4.2. Aerodynamic Exchange¶

ADELM diagnoses four aerodynamic conductances under a neutral-stability approximation: soil_aerodynamic_conductance for soil-surface exchange, leaf_boundary_layer_conductance for leaf-scale transfer, above_canopy_aerodynamic_conductance for turbulent exchange above the canopy, and canopy_aerodynamic_conductance as the series combination of the two canopy-side conductances.

1. Soil aerodynamic conductance¶

Soil aerodynamic conductance \(g_{\mathrm{a,soil}}\) (soil_aerodynamic_conductance [m s-1; Diagnostic: aerodynamic conductance for water vapour transport between the soil surface and the canopy air]) is

(4.2.1)¶\[g_{\mathrm{a,soil}} = \frac{1}{r_{\mathrm{soil}}}\]

where \(r_{\mathrm{soil}}\) is the soil aerodynamic resistance between the soil roughness length and the canopy-top exchange layer:

(4.2.2)¶\[r_{\mathrm{soil}} = \frac{h_{\mathrm{c}}}{\eta\,K_h} \left[ \exp\!\left(\eta\left(1 - \frac{z_{\mathrm{soil}}}{h_{\mathrm{c}}}\right)\right) - \exp\!\left(\eta\left(1 - \frac{z_0 + d}{h_{\mathrm{c}}}\right)\right) \right]\]

Here canopy height \(h_{\mathrm{c}}\) is canopy_height [m; PFT-based parameter: canopy height], and \(z_{\mathrm{soil}}\) is soil_roughness_length [default: 0.01 m; Fixed parameter: aerodynamic roughness length for momentum over soil].

The canopy decay coefficient \(\eta\) controls how rapidly wind speed attenuates with depth into the canopy:

(4.2.3)¶\[\eta = \sqrt{\frac{c_f\,h_{\mathrm{c}}\,\mathrm{LAI}}{l_m}}\]

where \(\mathrm{LAI}\) is lai [m2 m-2; Driver: leaf area index] and \(c_f = 0.20\). The mixing length \(l_m\) sets the length scale of turbulent eddies within the canopy:

(4.2.4)¶\[l_m = 2\,r_u^3\,L_m\]

where the momentum length scale \(L_m\) is a canopy-structure quantity:

(4.2.5)¶\[L_m = \frac{4\,h_{\mathrm{c}}}{\mathrm{LAI}}\]

The canopy-top exchange coefficient \(K_h\) scales turbulent diffusivity at the canopy top:

(4.2.6)¶\[K_h = \kappa\,u_\ast\,(h_{\mathrm{c}} - d)\]

where friction velocity \(u_\ast\) measures the turbulent momentum flux:

(4.2.7)¶\[u_\ast = r_u\,u\]

with \(u\) given by wind_ms [m s-1; Driver: wind speed at reference height (10 m)]. The zero-plane displacement height \(d\) is the effective aerodynamic centre of the canopy, following a drag-area closure:

(4.2.8)¶\[d = \left[1 - \frac{1 - \exp(-\sqrt{c_d\,\mathrm{LAI}})}{\sqrt{c_d\,\mathrm{LAI}}}\right] h_{\mathrm{c}}\]

where \(c_d = 7.5\) is the canopy drag coefficient.

The aerodynamic roughness length \(z_0\) characterises the surface texture seen by the flow above the canopy:

(4.2.9)¶\[z_0 = \left(1 - \frac{d}{h_{\mathrm{c}}}\right) \exp\!\left(-\kappa\,r_u - \phi_h\right) h_{\mathrm{c}}\]

where \(\kappa\) is von_karman_constant [default: 0.41; Constant: von Karman constant] and \(\phi_h = \ln 2\). The friction-velocity-to-canopy-wind ratio \(r_u\) links above-canopy wind shear to within-canopy drag:

(4.2.10)¶\[r_u = \sqrt{c_{\mathrm{sub}} + c_{\mathrm{rough}}\,\frac{\mathrm{LAI}}{2}}\]

where \(c_{\mathrm{sub}} = 0.003\) and \(c_{\mathrm{rough}} = 0.3\), clipped to \([0.2,\,1.0]\).

2. Leaf boundary layer conductance¶

Leaf boundary layer conductance \(g_{\mathrm{b}}\) (leaf_boundary_layer_conductance [m s-1; Diagnostic: bulk conductance for water vapour across the laminar boundary layer of canopy leaves]) uses a forced-convection Sherwood-number formulation:

(4.2.11)¶\[g_{\mathrm{b}} = D_{\mathrm{v}}\,Sh\,\frac{1}{w}\,\frac{\mathrm{LAI}}{2}\]

where \(D_{\mathrm{v}}\) is water_vapour_diffusivity [m2 s-1; Diagnostic: molecular diffusivity of water vapour in air] and \(w_{\mathrm{leaf}}\) is canopy_leaf_width [m; PFT-based parameter: characteristic leaf width].

The Sherwood number \(Sh\) relates mass transfer to the flow regime at the leaf surface:

(4.2.12)¶\[Sh = 1.019\,\sqrt{Re}\]

where \(Re\) is the leaf Reynolds number, characterising the ratio of inertial to viscous forces at the leaf scale:

(4.2.13)¶\[Re = \frac{w\,u_{0.75}}{\nu}\]

where \(\nu\) is kinematic_viscosity_of_air [m2 s-1; Diagnostic: ratio of dynamic viscosity to air density]. The representative within-canopy wind speed \(u_{0.75}\) is evaluated at the \(0.75\,h_{\mathrm{c}}\) level by attenuating the canopy-top wind speed \(u_{\mathrm{c}}\) downward through the canopy:

(4.2.14)¶\[u_{0.75} = u_{\mathrm{c}}\, \exp\!\left(\frac{r_u\,(0.75\,h_{\mathrm{c}} - h_{\mathrm{c}})}{l_m}\right)\]

where \(u_{\mathrm{c}}\) is reconstructed from the logarithmic wind profile above the canopy:

(4.2.15)¶\[u_{\mathrm{c}} = \frac{u_\ast}{\kappa} \ln\!\left(\frac{h_{\mathrm{c}} - d}{z_0}\right)\]

3. Above-canopy aerodynamic conductance¶

ADELM diagnoses an above-canopy aerodynamic resistance \(r_{\mathrm{a,above}}\) and converts it to above_canopy_aerodynamic_conductance [m s-1; Diagnostic: aerodynamic conductance for water vapour transport from the canopy top to the reference height] via

(4.2.16)¶\[g_{\mathrm{a,above}} = \frac{1}{r_{\mathrm{a,above}}}\]

Two resistance formulations are used depending on canopy height.

For tall canopies (\(h_{\mathrm{c}} > 3\,\mathrm{m}\)), the resistance combines exponential attenuation inside the canopy, a transition layer, and a logarithmic profile to a 50 m reference height:

(4.2.17)¶\[r_{\mathrm{a,above}}^{\mathrm{over}} = \frac{\ln\!\left(\dfrac{z_{\mathrm{ref}} - d}{z_0}\right)}{\kappa^2 u_{50}} \left[ \frac{h_{\mathrm{c}}}{a(Z_w - d)} \left( \exp\!\left[a\left(1 - \frac{d+z_0}{h_{\mathrm{c}}}\right)\right] - 1 \right) + \frac{Z_w - h_{\mathrm{c}}}{Z_w - d} + \ln\!\left(\frac{z_{\mathrm{ref}} - d}{Z_w - d}\right) \right]\]

where \(a = 0.5\), \(z_{\mathrm{ref}} = 50\,\mathrm{m}\), and \(Z_w = 1.5 h_{\mathrm{c}} - 0.5 d\). The code first extrapolates the 10 m wind to \(u_{50}\) using an open-field log profile with roughness length \(0.03\,\mathrm{m}\).

For short canopies (\(h_{\mathrm{c}} \le 3\,\mathrm{m}\)), ADELM uses a double-logarithm resistance:

(4.2.18)¶\[r_{\mathrm{a,above}}^{\mathrm{short}} = \frac{ \ln\!\left(\dfrac{z_{\mathrm{eff}}}{z_0}\right) \ln\!\left(\dfrac{z_{\mathrm{eff}}}{0.1 z_0}\right) }{ \kappa^2 u U_0 }\]

with \(z_{\mathrm{eff}} = 2 + (1/0.63 - 1)d\) and

(4.2.19)¶\[U_0 = \frac{ \ln\!\left(\dfrac{2 + z_0}{z_0}\right) }{ \ln\!\left(\dfrac{10 - d}{z_0}\right) }\]

The diagnosed resistance is \(r_{\mathrm{a,above}} = r_{\mathrm{a,above}}^{\mathrm{over}}\) for tall canopies and \(r_{\mathrm{a,above}} = r_{\mathrm{a,above}}^{\mathrm{short}}\) for short canopies.

4. Canopy aerodynamic conductance¶

The canopy-scale conductance used by photosynthesis is the series combination of above-canopy and leaf boundary layer resistances:

(4.2.20)¶\[g_{\mathrm{a,can}} = \left( \frac{1}{g_{\mathrm{a,above}}} + \frac{1}{g_{\mathrm{b}}} \right)^{-1}\]

This combined quantity is diagnosed as canopy_aerodynamic_conductance [m s-1; Diagnostic: effective aerodynamic conductance for water vapour transport between the canopy and the atmosphere].