Estimating soil erosion using ¹³⁷Cs in the absence of reference sites: Application to truncated soil profiles

Soil erosion is a major land degradation process that affects ecosystem functions and services, requiring reliable methods for its assessment. The use of ¹³⁷Cs is valuable for estimating soil redistribution; however, its application is often limited by the lack of suitable reference sites. This study proposes a methodology to reconstruct the reference ¹³⁷Cs depth distribution and derive key erosion parameters using mechanically truncated profiles in situations where suitable undisturbed reference sites are unavailable. Two sites within the Panama Canal watershed were investigated: a truncated soil profile affected by land leveling and a pasture site under grazing. A reference ¹³⁷Cs depth distribution was reconstructed from the preserved lower portion of a truncated soil profile using a shifted exponential function, while the reference inventory (A_ref) was independently estimated from precipitation-based fallout models. This approach allowed the estimation of the relaxation mass depth (h₀) and the thickness of the removed soil layer. Erosion rates at the pasture site were quantified using the Profile Distribution Model (PDM) and the MODERN model. Both models yielded comparable erosion rates (1.5-2.5 Mg ha^-1 yr^-1), with good agreement under low erosion, although a slight systematic overestimation by PDM was observed. The estimated erosion rates are consistent with those reported from erosion plot measurements, supporting the validity of the approach. Furthermore, the results highlight the importance of accounting for uncertainty in reference inventory estimates by using a range of plausible A_ref values and expressing erosion rates as ranges. Overall, the proposed methodology provides a robust and practical alternative for applying the ¹³⁷Cs technique in disturbed landscapes, where suitable reference sites are unavailable and the underlying assumptions of the reconstruction are satisfied. The proposed approach could expand the applicability of the ¹³⁷Cs technique while reducing time, cost and field effort required for soil erosion assessment, compared to conventional monitoring approaches.