assimilation of scatterometer winds

Assimilation of Scatterometer

WindsAd.Stoffelen@KNMI.nl

Manager NWP SAF at KNMI

Manager OSI SAF at KNMI

PI European OSCAT Cal/Val project

Leader KNMI Satellite Winds Group

www.knmi.nl/scatterometer

2. Level 2 Wind Processing2. Level 2 Wind Processing

Observations Inversion Ambiguity Removal

Wind Field

INPUT OUTPUT

Observations Inversion Ambiguity Removal

Quality ControlQuality Control

Wind Field

INPUT OUTPUT

Quality

Monitor

),,,(m pfo

Geophysical Model FunctionGeophysical Model Function

A geophysical model function (GMF) relates ocean surface A geophysical model function (GMF) relates ocean surface wind speed and direction to the backscatter cross section wind speed and direction to the backscatter cross section measurements. measurements.

),,,(model pfo

: wind speed ø: wind direction w.r.t. beam view: incidence anglep: polarizationλ: microwave wavelength

InversionInversion• Bayesian approach: Bayesian approach:

– Find closest point on 3D or Find closest point on 3D or 4D manifold4D manifold

• The statistical error in finding this point is small The statistical error in finding this point is small and equivalent to a vector error of 0.5 m/s in windand equivalent to a vector error of 0.5 m/s in wind

• pp((zzM M ||zzS S ) ) exp{ - exp{ - ½½((zzM M - - zzSS))22/n/noise(oise(zz)) }}• pp((zzS S ) = ) = constant; constant; pp((oo

S S ) ) ≠≠ constantconstant

)()()( os

os

om

om

os PPP σσσσσ

Stoffelen and Portabella, 2006

625.0 ),()()( o

ssmms PPP σzzzzzz

Ambiguity removalAmbiguity removal

Scatterometer inversion produces Scatterometer inversion produces a set of wind (direction) solutions a set of wind (direction) solutions or ambiguitiesor ambiguities

Ambiguity removal is performed Ambiguity removal is performed with spatial filterswith spatial filters

N

i si

simi

zkp

zz

NMLE

1

21

som

oss

om dPPP vzzvvzv

sv

)()()|(

)()()( vvvvv PPP ss

Azimuthal diversityAzimuthal diversityM

LE

Wind direction ()

Local minima

Solution bands

0

180

MSS

Accounting for local Accounting for local minima, erratic winds minima, erratic winds are producedare produced

MSS accounts for lack MSS accounts for lack of azimuthal diversityof azimuthal diversity– A relative weight A relative weight

(probability) is derived (probability) is derived for every solutionfor every solution

– Suitable with a Suitable with a variational filtervariational filter

Meteorological balance Meteorological balance (2D-VAR)(2D-VAR)

Spatial filter:Spatial filter: Mass conservationMass conservation Continuity equationContinuity equation

00UU = = 00

Vertical motion < horizontal Vertical motion < horizontal motionmotion

Parameters:Parameters: Background error (variance)Background error (variance) Correlation lengthCorrelation length Rotation vs divergenceRotation vs divergence

Cost function:Cost function: )()(])[(])[()( 11bboo xxBxxxyRxyx TT HHJ

)()()( vvvvv PPP ss

Local minima MSS

NWP model

Local minima MSS

NOAA NOAA MSS @ MSS @ 25 km25 km

Improved coldfront

BetterAroundrain

50 kmPlots !

Remarks

• Scatterometer wind retrieval skill depends on viewing geometry

• Measurement error characterization is essential, notably for QC and AR

• Effective QC is very important for DA– Rain screening is especially relevant for Ku-band

• Variational AR accounts for full wind PDF

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Data assimilation

BO JJJ

2/exp|

2,1 2

2),(

BJBp

j B

jBujuBJ

vv

• The analysis minimizes the costfunction J by varying the controlvariables representing theatmospheric state, e.g., uj , the wind components of wind vector vj,

• At every observation point prior knowledge is available on the observed state from a sort-range forecast, called NWP background

• JB is a penalty term penalizing differences of, e.g., uj with the NWP background (subscript B)

• B denotes the expected background wind component error• JB differences should be spatially balanced according to our

knowledge of the NWP model errros• So, JB determines the spatial consistency of the analysis

(i.e., a low pass filter) Lorenc, Q.J.R.Meteorol.Soc., 1988

Wind error

model

13

• Error distributions: p(vSCAT |vB) = p(vSCAT |vTrue) p(vTrue |vB) • Combined NWP background and scatterometer error distribution

looks like a normal distribution in wind components with rather constant width as a function of wind speed

• In speed it is a skew distribution• In direction the width of the distribution depends on speed and

the distribution is periodic Wind component error model clearly simplest

Stoffelen, Q.J.R.Meteorol.Soc., 1998

p([u,v]SCAT |vB)

p([V,]SCAT |vB)

5%

Measurement Noise

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• noise is uniform in

measurement space (~5 % or 0.5 m/s VRMS)

Wind retrieval provides very accurate

S given

O , so

well-defined p(vS |

O)

NWP SAF Workshop | 14 April 201115

Observation error• The analysis control variables follow the NWP model spectrum (model balance)• Measured scales not represented by the NWP model state are attributed as observation representation error• The scatterometer wind vector representation error is about 1.5 m/s• In triple collocation scatterometer wind errors on NWP scale are estimated at about 1 m/s vector RMS

Vogelzang et al., 2011

v

16

p(vS |v)v

Prob

[a.u.]

NWP Scatterometer Observation

Scatterometer input Representation error

X

17

• Rotating beam (SeaWinds, OSCAT: mid swath)

• Fixed antennas (ASCAT: inner swath)

Broad MLE minima and closeby multiple ambiguous solutions are complicating scatterometer wind assimilation

true

Scatterometer Data AssimilationPosteriori Wind Probability given a set of measurements

Wind domain uncertainty u, v ~ 1.5 m/s

Measurement space noiseD ~ 5% (0.2 m/s)

0S = GMF(vS, .. ) Geophysical solution manifold

• ERS/ASCAT: Manifold in 3D measurement space• SeaWinds/NSCAT: Manifold in 4D measurement space

Stoffelen&Portabella, 2006

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Scatterometer data assimilation

• JO is a penalty term penalizingdifferences of the analysis control variables with the observations

• Choices:• Direct assimilation of 0

O Complex error PDFs

• Assimilate p(vS | 0O), like

in MSS and 2DVAR• Needs p information

• Assimilate ambiguitiesReduces wind solution space to max 4 points

• Assimilate selected solution

Reduces wind solution space to one point

Stoffelen & Anderson, Q.J.R.Meteorol.Soc., 1997

p(vS | 0O)

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Direct assimilation of 0O

Main uncertainty is in the wind domain

y: 0

x: wind

Stoffelen, PhD thesis,1998

• noise is narrow

leading to accurate wind retrieval

• Observation and background wind noise are relatively large leading to complex and skew error PDFs in measurement space

• Not compatible with BLUE, higher order statistics needed

Wind assimilation appears simplest

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p(vS |v) Ambiguities

v|ln2 0OpJ SCAT

o

ProbProb

v

Assimilate ambiguities

Reduces wind solution space to max 4 points (delta functions); solution wind PDF information is lost

22

Assimilate ambiguities

Scatterometer wind cost

ambiguous wind vectorsolutions ui ,vi

provided by wind retrieval procedure and complemented by estimated observation wind error, u = v

Stoffelen and Anderson, 1998

Derive probability Pi from MLE info

23

v|ln2 0OpJ SCAT

o

ProbProb

v

٧ Retains essential wind solution PDF information along the valley of solutions that generally exists

٧ Provides very good approximation to p(v | 0O)

Assimilate solution “valley”

p(vS |v) MSS

Portabella and Stoffelen, 2004

v

24

Prob

[a.u.]

NWP Scatterometer Observation from MSS

Scatterometer input Representation error

X

Portabella and Stoffelen, 2004

٧ Provides very good approximation to p(v | 0

O)

Assimilation of ambiguous winds

• Potentially provides multiple minima in3D/4D-Var

• Problem is very limitedfor ASCAT

• 2DVAR tests show <1% of wrong selection

• May be linearized byselecting one solutionat a time (inner loop)

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vtrue = (0,3.5) ms-1 v2 = -v1

u/v,O = 2 ms-1 p2 = p1 = .5u/v,B = 2 ms-1

<vA> = (0,3.25) ms-1

Monte Carlo simulation, Stoffelen & Anderson, 1997

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Assimilation of unambiguous winds• AR by 2DVAR well tested and independent of B• Broad B structure functions provide best AR skill

• Assimilation of scatterometer wind product is straightforward• Few spatially correlated outliers due to AR errors, but mainly in dynamic weather

NWP backgroundScatterometer wind Analysis

Prob

[a.u.]

27

Example

• Improved 5-day forecasts of tropical cyclone in ECMWF 4D-VAR

Isaksen & Stoffelen, 2000

RitaNo ERS Scatterometer With ERS

28

Another example

• ASCAT has smaller rain effect

Japan Meteorological Agency

29

Gebruik van scatterometersAssimilation ASCAT winds ECMWF from 12/6/’07Beneficial for U10 analysisOperational okt/nov 2007 (added to QuikScat&ERS)

Hans Hersbach & Saleh Abdalla, ECMWF

ECMWF analysis vs ENVISAT altimeter wind

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Underpredicted surge Delfzijl

31/10/’6 18Z 1/11/’06 4Z

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NWP Impact @ 100 km

Storm near

HIRLAM misses wave;SeaWinds should bebeneficial!

29 10 2002

32ERS-2 scatterometer wave train; missed by HiRLAM

NWP models miss wave;Next day forecast bust

33

Missed wave train in

QuikScat

34

Conclusions• ASCAT on board MetOp provides accurate daily global

ocean surface winds at high spatial resolution• NWP models lack such high resolution• MetOp-B due for launch in 2012 probably providing a

tandem ASCAT

Further information:

www.nwpsaf.org scat@knmi.nl

www.osi-saf.org

www.knmi.nl/scatterometer

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Geographical statistics for QuikSCAT, July 2009

Geographical statistics for ASCAT, July 2009

Rain flag removes stronger winds for QuikSCATThere are some regional differences

WISE 2004, Reading

Lack of cross-isobar flow in NWPQuikSCAT vs model wind dirStratify w.r.t. Northerly, Southerly wind direction.(Dec 2000 – Feb 2001)

•Large effect warm advection

•Small effect cold advection

•Similar results for NCEP

Hans Hersbach, ECMWF (2005)