2:2.2.1.2 Aerodynamic Resistance

The aerodynamic resistance to sensible heat and vapor transfer, $r_a$, is calculated:

$r_a=\frac{ln[(z_w-d)/z_{om}]ln\lfloor(z_p-d)/z_{ov}\rfloor}{k^2u_z}$ 2:2.2.3

where $z_w$ is the height of the wind speed measurement (cm), $z_p$ is the height of the humidity (psychrometer) and temperature measurements (cm), $d$ is the zero plane displacement of the wind profile (cm), $z_{om}$ is the roughness length for momentum transfer (cm), $z_{ov}$ is the roughness length for vapor transfer (cm), $k$ is the von Kármán constant, and $u_z$ is the wind speed at height $z_w$ (m s$^{-1}$).

The von Kármán constant is considered to be a universal constant in turbulent flow. Its value has been calculated to be near 0.4 with a range of 0.36 to 0.43 (Jensen et al., 1990). A value of 0.41 is used by SWAT+ for the von Kármán constant.

Brutsaert (1975) determined that the surface roughness parameter, $z_o$, is related to the mean height ($h_c$) of the plant canopy by the relationship $h_c/z_o$ = $3e$ or 8.15 where e is the natural log base. Based on this relationship, the roughness length for momentum transfer is estimated as:

$z_{om} = h_c/8.15 =0.123*h_c$ when $h_c \le 200cm$ 2:2.2.4

$z_{om}= 0.058*(h_c)^{1.19}$ when $h_c>200cm$ 2:2.2.5

where mean height of the plant canopy ($h_c$) is reported in centimeters.

The roughness length for momentum transfer includes the effects of bluff-body forces. These forces have no impact on heat and vapor transfer, and the roughness length for vapor transfer is only a fraction of that for momentum transfer. To estimate the roughness length for vapor transfer, Stricker and Brutsaert (1978) recommended using:

$z_{ov} =0.1*z_{om}$ 2:2.2.6

The displacement height for a plant can be estimated using the following relationship (Monteith, 1981; Plate, 1971):

$d=2/3*h_c$ 2:2.2.7

The height of the wind speed measurement, $z_w$, and the height of the humidity (psychrometer) and temperature measurements, $z_p$, are always assumed to be 170 cm.