wind energy meteorology modelling and measurements · the ”miuu-method” for modelling the wind...

KTH 14 Sep 2015

Wind Energy Meteorology

Modelling and measurements

Hans Bergström

Department of Earth Sciences, Uppsala University

email: [email protected]

Hans Bergström – Department of Earth Sciences

KTH 14 Sep 2015 Hans Bergström – Department of Earth Sciences 2

Planning for wind energy

Need for input from meteorology


Planning for wind energy

Examples of data input:

• wind resource

• wind speed distribution

• wind direction distribution

• wind shear

• turbulence


c

A

Uc

eA

U

A

cUf

1

)(

Wind speed distribution:

Commonly Weibull distribution used

U=wind speed (m/s)

f(U)=distribution (%)

A=scale parameter

c=shape parameter


1

2

1

2

)(

)(

z

z

zU

zU

Wind shear – how wind varies with height:

Commonly exponential profile used:

U=wind speed (m/s)

z1 and z2 two heights (m)

=climatologically estimated exponent (for

individual cases depending on roughness

and thermal stability)


How can a wind resource mapping be done?

We want to find out the average wind speed and

the wind distribution in order to be able to estimate

the wind energy production.

Two methods:

1) Measurements

2) Modelling


1640000 1660000 1680000 1700000 1720000 1740000 1760000

west-east (m)

Suorva

7460000

7480000

7500000

7520000

7540000

7560000

south

-nort

h (

m)

R

M

SJ

m/s

Wind measurements –

Poor geographical coverage.

Climatologically representative?

Modelling –

Good geographical coverage

but

different models may give different

results.


Major challenges:

1) Wind measurements:

How can they be made climatologically

representative? (Long-time correction)

2) Modelling:

To what extent can the model results be trusted?


Meteorological model:

a) Prognostic models (numerical or CFD (Computational Fluid Dynamic) models):

• Global circulation models – global forcast models

with a resolution of ca. 100 km.

• High resolution limited area models – local forcast

model with a resolution of ca. 10-50 km.

• Mesoscale models - higher order closure models –

good resolution of the boundary layer and a

horizontal resolution of 0.1-10 km.

• Large-eddy simulation models – resolves the larger

scales of turbulence, parameterizes the smaller

scales.

• Direct simulation models – resolves turbulence

down to scales of the order cm.

b) Analytical models, e.g. WASP.


Principles of analytical models for boundary

layer wind profile:

The boundary layer consists of two parts:

1) Surface layer (constant flux layer)

2) Transition layer (Ekman layer). Here wind

direction turns with height.

Different relations are used for these two layer.


Surface layer (Monin-Obukhov similarity theory):

Stationary and horizontally homogeneous conditions.

Based on a dimensionless wind gradient

where L is the Obukhov length:

u*=friction velocity, T=temperature, g=acc. of gravity, k=0.4, =heat

flux, z=height and z/L is a measure of stability.

)/(z

U

u

kzΦ

*m Lzf

Integration gives the wind profile:

z

z

m dzzk

uzU

0

*)(

''

3*

Twkg

TuL

''Tw

For neutral stability m=1 and we get a logarithmic wind profile:

0

* lnz

z

k

uU


Transition layer – Ekman layer:

Stationary and horizontally homogeneous conditions gives the equations

of motion:

where f is the Coriolis parameter;

(ug,vg) the geostrophic wind components;

turbulent momentum transports;

(u,v) the wind components. '' and '' wvwu

First order closure K-theory with constant Km gives:

z

vKwv

z

uKwu mm

'' ;''

With x-axis along the geostrophic wind ug=G and vg=0,

and we get:

2

2

2

2

z

vKGuf

z

uKfv

m

m

{

z

wvuuf

z

wuvvf

g

g

''0

''0{


Transition layer – Ekman layer (continued):

Boundary conditions: u=v=0 at z=0

u→G as z →∞

v →0 as z →∞

It is thus assumed that the winds become geostrophic away from the

surface. The solution will then be:

where

)sin(

)cos(1

zeGv

zeGu

z

z

{ mK

f

2

Wind increase and turns with increasing height


Principles of a meso-scale model.

Includes the following time dependent relations:

Momentum equation (Navier-Stokes eq.):

Determines the wind field.

Thermodynamic equation (energy eq.):

Determines the temperature field

Humidity equation:

Determines the humidity field (water vapour, clouds)

Turbulent kinetic energy equation:

Determines atmospheric turbulence

This system of equations must be solved numerically.


Principle of a numerical model:

Equations solved for grid points (volumes).


’Simple’ model:

• Take in a simple way care of

effects of surface roughness

and topography.

•Limitations:

• thermal stability

• complexity of

topography

• low-level jets

•Advantages:

• fast to run

• high resolution

•WASP is an example of such a

model.

’Advanced’ model:

• Physically more complete

•Directly calculates the wind in

three dimensions

•Limitations:

• takes a longer time to run

on the computer

•Advantages:

• takes care of thermal

differences

• takes care of complex

topography

• generates low-level jets

• Examples of such models are

MIUU, WRF, COAMPS


Daily variation of wind speed – influence of stability.

Shows the importance to include thermal stability!

Stable conditions nighttime (colder at surface), unstable

daytime (warmer at surface).


The MIUU-model Developed by Leif Enger and others at the Department of Meteorology, Uppsala University

Meso-scale 3 dim. model., higher-order turbulence

closure scheme, terrain influenced coordinates,

surface energy balance scheme

Prognostic equations for:

wind, temperature, humidity and turbulent kinetic

energy

Model input: horisontal air pressure gradient,

solar radiation, surface roughness, land use, elevation,

clouds, ground and water temperatures.

Initialized with: Profiles of temperature and humidity.


Some test with the MIUU-model

Heterogeneous offshore wind fields caused by

temperature differences between land and sea.

Gives:

•’Special’ internal boundary layers

• Sea-breezes

• Low-level jets – advected & others


Are the heterogeneous offshore winds

seen in observations?

Field experiment:

May 1997 field experiment in the Baltic

Sea area, including airborne measurements

with UK Met Office Hercules aircraft.


3 May 1997 forecast

Homogeneous winds

Model data at 90 m

Aircraft

measurements

at 75 m height

0 50 100 150 200 250 300 350 400

km

MIUU-model 970503, 90 m - Baltic Sea, Central part with Gotland

0

50

100

150

200

250

km

4

6

8

10

12

14

16

m/s

Heterogeneous winds


Wind measurement

Wind model

(Karin Törnblom, 2005)

(Cecilia Johansson,

2005)

Measurements and modelling - Gotland


Wind measurement

Wind model

(Karin Törnblom, 2005)


Observations show heterogeneity in the wind field

even over large offshore areas where winds might

have been expected to be more homogeneous.

The reasons may sometimes just be guessed using

observations alone.

Meso-scale model results show similar

heterogeneities.

Model results may be used to understand and

explain what is observed.


Methods to determine the wind climate using meso-

scale models:

1) Model time series

2) Model randomly chosen days during a 30 year period

3) Use the MIUU-metoden


1) Time series:

Make model simulations for an as long time period as

possible, at least 1 year.

Advantage: Gives time series which may directly be

compared with observations.

Disadvantage: Results must be long-time corrected.

Many days must be simulated – at least 1 year.


2) Randomly chosen days during 30 years:

Model simulations made for a randomly chosen number of

365 days during a 30 year peirod.

Advantage: Gives directly the wind climate.

Disadvantage: Uncertainties regarding how well the

random choice of days represent the wind climate. Many

days must be modelled – are 365 enough?


The MIUU-method:

Model simulations are made for 192 cases which should

be representative for the wind climate. The cases

represent the four seasons, 3 strengths and 16 directions

of the geostrophic wind (horizontal pressure gradient).

Each simluated case made over a daily cycle.

Model results weighted together using long-time statistics

for the pressure gradient using data from climate stations

or from NCEP/ERA40 reanalysis.

Advantage: Gives directly the wind climate. Different

periods may be used for weighting making it possible to

study temporal variations of the wind climate. The method

is computationally effective.

Disadvantage: The uncertainty lies in how well the 192

cases represent the true wind climate.


The ”MIUU-method” for modelling the wind climate

MIUU-

model 192 cases

Statistics of air

pressure gradients

Wind climate

Mean wind, wind distribution

and energy production at

different heights.

Output

• Wind

• Temperature

• Humidity

•Turbulent energy

Input

•Topography

• Landuse

• Surface roughness

• Ground temp./hum.

• Cloudiness

• Longitude/latitude

•Time of year

• Air pressure field

• Initial profiles of

temperature and

humidity

KTH 14 Sep 2015 Hans Bergström – Department of Earth Sciences 30 Hans Bergström – Institutionen för geovetenskaper 30

Weighting together results from model runs: Is done for 16 directions and 3 strengths of the geostrophic wind.

Gives the climatological average wind speed:

)()()()()()()()(16

1

14

50

14

149

13

8

94

7

1

4 jfifiWUifiWUifiWUmonthU wd

j

u

i

u

i

u

i

CLIM

Where

• Um = modelled wind for 3 geostrophic wind speeds (m=4, 9 och 14 m/s)

• Wg= weighting factor for geostrophic wind speed (g=4, 9, 14 m/s)

• fu = probability for geostrophic wind speed (1 m/s bins)

for each geostrophic wind direction.

• fwd = probability for geostrophic wind direction (16 sectors)

Climatological monthly averages (Uclim) weighted together into annual

averages.


NOTE!

No wind measurements are used.

The model physics based upon primary driving

forces for the wind enough to determine the wind

climate.


How do the model results compare with wind observations?

Comparisons made for 84 sites in Sweden.


Comparisons wih wind observations at 84 sites

Correl.coeff.: 0.975

87 % within ±0.4 m/s

48 % within ±0.2 m/s

+: Sites with small scale

topographic variations not

resolved by the model.


Sites to 2008 Sites to 2010


Data from additional 38 sites (o) with measurements

2008 to 2010 included – all together 122 sites:


Comparisons between modelled and observed

winds may be used to regionally correct model

output – provided local systematic differences are

found.


+: diff. < -0.4 m/s

+: -0.4 < diff < -0.2

+: -0.2 < diff < 0.2

+: 0.2 < diff < 0.4

+: diff > 0.4 m/s

: small scale topography

Difference in wind speed (model)–U(observation):

No systematic

regional differences

found!

2010


If observations and model results don’t agree, is it

then allways the model results which are less

accurate?

No, also measurements may be ’erroneous’.

Reasons may be:

• Model and measurements may not ’see’ the

same ’reality’ (unresolved topography).

• Measurements during shorter time are not

always representative for a longer period – the

need to be ’long-time corrected’.

• Anemometers may also give errors (bad barings,

ice problems, ’over speeding’, angular response)

or be affected by the mast they are mounted on.


Long-time correction

Wind measurements need to be long-time

corrected as the wind may vary quite a lot from

one year to another.


Sea level pressure data from

1900-2000

Gives geographical variations of

the geostrophic wind

Bodö

Haparanda

Härnösand

Helsingfors

Visby

Lund

Nordby

Oksöy

Bergen

Stockholm

Göteborg

Denmark

Southern

Sweden



Denmark


Results using geostrophic winds:



The normal wind variability according to 18 years wind observations

at Näsudden, Gotland:

Average and standard deviation of the average as function of length

of measuring period.

±0.5 m/s after

measurements during 1 year


To long-time correct observations taken during a shorter time some

kind of long-time reference is needed.

This may be:

• Wind measurements from a nearby representative site.

• Winds from re-analysis data.

• Air pressure gradients (geostrophic winds) from re-analysis data.


Re-analysis data: Gridded global data dynamically interpolated

using some global weather model. Based on available but

geographically inhomogeneous observations. Gives information on

e.g. air pressure, wind, temperature, humidity …

NCEP/NCAR (US), ERA40/ERA Interim (ECMWF).


Long-time correction Wind measurements and also modelled winds may be inhomogeneous

in time, while the dynamically more basic air pressure field probably is

more homogeneous in time.

As the most important driving force for the wind is the horizontal air

pressure gradient, the geostrophic wind may be most suitable for long-

time corrections.

Measured wind against geostrophic wind:

Obervations every 6 hour: Monthly average:



The wind variability after long-time correction according to 18 years of

wind observatons at Näsudden, Gotland:

Long-time corrected average and standard deviation of the average

as function of length of measuring period.

±0.2 m/s after

measurements during 1 year


The uncertainty of the measurements may be reduced by 50 %

by the long-time correction:

Uncertainty with 95 % confidence using 1 year measurements

reduced:

from ±1.0 m/s using measurements directly

to ±0.4 m/s after long-time correction

Thus still a significant uncertainty!



Long time corrections following 3 sources:

1) Geostrophic wind (NCEP)

2) Danish wind index

3) Swedish wind index

Considerable differences!


How are long-time corrections (and modelled

climate) affected by the choice of period for which

the geostrophic statistics are taken from?

Period Number

of years

Resulting average

wind (m/s)

1991-2000 10 8,4

1981-1990 10 8,9

1981-2000 20 8,6

1971-2000 30 8,6

1961-1990 30 8,8

1900-2000 101 8,8

Denmark


Important to consider resolution using model results!

Comparing modelled annual average wind speed estimated

using:

5 km resolution 1 km resolution


How can the model resolution be increased to

more accurately catch terrain influences?

1) Use a numerical model to increase resolution.

Two models tested:

a) MIUU-model

b) COAMPS-model from US Navy

Similar model but non-hydrostatic

2) Use a more simple model to increase resolution. WASP-model may be used with e.g. results from the

MIUU-model 1 km2 wind mapping.

WASP used to estimate the wind climate with higher

resolution.


Tests for Fjällberget-Saxberget (Ludvika) • The wind climate estimated using the two numerical

models and the MIUU-method.

• Resolution: 1000 m, 300 m, 100 m.

No local wind observations used.

• For comparison a wind mapping was made using the

WASP-model with 100 m resolution.


1446000 1447000 1448000 1449000 1450000 1451000 1452000 1453000 1454000 1455000 1456000

Fjällberget - Saxberget

6661000

6662000

6663000

6664000

6665000

6666000

6667000

6668000

6669000

6670000

6671000

150

165

180

195

210

225

240

255

270

285

300

315

330

345

360

375

390

405

420

435

450

465

480

495

möh

Fjällberget – Saxberget, topography Height differences of the order 300 m over a horizontal distance

of 3-5 km


Result: 1 km grid

MIUU, 7.0-7.3 m/s COAMPS, 6.6-7.0 m/s


Result: 300 m grid

MIUU, 7.0-7.4 m/s COAMPS, 6.6-7.4 m/s


Result: 100 m grid

MIUU, 7.0-7.6 m/s COAMPS, 6.6-7.8 m/s


Comparison of modelled and observed wind profiles:

Good agreement with observations for both models using 100 m

resolution.

The MIUU-model best for low resolution.

A tendency that COAMPS with high resolution gives too high

winds.


Comparison between the MIUU-model and WASP

run using wind data from Fjällberget

MIUU, 7.0-7.6 m/s WASP, 6.4-7.6 m/s

but higher wind

in low level terrain


Conclusions from down-scaling tests:

•Both numerical models can be used for down-scaling of the

wind climate to 100 m resolution.

•Two differences can be noted:

•1) With low resolution the MIUU-model gives higher winds

•2) With high resolution the COAMPS®-model gives higher

local maxima above mountain tops.

•WASP gives generally smaller differences between higher and

lower elevation terrain. Inportant to be aware of choosing input

data.

KTH 14 Sep 2015 Hans Bergström – Institutionen för geovetenskaper 59

TO CONCLUDE

Numerical models and

measurements complement

each other.

Give together the most reliable

estimate of the wind climate.

wind energy meteorology modelling and measurements · the ”miuu-method” for modelling the wind...

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