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

Hybrid 4D-Var development at NRL: Results from two 3-month trials. David Kuhl 1 , Craig Bishop 2 , Tom Rosmond 3 , Elizabeth Satterfield 4 1 Naval Research Laboratory, Washington DC 2 Naval Research Laboratory, Monterey, CA 3 Science Application International Corp., Forks, WA.

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

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

  2. 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.

  3. 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

  4. 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

  5. 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

  6. 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.

  7. 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

  8. 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

  9. Conventional vs. Hybrid Anomaly Height Correlation SH • 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

  10. Anom. H.C. Conv.vs. Hybrid Jul-Aug 2010 Scorecard=1 Feb-Mar 2011 Scorecard=2

  11. Vect. Wind Conv.vs. Hybrid Jul-Aug 2010 Scorecard=0 Scorecard*=4 *=based on significance Feb-Mar 2011 Scorecard=0 Scorecard*=3

  12. Raobs.Conv.vs. Hybrid Jul-Aug 2010 Scorecard=0 Scorecard*=2 *=based on significance Feb-Mar 2011 Scorecard=0 Scorecard*=0

  13. 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

  14. Vect. Wind Conv.vs. Hybrid Jul-Aug 2010 Feb-Mar 2011

  15. 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

  16. Thank You.

  17. Anom. H.C. Conv.vs. Hybrid Jul-Aug 2010 Scorecard=1 Feb-Mar 2011 Scorecard=2

  18. Anom. H.C. Conv.vs. Hybrid Jul-Aug 2010 Feb-Mar 2011

  19. Raobs.Conv.vs. Hybrid Jul-Aug 2010 Feb-Mar 2011

  20. 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

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