Commentary Comment on ‘‘Determining soil carbon stock changes: Simple bulk density corrections fail’’ [Agric. Ecosyst. Environ. 134 (2009) 251–256] Alex. B. McBratney *, Budiman Minasny Faculty of Agriculture, Food & Natural Resources, The University of Sydney, Sydney, Australia Lee et al. (2009) showed the equivalent soil mass (ESM) approach for correcting bulk density changes when estimating soil carbon stock or density. The ESM approach from Ellert and Bethany (1995) attempts to correct for differences in bulk density from different sampling dates by calculating the mass of soil C in an equivalent soil mass per unit area. This is done by first designating the mass of the heaviest soil layer as the equivalent mass. The C density from subsequent sampling is then calculated by estimating the thickness of the deepest soil layer required to attain the equivalent mass. Lee et al. (2009) showed various calculations of the ESM approach. In this comment, we should like to point out that the material coordinate system, which is simpler and more general, is better for handling this issue. In fact, Gifford and Roderick (2003) have proposed the use of the mass (or material) coordinate system for soil C accounting. The material coordinate or Lagrange system was proposed by Smiles and Rosenthal (1968) for calculating water flux in swelling soils. It has been applied in calculating water flows in swelling soils (McGarry and Malafant, 1987; Ringrose-Voase et al., 2000).For C accounting, we based the C density on the mass of the soil mineral material. First, we calculate the mineral mass of each sampling layer from the bulk density r b (in kg m 3 ), mineral fraction f min (kg kg 1 ), and thickness z (m) of the layer: m ¼ z r b f min The mineral fraction can be estimated from the fraction of the soil that is not organic matter, which can be done by dry combustion. In the absence of this information, we can base it on the van Bemmelen factor ( f min =1  organic C concentration  1.724). Then we calculate the cumulative mass for each layer M (in kg m 2 ): M i ¼ X i l¼1 m l and similarly we calculate the cumulative C density for each layer. Afterwards, we plot the cumulative C density with cumulative mass. For example, Fig. 1 shows the hypothetical example from Table 1 of Lee et al. (2009). The cumulative C density is plotted against cumulative mineral mass on the two sampling dates. We can now view the C stock of the two dates on a common material coordinate system. For comparison of C stock between the two dates, we simply calculate the C stock at the equivalent cumulative mass. As we can see, there is no change in C stock due to the change in bulk density. Table 1 shows the calculation of the equivalent C concentration based on a linear interpolation between each layer: C t ¼ C t1 þðM t  M i1 Þ C i  C i1 M i  M i1 where C t is the cumulative C density at M t , C i is the cumulative C density at layer i, and M i is the cumulative mass at layer i. Fig. 2 illustrates the example when there is a decrease in soil C content. First there is no change in bulk density, but a decrease in C content (Fig. 2, time = 2a). And in the second scenario there is a decrease in C content and an increase in bulk density (Fig. 2, time = 3a). We believe the material coordinate approach is easier to apply than the ESM approach. The mass coordinate method is a more formal method and has been used for correcting water content changes in swelling soils (McGarry and Malafant, 1987; Ring- rose-Voase et al., 2000). The assumptions are, of course, the changes of density is isotropic, the carbon ‘moves’ together with Agriculture, Ecosystems and Environment 136 (2010) 185–186 ARTICLE INFO Article history: Received 30 September 2009 Received in revised form 1 December 2009 Accepted 9 December 2009 Available online 12 January 2010 Keywords: Soil Carbon Carbon accounting Material coordinate Bulk density Soil carbon stock Equivalent soil mass * Corresponding author. E-mail address: alex.mcbratney@sydney.edu.au (Alex. B. McBratney). Contents lists available at ScienceDirect Agriculture, Ecosystems and Environment journal homepage: www.elsevier.com/locate/agee 0167-8809/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.agee.2009.12.010