Comparison of ensemblebased and variationalbased data assimilation schemes in a QuasiGeostrophic mod

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Comparison of ensemble-based and
variational-based data assimilation schemes in a
Quasi-Geostrophic model.Shu-Chih Yang et al.
3D-Var
Hybrid (3DVar20 BVs)
12-hour 4D-Var
LETKF (40 ensemble)
24-hour 4D-Var
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Analysis increment (color shaded) vs.
dynamically fast growing errors (contours)
12Z Day 24
00Z Day 25
Initial increment (smoother) vs. BV
analysis increment vs. BV
LETKF
analysis increment vs. Final SV
Initial increment vs. Initial SV
12-hour 4DVAR
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Analysis increment (color shaded) vs.
dynamically fast growing errors (contours)
00Z Day 24
00Z Day 25
analysis increment vs. Final SV
Initial increment vs. Initial SV
24-hour 4DVAR
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3D-LETKF
time
to
t1
4D-LETKF
No-cost LETKF smoother (cross) apply at t0 the
same weights found optimal at t1, works for 3D-
or 4D-LETKF
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No-cost LETKF smoother
LETKF analysis at time i
LETKF Analysis
Smoother reanalysis
Smoother analysis at time i-1
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LETKF minimizes the errors of the day and thus
provides an excellent first guess to the 3D-Var
analysis
3DVar
3DVar with the background of the first 50 days
provided from LETKF
3DVar with the background provided from LETKF
(forecast mean)
LETKF
We conclude from this experiment that the errors
of the day (and not just ensemble averaging) are
important in LETKF and 3D-Var.
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ENSEMBLE KALMAN FILTER IN THE PRESENCE OF MODEL
ERRORS
Hong Li, Eugenia Kalnay

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• SPEEDY MODEL (Molteni 2003)
• T30L7 global spectral model
• total 96x48 grid points on each level
• State variables u,v,T,Ps,q
• Data Assimilation LETKF
• Methods to handle model errors
• Multiplicative inflation
• Dee da Silva (1998)
• Low-order (Danforth et al, MWR, 2007)

Dense Observations
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Control run 200 inflation Dee da
Silva Low-order
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Simultaneous estimation of inflation and
observation errors

• Hong Li
• Eugenia Kalnay

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Diagnosis of observation error statistics
(Navascues et al, 2006, Desroziers et al, 2006)
Desroziers et al 2006 and Navascues et al 2006
have only used these relations in a diagnostic
mode, from past 3D-Var/4D-Var stats!! Here we
estimate both and R online.
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Tests within LETKF with L40 model

Estimated R
Estimated
Rinit
Rt1.0
(2)

Starting with very wrong R the right R and
optimal inflation are recovered.
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online estimated observational errors
The original wrong specified R converges to the
right R quickly (about 5-days)
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• Back up slides

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Model error estimation schemes (1)

• 1. Covariance inflation

(Ideal KF)
(EnKF)
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2. Dee and daSilva bias estimation scheme (1998)
Model error estimation schemes (2)
Do data assimilation twice first for model error
then for model state (expensive)
and need to be tuned
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Model error estimation schemes (3)
3. Low-order scheme (Danforth et al, 2007
Estimating and correcting global weather model
error. Mon. Wea. Rev)

• Generate a long time series of model forecast
  minus reanalysis from the training period

model
NNR
NNR
t0
NNR
t6hr

• Danforth et al 2007 did not compute the IC
  errors. Here we are concerned with both the IC
  error and the model error

Time-mean model bias
Diurnal model error
Forecast error due to error in IC
State dependent model error
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Further explore the Low-order scheme
Correct the Diurnal and the state-dependent model
errors
Time-mean model bias
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Diurnal model errors
Leading EOFs for 925 mb TEMP

• Generate the leading EoFs from the forecast error
  anomalies fields for temperature.

pc1 pc2

• Lack of diurnal forcing generates wavenumber 1
  structure

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925hPa Temperature
Black line
Blue line
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State-dependent model errors
the local state anomalies (Contour) and the
forecast error anomalies (Color)
SVD2
SVD1
SVD4
SVD3
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Correct state-dependent model errors
500hPa Uwind
500hPa Height
Black line
Blue line
Univariate SVD (not account for the relations
between different variables)
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Adaptive sampling with the LETKF-based ensemble
spreadJunjie Liu

• Purpose
• Sample 10 adaptive DWL wind observations to get
  90 improvement of full coverage
• Compare ensemble spread method with other
  sampling strategies
• How the results are sensitive to the data
  assimilation schemes (3D-Var and LETKF)
• Note
• same adaptive observations from ensemble spread
  method are assimilated by both 3D-Var and LETKF

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500hPa zonal wind RMS error
Rawinsonde climatology uniform random
ensemble spread ideal 100
3D-Var
LETKF
RMSE

• With 10 adaptive observations, the analysis
  accuracy is significantly improved for both
  3D-Var and LETKF.
• 3D-Var is more sensitive to adaptive strategies
  than LETKF. Ensemble spread strategy gets best
  result among operational possible strategies

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500hPa zonal wind RMS error (2 adaptive obs)
Rawinsonde climatology uniform random
ensemble spread ideal 100
3D-Var
LETKF

• With fewer (2) adaptive observations, ensemble
  spread sampling strategy outperforms the other
  methods in LETKF
• For 3D-Var 2 adaptive observations are clearly
  not enough

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Analysis sensitivity study within LETKF

• The self sensitivity is the trace of the matrix
  S.
• It can show the analysis sensitivity with respect
  to
• different types of observations (e.g.,
  rawinsonde, satellite, adaptive observation and
  routine observations)
• the observations in different area (e.g., SH, NH)

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Analysis sensitivity of adaptive observation (one
obs. selected from ensemble spread method over
ocean) and routine observations (every grid point
over land) in Lorenz-40 variable model
10-day forecast RMS error
Analysis sensitivity

• About 17 information of the analysis comes from
  observations over land.
• About 85 information comes from observation for
  the adaptive observation (a single observation
  over ocean).
• The single adaptive observation is more
  important than single observation over land.