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Observation Targeting

ECMWF Predictability Training Course - April 2006. Observation Targeting. Andy Lawrence Predictability and Diagnostics Section, ECMWF Acknowledgements: Martin Leutbecher, Carla Cardinali, Alexis Doerenbecher, Roberto Buizza. ECMWF Predictability Training Course – April 2006. Contents.

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Observation Targeting

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  1. ECMWF Predictability Training Course - April 2006 Observation Targeting Andy Lawrence Predictability and Diagnostics Section, ECMWF Acknowledgements: Martin Leutbecher, Carla Cardinali, Alexis Doerenbecher, Roberto Buizza

  2. ECMWF Predictability Training Course – April 2006 Contents Introduction • What is Observation Targeting? Targeting Methodology • Example using a simple model • Kalman Filter techniques • Singular Vector techniques • Summary of research issues Operational targeting principles • Previous targeting campaigns • Operational structure and schedules • Results from ATReC 2003 • Verification of forecast impacts • Future of observation targeting

  3. Estimated ROUTINE observations = 10 6 Estimated TARGETED observations = 10 3 ECMWF Predictability Training Course - April 2006 What is observation targeting? Techniques that optimize a flexible component of the observing network on a day-to day basis with the aim to achieve specific forecast improvements.

  4. ECMWF Predictability Training Course - April 2006 The concept of observation targeting Use adjoint model transform algorithm to derive data-sensitive areas. Add extra observations Forecast anevent. OBS OBS OBS Improve forecast? Verify with corresponding analysis.

  5. ECMWF Predictability Training Course - April 2006 The concept of observation targeting Q: If we have the capability to addobservations in data-sensitive areas to improve the forecast of a specific event, can these locations be determined using objective (model-based) methods? OBS OBS OBS A: This is an optimization problem with two constraints: • Probability of making an analysis error at a particular location • The intrinsic ability of the flow at that location (i.e. sensitivity)

  6. ECMWF Predictability Training Course - April 2006 Where are observations needed to improve a 18-hour forecast? Sensitive areasVerification region

  7. ECMWF Predictability Training Course - April 2006 Where are observations needed to improve a 42-hour forecast?

  8. ECMWF Predictability Training Course - April 2006 Where are observations needed to improve a 66-hour forecast?

  9. ECMWF Predictability Training Course - April 2006 Methodology The Observation Targeting Question How do identify optimal sites for additional observations? OR How do we predict changes of forecast uncertainty due to assimilation of additional observations?

  10. ECMWF Predictability Training Course - April 2006 Methodology Information needed to answer this question: • Knowledge of the statistics of initial condition errors…and how they change due to an assimilation of additional observations. • Gaussian error statistics • Kalman filter techniques • Knowledge of the perturbation dynamics from the observation time to the forecast verification time • NWP studies suggest that perturbation dynamics are approximated by a linear propagator defined by ensemble-based techniques or tangent-linear/ adjoint techniques. For linear perturbation dynamics and Gaussian error statistics, optimal state estimation can be approximated by the Extended Kalman Filter… which can also be used to select optimal sites for additional observations.

  11. A perturbation placed at i=10, propagates ‘eastward’ at a speed of 25 degrees/day. ECMWF Predictability Training Course - April 2006 Extended Kalman Filter • A chaotic system, where a time unit of 1 represents 5 days dxi dt = -xi-2 xi-1 + xi-1 xi+1 – xi + F with i = 1,2,…40 x0 = x40 , x–1 = x39 , x41 = x1 and F = 8 Targeted observations in the framework of an Extended Kalman Filter (Illustration using the Lorenz-95 system - Leutbecher, 2003)

  12. ECMWF Predictability Training Course - April 2006 Planet L95: routine observing network For routine observations: Observations are constructed by adding noise (representing unbiased and uncorrelated normally distributed errors) to values taken from a ‘truth’ run..become available every 6 hours. Over land (positions 21-40) we have observations at all locations 0 = 0.05clim Over ocean (positions 1-20) we have observations at ‘cloud-free’ locations 0 = 0.15clim

  13. ECMWF Predictability Training Course - April 2006 Planet L95: forecast errors 2-day forecast errors for Europe

  14. ECMWF Predictability Training Course - April 2006 Planet L95: targeted observation A single observation over the ocean, with the error characteristics of a land observations is considered (i.e. at i=1,…20). The aim of this is to provide a better forecast over ‘Europe’ on Planet L95.

  15. ECMWF Predictability Training Course - April 2006 Covariance prediction with the Kalman filter (routine + additional observations) Covariance evolution within the Kalman filter: For Routine observations: Analysis Step at time tj(Pra)-1 = (Prf)-1 + HrTRr-1Hr Forecast Step tj tj+ Prf = M PraMT For Routine + additional observations at position i (where i = 1,…20) Analysis Step at time tj(Pia)-1 = (Prf )-1 + HrTRr-1Hr+ HiTRi-1Hi Forecast Step tj tj+ Pif= MPiaMT Optimal position i* (where i* gives the maximum reduction of forecast error variance) : maxi=1..20 trace ( LEu (Prf- Pif) LTEu )

  16. ECMWF Predictability Training Course - April 2006 Optimal position for an additional observation Distribution of optimal position for an additional observation in L95 ‘Atlantic’ (to improve the 2-day forecast over Europe)

  17. ECMWF Predictability Training Course - April 2006 Planet L95: Forecast impacts How to measure the improvements in forecast skill: • Compare with randomly placed observations • Compare with impact obtained with observations that actually reduce the forecast error the most ( although never achievable as it requires information at verification time; position depends on realization of actual errors!) • Compare with the impact of an observation added at a fixed site optimized for the forecast goal (a hard test). • No such test with NWP system and real observations yet. • How does last test look with L95?

  18. ECMWF Predictability Training Course - April 2006 Fixed location v. adaptive day-to-day location

  19. ECMWF Predictability Training Course - April 2006 Approximations of the Kalman Filter Method is good for a simple model, BUT an extended Kalman filter is too expensive for a full NWP model Targeting would require to run the Kalman filter several times (i.e. each configuration of the additional observations considered in the planning process is one among several feasible ones). • Solution: • Calculate forecast error variance in small relevant subspace! • Perturbations of ensemble members about the mean: a proxy for data assimilation scheme (ETKF). • Based on singular vector schemes computed with an estimate of the inverse of the routine analysis error covariance metric as the initial time metric.

  20. ECMWF Predictability Training Course - April 2006 Ensemble Transform Kalman Filter (ETKF) Used in targeting for Winter Storms Reconnaissance Program (WSRP)(Bishop, Etherton and Majumdar, 2001) • Assumes linearity. ‘linear combination of ensemble perturbations + ensemble mean = model trajectory’. • Assumes optimal data assimilation. • No covariance localisation. Reduction of forecast error variance using the ETKF (Majumdar, 2001) Signal = forecast error (routine +additional) – forecast error (routine)

  21. Singular Vector Schemes ECMWF Predictability Training Course - April 2006 • Singular vectors identify the directions (in phase space) that provide maximum growth over a finite period of time. • Dependent on model characteristics and optimization time • Growth is measured by the inner product (or metric or norm): • If the correct norm is used, the resulting ensemble captures the largest amount of forecast error variance at optimization time (assuming that the forecast error evolves linearly). • For targeting: Forecast error variance prediction from t0 to tv replaced by variance predictions in a singular vector subspace. • Data assimilation can either use a full Kalman filter or Optimal Interpolation.

  22. ECMWF Predictability Training Course - April 2006 Singular vector targeting method 1 Singular Vector-based reduced-rank estimate: • Initial time metric is the inverse of the routine analysis error covariance matrix (Pra)-1 • SV’s computed with this metric evolve into the leading eigenvectors of the routine error covariance matrix trace (LeuPf LTEu ) . • Compute variance of forecast errors only in a subspace of leading singular vectors trace (ÂnLEuPf LTEuÂnT) instead of trace (LEuPf LTEu ) Here, Ân denotes the projection on the subspace of the leading n (left) singular vectors of LEuM. • Data assimilation uses full Kalman filter

  23. ECMWF Predictability Training Course - April 2006 Reduced-Rank approximation of covariance forecast step Analysis error covariances in the subspace spanned by the leading n SV’s are represented by Routine network VnVnT where VnT ( Pra ) -1 Vn = I Modified network VniiTVnT where (Vn i )T ( Pra ) -1 (Vn i) = I The transformation matrix i is the inverse square root of the n x n matrix,Ci, that expresses the modified analysis error covariance metric in the basis of the singular vectors; Ci = VnT ( Pra ) -1 Vn = In +VnT HiTR –1 HiVn . Using these representations (of the aecm), the forecast error variance in the verification region becomes: trace (ÂnLEu ( Pfj+ ) LTEu ÂnT ) =nj=12j routine network trace (T diag (21… 2n )  ) modified network where j denotes the singular value of the j-th SV vj

  24. ECMWF Predictability Training Course - April 2006 Singular vector targeting method 2 Approximate full Kalman filter by replacing the routine forecast error covariance matrix Pfr by a static background error covariance matrix B (Optimal Interpolation scheme) • In the variance prediction (for targeting) and • In the assimilation algorithm Analysis error covariance matrix given by A-1 = B-1 + HTR-1H In L95 system, static background error covariance matrix B =  (xf - xt ) (xf - xt)T is a sample covariance matrix computed from (forecast – truth) differences from a 1000 day sample → combine with reduced-rank technique

  25. ECMWF Predictability Training Course - April 2006 L95 comparisons : SV reduced-rank schemes Method 1: Method 2: Full KF- SV subspace Optimal Interpolation – SV subspace

  26. ECMWF Predictability Training Course - April 2006 L95 comparisons : SV full rank v reduced-rank schemes Distribution of 2-day forecast errors over Europe Full KF v. Method 1 ( Reduced-rank Kalman filter) Full KF v. Method 2 ( Reduced-rank OI)

  27. SV dependency on initial time metric p1 p0 S S • For predictability studies, an appropriate metric is based on energy. • Total Energy provides a dynamical basis (has no knowledge of error statistics): • ||x||e2 = xTEx = ½ u2 + v2 + (cp/Tr) T2 dp dS + ½ Rd Tr pr ( ln psfc )2 dS ECMWF Predictability Training Course - April 2006 • Targeted observations should be directed to ‘sensitive’ regions of the atmosphere. • Correct metric is dependent on the purpose for making the targeted observations (study precursor developments or to improve forecast initial conditions).

  28. ECMWF Predictability Training Course - April 2006 Hessian Singular Vectors • The Hessian of the cost-function provides the estimate of the inverse of the analysis error covariance matrix: J(x) = Jb (x)+ Jo (x) J = B-1 + HTR-1H = A-1 • Initial error estimates are consistent with the covariance estimates of the variational data assimilation scheme (incorporates error statistics).

  29. Total energy SV v Hessian SV ECMWF Predictability Training Course - April 2006 TESV ‘Full’ Hessian SV ‘Partial’ Hessian SV J = Jb + Jo J = Jb

  30. ECMWF Predictability Training Course - April 2006 Hessian reduced-rank estimate • Similar to Kalman Filter/ OI- reduced rank estimate but is based on a subspace of Hessian Singular vectors vi computed with the metric Jroutine (using only observations from the routine network in Jo) (Leutbecher, 2003) • Efficient computation of the Hessian metric for modified observation network (routine + additional) in the subspace: Cij = vTiJmodvj = vTi (Jroutine + HTa R-1aHa) vj = ij + (Havi)TR-1aHavj • Estimate of forecast error variance reduction due to additional observations trace ([I – C-1] diag (21…. 2n)) where jdenotes the singular value of the routine Hessian SV vj

  31. ECMWF Predictability Training Course - April 2006 Comparison of flight track ranking Winter Storms Reconnaissance Program 2003 Additional observations on 4th Feb 00UT for forecast verification time: 6thFeb 00UT Hessian Reduced-rank estimate ETKF (Doerenbecher et al., 2003)

  32. ECMWF Predictability Training Course - April 2006 Summary & Research Issues Aim of observation targeting: Prediction of forecast error variance due to modifications of observing network. Factors that affect skill of forecast error variance predictions in operational NWP: • Covariance estimates • Skill of forecast error variance predictions depends on quality of background error covariance estimate…incorporate flow-dependant wavelet approach. • Account for correlations between observation error in current schemes (Important for satellite data with observation error correlations in space and between channels  optimal thinning - Liu & Rabier, 2003) • Predict spatial resolution of routine observations. Harder to do with day-to-day variability of targeted observations, particularly for satellite data affected by cloud.

  33. ECMWF Predictability Training Course - April 2006 Summary & Research Issues • Error dynamics • TL/AD model simplified due to resolution and physical process parameterisation. Advances in formulation (moist processes, sensitivity of observation targeting guidance to spatial resolution) should improve variance predictions. • Validity of tangent linear assumption: Gilmour et al. 2001: probably not useful beyond 24h; but measure of nonlinearity dominated by small scales Reynolds & Rosmond 2003: SV’s usefully up to 72h (diagnostic in SV-space and scale dependant diagnostic) • Reduced Rank SV’s (Subspace): How many SV’s are needed to reliably predict forecast error variance reductions? • L95: 1 SV is sufficient: the leading SV explains a large fraction of the total forecast error variance in the verification region (Rank 1KF  full KF) • NWP: For rank (LEuM)  number of grid-points in verification region times number of variables.

  34. ECMWF Predictability Training Course - April 2006 Summary & Research Issues • Contribution of model error? • To initial condition error at t0 • To growth of error from t0 to tv • Targeting methodology • Perhaps combination of SV and ensemble-based approach? (expensive, as requires a dedicated ensemble). • Does validity of linear transformation in ETKF technique extend further than the validity of the TL-approximation? • Observation types • Forecast error variance reductions can be determined for different observation types in sensitive areas. • Will the abundance of satellite data eliminate the need for in-situ measurements? • Satellite sampling is limited through cloud layers → in-situ measurements useful if dynamically-sensitive areas are beneath clouds.

  35. ECMWF Predictability Training Course - April 2006 Previous targeting campaigns Targeted observation techniques and methods were tested during numerous operational campaigns: FASTEX (Fronts and Atlantic Storm-Track Experiment 1997) Improving forecasting of atmospheric cyclone depressions forming in the North-Atlantic and reaching the west-coast of Europe. NORPEX (North Pacific Experiment 1998) North Pacific winter-season storms that affect the United States, Canada, and Mexico. WSRP (Winter Storms Reconnaissance Program 1999-2006) North-Eastern Pacific storms affecting the west-coast of the United States. Use of targeted observations has a positive effect on forecast skill (Majumdar et al. 2001) ATReC (Atlantic THORPEX Regional Campaign 2003) North-Atlantic storms affecting east-coast United States and Europe.

  36. Case selection: Decision made at tc on whether or not to commit additional observing resources at t0. Decide for which forecast verification time tv and whichregion R adaptive observations should be taken. NWP Centres ECMWF UK MO MF NCEP NRL Operations Centre ECMWF Predictability Training Course - April 2006 Operational Structure for Observation Targeting 1 2345 tctd t0tv time

  37. NWP Centres ECMWF UK MO MF NCEP NRL ECMWF Predictability Training Course - April 2006 Operational Structure for Observation Targeting 1 2345 tctd t0tv time 2. Sensitive area prediction: Compute which configuration for adaptive observations (to be taken at t0) is likely to best constrain error of forecast for (tv,R). Operations Centre

  38. NWP Centres ECMWF UK MO MF NCEP NRL Operations Centre Observation control centre ECMWF Predictability Training Course - April 2006 Operational Structure for Observation Targeting 1 2345 tctd t0tv time 3. Select and request additional observations at td.

  39. NWP Centres ECMWF UK MO MF NCEP NRL ECMWF Predictability Training Course - April 2006 Operational Structure for Observation Targeting 1 2345 tctd t0tv time 4. Observing platforms deployedatt0and observations taken. Operations Centre Data Monitoring Observation control centre AMDAR Radiosonde ASAP Res. Aircraft

  40. NWP Centres NWP Centres ECMWF ECMWF UK MO UK MO MF MF NCEP NCEP NRL NRL ECMWF Predictability Training Course - April 2006 Operational Structure for Observation Targeting 1 2345 tctd t0tv time 5. Forecast verification time at tv Operations Centre Operations Centre Data Monitoring Observation control centre AMDAR Radiosonde ASAP Res. Aircraft

  41. ECMWF Predictability Training Course - April 2006 Atlantic THORPEX Regional Campaign 2003 First field campaign in which multiple observing systems were used. Dropsondes from research aircraft, ASAP ships, AMDAR, land radiosonde sites. Observation targeting guidance to predict the sensitive areas based on • UKMO: ETKF based on ECWMF ensemble • Meteo-France: total energy SV’s run on a (possibly perturbed) trajectory • NRL: SV’s and sensitivity to observations • NCEP: ETKF based on combined ECWMF and NCEP ensembles. • ECWMF: 2 flavours of total energy SV’s and Hessian SV’s Config. initial norm TLM res. TLM physics TE-d42 Total Energy T42 dry TE-m95 Total Energy TL95 moist H-d42 Hessian T42 dry

  42. ECMWF Predictability Training Course - April 2006 ATReC_029_1: Obs. time: 20031208, 18UT ; Ver. time 20031211, 00 (54h opt) Dry TESV (ECMWF) Moist TESV (ECMWF) Hessian SV (ECMWF) ETKF (Met Office using ECMWF ensemble)

  43. ECMWF Predictability Training Course - April 2006 Sensitivity area prediction How do we determine where to send the observations? In ATReC 2003, level of agreement between the sensitive area predictions can be quantified in terms of geographical overlap. Sensitive area 1: Sj of area a Sensitive area 2: Sk of area a Geographical overlap Ojk = area ( Sj  Sk ) /a ECMWF calculated overlap ratios for a = 4 x 106 km2 (Leutbecher et al. 2004) SAP1 SAP2 Number of cases with overlap >0.50 SV TE-d42 SV TE-m95 42/43 98% SV TE-d42 SV H-d42 35/42 83% SV TE-d42 ETKF 31/67 46% SV H-d42 ETKF 32/67 48%

  44. DESIGNATED TARGET AREA ECMWF Predictability Training Course - April 2006 TESV vs Hessian SV vs ETKF ETKFsensitivity across Atlantic, main area 40-55N,20-30W; secondary max 45N60W (this is also secondary area for Hessian SVs). Main HSV and dry TESV centre is South tip of Greenland (and down to 50N), and back into Canada at 60N. Moist TESVs have significant area 35N65W (Odette)

  45. ECMWF Predictability Training Course - April 2006 Case 43: Obs. time 8th Dec 18UT, Verif. time 11th Dec 00UT Radiosonde, Satellite rapid-scan winds, AMDAR flights

  46. ECMWF Predictability Training Course - April 2006 Case 47: Obs time 11th Dec 18UT, Verif. Time 13th Dec 12UT Radiosondes, ASAP, Satellite, AMDAR

  47. ECMWF Predictability Training Course - April 2006 Case 36: Obs time 4th Dec 18UT, Verif. Time 6th Dec 12UT Radiosonde, ASAP, AMDAR

  48. ECMWF Predictability Training Course - April 2006 Case 37: Obs. Time 5th Dec 18UT, Verif. Time 7th Dec 12UT Radiosonde, ASAP, Satellite, AMDAR and Dropsondes

  49. ECMWF Predictability Training Course - April 2006 East Coast USA storm 5-7th December 2003 A major winter storm impacted parts of the Mid-Atlantic and Northeast United States during the 5th-7th. Snowfall accumulations of one to two feet were common across areas of Pennsylvania northward into New England. Boston, MA received 16.2 inches while Providence RI had the greatest single snowstorm on record with 17 inches, beating the previous record of 12 inches set December 5-6, 1981. (from http://www.met.rdg.ac.uk/~brugge/world2003.html) NASA-GSFC, data from NOAA GOES

  50. ATReC (routine + additional observations in target area) ECMWF Predictability Training Course - April 2006 Summary of ATReC forecast Impacts Control (routine observations) ATReC (routine + additional observations)

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