Download - Assimilation of Scatterometer Winds
Assimilation of Scatterometer
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
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• 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
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p(vS |v)v
Prob
[a.u.]
NWP Scatterometer Observation
Scatterometer input Representation error
X
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• 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
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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
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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
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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.]
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Example
• Improved 5-day forecasts of tropical cyclone in ECMWF 4D-VAR
Isaksen & Stoffelen, 2000
RitaNo ERS Scatterometer With ERS
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Another example
• ASCAT has smaller rain effect
Japan Meteorological Agency
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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
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Missed wave train in
QuikScat
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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 [email protected]
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)