Poeplau et al. (2017) recently outlined the systematic overestimation of soil
organic carbon (SOC) stocks due to incorrect application of bulk density and
rock fragment content in calculation of SOC stocks. Unfortunately, the method
they propose to rectify this is associated with a greater error (due to
assumption of rock density, extra calculation steps and propagation of
errors) than the simpler mass-balance-derived equation for SOC stock
calculations, outlined below. Using a mass balance approach to C stocks we
define

Using a mass balance approach on the mass proportion of C in the whole soil,
we obtain

Equation (8) is also mathematically equivalent to calculations according
to Eqs. (7) and (8) in Poeplau et al. (2017). However, the recommended use of the
mass of fine fraction for the calculations by Poeplau et al. (2017) also has a greater
potential error than using the mass proportion of rocks according to
Eq. (8). The advantage of using the rock mass to correct the stocks
is that rocks are (nearly) entirely conserved during sieving, whereas fine
soil mass is lost as dust during sieving, increasing uncertainty in the
calculations. In contrast, M4 (Eqs. 3 and 6) of Poeplau et al. (2017) requires
an estimation of rock density (they recommend assuming a rock density of
2.63 g cm

Unfortunately, the additional calculations required in M4 also increase the
uncertainty of the estimate due to error propagation. This can be
illustrated by calculating the error terms of both equations. The squared
relative error of Eq. (8) is

With regards to eliminating the depth,

Of key concern – and not addressed here – is the calculation of SOC stocks in stony soils, as here an accurate estimation of rock content is highly difficult. Estimating rock content from the profile face is highly error prone because 2-D surface areas are not representative of irregular 3-D structures, such as rocks. Therefore, estimating rock content from the profile face is not volumetric. Taking larger volumes of sample in very large cores to determine the bulk density of the whole soil would help to alleviate this issue, but this would be associated with more field and laboratory work. A systematic study into this issue, similar to the systematic evaluation of sources of error when upscaling to SOC analyses to landscape stocks (Goidts et al., 2009), could help to resolve the issue.

In summary, Poeplau et al. (2017) have clearly demonstrated the need to adjust for coarse fragments > 2 mm in SOC stock calculations. Unfortunately, their recommendation has added some confusion to the correct method of calculation of SOC stocks via the introduction of unfamiliar formulas. Whilst mathematically correct, their formulas are associated with larger errors than the standard equation, so they present no clear advantage. As such, we recommend the use of Eq. (8) for SOC stock calculations.

No data sets were used in this article.

The authors declare that they have no conflict of interest.

EUH is funded by the Bundesministerium für Bildung und Forschung grant no. 031B0026B. This work was supported by the German Research Foundation (DFG) and the Technische Universität München within the funding programme Open Access Publishing. Edited by: Bas van Wesemael Reviewed by: two anonymous referees