# Predict wind speed in a forest based on speed over and under canopy?

I am trying to understand the calculation of the wind speeds at forest edge. I am pretty new in wind simulation and profiles in general, so I am sorry if asking simple questions.

I have found that it is possible to calculate the wind speed as log wind profile based on friction velocity, roughness length ($${z0}$$), zero place displacement ($${d}$$), and von Karman's constant ($${k}$$). As I am working at forest edge, my estimates are:

z0 =  0.06          # m, roughness length, 1/10 of the surface roughness, forest:0.5-1m
d =   h/3*2         # m, zero place displacement, height (m) above the ground with 0 wind speed (2/3 or 3/4 of average height of obstacles)
k =   0.41      # no unit, von Karman constant


Formula:

# predict speeds for individual segments of the tree
u_z = frict_velocity/k*log((z-d)/z0)


However, it seems that friction velocity is not a constant, and needs to be calculated based on the wind speed measured at two heights. Well, I don't have two heights. The highest estimation I can get is that wind speed above canopy is $${12ms^{-1}}$$ and at the height $${d}$$ is 0, as estimated above. The formula is specified as shear velocity:

u_canopy = 12  # speed on canopy top
u_d = 0        # speed on height d, which is 0
z_canopy = 25  # height of the canopy, equals tree height
z_d = d        # height of the wind speed 0, equals to d

frict_velocity = k*(u_canopy - u_d)/log((z_canopy - d)/(z_d - d))


Well, this approach obviously predict just values higher than $${d}$$, even if all tree segments should have 0 value instead. Is my prediction of the wind speed on every segment $${z}$$ right? Or, is there a way how to simply use the "friction velocity" constant, as I don't have wind speed estimation at two vertical heights?

My goal is to predict wind speed on every segment ($${z}$$) and convert it to wind force to uproot the tree. The models should be included within a simulation study, so instead of specific single tree condition I am hoping to get some more general relationships.

• PS I think you might get a different result for coniferous forest compared to rain forest, because the trees are a different shape. The rainforest in Sarawak, Brunei and Malaya reaches a height of 260 feet in places. We found there was hardly any wind on the forest floor and it was all up in the canopy. Feb 6 '20 at 15:26