# 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.


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