Summary:

### Root Spacing Calculation

This section explains how to determine the root spacing within a soil layer, which is required to calculate the conductance along the soil-to-root pathway.

Key points:

1. The distance between roots (`dx_root,i`) is calculated based on the assumption that roots are uniformly distributed throughout the soil.

2. The root distance is calculated using the formula:
   `dx_root,i = (π * L_i)^(-1/2)`
   where `L_i` is the root length density (m/m³).

3. The root length density `L_i` is calculated as:
   `L_i = B_root,i / (ρ_root * CA_root)`
   where `B_root,i` is the root biomass density (kg/m³), `ρ_root` is the root density (kg/m³), and `CA_root` is the fine root cross-sectional area (m²).

4. The root biomass density `B_root,i` is calculated as:
   `B_root,i = (c_to_b * C_fineroot * r_i) / dz_i`
   where `c_to_b` is the conversion factor from carbon to biomass, `C_fineroot` is the fine root carbon amount (kg/m²), `r_i` is the root fraction in soil layer `i`, and `dz_i` is the thickness of soil layer `i`.

5. The fine root cross-sectional area `CA_root` is calculated as:
   `CA_root = π * r_root^2`
   where `r_root` is the root radius (m).