Transcript Hybrid 4DVAR development at NRL: Results from two 3

Hybrid 4D-Var development at NRL:
Results from two 3-month trials
b
0 _ Hybrid
P
David Kuhl1, Craig Bishop2, Tom Rosmond3,
Elizabeth Satterfield4
1Naval
Research Laboratory, Washington DC
2Naval Research Laboratory, Monterey, CA
3Science Application International Corp., Forks, WA.
4National Research Council/NRL, Monterey, CA
* 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.
b
0
NAVDAS-AR P
PNAVDAS  AR
 P0b

b
MP
 0


b
T
MP0 M  Q 
P0bMT
• Where:
– PNAVDAS  AR
is the error covariance matrix for NAVDAS-AR
specified at all time steps of the DA window
b
– P0 is the initial background error covariance matrix specified at
the beginning of the DA window (3 hours after previous analysis
time)
– M is the Tangent Linear Model (TLM)
– M T is the adjoint model
– Q is the model error covariance (opt. – not used)
• TLM and adjoint are used to propagate initial background
error covariance ( P0b ) forward and backward through data
assimilation window
Hybrid Assimilation
• Many groups (Buehner, Wang, Kleist) have
found that hybrid assimilation results in
improved analyses and forecasts
• With hybrid assimilation we combine the P0b
of the conventional and ensemble methods in
the linear fashion:
b
b
b
P0 _ Hybrid  (1  )P0 _ CONV   P0 _ ENS
• The resulting formulations incorporates
b
b
P
aspects of both P0 _ CONV and 0 _ ENS
• Bishop and Satterfield found theoretical
justification for hybrid based on variances
b
0 _ CONV
NAVDAS-AR Conventional P
1/2
P0b_ CONV  D1/2
C
D
CONV CONV CONV
• Variances ( DCONV ):
– 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 ( CCONV ):
– 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
b
0 _ ENS
Flow Dependent Ensemble P
• Where:
– x i  x is the ensemble perturbation
– K is the number of ensemble members
– C 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.
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   0.5
• Experiment comparison:
b
0 _ CONV
– Blue is win for Conventional P
b
– Red is win for Hybrid P0 _ 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
Anomaly Height Correlation SH
Anom. H.C. Conv. vs. Hybrid   0.5
Jul-Aug 2010
Scorecard=1
Feb-Mar 2011
Scorecard=2
Vect. Wind Conv. vs. Hybrid   0.5
Jul-Aug 2010
Scorecard=0
Scorecard*=4
*=based on
significance
Feb-Mar 2011
Scorecard=0
Scorecard*=3
Raobs. Conv. vs. Hybrid
Jul-Aug 2010
Scorecard=0
Scorecard*=2
*=based on
significance
Feb-Mar 2011
Scorecard=0
Scorecard*=0
  0.5
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
Vect. Wind Conv. vs. Hybrid   1.0
Jul-Aug 2010
Feb-Mar 2011
Conclusions/Future Work
• Conclusions:
b
– Ensemble enhancement of P0 improved analyses and
forecasts with Hybrid alpha=0.5
– Full ensemble experiment (a = 1.0 ) 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?
b
– Climatological ensemble for the static P0 . 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
Thank You.
Anom. H.C. Conv. vs. Hybrid  0.5
Jul-Aug 2010
Scorecard=1
Feb-Mar 2011
Scorecard=2
Anom. H.C. Conv. vs. Hybrid   1.0
Jul-Aug 2010
Feb-Mar 2011
Raobs. Conv. vs. Hybrid
Jul-Aug 2010
Feb-Mar 2011
  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