Uncertainty analysis of delta 13C method in soil organic matter studies

The delta 13C method is becoming increasingly popular to calculate turnover rates in soil organic matter studies. The method requires a lot input data, all of which exhibit a natural variability. We performed an uncertainty analysis on the calculations in the delta 13C method to evaluate the influence of uncertainty in the input data on the results of the calculations. Based on field measurements, we estimated the frequency distributions of the input data required for the delta 13C method (soil organic carbon, bulk density and delta 13C). From these frequency distributions, 200 randomly chosen data combinations were sampled, taking into account their mutual correlations (Monte Carlo sampling). The data combinations were used to calculate the soil organic C pools in the forest and pasture and the C loss since forest clearing. The uncertainty in output was described using frequency distributions. Uncertainty in the output was high, especially for net C loss (ranging between -79.3 and +63.5 Mg ha-1). An estimation of the C pools within +/- 10% of the estimated mean at the 90% confidence level requires 5 measurements in the forest and 7 in the pasture. Heterogeneity in delta 13C values of soil organic matter was the main reason for the higher sample number requirement in the pasture, compared to the forest. To estimate the C loss with the same precision requires 170 measurements in forest and pasture. Spatial variability of organic C and bulk density in forest and pasture was described by semivariograms. The semivariograms of forest and pasture differed mainly by the distance to which organic C and bulk density displayed spatial dependence (the range). The larger range of the pasture semivariograms was explained by the absence of trees. Spatial variability was the main source of the uncertainty in input data. However, variations due to sampling error and short scale variability (the nugget of a semivariogram) are considerable and should not be ignored.