Models for canopy turbulence by Katul et al (2004).
wind_canopyTurbulenceModel(zm, Cx, hm, d0, z0, model = "k-epsilon")
wind_canopyTurbulence(
zmid,
LAD,
canopyHeight,
u,
windMeasurementHeight = 200,
model = "k-epsilon"
)A numeric vector with height values (m).
Effective drag = Cd x leaf area density.
Canopy height (m).
Zero displacement height (m).
Momentum roughness height (m).
Closure model.
A numeric vector of mid-point heights (in cm) for canopy layers.
A numeric vector of leaf area density values (m3/m2).
Canopy height (in cm).
Measured wind speed (m/s).
Height of wind speed measurement with respect to canopy height (cm).
Function wind_canopyTurbulenceModel returns a data frame of vertical profiles for variables:
z1: Height values.
U1: U/u*, where U is mean velocity and u* is friction velocity.
dU1: dUdz/u*, where dUdz is mean velocity gradient and u* is friction velocity.
epsilon1: epsilon/(u^3/h) where epsilon is the turbulent kinetic dissipation rate, u* is friction velocity and h is canopy height.
k1: k/(u*^2), where k is the turbulent kinetic energy and u* is friction velocity.
uw1: <uw>/(u*^2), where <uw> is the Reynolds stress and u* is friction velocity.
Lmix1: Mixing length.
Function wind_canopyTurbulence returns a data frame of vertical profiles for transformed variables:
zmid: Input mid-point heights (in cm) for canopy layers.
u: Wind speed (m/s).
du: Mean velocity gradient (1/s).
epsilon: Turbulent kinetic dissipation rate.
k: Turbulent kinetic energy.
uw: Reynolds stress.
Implementation in Rcpp of the K-epsilon canopy turbulence models by Katul et al (2004) originally in Matlab code (https://nicholas.duke.edu/people/faculty/katul/k_epsilon_model.htm).
Katul GG, Mahrt L, Poggi D, Sanz C (2004) One- and two-equation models for canopy turbulence. Boundary-Layer Meteorol 113:81–109. https://doi.org/10.1023/B:BOUN.0000037333.48760.e5
#Default species parameterization
data(SpParamsMED)
#Load example plot plant data
data(exampleforest)
#Canopy height (in m)
h= max(exampleforest$treeData$Height/100)
d0 = 0.67*h
z0 = 0.08*h
#Height values (cm)
z = seq(50,1000, by=50)
zm = z/100 # (in m)
# Leaf area density
lad = vprofile_leafAreaDensity(exampleforest, SpParamsMED, draw = FALSE,
z = c(0,z))
# Effective drag
Cd = 0.2
Cx = Cd*lad
# canopy turbulence model
wind_canopyTurbulenceModel(zm, Cx,h,d0,z0)
#> z1 U1 dU1 epsilon1 k1 uw1 Lmix1
#> 1 0.5 0.8550725 0.01611031 0.003070609 0.2077187 -0.003156593 1.056
#> 2 1.0 0.8623221 0.01611031 0.003843443 0.2159537 -0.003156593 1.056
#> 3 1.5 0.8738023 0.02441644 0.004755993 0.2297953 -0.004942526 1.056
#> 4 2.0 0.8850883 0.02401959 0.005692790 0.2493185 -0.005070773 1.056
#> 5 2.5 0.8961739 0.02361695 0.006639946 0.2755342 -0.005246501 1.056
#> 6 3.0 0.9070512 0.02320348 0.007547697 0.3086430 -0.005459465 1.056
#> 7 3.5 0.9349807 0.05684244 0.009551333 0.3575494 -0.014396237 1.056
#> 8 4.0 0.9965002 0.12321936 0.014064599 0.4349114 -0.034388602 1.056
#> 9 4.5 1.1024788 0.21128611 0.022773360 0.5553624 -0.066520792 1.056
#> 10 5.0 1.2634226 0.32048042 0.038565340 0.7400501 -0.116225228 1.056
#> 11 5.5 1.4877301 0.44675159 0.065766621 1.0150209 -0.189347190 1.056
#> 12 6.0 1.7796965 0.58198655 0.109530957 1.4054661 -0.289757506 1.056
#> 13 6.5 2.1380296 0.71498586 0.173799260 1.9255898 -0.416170718 1.056
#> 14 7.0 2.5557528 0.83425304 0.258167007 2.5681284 -0.560379831 1.056
#> 15 7.5 3.0008802 0.88979336 0.346410777 3.2493215 -0.672082116 1.056
#> 16 8.0 3.4676143 0.93344426 0.430499881 3.9433012 -0.776599671 1.056
#> 17 8.5 3.9520287 0.96904099 0.499662705 4.6222636 -1.038149018 1.256
#> 18 9.0 4.3415186 0.77968801 0.523301827 5.0622764 -1.013427511 1.456
#> 19 9.5 4.6691390 0.65607082 0.532374145 5.3806174 -1.000000000 1.656
#> 20 10.0 4.9525037 0.56759594 0.538793103 5.6312500 -1.000000000 1.856