Calculated data

1. Purpose and source article

The method follows the Methods section of Hu, T., Malone, S. L., Rumpel, C. and Chabbi, A. (2024): Maximizing soil organic carbon stocks through optimal ploughing and renewal strategies in (Ley) grassland. Communications Earth & Environment 5, 38, doi:10.1038/s43247-024-01202-3.

The article is a model study of one grassland site in France. It gives a carbon balance (Eq. 1 to 7) and the flux methods: a $u_*$ threshold of 0.1 m s⁻¹, a plausibility limit of ±50 µmol m⁻² s⁻¹ and gap filling after Reichstein et al. 2005.

We calculate these products from our eddy-covariance data:

• GPP and Reco with the night-time method of Reichstein et al. 2005, for all six sites.
• Gap-filled NEE for Maktau (quality filter, $u_*$ filter, MDS gap filling).
• Daily, monthly and annual sums of NEE, GPP and Reco in g C m⁻².
• The NECB per site and year, with a carbon table of harvests and organic inputs.

We cannot calculate NPP, heterotrophic respiration (R_h), C_input, SCB and RCB (Eq. 3 to 7). These need a soil model or repeated soil carbon samples. No site measures leached carbon, fire, volatile losses or erosion.

2. Sign conventions

3. Equations

Hu et al. 2024 give these equations. The numbers are the numbers of the article.

1. Eq. 1$$\mathrm{NECB} = \mathrm{NEE} + C_{\mathrm{exo}} - C_{\mathrm{harvest}} - C_{\mathrm{D}} - C_{\mathrm{fire}} - C_{\mathrm{volatile}} - C_{\mathrm{CH_4}} - C_{\mathrm{erosion}}$$
2. Eq. 2$$\mathrm{NECB} = \mathrm{NEE} - C_{\mathrm{harvest}}$$
3. Eq. 3$$\mathrm{NEE} = \mathrm{NPP} - R_{\mathrm{h}}$$
4. Eq. 4$$\mathrm{NECB} = \mathrm{NPP} - R_{\mathrm{h}} - C_{\mathrm{harvest}}$$
5. Eq. 5$$C_{\mathrm{input}} = \mathrm{NPP} - C_{\mathrm{harvest}}$$
6. Eq. 6$$\mathrm{NECB} = C_{\mathrm{input}} - R_{\mathrm{h}}$$
7. Eq. 7$$\mathrm{RCB} = \mathrm{NECB} - \mathrm{SCB}$$

C_exo is the carbon in manure and organic fertiliser. C_harvest is the carbon that leaves the field in grain, straw or cut grass. C_CH4 is the carbon lost as methane. The article keeps only Eq. 2.

Our NEE is positive for an emission. Thus Eq. 1, without the terms that no site measures, becomes (g C m⁻² yr⁻¹, positive = gain):

4. Inputs and variables

The calculation reads the harmonised database. Days and years are local calendar days and years (Finnish sites UTC+2, Maktau UTC+3). The temperature for the respiration model is the air temperature at all sites.

• Night: incoming shortwave radiation sw_in < 10 W m⁻². Where sw_in is missing, PPFD < 20 µmol m⁻² s⁻¹.
• VPD: the value of the source file. Where the file has no VPD, we use the Magnus formula:

5. Night-time partitioning

At night, there is no photosynthesis. Thus the measured night NEE is the respiration. The respiration follows Lloyd and Taylor (1994):

$E_0$ (K) is the temperature sensitivity. $R_{\mathrm{ref}}$ (µmol m⁻² s⁻¹) is the respiration at 15 °C. We write the exponent with:

The steps per site and local calendar year:

1. Night sample. Rows with the night flag, a measured NEE and a temperature. At Qvidja and Maktau, rows with $u_*$ < 0.1 m s⁻¹ are not used. Negative night fluxes stay in the sample.
2. $E_0$ from short windows. Windows of 15 days (±7 days), one every 5 days. A window needs more than 6 values and a temperature range of at least 5 K. A least-squares fit gives $R_{\mathrm{ref}}$ and $E_0$. Then the fit removes the residuals outside the 5 to 95 % band and fits again. A window is valid when:$$E_0 - \mathrm{SE} > 30\ \mathrm{K} \quad\text{and}\quad E_0 + \mathrm{SE} < 350\ \mathrm{K}$$(with the soil temperature, the upper limit is 550 K). The annual $E_0$ is the mean of the 3 valid windows with the smallest standard error (SE). Fallbacks, in this order: fewer than 3 valid windows → mean of the valid windows; no valid window → one fit on all nights of the year; no fit → the value of the nearest year of the same site; else no Reco and GPP for the year.
3. $R_{\mathrm{ref}}$ from short windows. Windows of 7 days, one every 4 days, with $E_0$ fixed. A window needs more than 2 values. The closed-form least-squares value is:$$R_{\mathrm{ref}} = \frac{\sum_i \mathrm{NEE}_i\, f_i}{\sum_i f_i^2},\quad f_i = \exp\big(E_0\, g(T_i)\big)$$A negative value is not used. Between the window centres, the value is linear. Rows more than 14 days from a usable window get a low quality flag.
4. Temperature for every row. Linear interpolation fills gaps up to 3 hours. The mean diurnal course (same time ±1 h, over ±7, ±14, ±30 days) fills longer gaps.
5. Reco and GPP for every row.$$R_{\mathrm{eco}}(t) = R_{\mathrm{ref}}(t)\,\exp\big(E_0\, g(T(t))\big)$$$$\mathrm{GPP} = R_{\mathrm{eco}} - \mathrm{NEE}_f$$We do not set GPP to zero at night. Thus $\mathrm{NEE}_f = R_{\mathrm{eco}} - \mathrm{GPP}$ holds in every row.

6. Maktau: filter, $u_*$ and gap filling

Maktau has a measured CO₂ flux (FC), a quality flag and $u_*$, but no gap-filled NEE. The calculation:

1. Keeps rows with a quality flag of 1 or less. Rows without a flag are not used.
2. Keeps $|\mathrm{FC}| < 50\ \mu\mathrm{mol\,m^{-2}\,s^{-1}}$.
3. Keeps $u_* \ge 0.1\ \mathrm{m\,s^{-1}}$ (the threshold of the article). The moving point test of Papale et al. 2006 also runs, but its results change too much between years (6 temperature classes, 20 $u_*$ classes). We do not apply it.
4. Fills the gaps with marginal distribution sampling (MDS, Reichstein et al. 2005). Similar conditions: sw_in ±50 W m⁻², air temperature ±2.5 °C, VPD ±5 hPa, at least 2 values.

Result: 38 235 of 52 648 flux rows stay. 10 480 rows have no flag, 2 704 rows have a bad flag and 1 229 rows have a low $u_*$.

A row without VPD skips the 3-driver steps. The MDS value of a long gap is a model, not a measurement. The annual table marks those years as not reliable.

7. Sums and units

One 30-minute value of 1 µmol CO₂ m⁻² s⁻¹ is this mass of carbon:

The sums use the local day, month and calendar year. When one row of a period has no value, the sum of the period is empty. An annual sum is reliable when the measured fraction is at least 20 % and the longest gap is 30 days or less.

Haltiala uncertainty

Haltiala has ten gap-filling models (NEE_F1 to NEE_F10). We sum each model per year (S_k). Then we calculate the standard deviation of the ten sums:

8. Results

Temperature sensitivity per site and year

Annual sums

Net ecosystem carbon balance

9. Management carbon

The carbon table lists harvests and organic inputs from the management files of the sites and from the two Qvidja papers (Heimsch et al. 2021 and 2024). Rules:

• Dry mass from the fresh mass and the dry-matter fraction, or the dry mass of the file:

• Carbon fraction: Qvidja 0.42 (both Qvidja papers), Haltiala 0.50 (management file), Viikki 0.42 (assumed).
• An organic input without a carbon content gets no carbon value. Then the NECB is a lower bound. The Qvidja molasses fertiliser of 2018 and 2019 uses the value of Heimsch et al. 2021.
• Grazing gets no carbon value.
• Anttila, Särkisuo and Maktau have no harvest data. For Maktau we give no NECB.

10. Validation

At Anttila, our annual GPP and Reco are within 1.2 % of the night-time partitioning of the data provider. The half-hourly $R_{\mathrm{ref}}$ agrees well (r = 0.97 to 0.98), but $E_0$ is different. $E_0$ and $R_{\mathrm{ref}}$ compensate each other in the annual sums. Särkisuo 2022 is 5 % below the provider.

At Qvidja, our GPP and Reco are 15 to 31 % below the provider. The provider used a daytime method. Its night Reco is about 55 % above the measured night NEE. Our method follows the measured night flux. We report this difference and do not correct it.

Our Qvidja NEE sums are more negative than Heimsch et al. 2024, because the current file has a later processing version. The paper includes the carbon of grazing, thus the NECB values are not directly comparable.

Haltiala: the annual NEE is equal to the mean of the ten model sums within 0.15 g C m⁻² (table in section 7).

11. Limits and open questions

• Viikki measures NEE in about 20 % of the periods. It has few valid $E_0$ windows, and the $R_{\mathrm{ref}}$ interpolation spans long winter gaps.
• Maktau: only 2019 is almost complete. 2018 and 2023 use $E_0$ of a neighbour year. 2023 has no Reco, because the few measured night fluxes are negative.
• Anttila, Särkisuo, Haltiala and Viikki have no $u_*$ in the files. We use the quality flag of the provider.
• Särkisuo 2023 has an 84-day gap in the air temperature. Thus it has no annual GPP and Reco.
• The NECB is a lower bound in years with an organic input of unknown carbon content. One compost application can hold about 500 g C m⁻², more than the annual NEE.
• The Viikki yields have no unit. The Haltiala 2025 yield can be a fresh mass. Two Qvidja dry-matter fractions are not certain.

12. How to reproduce

Run these commands in the repository. The full method description is in docs/calculated.md.

npm run build:db     # db/*.parquet from the source files
npm run calc         # data/calculated/* (GPP, Reco, sums, NECB, validation)
npm run site:build   # copies the tables to the site and builds this page

The parameters are in scripts/lib/calc/constants.ts. This run used the options --ustar fixed, --temp ta and--gpp-night keep.