil erosion estimations. The objectives of this study are to: 1) characterize the effect of sample size on the estimates of mean inventories; 2) evaluate the sensitivity of the estimated soil redistribution to sample size using a new 137Cs model; 3) compare erosion detection limits among five conversion models; and 4) assess three spatial interpolation methods. Two small watersheds were sampled in an irregular grid design, and 30 samples were taken on a reference site. A moving window scheme was used to compute the 7-point and 11-point means of 137Cs inventories. The Welch’s modified t-test was used to test the mean estimates and to compute the detection limits for the replicated samples. Five models were selected to convert 137Cs inventories to soil redistribution rates. Since most single samples without replication yielded insignificant test results, the 137Cs technique cannot be used to estimate soil erosion at a single point due to random spatial variation. With 30 reference samples, 7 replicate samples on the sampling site provided reliable estimations of 137Cs inventories and soil redistribution. The spatial patterns of the estimated 137Cs inventories and soil redistribution became more regular and systematic as sample size increased, which agreed increasingly well with topography and surface hydrology. Replicate samples can be taken from each landform element or slope position where the erosion rate is expected to be uniform. Alternatively, a systematic grid sampling scheme can be used, and the nearest neighbors can be treated as replicates to calculate moving averages. The Type I and II errors with replicated samples showed that all sampling positions should be included in calculating watershed or area mean erosion rates even though the Type I errors indicated insignificant redistribution rates for some samples. Due to the lack of spatial autocorrelation, spline and inverse distance weighting methods performed better than kriging for interpolation. Detection limits and magnitudes of soil redistribution varied substantially with conversion models, depending on their sensitivities to changes in 137Cs inventories.