Compute the aerodynamic conductance for sensible and latent heat above the canopy following Van de Griend and Van Boxel (1989).
G_bulk( Wind, ZHT, Z_top, Z0 = Z_top * 0.1, ZPD = Z_top * 0.75, alpha = 1.5, ZW = ZPD + alpha * (Z_top - ZPD), LAI, extwind = 0, vonkarman = Constants()$vonkarman )
| Wind | Average daily wind speed above canopy (m s-1) |
|---|---|
| ZHT | Wind measurement height (m) |
| Z_top | Average canopy height of the taller crop (m) |
| Z0 | Roughness length (m). Default: |
| ZPD | Zero-plane displacement (m), Default: |
| alpha | Constant for diffusivity at top canopy. Default: |
| ZW | Top height of the roughness sublayer (m). Default: |
| LAI | Leaf area index of the upper layer (m2 leaf m-2 soil) |
| extwind | Extinction coefficient. Default: |
| vonkarman | Von Karman constant, default to |
The bulk aerodynamic conductance (m s-1)
alpha can also be computed as:
$$alpha=\frac{zw-d}{Z_{top}-d}$$
The bulk aerodynamic conductance \(ga_{bulk}\) is computed as follow:
$$ga_{bulk}=\frac{1}{r1+r2+r3}$$
where r1, r2 and r3 are the aerodynamic resistances of the inertial
sublayer, the roughness sublayer and the top layer of the canopy respectively. Because
wind speed measurements are more often made directly in the roughness sublayer, the
resistance in the inertial sublayer r1 is set to 0 though. r2 and
r3 are computed using the equation 43 of Van de Griend and Van Boxel (refer to
the pdf of the web version
of the help file for Latex rendering) :
$$r2=\int_{zh}^{zw}\frac{1}{K''}$$
with $$K''= kU_*(z_w-d)$$
And:
$$r3=\int_{(z2+z1)/2}^{zh}\frac{1}{K'''}\mathrm{d}z$$
with $$K'''= U_z\frac{K_h}{U_h}$$
Integration of r2 and r3 equations give:
$$\frac{(\ln(ZPD-ZW)^2-\ln(ZPD-Z2)^2)}{(2kU_*)}$$
simplified in:
$$r2= \frac{1}{kU_*}\ln(\frac{ZPD-ZW}{ZPD-Z2})$$
and finaly: $$r3= \frac{Uh}{Kh}\ln(\frac{Uh}{U_{interlayer}})$$
Van de Griend, A.A. and J.H. Van Boxel, Water and surface energy balance model with a multilayer canopy representation for remote sensing purposes. Water Resources Research, 1989. 25(5): p. 949-971.
G_interlay() and GetWind(), which is used internaly.
# The bulk aerodynamic conductance for a coffee plantation managed in agroforestry system: G_bulk(Wind=3,ZHT=25,Z_top=24,LAI = 0.5,extwind = 0.58)#> [1] 1.046699