Stoichiometric O$_2$ Demand from Reduced-Pool Inventories

Computes the complete-oxidation O$_2$ demand for a given rhizosphere reduced-pool inventory and compares it to the specified O$_2$ stock on the same dry-soil mass basis:

$$O_2^{\mathrm{demand}} = \sum_{j} n_j \cdot s_j$$

where $n_j$ is the molar inventory (mmol kg$^{-1}$) of reduced species $j$ and $s_j$ is the stoichiometric O$_2$ coefficient for complete oxidation to the specified endpoint.

Stoichiometric coefficients follow the electron balance table of Ghotbi, Ghotbi, Mühling and Stukenbrock (Box 1 of the mechanistic review, submitted):

Reduced pool	Endpoint	O$_2$ (mol mol$^{-1}$)
Fe$^{2+}$	Fe(III) oxyhydroxide	0.25
Mn$^{2+}$	MnO$_2$	0.50
HS$^{-}$	SO$_4^{2-}$	2.00
FeS (mackinawite)	Fe(III) + SO$_4^{2-}$	2.25
FeS$_2$ (pyrite)	Fe(III) + 2SO$_4^{2-}$	3.75
NH$_4^+$	NO$_3^-$	2.00
CH$_4$	CO$_2$	2.00
Acetate equivalents	CO$_2$	2.00

The O$_2$ deficit ratio (O2_deficit_ratio) is $O_2^{\mathrm{demand}} / O_2^{\mathrm{supply}}$: values $>1$ indicate that the specified O$_2$ stock is smaller than the demand. This stock ratio does not determine recovery or account for continuing O2 delivery.

Usage

rri_o2_demand(
  soil_df,
  fe2_col = NULL,
  mn2_col = NULL,
  hs_col = NULL,
  fes_col = NULL,
  fes2_col = NULL,
  nh4_col = NULL,
  ch4_col = NULL,
  acetate_col = NULL,
  ch4_unit = c("mmol_kg", "umol_kg"),
  acetate_basis = c("acetate", "carbon"),
  o2_supply_col = NULL,
  custom_coefs = NULL,
  bulk_density = NULL,
  theta_v = NULL,
  particle_density = 2.65,
  return_components = TRUE
)

Arguments

soil_df: Data frame with soil chemistry (rows = samples).
fe2_col: Character or NULL. Column for Fe$^{2+}$ (mmol kg$^{-1}$). Default stoichiometric coefficient: 0.25.
mn2_col: Character or NULL. Column for Mn$^{2+}$ (mmol kg$^{-1}$). Coefficient: 0.50.
hs_col: Character or NULL. Column for HS$^{-}$ (mmol kg$^{-1}$). Coefficient: 2.00.
fes_col: Character or NULL. Column for FeS/mackinawite (mmol kg$^{-1}$). Coefficient: 2.25.
fes2_col: Character or NULL. Column for FeS$_2$/pyrite (mmol kg$^{-1}$). Coefficient: 3.75.
nh4_col: Character or NULL. Column for NH$_4^+$ (mmol kg$^{-1}$). Coefficient: 2.00.
ch4_col: Character or NULL. Column for CH$_4$.
acetate_col: Character or NULL. Column for dissolved organic matter expressed as acetate or acetate-carbon equivalents.
ch4_unit: Character. Unit of ch4_col: "mmol_kg" (default) or "umol_kg".
acetate_basis: Character. "acetate" (default; 2 mol O2 per mol acetate) or "carbon" (1 mol O2 per mol acetate-C).
o2_supply_col: Character or NULL. Column for an explicitly defined O$_2$ inventory (mmol O$_2$ kg$^{-1}$). If NULL, deficit ratio is not computed.
custom_coefs: Optional named numeric vector to override or extend the built-in stoichiometric coefficients. Names must match the argument names above (e.g., c(fe2_col = 0.25)). Useful for system-specific endpoint assumptions.
bulk_density: Numeric of length one or nrow(soil_df). Soil bulk density (g cm$^{-3}$) for volumetric conversion of demand to mmol O$_2$ L$^{-1}$ porewater. Set to NULL to skip volumetric conversion.
theta_v: Numeric of length one or nrow(soil_df), or NULL. Volumetric water content (L water L$^{-1}$ bulk soil). When omitted and bulk_density is supplied, saturated porosity is estimated as 1 - bulk_density / particle_density.
particle_density: Numeric. Particle density in g cm$^{-3}$ used only for the saturated-porosity estimate. Default 2.65.
return_components: Logical. If TRUE (default), return a per-species contribution matrix.

Value

A list:

o2_demand: Numeric vector (mmol O$_2$ kg$^{-1} dry soil$) of complete-oxidation O$_2$ demand per sample.
o2_deficit_ratio: Per-sample $O_2^{\mathrm{demand}} / O_2^{\mathrm{supply}}$. Values $>1$ indicate demand exceeds the specified stock. NA when o2_supply_col is absent.
o2_demand_vol: Volumetric O$_2$ demand (mmol L$^{-1}$ porewater); NA if bulk_density is NULL.
n_species_used: Integer. Number of reduced-pool columns found.
n_species_observed: Integer vector. Number of species with a finite inventory in each row, so a low demand from sparse data is not mistaken for a low demand from a small inventory.
species_coverage: Per-row fraction of the requested species that were observed. Columns named but absent from soil_df count against coverage.
interpretation: Character. A one-line reminder that the ratio compares a demand to a stock, not to a delivery rate.
ch4_unit_used, acetate_basis_used: The resolved values of ch4_unit and acetate_basis, recorded because both change the numbers returned.
components: Data frame (one row per species) with: species, n_observed, stoich_coef, mean_inventory_mmol, mean_o2_contribution, fraction_total_demand. Returned only when return_components = TRUE.
stoich_table: Data frame of the coefficients actually applied, one row per species found, including any custom overrides: species_arg, column_used, stoich_coef_O2, endpoint. Species not present in soil_df are absent.

Details

Interpretation — the 26-fold contrast.

The mechanistic review (Ghotbi et al., submitted) provides a worked example: a Fe-rich rhizosphere containing 50 mmol Fe(II) kg$^{-1}$, 5 mmol FeS kg$^{-1}$, 2 mmol Mn(II) kg$^{-1}$, 2 mmol NH$_4^+$ kg$^{-1}$, 2 mmol acetate kg$^{-1}$, and 0.5 mmol CH$_4$ kg$^{-1}$ has a complete-oxidation O$_2$ ceiling of $\approx 34$ mmol O$_2$ kg$^{-1}$, versus only $\approx 1.3$ mmol O$_2$ kg$^{-1}$ in an illustrative initial pore-gas stock: about a 26-fold contrast. The assumed stock is not air-saturated porewater. Continuing atmospheric and root O2 delivery can replenish it. Accessibility, reaction kinetics and transport determine realized demand during an event.

Pyrite stoichiometry.

Complete pyrite oxidation to sulfate and Fe(III) oxyhydroxide releases 4 mol H$^+$ mol$^{-1}$ FeS$_2$ and consumes 3.75 mol O$_2$: FeS$_2$ + 15/4 O$_2$ + 7/2 H$_2$O → Fe(OH)$_3$ + 2H$_2$SO$_4$. Partial oxidation to sulfur intermediates (S$^0$, thiosulfate) requires fewer moles; adjust via custom_coefs.

pH coupling.

Under the applicable rate law, homogeneous abiotic Fe(II) oxidation increases $\approx$100-fold per unit pH rise (Stumm & Lee, 1961; Millero et al., 1987). The stoichiometric demand computed here is for complete oxidation and is independent of pH, but actual O$_2$ consumption rates will be pH-modulated. This function reports a stoichiometric potential demand, not a thermodynamic limit or rate.

References

Ghotbi, M., Ghotbi, M., Mühling, K. H., & Stukenbrock, E. H. Rhizosphere redox recovery after hydrological disturbances: mechanisms across the soil–plant–microbiome continuum. Submitted to Soil Biology & Biochemistry.

Stumm, W., & Lee, G. F. (1961). Oxygenation of ferrous iron. Industrial & Engineering Chemistry, 53, 143–146. doi:10.1021/ie50614a030

Millero, F. J., Sotolongo, S., & Izaguirre, M. (1987). The oxidation kinetics of Fe(II) in seawater. Geochimica et Cosmochimica Acta, 51, 793–801. doi:10.1016/0016-7037(87)90093-7

Examples

## Reproduce the worked example from Box 1 of the mechanistic review
worked_example <- data.frame(
  Fe2 = 50.0, # mmol kg-1
  FeS = 5.0,
  Mn2 = 2.0,
  NH4 = 2.0,
  acetate = 2.0,
  CH4 = 0.5, # mmol kg-1; set ch4_unit = "umol_kg" for umol input
  O2_pw = 1.3 # assumed initial O2 stock, mmol/kg; NOT air-saturated porewater
)

demand <- rri_o2_demand(
  soil_df = worked_example,
  fe2_col = "Fe2",
  mn2_col = "Mn2",
  fes_col = "FeS",
  nh4_col = "NH4",
  acetate_col = "acetate",
  ch4_col = "CH4",
  o2_supply_col = "O2_pw",
  return_components = TRUE
)

demand$o2_demand # should be ~34 mmol O2 kg-1
#> [1] 33.75
demand$o2_deficit_ratio # should be ~26
#> [1] 25.96154
demand$components
#>   species n_observed stoich_coef mean_inventory_mmol mean_o2_contribution
#> 1     Fe2          1        0.25                50.0                12.50
#> 2     Mn2          1        0.50                 2.0                 1.00
#> 3     FeS          1        2.25                 5.0                11.25
#> 4     NH4          1        2.00                 2.0                 4.00
#> 5     CH4          1        2.00                 0.5                 1.00
#> 6 acetate          1        2.00                 2.0                 4.00
#>   fraction_total_demand
#> 1                0.3704
#> 2                0.0296
#> 3                0.3333
#> 4                0.1185
#> 5                0.0296
#> 6                0.1185

Reduced pool	Endpoint	O\(_2\) (mol mol\(^{-1}\))
Fe\(^{2+}\)	Fe(III) oxyhydroxide	0.25
Mn\(^{2+}\)	MnO\(_2\)	0.50
HS\(^{-}\)	SO\(_4^{2-}\)	2.00
FeS (mackinawite)	Fe(III) + SO\(_4^{2-}\)	2.25
FeS\(_2\) (pyrite)	Fe(III) + 2SO\(_4^{2-}\)	3.75
NH\(_4^+\)	NO\(_3^-\)	2.00
CH\(_4\)	CO\(_2\)	2.00
Acetate equivalents	CO\(_2\)	2.00

Stoichiometric O\(_2\) Demand from Reduced-Pool Inventories