Transcript Powerpoint

Assimilation of
Scatterometer
Winds
[email protected]
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 Processing
INPUT
Observations
OUTPUT
Ambiguity
Removal
Inversion
Wind
Field
 om  f ( ,  , , p  )
Quality
Control
Quality
Monitor
Geophysical Model Function
A geophysical model function (GMF) relates ocean surface
wind speed and direction to the backscatter cross section
measurements.

model
o
 f ( ,  , , p  )
: wind speed
ø: wind direction w.r.t. beam view
: incidence angle
p: polarization
λ: microwave wavelength
Inversion
• Bayesian approach:
P(σ os σ om )  P(σ om σ os )  P(σ os )
P(z s z m )  P(z m z s )  P(z s ),
z  σ o 
0.625
– Find closest point on 3D or
4D manifold
• The statistical error in finding this point is small and
equivalent to a vector error of 0.5 m/s in wind
• p(zM |zS )  exp{ - ½(zM - zS)2/noise(z) }
• p(zS ) = constant; p( oS ) ≠ constant
Stoffelen and Portabella, 2006
Ambiguity removal


 
1 N zmi  z si
MLE  
N i 1 kp z si
2
P( v | z om )   P( v v s )  P(z os z om )dv s
vs
 Scatterometer inversion produces
a set of wind (direction) solutions
or ambiguities
P( v v s )  P( v s v)  P( v)
 Ambiguity removal is performed
with spatial filters
Azimuthal diversity


 Accounting for local
minima, erratic winds
are produced
 MSS accounts for lack
of azimuthal diversity
0
– A relative weight
(probability) is derived
for every solution
– Suitable with a
variational filter
180
Local minima
MSS
Solution bands
Wind direction ()
Meteorological balance (2D-VAR)
P( v v s )  P( v s v)  P( v)
Cost function: J (x)  (y o  H [x])T R 1 (y o  H [x])  (x  xb )T B 1 (x  xb )
Spatial filter:
 Mass conservation
 Continuity equation
 0U = 0
 Vertical motion < horizontal
motion
 Parameters:
 Background error (variance)
 Correlation length
 Rotation vs divergence
Local minima
MSS
NWP model
Local minima
MSS
NOAA
MSS @ 25
km
50 km
Plots !
Improved cold
front
Better
Around
rain
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
Data assimilation
• The analysis minimizes the cost
function J by varying the control
variables representing the
J

J

J
O
B
atmospheric state, e.g., uj , the wind
components of wind vector vj,
2
 (u  u
• At every observation point prior
)
B, j 
 j
knowledge is available on the

observed state from a sort-range J B   
2

B
j  1,2 
forecast, called NWP background

• JB is a penalty term penalizing
p v | v B  exp  J B / 2
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

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p([u,v]SCAT |vB)
Wind
error
model
p([V,]SCAT |vB)
• 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
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5%
Measurement
Noise
•  0 noise is uniform in
measurement space
(~5 % or 0.5 m/s VRMS)
 Wind retrieval provides very
accurate  0S given  0O , so
well-defined p(vS |  0O)
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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
15
Vogelzang et al., 2011
NWP SAF Workshop | 14 April 2011
v input
Scatterometer
p(v
|v)
S
Representation
error
v
X
Prob
NWP
Scatterometer
Observation
[a.u.]
16
• Rotating beam (SeaWinds, OSCAT: mid swath)
true
• Fixed antennas (ASCAT: inner swath)
Broad MLE minima and closeby multiple ambiguous
solutions are complicating scatterometer wind assimilation
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Scatterometer Data Assimilation
Posteriori Wind Probability given a set of
measurements
Wind domain uncertainty
u, v ~ 1.5 m/s
Measurement space noise
D ~ 5% (0.2 m/s)
 0S = GMF(vS, .. )
Geophysical solution manifold
• ERS/ASCAT: Manifold in 3D measurement space
• SeaWinds/NSCAT: Manifold in 4D measurement
Stoffelen&Portabella, 2006
space
Scatterometer data
assimilation
• JO is a penalty term penalizing
differences of the analysis
control variables with the
observations
• Choices:
p(vS |  0O)
• Direct assimilation of  0O
Complex error PDFs
• Assimilate p(vS |  0O), like
in MSS and 2DVAR
• Needs p information
• Assimilate ambiguities
Reduces 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
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Direct assimilation of
•  0 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
0

O
y: 0
x: wind
 Main uncertainty is in the wind domain
Stoffelen, PhD thesis,1998
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Assimilate ambiguities
v
Prob
Jo
SCAT

 2 ln p  | v
p(vS |v)
0
O
Prob

Ambiguities
Reduces wind solution space to max 4 points
(delta functions); solution wind PDF information is lost
21
Assimilate ambiguities
Scatterometer wind cost
ambiguous wind vector solutions ui ,vi
provided by wind retrieval procedure
and complemented by estimated
observation wind error, eu = ev
Stoffelen and Anderson, 1998
 Derive probability
Pi from MLE info
22
Assimilate solution “valley”
v
Prob
p(vS |v)
Jo
SCAT

 2 ln p  | v
0
O
Prob

MSS
٧ Retains essential wind solution PDF information along the
valley of solutions that generally exists
٧ Provides very good approximation to p(v |  0O)
Portabella and Stoffelen, 2004
23
Scatterometer input
Representation
error
v
X
Prob
٧ Provides very
good
approximation
to p(v |  0O)
NWP
Scatterometer
Observation
from MSS
[a.u.]
Portabella and Stoffelen, 2004
24
Assimilation of ambiguous
winds
• Potentially provides
multiple minima in
3D/4D-Var
• Problem is very limited
for ASCAT
• 2DVAR tests show
<1% of wrong selection
• May be linearized by
selecting one solution
at a time (inner loop)
vtrue = (0,3.5) ms-1
eu/v,O = 2 ms-1
eu/v,B = 2 ms-1
v2 = -v1
p2 = p1 = .5
<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
Prob
[a.u.]
Scatterometer wind
NWP background
Analysis
• Assimilation of scatterometer wind product is
straightforward
• Few spatially correlated outliers due to AR errors,
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but mainly in dynamic weather
Example
• Improved 5-day forecasts of
tropical cyclone in ECMWF
4D-VAR
No ERS Scatterometer
With ERS
Rita
Isaksen & Stoffelen, 2000
27
Another example
Japan Meteorological Agency
• ASCAT has smaller rain effect
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Assimilation ASCAT winds ECMWF from 12/6/’07
Beneficial for U10 analysis
Operational okt/nov 2007 (added to
QuikScat&ERS)
Gebruik van scatterometers
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
30
NWP Impact @ 100 km
29 10 2002
Storm near
HIRLAM
misses wave;
SeaWinds
should be
beneficial!
31
NWP models
miss wave;
Next day
forecast bust
ERS-2 scatterometer wave train; missed by HiRLAM
32
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 QuikSCAT
There are some regional differences
Lack of cross-isobar flow in NWP
QuikSCAT vs model wind dir
Stratify 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)
WISE 2004, Reading