Hurricane Synoptic Surveillance Using The Ensemble Transform Kalman Filter


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Hurricane Synoptic Surveillance Using The Ensemble Transform Kalman Filter

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Hurricane Synoptic Surveillance Using The Ensemble Transform Kalman Filter

  1. 1. Hurricane synoptic surveillance using the Ensemble Transform Kalman Filter Sharanya J. Majumdar (RSMAS/MPO Univ. of Miami) Collaborators: Sim Aberson (HRD), Craig Bishop (NRL Monterey), Brian Etherton (UNC Charlotte), James Franklin (TPC/NHC), Istvan Szunyogh (U.Maryland), Zoltan Toth (EMC), Chun-Chieh Wu (National Taiwan University) Acknowledgment: NOAA Joint Hurricane Testbed NOAA/NCEP/EMC, October 28th 2004
  2. 2. Florida: Under the Gun in 2004
  4. 5. Ensemble Transform Kalman Filter (ETKF) <ul><li>Outline of talk </li></ul><ul><ul><ul><li>Targeted Observations: </li></ul></ul></ul><ul><ul><ul><ul><li>Theory </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Main Results from Winter Storm Reconnaissance </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Tropical Cyclones </li></ul></ul></ul></ul><ul><li>ETKF publications </li></ul><ul><ul><ul><li>Theory: Bishop et al. (MWR, 2001) </li></ul></ul></ul><ul><ul><ul><li>Data assimilation: Etherton and Bishop (MWR, 2004) </li></ul></ul></ul><ul><ul><ul><li>Ensemble generation: Wang and Bishop (JAS, 2003, 2004) </li></ul></ul></ul><ul><ul><ul><li>Targeted Observations: Majumdar et al. (QJRMS 2001, MWR 2002, QJRMS 2002) </li></ul></ul></ul>
  5. 6. How the ETKF works I <ul><li>Given ensemble forecasts initialized at time t i , how do we choose the optimal deployment of observations to improve a forecast between times t a and t v ? </li></ul><ul><li>ETKF specifies error covariance matrices for routine (r) and targeted (q) observational networks, in the form </li></ul><ul><li>P f = Z f Z fT </li></ul>t i t d t a t v Ensemble Initialization time Decision time Adaptive sampling (analysis) time Verification time t
  6. 7. How the ETKF works II <ul><li>1: Kalman Filter error statistics equations to produce error covariances for the routine observational network: </li></ul><ul><ul><ul><li>P r = P f – P f H rT ( H r P f H rT +R r ) -1 H r P f </li></ul></ul></ul><ul><ul><ul><li>2: Update forecast error covariance matrix for q th set of targeted observations (repeat Q > 100 times): </li></ul></ul></ul><ul><ul><ul><li>P q = P r – P r H qT ( H q P r H qT +R q ) -1 H q P r </li></ul></ul></ul><ul><li>ETKF predicts “ signal covariance ” S q : reduction in forecast error covariance for qth deployment of adaptive observations: </li></ul><ul><li>S q = P r – P q = M P r (t a ) H qT ( H q P r (t a ) H qT +R q ) -1 H q P r (t a ) M T </li></ul><ul><li>= Z r (t v ) T r C q  q (  q +I) -1 C qT T rT Z rT (t v ) </li></ul><ul><li>“ Signal variance ” = diagonal of S q , calculated rapidly </li></ul>
  7. 8. Main results from WSR programs <ul><li>60-80% of forecasts improved because of targeted observations </li></ul><ul><li>12-hour gain in forecast lead time </li></ul><ul><li>RMS forecast errors reduced by 10-20% </li></ul><ul><li>Improvement similar to that achieved in last 20 years of advances in numerical modeling and data acquisition </li></ul>Toth et al. (2000) (based on data from winters 1998-2002)
  8. 9. Signals and Signal Variance Squared NCEP MRF signal 1/2 (u’ 2 +v’ 2 ) + (c p /T r ) T’ 2 valid at analysis time t a Predicted ETKF signal variance S q , using ensembles initiated 36h prior to analysis time t a
  9. 10. Summary Maps of Signal Variance <ul><li>ETKF predicts signal variance (reduction in forecast error variance) for all feasible deployments of targeted observations. </li></ul><ul><li>Summarize these predictions in the form of a map or bar chart. </li></ul>
  10. 11. Aim: to improve a 24-hr forecast on the West Coast t a t a ETKF Summary map of Signal Variance S q , for many different q. Summary bar chart t v t v Good Poor
  11. 12. Shortcomings of ETKF targeting strategy <ul><li>Inconsistency between imperfect error covariance in ETKF and operational data assimilation scheme </li></ul><ul><li>Limited # ensemble members gives a rank-deficient P : leads to spurious correlations </li></ul><ul><li>Ensemble mean and variance predictions must be reasonably accurate </li></ul><ul><li>Theory is (quasi) linear </li></ul>
  12. 13. Serial adaptive sampling <ul><li>Many combinations and permutations of adaptive observations are available. </li></ul><ul><li>Suppose that two sets of observations can be deployed simultaneously. </li></ul><ul><li>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 . </li></ul><ul><li>Reduces observational redundancy. </li></ul>
  13. 14. Serial adaptive sampling during Winter Storm Reconnaissance Flight track number Flight track number
  14. 15. Questions <ul><li>1. Can an ETKF predict signal variance for any deployment of targeted observations? </li></ul><ul><li>2. Is the signal variance related to the reduction in forecast error variance? </li></ul><ul><li>Investigate using WSR flights, and 2 parallel NCEP MRF analysis-forecast cycles (with and without targeted data) </li></ul>
  15. 16. Evolution of operational signal over 84h
  16. 17. Evolution of predicted ETKF signal variance over 84h
  17. 20. Answer to Question 1 YES : a linear, increasing relationship is found to exist between the ETKF predicted signal variance, and the sample variance of operational signal realizations. Q2: Is the operational signal variance related to the reduction in operational forecast error variance?
  18. 21. Signal realization versus forecast error reduction , at verification time t v
  19. 22. WSR01: Signal Variance vs Reduction in Forecast Error Variance
  20. 23. Rescaled ETKF Signal Variance Reduction in NCEP forecast error variance Final Result from WSR01
  21. 24. Summary and Conclusions 1 <ul><li>In the mid-latitudes, ETKF has demonstrated the ability to predict the reduction in forecast error variance due to any set of targeted observations. </li></ul><ul><li>There is potential to: </li></ul><ul><li>(i) select good observing locations from bad locations </li></ul><ul><li>(ii) select good flight days from bad flight days </li></ul><ul><li>(iii) predict quantitatively the economic benefits of new observational networks </li></ul><ul><li>Now, how about the tropics?? </li></ul>
  22. 25. Targeted observations to improve tropical cyclone forecasts <ul><li>Current operational synoptic surveillance strategy at NHC: combination of uniform sampling and ensemble spread. </li></ul><ul><li>Is the ETKF a viable objective strategy to deploy aircraft-borne observations around hurricanes and typhoons? </li></ul><ul><li>Problems: </li></ul><ul><li>1. Error statistics are highly non-Gaussian </li></ul><ul><li>2. Linearity assumptions in ETKF may be violated </li></ul><ul><li>3. Ensemble initialization in tropics is questionable </li></ul><ul><li>Acknowledgment: NOAA Joint Hurricane Testbed </li></ul>
  23. 26. Typhoon Nida: May 17 2004, 12Z SPREAD ETKF
  24. 27. Typhoon Conson: June 8 2004, 12Z SPREAD ETKF
  25. 28. Typhoon Aere: August 24 2004, 12Z SPREAD ETKF SPREAD ETKF
  26. 29. Latest ETKF Summary for Aere
  27. 30. Latest flight tracks for 12Z August 24th 2004, based on ETKF and ensemble spread output. Maps produced during Sim’s seminar!
  28. 31. NOGAPS Singular Vector Sensitivity Summary, first 5 SVs. T79L30 (+48h, -48h) (Courtesy M. Peng, C. A. Reynolds of NRL Monterey) ISABEL: 00Z 14 Sep 2003 SPREAD ETKF
  29. 32. SPREAD ETKF
  30. 33. ETKF PREDICTED SIGNAL VAR. ACTUAL NCEP GFS SIGNAL ETKF predicts the variance of the “signal” : the influence of the targeted observations on the operational forecast. Preliminary result from Hurricane Isabel ETKF used 20-member 1-deg res NCEP GFS Ensemble, initialized 24-36h prior to targeted observing time. Influence on GFS analysis Influence on 1-day forecast Influence on 2-day forecast
  31. 35. Isabel maintained a westward motion until 13 September 2003, moving along the south side of the Azores-Bermuda High. Isabel approached a weakness in the western portion of the High, which allowed the hurricane to turn to the WNW on the 13th, NW on 15th, and NNW on 16th. At 00Z 14th, there were several features in the deep layer mean flow around Isabel. A cyclonic circulation was located near the Carolina coastline. And anti-cyclonic circulation was located to the south of Newfoundland. Just to the south of this feature was a smaller anti-cyclonic circulation. The cyclonic circulation over the eastern US seaboard and the anti-cyclonic circulation in the north Atlantic would help guide Isabel to the northwest over time. In addition, there was another cyclonic circulation to the east of Isabel, and a short-wave trough moving into the Central United States. Ensemble spread at 00Z 14th was mostly associated with Isabel. In addition, there was a lesser amount of ensemble spread to the northwest of Isabel, associated with the cyclonic circulation near the eastern US seaboard. There were also regions of spread to the east of Isabel, to the northeast of Isabel, and over the south-central United States. None of these regions was appropriate for aircraft observations, but the area of spread associated with the cyclonic circulation near the eastern US seaboard was sampled. The ET KF selection for observing sites on the 14th at 00Z concentrated on two areas: Isabel, and the anti-cyclone to the North of Isabel. These were considered to be the two most important and poorest observed features. While the trough in the eastern United States was important, the ET KF did not select it as a target area, in contrast to the ensemble spread, which did depict uncertainty in the east coast cut-off low. Hurricane Isabel: Targeting Discussion, 00Z 14 Sep 2003
  32. 36. NOGAPS Singular Vector Sensitivity Summary, first 5 SVs. T79L30 (+48h, -48h) (Courtesy M. Peng, C. A. Reynolds of NRL Monterey) ISABEL: 00Z 15 Sep 2003 SPREAD ETKF
  33. 38. At 00Z on the 15th, the deep layer mean flow had changed since the 14th. Now there were two primary features of interest (in addition to Isabel) - the anti-cyclonic circulation to the north of Isabel, and a trough along the eastern United States. The shortwave in the central US caught up to the cut-off low along the east coast to form one feature. Also of importance was a long-wave trough over the central United States. Isabel was to travel between this trough in the central United States and the anti-cyclone off the coast of the Maritime Provinces of Canada. Ensemble spread at 00Z on the 15th was greatest near Isabel, to the east of Isabel, and near the short-wave trough over the eastern United States. The ET KF gave the greatest support to sampling the storm. Secondary targets were (a) the east coast US short wave, (b) the anti-cyclone south of the Canadian Maritimes, and (c) an anti-cyclone to the east of Isabel. Given logistical constraints, the anti-cyclone to the east of Isabel could not be a target area, though the flight did go as far east as possible. The short-wave trough in the eastern US was sampled, however, the anti-cyclone to the north of Isabel was not. Hurricane Isabel: Targeting Discussion, 00Z 15 Sep 2003
  34. 39. SPREAD ETKF
  35. 40. NOGAPS Singular Vector Sensitivity Summary, first 5 SVs. T79L30 (+48h, -48h) (Courtesy M. Peng, C. A. Reynolds of NRL Monterey) ISABEL: 00Z 16 Sep 2003 SPREAD ETKF
  36. 41. SPREAD ETKF
  37. 42. SPREAD ETKF
  38. 43. SPREAD ETKF
  39. 44. SPREAD ETKF
  40. 45. SPREAD ETKF
  41. 46. 2004 Hurricane Season <ul><li>A combination on uniform sampling , ensemble spread and ETKF (using GFS ensembles) were used to design G-IV synoptic surveillance tracks. </li></ul><ul><li>Summary map maxima were traversed by an automated “travelling salesman” algorithm (Aberson and Leighton) to plot coordinates. </li></ul>
  42. 47. SPREAD ETKF
  43. 48. SPREAD ETKF
  44. 49. SPREAD ETKF
  45. 50. Typhoon Mindulle: June 27 2004, 12Z (DOTSTAR) SPREAD ETKF
  46. 51. Typhoon Aere: August 23 2004, 12Z (DOTSTAR) SPREAD ETKF
  48. 53. Hurricane Ivan: September 15 2004, 00Z
  49. 54. SPREAD ETKF Hurricane Jeanne: September 24 2004, 00Z
  50. 55. Hurricane Jeanne: September 25 2004, 00Z
  51. 56. Summary and Conclusions 2 <ul><li>ETKF is a theoretical improvement over ensemble spread: accounts for observational networks and future forecasts. </li></ul><ul><li>Reality: ETKF and ensemble spread maps often similar in vicinity of TC (within flight range). Dependent on ensemble. </li></ul><ul><li>Quantitative tests required to evaluate ETKF’s predictions of signal variance and reduction in forecast error variance. </li></ul><ul><li>Systematic comparison between ETKF targets vs ECMWF and NRL Singular vector targets is under way. Both ETKF and SV targets often suggest flying BEHIND the storm, which is contrary to the NHC’s thoughts. </li></ul><ul><li>Real-time maps </li></ul>
  52. 57. Future Work <ul><li>Synoptic Interpretation of ETKF and Spread targets </li></ul><ul><li>Need to UNDERSTAND how G-IV observations are affecting hurricane forecast. </li></ul><ul><li>Which levels and variables are most important to observe? </li></ul><ul><li>Would hurricane forecasts benefit from further observations over land? </li></ul><ul><li>Extend targeting and data denial experiments for satellite observations. </li></ul>