Mattias Mohr, Johan Arnqvist, Hans Bergström Uppsala University (Sweden)
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Transcript of Mattias Mohr, Johan Arnqvist, Hans Bergström Uppsala University (Sweden)
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?