### 2.11.1.2. Root Spacing[¶](#root-spacing "Permalink to this headline")

To determine the conductance along the soil to root pathway (section [2.11.2.1.3](#soil-to-root)) an estimate of the spacing between the roots within a soil layer is required. The distance between roots \\(dx\_{root,i}\\) (m) is calculated by assuming that roots are distributed uniformly throughout the soil ([Gardner 1960](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#gardner1960))

(2.11.2)[¶](#equation-11-12 "Permalink to this equation")\\\[dx\_{root,i} = \\left(\\pi \\cdot L\_i\\right)^{- \\frac{1}{2}}\\\]

where \\(L\_{i}\\) is the root length density (m m \-3)

(2.11.3)[¶](#equation-11-13 "Permalink to this equation")\\\[L\_{i} = \\frac{B\_{root,i}}{\\rho\_{root} {CA}\_{root}} \\ ,\\\]

\\(B\_{root,i}\\) is the root biomass density (kg m \-3)

(2.11.4)[¶](#equation-11-14 "Permalink to this equation")\\\[B\_{root,i} = \\frac{c\\\_to\\\_b \\cdot C\_{fineroot} \\cdot r\_{i}}{dz\_{i}}\\\]

where \\(c\\\_to\\\_b = 2\\) (kg biomass kg carbon \-1) and \\(C\_{fineroot}\\) is the amount of fine root carbon (kg m \-2).

\\(\\rho\_{root}\\) is the root density (kg m \-3), and \\({CA}\_{root}\\) is the fine root cross sectional area (m 2)

(2.11.5)[¶](#equation-11-15 "Permalink to this equation")\\\[CA\_{root} = \\pi r\_{root}^{2}\\\]

where \\(r\_{root}\\) is the root radius (m).

