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MPO 674 Lecture 22 4/2/15

MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD f -1 =0.25 H-4DENVAR f -1 =0.25 4DENVARTLMADJ

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Page 1: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

MPO 674 Lecture 22

4/2/15

Page 2: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Single Observation Examplefor 4D Variants

D. Kleist et al.

4DVAR

H-4DVAR_ADbf-1=0.25

H-4DENVARbf-1=0.25

4DENVARTLMADJ

TLMADJ

ENSONLY

ENSONLY

Page 3: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Lorenz, E.N., and K.A. Emanuel, 1998: Optimal Sites for Supplementary Weather Observations: Simulation with a Small Model. J. Atmos. Sci., 55, 399–414.

Page 4: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ
Page 5: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Lorenz, E.N., and K.A. Emanuel, 1998: Optimal Sites for Supplementary Weather Observations: Simulation with a Small Model. J. Atmos. Sci., 55, 399–414.

Page 6: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

UYonsei MM5SV NRL SV JMA SV

ECMWF SV UMiami-NCEP ETKF UKMO ETKF

Targeted observing guidance (Typhoon Sinlaku, 2008)

Page 7: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Sensitivity Methods

• Observation sensitivity– ETKF– Adjoint Observation Sensitivity / Impact

• Analysis sensitivity– Singular Vectors (done)– Adjoint Sensitivity (done)– Ensemble Sensitivity

Page 8: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Signals and Signal VarianceSquared NCEP MRF signal

1/2 (u’2+v’2) + (cp/Tr) T’2

valid at analysis time ta

Predicted ETKF signal variance Sq, using ensembles initiated 36h prior

to analysis time ta

Page 9: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

tata

ETKF Summary map of Signal

Variance Sq, for many different q.

Summary bar chart

tv tv

GoodPoor

Aim: to improve a

24-hr forecast on the West Coast

Page 10: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Evolution of operational

signal over 84h

Page 11: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Evolution of predicted ETKF signal variance

over 84h

Page 12: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ
Page 13: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Signal realization versus forecast

error reduction, at verification time tv

Page 14: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

0ld method: ETKF-based Pr

Heavy emphasis on TC (obvious target)

Secondary targets in areas of high ensemble variance over ocean, downstream of TC

Page 15: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

New method: Ensemble transform based on operational analysis error variance

Less emphasis on TC

Secondary targets: often upstream, in subtropical jet and mid-latitude troughs

Page 16: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Suppose we wish to sample through 4 days of Typhoon Ewiniar (2006) as it recurves.

Can one identify spatio-temporal continuity of ETKF target regions?

Extension into medium-range (forecasts beyond 2 days)

Page 17: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

-4 days

Page 18: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

-3.5 days

Page 19: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

-3 days

Page 20: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

-2.5 days

Page 21: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

-2 days

Page 22: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

-1.5 days

Page 23: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

-1 day

Page 24: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

-0.5 days

Page 25: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

0 days

Page 26: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Serial adaptive sampling

• Many combinations and permutations of adaptive observations are available.

• Suppose that two sets of observations can be deployed simultaneously.

• First, find the optimal first deployment. Next, calculate the best second deployment given that the first set of observations are to be assimilated by the ETKF at the same time.

• Reduces observational redundancy.

Page 27: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Flight track number Flight track number

Serial adaptive sampling during

Winter Storm Reconnaissance

Page 28: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Shortcomings of ETKF targeting strategy

• Inconsistency between imperfect error covariance in ETKF and operational data assimilation scheme

• Limited # ensemble members gives a rank-deficient P : leads to spurious correlations

• Ensemble mean and variance predictions must be reasonably accurate

• Theory is (quasi) linear

Page 29: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Dependence of SVs on the analysis-time norm: Hurricane Charley (2004)

Using NAVDAS analysis error variance as constraint pushes primary target northward into Canada. 2-day growth diminished from 54.4 to 36.4.

NOGAPS Total-Energy SV NOGAPS Variance SV

NAVDAS Analysis Error Variance

Reynolds

Page 30: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Ensemble Sensitivity (from Ryan

Torn)

Page 31: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Overview

• Want to understand how initial condition errors associated with vortex and environment regulate the predictability of TC genesis

• Focus on two forecasts initialized roughly 48 h prior to genesis, one for Karl and another for Danielle

R. Torn

Page 32: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Karl Forecast

R. Torn

Page 33: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Methods

• Use ensemble-based sensitivity analysis to compute the sensitivity of 48 h 850 hPa circulation associated with the pre-genesis system to the initial conditions

R. Torn

Page 34: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Sensitivity

R. Torn

Sensitivity of 48-h 850 hPa circ to 0-h 850 hPa circ

Sensitivity of 48-h 850 hPa circ to 0-h 400 hPa theta-e

Page 35: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Vortex Sensitivity

• Most of the sensitivity appears to be associated with the pre-genesis system itself

• Instead compute sensitivity of forecast to vortex-average quantities at each vertical level for different lead times.

R. Torn

Page 36: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Vortex Sensitivity

R. Torn

Page 37: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Upwind Moisture Sensitivity

• Interesting to see the sensitivity of upwind moisture to the initial moisture field

• Compute sensitivity as before, except metric is now 0-48 h upwind moisture in 400-600 hPa layer

R. Torn

Page 38: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Upwind Moisture Sensitivity

R. Torn

Page 39: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Danielle Forecast

R. Torn

Page 40: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Danielle Sensitivity

R. Torn

Sensitivity of 48-h 850 hPa circ to 0-h 850 hPa circ

Sensitivity of 48-h 850 hPa circ to 0-h 400 hPa theta-e

Increase theta-e to the south stronger circulation

Decrease theta-e to the north stronger circulation

Page 41: MPO 674 Lecture 22 4/2/15. Single Observation Example for 4D Variants D. Kleist et al. 4DVAR H-4DVAR_AD  f -1 =0.25 H-4DENVAR  f -1 =0.25 4DENVARTLMADJ

Danielle Sensitivity

R. Torn

Forecast of pre-Danielle has less “memory” of the initial vortex than Karl. Lower-level sensitivity of q and theta-e.