**Submitted to:** Geoderma

**Publication Type:** Peer Reviewed Journal

**Publication Acceptance Date:** 10/6/2014

**Publication Date:** 10/28/2014

**Citation:** Zhang, X.J., Zhang, G., Wei, X. 2014. How to make 137Cs erosion estimation more useful: An uncertainty perspective. Geoderma. 239-240:186-194.

**Interpretive Summary:** The fallout radionuclide cesium-137 has been widely used as a tracer to provide quantitative soil redistribution estimates over a landscape at a point scale in the past 50 years. This tracing technique assumes that the spatial distribution of fallout cesium-137 derived from nuclear bomb tests is initially uniform. This work showed that the key assumption is violated due to substantial spatial variability of cesium-137 inventory in soil. The spatial variability of cesium-137 is the predominant contributor to prediction errors when using the technique. In the presence of substantial spatial variation, the cesium-137 technique is not suitable for estimating point soil redistribution rates as is widely perceived in the literature. The point estimates are not true redistribution values, and may be termed pseudo estimates because the random spatial variation of cesium-137 is erroneously attributed to a result of soil redistribution. However, the random contributions to the cesium-137 inventory or the resultant pseudo estimates of soil redistribution may be cancelled out theoretically if only the mean values are sought for a uniform area with a sizable number of independent samples. In the light of the cesium-137technique's inability to estimate point erosion rates, it is advisable to combine independent samples for each landform unit to estimate the mean soil redistribution rate for the unit with minimal cesium-137 measurement cost and in quick turnaround. This result will be useful to erosion scientists or soil conservationists who estimate soil erosion and deposition rates using the cesium-137 tracing technique.

**Technical Abstract:** The cesium-137 technique has been widely used in the past 50 years to provide quantitative soil redistribution estimates at a point scale. Recently its usefulness has been challenged by a few researchers questioning the validity of the key assumption that the spatial distribution of fallout cesium-137 in soil is initially uniform. This work is intended to reconcile the opposing opinions by developing a new concept and insights. We examined the key assumption and provided remediation if violated, conducted a thorough model validation in a unit watershed, performed sophisticated sensitivity and uncertainty analyses, and developed general guidelines for better use of the technique. The key assumption necessitates that (1) atmospheric deposition with precipitation is spatially uniform, (2) transfer to soil is spatially homogenous, and (3) no redistribution of free cesium-137 occurs during the transfer processes. Data from dense raingauge networks in several US watersheds show that mean precipitation is relatively uniform at a local scale. Elements (2) and (3) are generally invalid due to spatial variations in vegetation interception, vegetation type and cover, ground residue cover, soil properties, water infiltration rates, surface random roughness, and micro-topography. Fortunately, these variations are typically random in nature and thus can be resolved statistically by increasing sample number and by interpreting soil redistribution rates in terms of mean value for a uniform area. Compared with the measured net mean soil loss, the relative errors of the estimates with (without) Kriging were -17 (28), 106 (141), and 100% (133%) for the proportional model (PM), simple mass balance model, and improved mass balance model, indicating that PM performed better under the study condition and that Kriging improved estimates by effectively increasing sample size. Uncertainty analysis showed that the spatial variabilities on both reference and redistribution sites were predominant contributors to overall uncertainty, followed by particle size correction factor P, with negligible contributions from bulk density and tillage depth, showing that close attention must be paid to cesium-137 spatial variability and factor P. In the presence of substantial spatial variation, the cesium-137 technique is not suitable for estimating point soil redistribution rates as is widely perceived in the literature. The point estimates are not true redistribution values, and may be termed pseudo or fictitious estimates because the random spatial variation of cesium-137 is erroneously attributed to a result of soil redistribution. However, the random contributions to the cesium-137 inventory or the resultant pseudo estimates of soil redistribution may be cancelled out theoretically if only the mean values are sought for a uniform area. In the light of the cesium-137 technique's inability to estimate point erosion rates, it is advisable to combine independent samples for each landform unit to estimate the mean soil redistribution rate for the unit with minimal cesium-137 measurement cost in no time. To obtain quantitative soil redistribution estimates, model application must be strictly scrutinized. The spatial variability on both reference and redistribution sites must be well quantified and considered. Particle size correction factor P should be directly measured. Probability-based sampling design is preferred and sufficient sample size should be taken. More importantly, a model cannot be applied to conditions under which its assumptions are noticeably violated, unless the model is properly modified to overcome the violation.