Meteorological Training Course, 20 March 2009 1/25 Using Combined Prediction Systems (CPS) for wind energy applications European Centre for Medium-Range

Meteorological Training Course, 20 March 2009 1/25

Using

Combined Prediction Systems (CPS)

for wind energy applications

European Centre for Medium-Range Weather Forecasts (ECMWF) Michael Denhard, Renate Hagedorn


Safe Wind

“Multi-scale data assimilation, advanced wind modelling and

forecastingwith emphasis to extreme weather

situations for a safe large-scale windpower integration.”

EU-FP7 project


September 2008

August 2012

Safe Wind


TIGGE (10 global EPS)

Thorpex Interactive Grand Global Ensemble

TIGGE-LAM: archive at ECMWF (-24 hours)

COSMO LEPS

Limited area medium range

ensemble

(2-5 days)GLAMEPS LAMEPS (Hungary) ALADIN-LAEF (Austria)NORLAMEPS (Norway)

AEMET SREPSSpain

MOGREPS - NAEUK

COSMO SREPSItaly

SRNWP-PEPS“Poor mans” ensemble

Eumetnet, Germany

PEACEFrance

Limited area short range ensembles (1-3 days)

Numerical forecast systems in Europe

global high resolution

models


SafeWind WP5: Summary

• 6 Tasks, 11 Deliverables, 5 (direct) Partners

ForWind(OL), ARMINES, ECMWF, ENERGINET

ECMWF, ForWind(OL)

ForWind(OL), ECMWF, Meteo France

ForWind(OL), ECMWF

ECMWF, ForWind(OL), MeteoFrance

ECMWF, ForWind(OL)

Partners

CPS applied to wind power forecasts5.6

Combined meteorological Prediction Systems5.5

Weather regime dep. Extreme Forecast Index5.4

Use of Local Area Model EPS5.3

Evaluation of novel ensemble techniques5.2

Probabilistic verification tool (wind gust verif.)5.1

DescriptionTask


Combination of:

ECMWF Ensemble Perturbations (50 )

ECMWF EPS control (1)

ECMWF high resolution model forecast (1)

Combined Prediction System


ECMWF high resolution deterministic system

Sea Level Pressure und 10 m Winds 00 UTC, 12 December 2005

Anlysis and forecasts (a) T799L91 and (b) T511L60ECMWFglobal high

resolution deterministi

c model


RMSE Wind Power% installed capacity (~60MWatt)

RMSE Wind speedmodel level 88 (116m)

5 best members

OpFC: deterministic high resolution model of ECMWF

Single point forecasts at the FINO1-site (100m)mean RMSE (Dec 2007 - July 2008)

EPS mean EPS control


12.-14. June 2008



Brier-Score based combination

Mark Rodwell et. al.


The forecast of a combined prediction system is:

11

K

kkw

K

kkk fwf

1

kf

In principal there are two ways of determining the weights:

calculate the forecast skill of each component of the CPS separately and determine the weights according to the differences of the score values of the subsystems

optimize an overall score value of the CPS forecasts by changing the weights of its components


with

is the forecasted probability of system k : • a single deterministic forecast,

• a group of forecasts with predefined equal skill

• or any other probabilistic forecast

kjkf


i

ii of

X

Ni ,...,1

If the observable

is binned in categories

is 2, no matter what the distance between the outcomes is !

ilio

jl

and kjkf


Combining deterministic and probabilistic forecast systems


S

sststt of

SBS

1

2)(1

Ss ,...,1

:

forecast observation pairs of the sample.

t Xto exceed threshold of observable tf

to

forecasted probability

observed probability

Brier Score


S

s

N

t

t

isisi

N

tt of

NSBS

NRPS

1

1

1

2

1

1

1 1

11

1

1

Summing over all Brier Scores of possible event thresholds leads to:

The RPS measures the difference between the cumulative density function of the forecast and the observation.

This enables the RPS to measure the overall difference between all kinds of probability distributions, including deterministic delta functions.

Ranked Probability Score (RPS)


Ranked Probability Score

category

f(y)

category

F(y)1

PD

F

CD

F


Weighting of ensemble components

One may distinguish between three different ways of estimating the weights:

single skill, by measuring the forecast skill of each component separately and setting the weights according to the differences between the individual scores.

multiple skill, by using analytical or regression methods to jointly determine the weights.

iterative, by starting from a first guess for the weights and minimizing a penalty function or a score until convergence is reached.


2k

K

kk

kkw

1

2

2

/1

/1

Total Error Variance

of the individual model forecasts k can be used to estimate the weights

This only holds, if the errors of the models are linearily independent, which indeed is not the case for numerical weather forecasts.


j

kjkjjk Kkee ,...,1,min 222

-4

-3

-2

-1

0

1

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Eigenvektor

Eig

en

ve

kto

rko

mp

on

en

te

1 2 3 4 5 6 7 8 9 10 11 12 13 14Model

Explained variance of 1st EOF: 80,5%

Eig

enve

cto

r c

om

po

nen

t

Eigenvector

-4

-3

-2

-1

0

1

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Eigenvektor

Eig

en

ve

kto

rko

mp

on

en

te

1 2 3 4 5 6 7 8 9 10 11 12 13 14Model

Explained variance of 1st EOF: 80,5%

Eig

enve

cto

r c

om

po

nen

t

Eigenvector

EOF-filter


0

20

40

60

80

100

en

se

mb

le s

ize

total MLR coefficients >0

Number of predictors (ensemble size of the CPS) in a reduced MLR-model with positive coefficients

Linear Regression of single members

COMO-DE-LAF ensemble

(COMSO-DE) with 4

delayed members SRNWP-PEPS (PEPS)

with 17 members COSMO-LEPS (LEPS)

with 16 members. PEPS/COSMO-DE CPS: (+) add lagged LEPS systems


0

5

10

15

20

25

2 3 6 8 9 10 11 12 13 15 1 2 3 4 2 7 9 13 2 4 6 10 13 1 4 7 10 2 4 1 5 11 15

model-number in subsystem

wei

gh

t (r

edu

ced

ML

R w

ith

w>

0)

PEPS/COSMO-DE (+) LEPS -1 (+) LEPS -2 (+) LEPS -3 (+) LEPS -4 (+) LEPS -5

SRNWP-PEPS COSMO-DELAF

LEPS -1 LEPS -5LEPS -2 LEPS -3 LEPS -4




4

4.5

5

5.5

6

6.5

COSMO-D

E

LEPS (-

1)PEPS

PEPS/COSM

O-DE

(+) L

EPS -1

(+) L

EPS -2

(+) L

EPS -3

(+) L

EPS -4

(+) L

EPS -5

RM

SE

MLR w>0 (T) MLR w>0 (V) MLR (T) MLR (V)

12h accumulated precipitation (6UTC to 18UTC) summer 2007

• training (70%,T)• validation (30%,V)

The full regression model (MLR) is compared with a reduced model (MLR w>0) with positive coefficients


Methods for estimating Weights of CPS members

Error Variance problem: covariances of forecast errors

EOF-Filter reduce covariances of forecasts errors

Best Member statistic

Multiple Linear Regression (MLR)iterate until all coefficients are positive

Brier Score/ Ranked Probability Score (under investigation!)

analytical solution

Combined System

[ ]


0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7 8 9 10

lead time [days]

wei

gh

t [%

].

hres - ErrorV ctrl - ErrorVhres - EOF ctrl - EOFhres - BestMember ctrl - BestMemberhres - MLR ctrl - MLR

Combined System

10 m Windspeed, 01.07.2008

Training period: 30 days

Forecast validation:10 days

Mean for Europe

ECMWFhres: deterministic run

ECMWF-EPSctrl: control runpert: 50 perturbations

pert ~ 2% per member


Combined System

Ranked Probability Skill Score (RPSS) relative to raw EPS

0

2

4

6

8

10

12

0 1 2 3 4 5 6 7 8 9 10

lead time [days]

RP

SS

[%

].

ErrorV EOF BestMember MLR

10 m Windspeed, 01.07.2008


Summary

Started Safe Wind Project

First Results for Combined Systems

Does sorting out members really generate better probabilistic forecasts ?

Documents

Meteorological Training Course, 20 March 2009 1/25 Using Combined Prediction Systems (CPS) for wind energy applications European Centre for Medium-Range