Ensemble-based adaptive sampling and data assimilation issues in tropical cyclones

1
Ensemble-based adaptive sampling and data
assimilation issues in tropical cyclones

• Sharanya J. Majumdar (RSMAS/U.Miami)
• Collaborators, present and future
• Carolyn Reynolds, Xuguang Wang, Sim Aberson,
  Craig Bishop, Roberto Buizza, Yongsheng Chen, Tom
  Hamill, Melinda Peng
• EnKF Workshop, Austin TX, 10-12 Apr 2006

2
HURRICANE WILMA, 24th October 2005
3
2 topics

• Adaptive Sampling
• ETKF tested as an alternative to uniform sampling
  / ensemble spread for hurricane synoptic
  surveillance
• How do targets compare with Singular Vectors?
• Data Assimilation
• Limited development and application of EnKFs to
  tropical cyclones

4
(No Transcript)
5
Targeted Observing Strategies
ETKF and SV-based targeting products are compared
for 78 cases. All techniques use the same
flow-dependent verification region centered on
the official forecast position of the tropical
cyclone.
6
ETKF Adaptive Sampling

• STEP 1 Error covariance matrix for ROUTINE obs
  network
• Pr(t) Pf - Pf HrT (Hr Pf HrT Rr)-1 Hr Pf and
  Zr Zf Tr
• STEP 2 Using SERIAL ASSIMILATION theory,
  covariance update for qth possible ADAPTIVE
  observational network
• Pq(t) Pr - Pr HqT (Hq Pr HqT Rq)-1 Hq Pr
• Zr(t)ZrT(t) Zr(t) Cq Gq (Gq I)-1 CqT
  ZrT(t)
• Pr - Sq
• Holds for any time t if linear dynamics are
  obeyed.
• Sq is reduction in error covariance due to
  adaptive obs.

7
Signals and Signal Variance

• Signal sq zr zq
• Pr HqT (Hq Pr HqT Rq)-1 (yq Hq zr)
• Kq (yq Hq zr)
• Signal covariance
• Sq E(sq sqT)
• Kq E((yq Hq zr) (yq Hq zr)T) KqT
• Kq (Rq Hq E(zr yqT)E(yq zrT) HqT Hq Pr
  HqT)KqT
• Kq (Hq Pr HqT Rq) KqT new obs
  uncorrelated w/analysis
• Pr HqT (Hq Pr HqT Rq)-1 Hq Pr
• Hence, the ETKF predicts SIGNAL COVARIANCE, which
  is precisely equal to the reduction in
  analysis/forecast error covariance.

8
Targeted Observing Strategies

• Ensemble Transform Kalman Filter (ETKF) uses
  ensemble forecasts to predict reduction in
  forecast error variance due to qth set of extra
  observations
• ETKF maps show 850-200hPa wind signal variance as
  a function of observation location.
• ECMWF ensemble (50 1o resolution members
  initialized 60h prior to to).
• NCEP GFS ensemble (20 1o resolution members
  initialized 48-60h prior to to).
• Total-Energy Singular Vectors (TESVs) represent
  structures that grow optimally from to into the
  verification region at tv.
• Maximizes ltPx(tv) EPx(tv)gt / ltx(to) Ex(to)gt
• TESV maps show the weighted average of
• Leading 10 TESVs computed from TL95 L60
  resolution ECMWF mode.
• Leading 3 TESVs computed from T79 L30 resolution
  NOGAPS model.
• Ensemble Spread
• Synoptic surveillance missions conducted by the
  NOAA G-IV aircraft are planned using a
  combination of uniform sampling around the
  tropical cyclone and the spread of the NCEP GFS
  Deep Layer Mean (850-200hPa ) wind.

9
Examples Ivan. Observation Time 2004090900
SV targets in vicinity of storm. ETKF targets
near the storm and to the NE.
Majumdar et al. 2006, MWR
10
Examples Ivan. Observation Time 2004091600
SV targets in vicinity and to NW of storm. ETKF
targets near the storm.
Majumdar et al. 2006, MWR
11
Composites of Close Targets
SVs exhibit an annular structure around the storm
center. ETKF targets are a maximum at the storm
center.
12
Composites of Far Targets
SV maxima occur to the northwest. ETKF maxima
often occur to the north and east.
13
Variance Singular Vectors

• To date, the most commonly used optimals are
  total energy singular vectors.
• Need to combine error growth optimization with
  realistic estimates of analysis error covariance.
• Do SV structures and growth rates change when
  this is considered?

14
Variance Singular Vectors (courtesy Carolyn
Reynolds)
ETKF ECMWF Analysis Error Variance
NAVDAS 3d-Var Analysis Error Variance
Charley 0814 NRL NAVDAS TESV
Charley 0814 ETKF VAR SV
Using the ECMWF ETKF error variance as
initial-time constraint pushes primary target
downstream. 2-day growth diminished from 54.5 to
9.0.
15
Conclusions and Issues

• ETKF and TESV targets often differ, indicating
  the respective constraints and limitations.
• Constraining AEC optimals (SVs) using the ETKF
  variance can produce targets similar to ETKF
  regions. Perturbation growth is damped
  considerably.
• ETKF results are sensitive to the ensemble used.
• Sampling errors can lead to spurious correlations
  (and targets) far from region of interest.
• Potential solutions
• time-dependent localization techniques
• larger ensembles.

16
DA in Hurricanes

• Artificial operational methods
• Bogus Vortex (NOGAPS, UKMO)
• Relocation (NCEP GFS Ensemble)
• Vortex Spin-Up (GFDL)
• Research methods
• Bogus / 4d-Var (Zou, Xiao, Pu etc)
• EnKF assimilating position (Lawson and Hansen
  2006, Chen and Snyder 2006)
• EnKFs assimilating physical variables?

17
A spun-up hurricane
18
Hurricane Structure

• Primary Circulation
• Low-pressure vortex in gradient-wind balance
• Secondary Circulation
• Low-level cyclonic inflow
• Upper-level anticyclonic outflow
• Eye subsidence of warm, dry air
• Eyewall moist updrafts due to sensible and
  latent heat release
• Spiral rainbands

19
Hurricane Dynamics

• External Influences Environmental Interactions
• Vertical wind shear
• Interaction with trough
• Entrainment of dry air
• Internal Influences
• Air-sea fluxes of heat and momentum
• Core asymmetries
• Imbalanced adjustment processes
• Eyewall cycles
• Does an EnKF account for these processes?
• Data assimilation
• AEC Optimals (Hamill et al. 2002), Synoptic
  Analysis (Hakim and Torn 2005)

20
PRELIMINARY RESULTS (Xuguang Wang,
NOAA/CIRES) (1) Assimilation of single v ob 5
m/s higher than background v
21
(2) EnKF-based covariance of decrease in central
SLP with T and v
22
Observations in Hurricanes

• Satellite
• GOES winds (include rapid-scan)
• AIRS, AMSR-E temp. and water vapor, 15km res
• Aircraft
• GPS Dropwindsondes
• Dual Doppler Radar (3-d wind fields and Z)
• Stepped-Frequency Microwave Radiometer
• UAVs