This document provides an overview of wind energy meteorology research topics at the Institute of Physics / ForWind, including:
1) Forecasting of wind power and offshore wind energy meteorology using numerical weather prediction and physical/statistical models.
2) Numerical modelling of atmospheric boundary layer flow and wakes in wind farms using mesoscale modelling, Large Eddy Simulation (LES), and Reynolds-averaged Navier-Stokes (RANS) models.
3) Research on offshore-specific wind conditions, turbulence, vertical wind profiles, and air-sea interactions using measurements from platforms like FINO-1.
The document outlines the basic meteorological concepts required to study these topics, such as atmospheric dynamics,
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Basics of Wind Meteorology - Dynamics of Horizontal Flow
1. WIND ENERGY METEOROLOGY
SS 2011
Detlev Heinemann
ENERGY METEOROLOGY GROUP
INSTITUTE OF PHYSICS
OLDENBURG UNIVERSITY
FORWIND – CENTER FOR WIND ENERGY RESEARCH
Montag, 18. April 2011
2. WIND ENERGY METEOROLOGY
Contents
I. Basic Meteorology
- Dynamics of Horizontal Flow
(forces, equation of motion, geostrophic wind,
frictional effects, primitive equations, general circulation)
- Atmospheric Boundary Layer
(turbulence, vertical structure, special BL effects)
II. Atmospheric Flow Modeling
- Model classes: Linear, RANS, LES, ..
- Application: Wind farm modeling
III. Offshore-Specific Conditions
IV. Resource Assessment & Wind Power Forecasting
V. Wind Measurements & Statistics
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3. WIND ENERGY METEOROLOGY
INTRODUCTION
Research related to wind energy
meteorology at the Institute of Physics /
ForWind
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4. WIND ENERGY METEOROLOGY
RESEARCH TOPICS
Forecasting of wind power
Offshore wind energy meteorology
Numerical modelling of wind flow
Turbulent characteristics of wind flow
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5. WIND ENERGY METEOROLOGY
WIND POWER FORECASTING
Numerical Weather Prediction
Wind speed, direction
Spatial Refinement
roughness, orography, thermal stability Forecasting
local
Wind farm power output
power characteristics, shading losses
Correction of systematic errors
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6. WIND ENERGY METEOROLOGY
WIND POWER FORECASTING
PHYSICAL MODELS
Input:
- wind speed forecasts at hub height
- roughness parameter / orography
- thermal stability
- wind farm geometry
- power curve
- produced power ('measurement')
for correction (model output statistics)
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7. WIND ENERGY METEOROLOGY
WIND POWER FORECASTING
STATISTICAL MODELS
Input:
- wind speed forecasts at hub height
- produced power ('measurement')
as training data (e.g., in a Neural Net)
statistically derived wind power curve includes:
- wind farm effects (wake effects)
- regional/local situation (roughness, orography, etc.)
- regular updates ensure adaptation to changes
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8. WIND ENERGY METEOROLOGY
Example: Vertical wind profile
comparison of different
theoretical vertical profiles
with IEC standard
large deviations of real
profiles
importance of
atmospheric stability over
the ocean
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9. WIND ENERGY METEOROLOGY
Example: Vertical wind profile
comparison of different
theoretical vertical profiles
with IEC standard
large deviations of real
profiles
importance of
atmospheric stability over
the ocean
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11. WIND ENERGY METEOROLOGY
Offshore Wind Energy
measurement
platform FINO-1
test field Alpha
Ventus
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12. WIND ENERGY METEOROLOGY
Numerical Modelling of Atmospheric Boundary
Layer Flow
Application: Offshore, complex terrain, thermally induced flow
Tasks: - Parametrisation of local and small-scale effects (turbulence!)
- coupling of differnet scales
e.g: meso scale models and Large Eddy Simulation (LES)
to couple the synoptic scale flow and wakes behind
wind turbines
important for: turbine design, resource assessment, forecasting
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13. WIND ENERGY METEOROLOGY
Offshore Wind Resources
Modelling the atmospheric boundary layer wind field
in offshore wind farms
extension of knowledge of the marine atmopheric boundary layer
with respect to wind energy applications
vertical structure of wind fields over the ocean
turbulence in offshore wind farms
influence of wakes in large offshore wind farms on local wind fields
modlling the influence of air sea interaction
interaction of wind and waves
reliable data for turbine design
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14. WIND ENERGY METEOROLOGY
OFFSHORE WIND RESOURCES
Meso Scale Modelling
high resolution up to 1 km
Resource assesment and forecasting
Offshore and coastal regions
complex terrain
extreme events on long time scales
time scales from hours to decades
no small-scale turbulence resolved
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15. WIND ENERGY METEOROLOGY
OFFSHORE WIND RESOURCES
mean wind speed
in m/s for the period
2004-2006.
calculated with the
mesoscale model WRF
and data from the
measurement platform
FINO-1
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16. WIND ENERGY METEOROLOGY
WAKE MODELLING IN WIND FARMS
Calculation of wind speed
deficit in single wake with
Ainslie model (Reynolds-Solver)
‣Superposition of multiple
wakes (wind farm situation)
‣Influence of turbulence
intensity on wake shape
‣Estimation of yearly power
production based on the wind
speed distribution
‣Application of Large Eddy
Simulation (LES)
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17. WIND ENERGY METEOROLOGY
TURBINE DYNAMICS
wind induced turbine
dynamics are in time scale
of sec and below
knowledge of wind
characteristics in time
scale of sec necessary
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18. WIND ENERGY METEOROLOGY
Windböe - was ist dies?
WIND GUSTS
uτ := v(t + τ ) − v(t) ur := v(x + r) − v(x)
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19. WIND ENERGY METEOROLOGY
STATISTICS OF WIND GUSTS
(Wind fluctuations)
P(uτσ−1)
τ=4s
1/hour
~106
1/100 years
Boundary-Layer Meteorology 108 (2003)
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20. WIND ENERGY METEOROLOGY
WIND TURBINE POWER CURVES:
data sheets vs. reality
Wind turbine power output is result of nonlinear dynamic processes
But:
power curve P(v) is usually taken
from simplified data sheets
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21. WIND ENERGY METEOROLOGY
WIND TURBINE POWER CURVES:
data sheets vs. reality
individual power curves according to the meteorological
situation
governing parameter:
- wind direction,
- atmospheric stability,
- turbulence intensity
aim: „learning“ power curves
integration in forecasting schemes
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22. WIND ENERGY METEOROLOGY
I BASIC METEOROLOGY
I-1 Dynamics of Horizontal Flow
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23. WIND ENERGY METEOROLOGY
Dynamics of Horizontal Flow
Newton’s second law
in each of the three directions in the If the coordinate system is accelerated,
coordinate system, the acceleration a apparent forces are introduced to
experienced by a body of mass m in compensate for this acceleration of the
response to a resultant force ΣF is given coordinate system.
by
In a rotating frame of reference two
different apparent forces are required:
‣ a centrifugal force that is experienced
by all bodies, irrespective of their
motion,
This equation describes the motion in an ‣ and a Coriolis force that depends on
inertial (i.e. nonaccelerating) frame of the relative velocity of the body in the
reference. plane perpendicular to the axis of
rotation (i.e., in the plane parallel to
the equatorial plane).
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24. WIND ENERGY METEOROLOGY
Real Forces
‣ Gravitation
‣ Pressure gradient force
‣ Frictional force
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25. WIND ENERGY METEOROLOGY
Insert: Total & local time derivatives
Atmospheric variables typically depend on both time and space:
ψ = ψ(t,x,y,z)
total time derivative d/dt
rate of change following an air parcel as it moves along its three-
dimensional trajectory through the atmosphere (Eulerian)
local derivative ∂/∂t
rate of change at a fixed point in rotating (x, y, z) space
(Lagrangian)
Related by chain rule:
advection terms
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26. WIND ENERGY METEOROLOGY
Hydrostatic Equation & Geopotential (I)
Atmopheric pressure at any height is
due to the force per unit area exerted
by the weight of the air above that
+ height.
--> atmospheric pressure decreases
with increasing height
Net upward force due to the
decrease in atmospheric pressure
with height: -δp
Wallace & Hobbs (2006)
Net downward force due to gravi-
tational force acting on the slab: gρδz
If the net upward force on the slab equals the downward force:
Atmosphere is in hydrostatic balance.
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27. WIND ENERGY METEOROLOGY
Hydrostatic Equation & Geopotential (II)
For an atmosphere in hydrostatic balance, the
balance of forces in the vertical requires that
Note: δp is negative!
or, with δz -> 0:
Balance of
gravitational force
Hydrostatic Equation and
vertical component of
pressure gradient force
Integration then yields:
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28. WIND ENERGY METEOROLOGY
Hydrostatic Equation & Geopotential (III)
The geopotential at any point in the Earth’s atmosphere is defined
as the work that must be done against the Earth’s gravitational
field to raise a mass of 1 kg from sea level to that point.
In other words, is the gravitational potential per unit mass.
units of geopotential: Jkg-1 or m2s2.
dΦ = gdz = - 1/ρ dp
The geopotential Φ(z) at height z is thus given by
with Φ(z=0) = 0 at sea level.
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29. WIND ENERGY METEOROLOGY
Hydrostatic Equation & Geopotential (IV)
Definition of the geopotential height Z:
g0 is the globally averaged acceleration due to gravity at the Earth’s
surface (9.81ms-2).
Geopotential height is often used as the vertical coordinate in
atmospheric applications in which energy plays an important role
(e.g., in large-scale atmospheric motions).
The values of z and Z are almost the same in the lower atmosphere
where g≅g0.
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30. WIND ENERGY METEOROLOGY
Pressure Gradient Force
The pressure gradient
force is directed down
the horizontal pressure
gradient ∇p from higher
toward lower pressure.
The x-component of the pressure gradient force
acting on a fluid element:
The horizontal components of the pressure gradient
force and acceleration, respectively, then are:
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31. WIND ENERGY METEOROLOGY
Frictional Force
frictional force (per unit mass):
τ represents the vertical compo- Free atmosphere (above the
nent of the shear stress (i.e., the boundary layer):
rate of vertical exchange of hori- Frictional force << pressure
zontal momentum) in units of gradient force, Coriolis force
Nm-2 due to the presence of smal- Within the boundary layer:
ler, unresolved scales of motion. Frictional force ~ other terms in
the horizontal equation of motion
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32. WIND ENERGY METEOROLOGY
Shear Stress
The shear stress σs at the Earth’s surface is in the opposing
direction to the surface wind vector Vs.
Approximation by the empirical relationship:
where
ρ density of the air
CD dimensionless drag coefficient (varying with
surface roughness and static stability
Vs surface wind vector
Vs (scalar) surface wind speed
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34. WIND ENERGY METEOROLOGY
Coriolis Force – Mathematical Description
transformation of coordinates between the inertial reference frame and
1 the reference frame rotating with the angular velocity of the earth ...
2 … and applied to the wind velocity vector v=d‘r/dt …
…and substituting (1) in (2) adds two new
3 components: the Coriolis acceleration (2nd
term) plus the centripetal acceleration (3rd
term)
4 The Coriolis force and acceleration in vector notation …
5
… and the horizontal component only.
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35. WIND ENERGY METEOROLOGY
Coriolis Force – Properties
‣ The Coriolis force is proportional the the object’s velocity, i.e., it is only
acting on moving objects.
‣ The Coriolis force acts perpendicular to the direction of a moving object.
‣ In the northern hemisphere this results in a deflection of the horizontal
wind vector to the right, in the southern hemisphere to the left.
‣ Consequently, the Coriolis force only affects the direction, not the velocity.
No work on the object is performed.
‣ The Coriolis force vanishes at the equator and is maximum at the poles.
Ω = (0, Ω cos φ , Ω sin φ) is the vector of the earth’s rotation with (|Ω| = 7.29 · 10−5 rad s−1).
f = 2 Ω sin φ ( ~10 −4 s −1 in midlatitudes) is the Coriolis parameter.
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36. WIND ENERGY METEOROLOGY
Equation of Motion (I)
Horizontal motions of fluid In component form:
elements in the atmosphere are
governed by the acting forces:
Fh = Fp,h + Fc,h + Ffr,h
The individual acceleration of fluid
elements (air parcels) thus is:
dvh/dt = ah = ap,h + ac,h + afr,h 1) Notes:
1) dvh/dt is the Lagrangian time derivative
Then the horizontal equation of
motion can be written: of the horizontal velocity component
experienced by an air parcel as it moves
about in the atmosphere.
2 ) Accelaration is due to a change in
velocity of the motion as well as due to
a change in direction of the motion.
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37. WIND ENERGY METEOROLOGY
Equation of Motion (II)
The density dependence can be eliminated by substituting
Fp = -1/ρ ∇p by Fp = - ∇Φ:
Here, the horizontal wind field is defined on surfaces of constant
pressure (∇p=0) instead of surfaces of constant geopotential (∇Φ=0).
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40. WIND ENERGY METEOROLOGY
The Geostrophic Wind: Example
Low pressure system over Great
Britain
Δp = 32 hPa
Δx = 600 km
latitude: Φ = 54°N
Coriolis parameter:
f = 2 Ω sinΦ = 1.18 10-4 s -1
vg = - 1 / (1.2 kgm -3 x 1.18 10-4 s -1) x
(32 hPa / 0.6 106 m)
= 38 ms-1
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41. WIND ENERGY METEOROLOGY
Balances of the Horizontal Wind Field
The geostrophic balance Balance of boundary layer flow
The horizontal components of the The pressure gradient force Fp,h is balanced
pressure gradient force Fp,h and the by the sum of the Coriolis force Fc,h and the
Coriolis force Fc,h are balanced. vg is the frictional force Ffr.
geostrophic wind. The stronger the frictional force Ffr, the larger
the angle between vfr and vg and the more
subgeostrophic the surface wind speed vfr.
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42. WIND ENERGY METEOROLOGY
The Primitive Equations (I)
The horizontal equation of motion is part of a complete system of
equations that governs the evolution of large-scale atmospheric
motions – the socalled primitive equations.
The other primitive equations relate to the vertical component of
the motion and to the time rates of change of the thermodynamic
variables p, ρ, and T.
Equations containing time derivatives are prognostic equations. The
remaining so-called diagnostic equations describe relationships
between the dependent variables that apply at any instant in time.
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43. WIND ENERGY METEOROLOGY
The Primitive Equations (II)
horizontal equation of motion
hydrostatic/hypsometric equation
thermodynamic energy equation
(κ=0.286, ω=dp/dt)
continuity equation
Five equations in five dependent variables: u, v, ω, Φ, and T.
The fields of diabatic heating J and friction F need to be parameterized.
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