SPC–Methane Offsetting Tool (TCE/IRF framework)

This tool calculates the equivalence between a methane pulse and a semi-persistent carbon (SPC) pool of soil applied biochar using the Time-integrated Climate Effect (TCE) framework.

You can either determine the mass of SPC (in $\text{tCO}_2\text{e}$ at $t=0$) required to offset a given methane emission $M_{\mathrm{CH4}}$ over a specified SPC delivery horizon $H$, or determine the amount of emitted methane that is possible to offset with a given amount of SPC.

For the calculation we use the impulse response function, the SPC retention function, and the time dependent total climate effect (TCE) of methane emissions and biochar SPC removals:

1. CO$_2$ impulse response function (IRF)

The atmospheric decay of a CO$_2$ pulse is represented by a multi-exponential impulse response function (Jeltsch-Thömmes & Joos, 2019):

The analytic time-integral of the IRF over a horizon $T$ is:

$$\int_{0}^{T} \mathrm{IRF}(t)\,\mathrm{d}t = a_0\,T + \sum_{j=1}^{5} a_j \tau_j \left(1-e^{-T/\tau_j}\right)$$

IRF Parameter Set (Bern3D model)

Reference: Jeltsch-Thömmes, A., and Joos, F. (2019). A compilation of atmospheric CO2 and carbon isotope impulse response functions. Climate of the Past.

2. SPC Retention Curve

The retention of SPC in soil follows a bi-exponential decay (Schmidt et al., 2025):

Parameters:

• $\alpha_1 = 0.1787, k_1 = 0.5337$
• $\alpha_2 = 0.8237, k_2 = 0.00997$

3. The Offset Calculation

To calculate the offset, we equate the cumulative warming of methane with the cumulative cooling of the SPC sink.

Step A: Calculate Methane TCE

Using a 100-year horizon ($T=100$) and $\mathrm{GWP}_{100} = 27.0$ for biogenic methane (27.9 for mixed, 29.8 for fossil):

$$\mathrm{TCE}_{\mathrm{CH4}}(100) = M_{\mathrm{CH4}} \cdot \mathrm{GWP}_{100} \cdot \int_{0}^{100} \mathrm{IRF}(t)\,\mathrm{d}t$$

Step B: Calculate the Kernel Integral $I(H)$

The cooling effect depends on the interaction between SPC retention and the CO$_2$ IRF over horizon $H$:

$$I(H) = \int_{0}^{H} f_{\mathrm{SPC}}(t) \cdot \mathrm{IRF}(t) \,\mathrm{d}t$$

The analytic solution for $I(H)$ is a sum of integrals for each combination of SPC and IRF terms:

Step C: Solve for the Unknown

4. Remaining SPC at Year $H$

The amount of carbon physically remaining in the soil at the end of the period is:

Remaining SPC($H$) $= M_{\mathrm{SPC}} \cdot f_{\mathrm{SPC}}(H)$

For comparability with the former EasyCert methane compensation calculator, this tool provides an optional legacy mode that uses $\mathrm{GWP}_{100}=25$ and a 1-year left Riemann sum approximation. However, the newly adopted method provides:

• Flexible $\mathrm{GWP}_{100}$ aligned with IPCC AR6 values.
• Continuous-time integration for higher physical accuracy.

1) Alignment with current scientific consensus

Using source-specific AR6-consistent values (natural, mixed, fossil) improves scientific accuracy. The new CRCF regulation and EU Delegated Regulation (EU) 2020/1044 mandates specific values which our "mixed" setting reflects.

2) Consistency with TCE definition

The Time-integrated Climate Effect (TCE) is fundamentally a continuous integral:

$$\mathrm{TCE}_{\mathrm{CH4}}(100)=M_{\mathrm{CH4}}\cdot \mathrm{GWP}_{100}\cdot \int_{0}^{100} \mathrm{IRF}(t)\,\mathrm{d}t$$

3) Avoidance of discretization artefacts

Former methods used a 1-year left Riemann sum:

$$\int_{0}^{H} f(t)\,\mathrm{d}t \approx \sum_{k=0}^{H-1} f(k)\cdot \Delta t, \qquad \Delta t = 1~\text{yr}.$$

The analytic integral removes these artefacts, especially critical during the non-linear decay in early years.

4) Internal consistency of the offset condition

Offsetting is defined by equality of the integrated climate effects:

$$\mathrm{TCE}_{\mathrm{CH4}}(100) + \mathrm{TCE}_{\mathrm{SPC}}(H)=0$$

5) Method Comparison Table

API Reference:
POST https://dev.ithaka-institut.org/api/calc

Example Payloads

{
  "mode": "offset_mode",
  "h_horizon": 20.0,
  "gwp_type": "fossil",
  "ch4_offset": 1.0
}

{
  "mode": "sink_mode",
  "h_horizon": 10.0,
  "gwp_type": "biogenic",
  "spc_initial": 100.0
}