Hybrid 4D-Var development at NRL: Results from two 3-month trials

David Kuhl1, Craig Bishop2, Tom Rosmond3, Elizabeth Satterfield4

1Naval Research Laboratory, Washington DC2Naval Research Laboratory, Monterey, CA

3Science Application International Corp., Forks, WA.4National Research Council/NRL, Monterey, CA

P0 _ Hybridb

* Xu et al. 2005 NAVDAS-AR 4DVAR system(Navy’s Operational Global Modeling System)

Overview

• Goal: Investigate impact of enhancing the conventional initial background error covariance of the NAVDAS-AR 4D-Var setup with an ensemble background error covariance. We refer to this as hybrid system.

• Result: The hybrid system improves the 4D-Var DA.

NAVDAS-AR

• Where:– is the error covariance matrix for NAVDAS-AR specified

at all time steps of the DA window

– is the initial background error covariance matrix specified at the beginning of the DA window (3 hours after previous analysis time)

– is the Tangent Linear Model (TLM)

– is the adjoint model

– is the model error covariance (opt. – not used)

• TLM and adjoint are used to propagate initial background error covariance ( ) forward and backward through data assimilation window

PNAVDAS AR

P

0b P

0bMT

MP0b MP

0bMT Q

P0b

PNAVDAS AR

P0b

M

MT

Q

P0b

Hybrid Assimilation

• Many groups (Buehner, Wang, Kleist) have found that hybrid assimilation results in improved analyses and forecasts

• With hybrid assimilation we combine the of the conventional and ensemble methods in the linear fashion:

• The resulting formulations incorporates aspects of both and

• Bishop and Satterfield found theoretical justification for hybrid based on variances

P0 _ Hybridb (1 )P0 _ CONV

b P0 _ ENSb

P0b

P0 _ CONVb P0 _ ENS

b

NAVDAS-AR Conventional

• Variances ( ): – Geo-pot. height and temperature are in exact hydrostatic balance– Geo-pot. height and winds are approximately geostropically balanced in

the extratropics and independent in tropics

• Correlations ( ): – Isotropic correlation model based on balanced and unbalanced

correlations separable in the vertical and horizontal (see Chapter 4 Daley and Barker 2001)

• Strengths: – High rank– Preserves some aspects of geophysical balances

• Weakness: – Not flow dependent– Horizontal length scale independent of height may not apply in both

troposphere and stratosphere– Balance assumptions are incorrect in boundary layer and stratosphere

P0 _ CONVb

P0 _ CONVb DCONV

1/2 CCONV DCONV1/2

CCONV

DCONV

Flow Dependent Ensemble

• Where:– is the ensemble perturbation– is the number of ensemble members– is localization matrix

• Ensembles: 9-banded Ensemble Transform (ET) (McLay et. al 2010)– Mean: 3-hour forecast of 4D-var analyses at high resolution – Covariances (balance of):

• Operational 3D-Var analysis error variances• 3-hour forecast of ensemble members at low resolution

• Strength: – Flow dependent errors of the day – Multivariate balances implied by the localized ensemble correlations

• Weakness: – Localization damages geophysical balances– Cycled ensembles (generated in the manner of a Kalman filter) almost

inevitably result in variances that are too small in some regions and too large in others. Getting this correct is a work in progress.

P0 _ ENSb

C

x i x

K

Experimental Setup

• 2 Experiments • Jun. 1, 2010 to Sep. 1 2010• Jan. 1, 2011 to Apr. 1, 2011

• Discard 1st month of each analysis for Radiance Bias correction (VAR-BC) spin-up of ensemble

• Model resolution (operational): • T319L42 outer (960x480 Gaus. Grid)• T119L42 inner (360x180 Gaus. Grid)

• Ensemble resolution (same as inner): T119L42• Number of Ensemble Members: 80 (size of operational

ensemble)• Assimilating conventional observations and all operational

radiances except Aqua and MHS

Verification Metrics:Score Card

– Anomaly Correlations:– Statistically significantly better with confidence level of 95%

– All of the rest:– Statistically significantly better with confidence level of 95%– And error must be at least 5% less than the control

Conventional vs. Hybrid• Experiment comparison:

– Blue is win for Conventional

– Red is win for Hybrid• Percentage reduction/increase of

anomaly height correlation relative to conventional– Anomaly height correlation is

computed relative to self analysis at different forecast lead times 0-5 days

– Forecasts were launched every 12 hours after one month spin-up for bias correction

• Statistical significance of anomaly height correlation difference

• Green Boxes show scorecard– Presented here 2 wins for Hybrid in SH

Anomaly Height Correlation

P0 _ CONVb

P0 _ Hybridb

Anomaly Height Correlation SH

0.5

Anom. H.C. Conv. vs. Hybrid

Jul-Aug 2010Scorecard=1

Feb-Mar 2011Scorecard=2

0.5

Jul-Aug 2010Scorecard=0

Scorecard*=4

Feb-Mar 2011Scorecard=0

Scorecard*=3

Vect. Wind Conv. vs. Hybrid 0.5

*=based onsignificance

Jul-Aug 2010Scorecard=0

Scorecard*=2

Feb-Mar 2011Scorecard=0

Scorecard*=0

Raobs. Conv. vs. Hybrid 0.5

*=based onsignificance

Score Card Results

• No statistical significance in either TC tracks or buoy wind speed verification

• Classic Counting (RMS and Vect. Wind need 5% less than control)– Jul-Aug 2010: 1 points– Feb-Mar 2011: 2 points

• Only 95% significance– Jul-Aug 2010: 7 points– Feb-Mar 2011: 5 points

• Upgrade to 3D-Var: 1 point• Upgrade to 4D-Var (with other changes): 4 points

Jul-Aug 2010

Feb-Mar 2011

Vect. Wind Conv. vs. Hybrid 1.0

Conclusions/Future Work

• Conclusions:– Ensemble enhancement of improved analyses and

forecasts with Hybrid alpha=0.5– Full ensemble experiment ( ) shows marked

improvement to tropical vector winds• Regional tuning of alpha may produce better impacts

• Future Work:– Can large ensemble remove need for TLM and adjoint?– Climatological ensemble for the static . At low resolutions we

saw very promising results in this direction– Tuning of the localization and alpha

• Adaptive ensemble covariance localization• Bishop and Satterfield equation method for determining

alpha

P0b

P0b

Thank You.

Anom. H.C. Conv. vs. Hybrid

Jul-Aug 2010Scorecard=1

Feb-Mar 2011Scorecard=2

0.5

Jul-Aug 2010

Feb-Mar 2011

Anom. H.C. Conv. vs. Hybrid 1.0

Jul-Aug 2010

Feb-Mar 2011

Raobs. Conv. vs. Hybrid 1.0

TC Tracks and Buoy

• Tropical cyclone Track error– At lead time 4 days– Number of verification dates with storms in them:

• Jul-Aug 2010: 42• Feb-Mar 2011: 27

– No significant difference between either experiment• Global Buoy Surface Wind Speed Error

– At lead time 3 days– No significant difference between either experiment