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

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 PengEnKF Workshop, Austin TX, 10-12 Apr 2006

HURRICANE WILMA, 24th October 2005

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

ttii ttoottvv

Initialization timeInitialization time Observing timeObserving time Verification timeVerification time

tt

2 days 2 days

ETKF: Adaptive SamplingSTEP 1: Error covariance matrix for ROUTINE obs

networkPr(t) = Pf - Pf HrT (Hr Pf HrT + Rr)-1 Hr Pf and Zr = Zf Tr

STEP 2: Using SERIAL ASSIMILATION theory, covariance update for q’th possible ADAPTIVE observational network

Pq(t) = Pr - Pr HqT (Hq Pr HqT + Rq)-1 Hq Pr

= Zr(t)ZrT(t) – Zr(t) Cq q (q + 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.

Majumdar et al. 2006, MWR

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

Examples: Ivan. Observation Time 2004091600

SV targets in vicinity and to NW of storm. ETKF targets near the storm.

Composites of “Far” Targets

SV maxima occur to the northwest. ETKF maxima often occur to the north and east.

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?

Variance Singular Vectors (courtesy Carolyn Reynolds)

Using the ECMWF ETKF error variance as initial-time constraint pushes primary target downstream. 2-day growth diminished from 54.5 to 9.0.

Charley 0814 NRL NAVDAS TESV Charley 0814 ETKF VAR SV

ETKF ECMWF Analysis Error VarianceNAVDAS 3d-Var Analysis Error Variance

1) ETKF and TESV targets often differ, indicating the respective constraints and limitations.

2) Constraining AEC optimals (SVs) using the ETKF variance can produce targets similar to ETKF regions. Perturbation growth is damped considerably.

3) ETKF results are sensitive to the ensemble used.

4) Sampling errors can lead to spurious correlations (and targets) far from region of interest.

Potential solutions:

a) time-dependent localization techniques

b) larger ensembles.

Conclusions and Issues

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?

A “spun-up” hurricane

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)

PRELIMINARY RESULTS (Xuguang Wang, NOAA/CIRES)

(1) Assimilation of single v ob:

5 m/s higher than background v

(2) EnKF-based covariance of decrease in central SLP with T and v

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