= Water-filled pore space
{title2=$V_w/V_p$}
<Water-filled pore space> is the fraction of a <soil> sample's pore <volume> occupied by <water>. If $V_w$ is water volume and $V_p$ is total pore volume, the fraction is $V_w/V_p$; multiplying by one hundred expresses it as a percentage. The denominator is the pore volume, whereas <volumetric soil water content> uses the entire sample volume.<Effect of Water-Filled Pore Space on Carbon Dioxide and Nitrous Oxide Production in Tilled and Nontilled Soils by D. M. Linn and J. W. Doran>[Abstract, water-filled porosity determined from water content and total porosity]{ref}
Let total sample volume be $V$, <porosity> be $\varepsilon=V_p/V$, and <volumetric soil water content> be $\theta=V_w/V$. Then
$$
\frac{V_w}{V_p}=\frac{\theta}{\varepsilon}.
$$
For matching dry-solid mass $M_s$, <soil bulk density> is $\rho_b=M_s/V$ and <soil-particle density> is $\rho_s=M_s/V_s$. Under an additive solid-and-pore volume model,
$$
\varepsilon=1-\frac{V_s}{V}=1-\frac{\rho_b}{\rho_s}.
$$
These identities require compatible volume definitions; shrinkage or swelling can change the measured sample geometry.
Consider two hypothetical samples with $\theta=0.30$ and $\rho_s=2.65\,\mathrm{g\,cm^{-3}}$. For $\rho_b=1.325\,\mathrm{g\,cm^{-3}}$, porosity is $0.50$ and water-filled pore space is $0.60$. For $\rho_b=1.59\,\mathrm{g\,cm^{-3}}$, the corresponding values are $0.40$ and $0.75$. Equal water per total volume fills different fractions of the available pores. This compares two stipulated samples, rather than assuming a compaction process preserves every other quantity.
The 1984 study related water-filled porosity to <carbon dioxide> production, oxygen uptake and <nitrous oxide> production. Its reported maximum aerobic activity near sixty percent applies to the studied conditions, rather than a universal threshold.<Effect of Water-Filled Pore Space on Carbon Dioxide and Nitrous Oxide Production in Tilled and Nontilled Soils by D. M. Linn and J. W. Doran>[Abstract, laboratory and tillage comparisons]{ref} Pore occupancy describes geometry; pore connectivity and biological demand also matter when interpreting gas exchange.
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