Estimating variability in soil organic carbon storage using the method of statistical differentials

The diverse nature of soils introduces uncertainty into the estimation of soil organic carbon (SOC) storage. Laboratory analyses indicate C concentration in soils, but the soil layer thickness, bulk density, and percent of fragments > 2 mm. must be known in order to estimate SOC storage. Ideally, measurements of SOC concentration are performed on the same soil samples used to determine bulk density and percent of fragments > 2 mm, but this is frequently not possible. Often measurements of SOC concentration, bulk density, and percent of fragments > 2 mm are obtained separately from the same soil layer, which causes propagation of error when estimating SOC storage. Furthermore, measurements of bulk density and percent of fragments > 2 nun are more difficult to obtain than measurements of SOC concentration. Because of this, samples of bulk density and percent of fragments > 2 mm. are often taken independently and less frequently than samples for SOC concentration. The objective of this study was to derive an estimation method for the variability in SOC storage estimates as a function of SOC concentration, bulk density, percent of fragments > 2 mm, and soil thickness. The method of statistical differentials, also known as the delta method, was used to obtain an estimate of the variability in SOC storage estimates. The variance estimation procedure is illustrated using previously published data for the Russian Chernozem under different management regimes. The method of statistical differentials is a valuable tool for obtaining variance estimates in a large class of problems with similar characteristics.