# Aerodynamic Resistance

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

&#x20;             $$r_a=\frac{ln[(z_w-d)/z_{om}]ln\lfloor(z_p-d)/z_{ov}\rfloor}{k^2u_z}$$                                    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:

&#x20;          $$z_{om} = h_c/8.15 =0.123*h_c$$       $$h_c \le 200cm$$        2:2.2.4

&#x20;          $$z_{om}= 0.058*(h_c)^{1.19}$$                 $$h_c>200cm$$          2:2.2.5

where mean height of the plant canopy ($$h_c$$) is reported in centimeters.&#x20;

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:

&#x20;    $$z_{ov} =0.1*z_{om}$$                                                                       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&#x20;

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.

