# 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 12 m/s 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. – Michael Walsby Feb 6 '20 at 15:26