A simple soil mass correction for a more accurate determination of soil carbon stock changes

Our approach uses hypothetical 30 cm fixed depth samples taken at three successive time points (t0, t1, and t2) with prescribed changes in SOC (1.4% to 1.6%) and BD (1.5–1.1 g cm⁻³) over these time points (Table 1). The 30 cm soil depth is the common international standard for sampling and analysis required for SOC stock assessment and adhered to by carbon accounting and market organizations^6,18. The changes we adopted (a 27% decrease in BD and a 14% increase in SOC) while relatively large, are consistent with those reported in the literature. For example, Reganold and Palmer reported a 25% decrease in BD (1.2–0.9 g cm⁻³) in neighboring farms with differing management practices²³, and Syswerda et al. observed a 17% increase in SOC concentration (10.4–12.2 g C kg soil⁻¹) when converting from a conventionally to organically managed row crop rotation²¹.

In Table 1, the total soil mass, mineral soil mass, and the SOC stock of the fixed depth samples were calculated by equations as described in the introduction from our prescribed changes in BD and SOC values.

Scenarios

We compared hypothetical ESM correction scenarios with our 30 cm fixed depth sample at each time point (Table 2, Figs. 2, 3).

Scenario 1

We carried out the ESM correction on a 30 cm sample and assumed that the sample was homogenous throughout the profile, with constant SOC and BD values at each time point.

To correct for the error in SOC stock estimation when using fixed depth soil sampling, we used  Eqs.2a, 2b and 2c that consider changes in BD^28,35. The adjusted soil depth resulting from the change in BD is calculated as:

where M_i = Initial mineral soil mass per area (left[frac{M}{{L}^{2}}right]) , M_n = New mineral soil mass per area (left[frac{M}{{L}^{2}}right]) , D_a = Adjusted soil surface depth (left[Lright]) , BD_i = Initial bulk density (left[frac{M}{{L}^{3}}right]) , BD_n = New bulk density (left[frac{M}{{L}^{3}}right]) , SOC_i = Initial SOC as a decimal percent (left[frac{M}{M}right]) , SOC_n = New SOC as a decimal percent (left[frac{M}{M}right]) , D_i = Initial depth (left[Lright]).

To conform with Eq. (2a), an increase in SOC over time results in a displacement of some soil mineral mass from the sample, whereas a decrease in SOC over time requires some soil mineral mass to be replaced³⁴. Multiplying the BD by the mineral fraction of the soil (left(1-mathrm{k}*{mathrm{SOC}}right)) for each time point allowed us to compare equivalent mineral mass²⁸. The effect of a change in SOC on mineral mass is small, with a 1% change in SOC equating to approximately a 2% change in apparent depth. This adjustment relates SOC per unit of mineral mass of the fine fraction (< 2 mm) and is unaffected by the coarse fraction (> 2 mm)²⁰. The corrected apparent depth can then be used to calculate the corrected SOC stock of a single layer, fixed depth sample (Eq. 3).

Scenario 2

In ESM correction scenarios 2a, 2b, and 2c, we imposed variable, dynamic BD and SOC values with depth over time (Table 2, Figs. 2, 3). To investigate these profiles, we determined the SOC and BD values throughout the soil depth by separating the soil into one (1) cm depth increments (i.e., 0–1 cm, 1–2 cm, etc.). We refer to this calculated incremental profile as the scenario 2 baseline. We assumed that our prescribed SOC concentration varied with depth following an exponential decay. To represent this decay, we simulated the global average distribution of SOC concentration with depth on crop land³⁶, following the distribution from Hobley and Wilson³⁷ (Eq. 4),

where SOC (d) is the SOC concentration at depth (d), ({SOC}_{infty }) is the infinity SOC concentration, SOC₀ is the SOC concentration at the soil surface, and k is the decay rate. We solved for the decay rate, initial SOC₀, and infinity ({SOC}_{infty }) to fit the global average distribution for the 30 cm profile³⁶ and then scaled the SOC concentration to our 30 cm fixed depth sample’s average SOC (1.4%) at t0 (Fig. 3).

In scenarios 2a, 2b, and 2c, the BD increased linearly with depth^38,39. At the initial time point (t0), we varied the BD values by ± 10% of the BD average over the 30 cm depth, such that for example, BD at t0 (profile average of 1.5 g cm⁻³) was 1.35 g cm⁻³ and 1.65 g cm⁻³ for the upper (0–1 cm) and lower (29–30 cm) depth increment, respectively. For each sequential time point, as the average BD decreased, the soil expanded. To determine the expansion, the depth of the initial sample (e.g., at t0) that filled the 30 cm depth in the subsequent sample (e.g., at t1) was calculated as the initial depth multiplied by the ratio of the average initial BD over the average new BD (e.g., 1.5/1.3 = 1.15 for t0/t1).

The linear increase in BD with depth of each following time point maintained the average BD of scenario 1. We then varied the new BD by ± the percent change in the average BD between the time periods (see annotated scripts “main.R” and “functions.R” in Supplementary Material 1 for the development of the theoretical dataset). We then divided each initial BD increment (using soil mass for every 1 cm depth increment) by the new BD in the expanded increment (using soil mass for every > 1 cm depth increment) to determine the expanded depth of each increment. The SOC value at the initial time represented the same, now expanded, (> 1 cm) increments, as SOC is a ratio of mass. We used a linear decay rate that was twice that of the percent change in BD between time points to maintain an average BD that was consistent with scenario 1. To model the subsequent fixed depth sample, the BD and SOC concentration values of this expanded soil profile were then interpolated back to the 30 × 1 cm increments of the scenario 2 baseline depth. This calculation preserved the prescribed average BD of the new time point by only expanding the initial SOC concentration.

We adjusted the SOC concentration of the next time point to maintain the average SOC concentrations of the 30 cm fixed depth sample, (see annotated scripts “main.R” and “functions.R” in Supplementary Material 1). Because the BD changed between time points and because the SOC stock in the 30 cm fixed depth sample was known, we determined the change in SOC stock between time points by subtracting the average SOC stock in the prior sample from the new sample. We then weighted this change across the 30 cm profile using the distribution of the global soil SOC in the top 30 cm to simulate SOC stratification with reduced tillage or agricultural intensification⁴⁰. We then multiplied this change by the BD to convert back to SOC concentration and added the delta ((Delta )) SOC value to the prior sample. A worked example is shown in Supplementary Material 2 “Correction Example”.

At each time point we split the soil profile at 10 cm and 15 cm depth intervals to create samples for scenarios 2a (3 soil intervals) and 2b (2 soil intervals), respectively. Note that scenario 2c is mathematically equivalent to scenario 1—with only one sample depth interval (30 cm) the sample contains no data on varying SOC or BD. The samples for 2a and 2b were generated by summing the total mass per area and SOC stock values from the scenario 2 baseline to produce single sample values of total soil mass per area and SOC concentration values per depth interval (as would be determined in a laboratory) and calculating BD and mineral mass.

In scenario 2, any required additional mineral mass and the associated SOC values were ‘placed’ at the base of the sample to represent a soil profile that had expanded below the fixed 30 cm depth. To account for this, we calculated the increase in adjusted sample depth and accumulated additional soil mineral mass with the lowest sample depth interval of each split sample (Eqs. 5 and 6).

where (mathrm{ Delta D}) is the apparent change in depth needed to generate the same mineral mass of the initial sample and the subscript j is the number of sample depth intervals from 1 to j.

Varying BD linearly with depth introduces additional complexity in the calculation of the apparent depth. Each sample depth interval may expand (or contract in cases not explored here) at differing rates. Here, the over or under sampling of soil mineral mass is no longer constant with depth and the correction for apparent depth (Da) is estimated with linear interpolation using the BD of each sampling depth interval (i.e., 10 cm, 15 cm, or 30 cm). To do so, we calculated the mineral mass in each depth interval, determined their difference between the initial sample time point and new sample time point, and converted the change in mineral mass to a depth, where:

where j_bottom is the lowest sample depth interval, and other terms are as previous. Using Eqs. (5), (6), and (7), with variable BD and SOC values, SOC stock can be corrected using samples split into the 10 cm and 15 cm sampling depth intervals.

Source: Ecology - nature.com