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, 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 titititi totototo tvtvtvtv Initialization time Observing time Verification time t 2 days

Targeted Observing Strategies titititi totototo tvtvtvtv Initialization time Observing time Verification time t 2 days 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.

ETKF: Adaptive Sampling STEP 1: Error covariance matrix for ROUTINE obs network P r (t)= P f - P f H rT (H r P f H rT + R r ) -1 H r P f and Z r = Z f T r STEP 2: Using SERIAL ASSIMILATION theory, covariance update for q’th possible ADAPTIVE observational network P q (t)= P r - P r H qT (H q P r H qT + R q ) -1 H q P r = Z r (t)Z rT (t) – Z r (t) C q  q (  q + I) -1 C qT Z rT (t) = P r - S q Holds for any time t if linear dynamics are obeyed. S q is reduction in error covariance due to adaptive obs.

Signals and Signal Variance Signal s q = z r – z q = P r H qT (H q P r H qT + R q ) -1 (y q – H q z r ) = K q (y q – H q z r ) Signal covariance S q = E(s q s qT ) = K q E((y q – H q z r ) (y q – H q z r ) T ) K qT = K q (R q – H q E(z r y qT )–E(y q z rT ) H qT + H q P r H qT )K qT = K q (H q P r H qT + R q ) K qT [new obs uncorrelated w/analysis] = P r H qT (H q P r H qT + R q ) -1 H q P r Hence, the ETKF predicts SIGNAL COVARIANCE, which is precisely equal to the reduction in analysis/forecast error covariance.

Targeted Observing Strategies Ensemble Transform Kalman Filter (ETKF) uses ensemble forecasts to predict reduction in forecast error variance due to q th set of extra observations ETKF maps show hPa wind signal variance as a function of observation location. ECMWF ensemble (50 1 o resolution members initialized 60h prior to t o ). NCEP GFS ensemble (20 1 o resolution members initialized 48-60h prior to t o ). Total-Energy Singular Vectors (TESVs) represent structures that grow optimally from t o into the verification region at t v. Maximizes / 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 ( hPa ) wind.

Majumdar et al. 2006, MWR Examples: Ivan. Observation Time SV targets in vicinity of storm. ETKF targets near the storm and to the NE.

Majumdar et al. 2006, MWR Examples: Ivan. Observation Time SV targets in vicinity and to NW of storm. ETKF targets near the storm.

Composites of “Close” Targets SVs exhibit an annular structure around the storm center. ETKF targets are a maximum at the storm center.

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 TESVCharley 0814 ETKF VAR SV ETKF ECMWF Analysis Error Variance NAVDAS 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 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

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