Mattias Mohr, Johan Arnqvist, Hans BergströmUppsala University (Sweden)

Simulating wind and turbulence profiles in and above a forest canopy using the MIUU mesoscale model

Project and Goals

• Project: Wind power over forests (Vindforsk III)

• Better estimation of energy yield (wind resource)

• Better estimation of turbine loads (wind shear, turbulence, forest clearings)

• Models should be developed for these purposes

MIUU mesoscale model

• Used for wind resource mapping of Sweden (e.g. www.weathertech.se)

• Higher order closure, prognostic TKE, no terrain smoothing, 1km resolution

• Very high resolution in PBL (for canopy modelling: 1, 3, 6, 10, 16, 24, 35, 52, … m)

Wind profile over forests (conceptual)

How to include this in model?

• Drag term for horizontal wind components (u, v)

LAD | horizontal | u (same for v-component)

where u = hor. wind speed, Cd = 0.2 (drag coefficient), LAD = leaf area density (Lalic and Mihailovic (2004))

How to include this in the model?

• Production/dissipation term in TKE equation

LAD | horizontal | 3 - | horizontal | q2

where q2 = turbulent kinetic energy, βp = canopy TKE-production coefficient, βd = canopy dissipation coefficient

These terms seem to make little difference.

”Elevated” Monin Obukhov theory in model

• Substitute all terms with elevation above ground through elevation above zero displacement

• Replace MO-similarity theory terms below zero displacement height with something else (what?)

• Lower boundary conditions have to be modified

Master length scale• Master length scale within forest has to be

modified

• We chose simple model of Inoue (1963):

l = 0.47 · (h – d) ≈ 2m

• Length scale constant with height within canopy

• However, this has very little influence on results

Energy balance

• Has to be solved at each model level within canopy

• Shortwave radiation follows roughly Beer’s law S↓ = S↓0 · exp(-0.5 · )

• Longwave radiation (Zhao and Qualls, 2006)

Summary

Basic equations

Include drag termF=Cd |U|U

Solve the energy balance for each forest level

Determine the radiative heating

Short wave balance

Long wave balance

Source/sink from phase changes of

water

Turbulence closure

Include equations for TKE-

produktion, dissipation

Determine master

length scale in forest

Start with idealised 1D simulations• Compare new simulated profiles with profiles from bulk

layer model version and measurements

• Use forest drag terms in horizontal momentum equations and canopy energy balance (not in TKE equation)

• Run 24 hours (diurnal cycle) and take mean value

• Parameters used: 10m/s geostr. wind, average temperature profile, z0 = 1m, h = 20m, LAI = 5, pine forest, total cloudiness = 50%

Preliminary 1D results

0 1 2 3 4 5 6 7 80

20

40

60

80

100

120

140

Wind speed (m/s)

Hei

ght a

bove

gro

und

(m)

1D Model Runs with Canopy

Bulk surface roughnessCanopy Drag TermLogarithmic wind profile

Comparison with measurements

0 1 2 3 4 5 6 7 80

20

40

60

80

100

120

140

Wind speed (m/s)

Hei

ght a

bove

gro

und

(m)

1D Model Runs with Canopy

Bulk surface roughnessCanopy Drag TermMeasurements

Comparison with turbulence measurements

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

20

40

60

80

100

120

140

TKE (m2/s2)

Heig

ht a

bove

gro

und

(m)

1D Model Runs with Canopy

Bulk surface roughnessCanopy Drag TermMeasurements

Summary & Conclusions

• Preliminary 1D results promising

• Still a lot of work to do (lower boundary conditions, canopy energy balance, length scale…)

• Vertical resolution of 1D results might be too time-consuming to run in 3D

• Is vertical resolution of 3D runs (2, 6, 12, 21, 33, 49, 72, 103, …m) enough for canopy model?