Ensemble Data Assimila.on and Uncertainty Quan.fica.on

Transcription

1 Ensemble Data Assimila.on and Uncertainty Quan.fica.on Jeffrey Anderson, Alicia Karspeck, Tim Hoar, Nancy Collins, Kevin Raeder, Steve Yeager Na.onal Center for Atmospheric Research Ocean Sciences Mee.ng 24 Feb

2 What is Data Assimila.on? Observa.ons combined with a Model forecast + to produce an analysis (best possible es.mate). Ocean Sciences Mee.ng 24 Feb

3 What is Ensemble Data Assimila.on? Use an ensemble (set) of model forecasts. Use sample sta.s.cs to get covariance between state and observa.ons. OYen assume that ensemble members are random draw. Ensemble methods I use are op.mal solu.on when: 1. Model is linear, 2. Observa.on errors are unbiased gaussian, 3. Rela.on between model and obs is linear, 4. Ensemble is large enough. Ocean Sciences Mee.ng 24 Feb

4 Atmospheric Ensemble Reanalysis, O(1 million) atmospheric obs are assimilated every day. Assimilation uses 8 members of 2 o FV CAM forced by a single ocean (Hadley+ NCEP-OI2) and produces a very competitive reanalysis. hpa GPH Feb Ocean Sciences Mee.ng 24 Feb

5 Ensemble Filter for Large Geophysical Models 1. Use model to advance ensemble (3 members here) to.me at which next observa.on becomes available. Ensemble state es.mate ayer using previous observa.on (analysis) Ensemble state at.me of next observa.on (prior) Ocean Sciences Mee.ng 24 Feb. 212

6 Ensemble Filter for Large Geophysical Models 2. Get prior ensemble sample of observa.on, y = h(x), by applying forward operator h to each ensemble member. Theory: observa.ons from instruments with uncorrelated errors can be done sequen.ally. Ocean Sciences Mee.ng 24 Feb

7 Ensemble Filter for Large Geophysical Models 3. Get observed value and observa.onal error distribu.on from observing system. Ocean Sciences Mee.ng 24 Feb

8 Ensemble Filter for Large Geophysical Models 4. Find the increments for the prior observa.on ensemble (this is a scalar problem for uncorrelated observa.on errors). Note: Difference between various ensemble filters is primarily in observa.on increment calcula.on. Ocean Sciences Mee.ng 24 Feb

9 Ensemble Filter for Large Geophysical Models. Use ensemble samples of y and each state variable to linearly regress observa.on increments onto state variable increments. Theory: impact of observa.on increments on each state variable can be handled independently! Ocean Sciences Mee.ng 24 Feb

10 Ensemble Filter for Large Geophysical Models 6. When all ensemble members for each state variable are updated, there is a new analysis. Integrate to.me of next observa.on Ocean Sciences Mee.ng 24 Feb. 212

11 Ensemble Filter for Lorenz Variable Model 4 state variables: X1, X2,..., X4. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. Acts something like synop.c weather around a la.tude band. time Ocean Sciences Mee.ng 24 Feb

12 Ensemble Filter for Lorenz Variable Model 4 state variables: X1, X2,..., X4. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. Acts something like synop.c weather around a la.tude band. time Ocean Sciences Mee.ng 24 Feb

13 Ensemble Filter for Lorenz Variable Model 4 state variables: X1, X2,..., X4. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. Acts something like synop.c weather around a la.tude band. time Ocean Sciences Mee.ng 24 Feb

14 Ensemble Filter for Lorenz Variable Model 4 state variables: X1, X2,..., X4. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. Acts something like synop.c weather around a la.tude band. time Ocean Sciences Mee.ng 24 Feb

15 Ensemble Filter for Lorenz Variable Model 4 state variables: X1, X2,..., X4. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. Acts something like synop.c weather around a la.tude band. time Ocean Sciences Mee.ng 24 Feb

16 Ensemble Filter for Lorenz Variable Model 4 state variables: X1, X2,..., X4. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. Acts something like synop.c weather around a la.tude band. time Ocean Sciences Mee.ng 24 Feb

17 Ensemble Filter for Lorenz Variable Model 4 state variables: X1, X2,..., X4. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. Acts something like synop.c weather around a la.tude band. time Ocean Sciences Mee.ng 24 Feb

18 Ensemble Filter for Lorenz Variable Model 4 state variables: X1, X2,..., X4. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. Acts something like synop.c weather around a la.tude band. time Ocean Sciences Mee.ng 24 Feb

19 Ensemble Filter for Lorenz Variable Model 4 state variables: X1, X2,..., X4. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. Acts something like synop.c weather around a la.tude band. time Ocean Sciences Mee.ng 24 Feb

20 Ensemble Filter for Lorenz Variable Model 4 state variables: X1, X2,..., X4. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. Acts something like synop.c weather around a la.tude band. time Ocean Sciences Mee.ng 24 Feb

21 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 2 truth ensemble Ocean Sciences Mee.ng 24 Feb

22 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 4 truth ensemble Ocean Sciences Mee.ng 24 Feb

23 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 6 truth ensemble Ocean Sciences Mee.ng 24 Feb

24 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 8 truth ensemble Ocean Sciences Mee.ng 24 Feb

25 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 1 truth ensemble Ocean Sciences Mee.ng 24 Feb

26 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 112 truth ensemble Ocean Sciences Mee.ng 24 Feb

27 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 114 truth ensemble Ocean Sciences Mee.ng 24 Feb

28 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 116 truth ensemble Ocean Sciences Mee.ng 24 Feb

29 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 118 truth ensemble Ocean Sciences Mee.ng 24 Feb

30 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 12 truth ensemble Ocean Sciences Mee.ng 24 Feb

31 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 122 truth ensemble Ocean Sciences Mee.ng 24 Feb

32 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 124 truth ensemble Ocean Sciences Mee.ng 24 Feb

33 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 126 truth ensemble Ocean Sciences Mee.ng 24 Feb

34 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 128 truth ensemble Ocean Sciences Mee.ng 24 Feb

35 Lorenz- 96 is sensi.ve to small perturba.ons Introduce 2 ensemble state es.mates. Each is slightly perturbed for each of the 4- variables at.me. Refer to unperturbed control integra.on as truth.. time 13 truth ensemble Ocean Sciences Mee.ng 24 Feb

36 Assimilate observa.ons from 4 random loca.ons each step. Observa.ons generated by interpola.ng truth to sta.on loca.on. Simulate observa.onal error: Add random draw from N(, 16) to each. Start from climatological 2- member ensemble. time 21 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

37 Assimilate observa.ons from 4 random loca.ons each step. Observa.ons generated by interpola.ng truth to sta.on loca.on. Simulate observa.onal error: Add random draw from N(, 16) to each. Start from climatological 2- member ensemble. time 23 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

38 Assimilate observa.ons from 4 random loca.ons each step. Observa.ons generated by interpola.ng truth to sta.on loca.on. Simulate observa.onal error: Add random draw from N(, 16) to each. Start from climatological 2- member ensemble. time 2 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

39 Assimilate observa.ons from 4 random loca.ons each step. Observa.ons generated by interpola.ng truth to sta.on loca.on. Simulate observa.onal error: Add random draw from N(, 16) to each. Start from climatological 2- member ensemble. time 27 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

40 Assimilate observa.ons from 4 random loca.ons each step. Observa.ons generated by interpola.ng truth to sta.on loca.on. Simulate observa.onal error: Add random draw from N(, 16) to each. Start from climatological 2- member ensemble. time 29 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

41 Assimilate observa.ons from 4 random loca.ons each step. Observa.ons generated by interpola.ng truth to sta.on loca.on. Simulate observa.onal error: Add random draw from N(, 16) to each. Start from climatological 2- member ensemble. time 211 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

42 Assimilate observa.ons from 4 random loca.ons each step. Observa.ons generated by interpola.ng truth to sta.on loca.on. Simulate observa.onal error: Add random draw from N(, 16) to each. Start from climatological 2- member ensemble. time 213 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

43 Assimilate observa.ons from 4 random loca.ons each step. Observa.ons generated by interpola.ng truth to sta.on loca.on. Simulate observa.onal error: Add random draw from N(, 16) to each. Start from climatological 2- member ensemble. time 21 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

44 Assimilate observa.ons from 4 random loca.ons each step. Observa.ons generated by interpola.ng truth to sta.on loca.on. Simulate observa.onal error: Add random draw from N(, 16) to each. Start from climatological 2- member ensemble. time 217 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

45 Assimilate observa.ons from 4 random loca.ons each step. This isn t working very well. Ensemble spread is reduced, but..., Ensemble is inconsistent with truth most places. time 219 truth ensemble obs Confident and wrong. Confident and right. Ocean Sciences Mee.ng 24 Feb

46 Some Error Sources in Ensemble Filters 2. Obs. operator error; Representa.veness 3. Observa.on error 4. Sampling Error; Gaussian Assump.on. Sampling Error; Assuming Linear Sta.s.cal Rela.on 1. Model error Ocean Sciences Mee.ng 24 Feb

47 Observa.ons impact unrelated state variables through sampling error. Expected Sample Correlation Members.1 2 Members 4 Members 8 Members True Correlation Plot shows expected absolute value of sample correla.on vs. true correla.on. Unrelated obs. reduce spread, increase error. Apack with localiza.on. Don t let obs. Impact unrelated state. Ocean Sciences Mee.ng 24 Feb

48 Lorenz- 96 Assimila.on with localiza.on of observa.on impact. Localization from Hierarchical Filter time 21 truth ensemble obs No Localization time 21 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

49 Lorenz- 96 Assimila.on with localiza.on of observa.on impact. Localization from Hierarchical Filter time 23 truth ensemble obs No Localization time 23 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

50 Lorenz- 96 Assimila.on with localiza.on of observa.on impact. Localization from Hierarchical Filter time 2 truth ensemble obs No Localization time 2 truth ensemble obs Ocean Sciences Mee.ng 24 Feb. 212

51 Lorenz- 96 Assimila.on with localiza.on of observa.on impact. Localization from Hierarchical Filter time 27 truth ensemble obs No Localization time 27 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

52 Lorenz- 96 Assimila.on with localiza.on of observa.on impact. Localization from Hierarchical Filter time 29 truth ensemble obs No Localization time 29 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

53 Lorenz- 96 Assimila.on with localiza.on of observa.on impact. Localization from Hierarchical Filter time 211 truth ensemble obs No Localization time 211 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

54 Lorenz- 96 Assimila.on with localiza.on of observa.on impact. Localization from Hierarchical Filter time 213 truth ensemble obs No Localization time 213 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

55 Lorenz- 96 Assimila.on with localiza.on of observa.on impact. Localization from Hierarchical Filter time 21 truth ensemble obs No Localization time 21 truth ensemble obs Ocean Sciences Mee.ng 24 Feb. 212

56 Lorenz- 96 Assimila.on with localiza.on of observa.on impact. Localization from Hierarchical Filter time 217 truth ensemble obs No Localization time 217 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

57 Lorenz- 96 Assimila.on with localiza.on of observa.on impact. Localization from Hierarchical Filter This ensemble is more consistent with truth. time 219 truth ensemble obs No Localization time 219 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

58 Localiza.on computed by empirical offline computa.on. Localization from Hierarchical Filter 1 time 219 truth ensemble obs Sample Observation Localizations Ocean Sciences Mee.ng 24 Feb

59 Some Error Sources in Ensemble Filters 2. Obs. operator error; Representa.veness 3. Observa.on error 4. Sampling Error; Gaussian Assump.on. Sampling Error; Assuming Linear Sta.s.cal Rela.on 1. Model error Ocean Sciences Mee.ng 24 Feb

60 Assimila.ng in the presence of simulated model error. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. For truth, use F = 8. In assimila.ng model, use F = 6. Time evolu.on for first state variable shown. Assimila.ng model quickly diverges from true model. Ocean Sciences Mee.ng 24 Feb

61 Assimila.ng in the presence of simulated model error. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. For truth, use F = 8. In assimila.ng model, use F = 6. time 31 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

62 Assimila.ng in the presence of simulated model error. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. For truth, use F = 8. In assimila.ng model, use F = 6. time 36 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

63 Assimila.ng in the presence of simulated model error. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. For truth, use F = 8. In assimila.ng model, use F = 6. time 311 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

64 Assimila.ng in the presence of simulated model error. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. For truth, use F = 8. In assimila.ng model, use F = 6. time 316 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

65 Assimila.ng in the presence of simulated model error. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. For truth, use F = 8. In assimila.ng model, use F = 6. time 321 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

66 Assimila.ng in the presence of simulated model error. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. For truth, use F = 8. In assimila.ng model, use F = 6. time 326 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

67 Assimila.ng in the presence of simulated model error. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. For truth, use F = 8. In assimila.ng model, use F = 6. time 331 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

68 Assimila.ng in the presence of simulated model error. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. For truth, use F = 8. In assimila.ng model, use F = 6. time 336 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

69 Assimila.ng in the presence of simulated model error. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. For truth, use F = 8. In assimila.ng model, use F = 6. time 341 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

70 Assimila.ng in the presence of simulated model error. dxi / dt = (Xi+1 - Xi- 2)Xi- 1 - Xi + F. For truth, use F = 8. In assimila.ng model, use F = 6. time 346 truth ensemble obs This isn t working again! It will just keep gesng worse. Ocean Sciences Mee.ng 24 Feb

71 Reduce confidence in model prior to deal with model error Use infla.on. Simply increase prior ensemble variance for each state variable. Adap.ve algorithms use observa.ons to guide this. Probability Prior PDF Inflated S.D. Inflate SD by 1. Variance by 1. 2 Obs Ocean Sciences Mee.ng 24 Feb

72 Assimila.ng with Infla.on in presence of model error. Infla.on is a func.on of state variable and.me. Automa.cally selected by adap.ve infla.on algorithm inflation Adaptive State Space Inflation time 31 truth ensemble obs No Inflation time 31 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

73 Assimila.ng with Infla.on in presence of model error. Infla.on is a func.on of state variable and.me. Automa.cally selected by adap.ve infla.on algorithm inflation Adaptive State Space Inflation time 36 truth ensemble obs No Inflation time 36 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

74 Assimila.ng with Infla.on in presence of model error. Infla.on is a func.on of state variable and.me. Automa.cally selected by adap.ve infla.on algorithm inflation Adaptive State Space Inflation time 311 truth ensemble obs No Inflation time 311 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

75 Assimila.ng with Infla.on in presence of model error. Infla.on is a func.on of state variable and.me. Automa.cally selected by adap.ve infla.on algorithm inflation Adaptive State Space Inflation time 316 truth ensemble obs No Inflation time 316 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

76 Assimila.ng with Infla.on in presence of model error. Infla.on is a func.on of state variable and.me. Automa.cally selected by adap.ve infla.on algorithm inflation Adaptive State Space Inflation time 321 truth ensemble obs No Inflation time 321 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

77 Assimila.ng with Infla.on in presence of model error. Infla.on is a func.on of state variable and.me. Automa.cally selected by adap.ve infla.on algorithm inflation Adaptive State Space Inflation time 326 truth ensemble obs No Inflation time 326 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

78 Assimila.ng with Infla.on in presence of model error. Infla.on is a func.on of state variable and.me. Automa.cally selected by adap.ve infla.on algorithm inflation Adaptive State Space Inflation time 331 truth ensemble obs No Inflation time 331 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

79 Assimila.ng with Infla.on in presence of model error. Infla.on is a func.on of state variable and.me. Automa.cally selected by adap.ve infla.on algorithm inflation Adaptive State Space Inflation time 336 truth ensemble obs No Inflation time 336 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

80 Assimila.ng with Infla.on in presence of model error. Infla.on is a func.on of state variable and.me. Automa.cally selected by adap.ve infla.on algorithm inflation Adaptive State Space Inflation time 341 truth ensemble obs No Inflation time 341 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

81 Assimila.ng with Infla.on in presence of model error Infla.on is a func.on of state variable and.me. Automa.cally selected by adap.ve infla.on algorithm. It can work, even in presence of severe model error. inflation Adaptive State Space Inflation time 346 truth ensemble obs No Inflation time 346 truth ensemble obs Ocean Sciences Mee.ng 24 Feb

82 Uncertainty Quan.fica.on from an Ensemble Kalman Filter Ø (Ensemble) KF op.mal for linear model, gaussian likelihood, perfect model. Ø In KF, only mean and covariance have meaning. Ø Ensemble allows computa.on of many other sta.s.cs. Ø What do they mean? Not en.rely clear. Ø What do they mean when there are all sorts of error? Even less clear. Ø Must Calibrate and Validate results. Ocean Sciences Mee.ng 24 Feb

83 Obs DART Current Ocean (POP) Assimila.on DATM 3D state 2D forcing from CAM assimila.on POP Coupler 3D restart 2D forcing Ocean Sciences Mee.ng 24 Feb

84 World Ocean Database T,S observa.on counts These counts are for 1998 & 1999 and are representa.ve. FLOAT_SALINITY 682 FLOAT_TEMPERATURE 3932 DRIFTER_TEMPERATURE MOORING_SALINITY MOORING_TEMPERATURE BOTTLE_SALINITY 798 BOTTLE_TEMPERATURE CTD_SALINITY CTD_TEMPERATURE STD_SALINITY 674 STD_TEMPERATURE 677 XCTD_SALINITY 3328 XCTD_TEMPERATURE 79 MBT_TEMPERATURE 826 XBT_TEMPERATURE 9333 APB_TEMPERATURE 8111 temperature observa.on error standard devia.on ==. K. salinity observa.on error standard devia.on ==. msu. Ocean Sciences Mee.ng 24 Feb

85 Physical Space: 1998/1999 SST Anomaly from HadOI- SST Coupled Free Run POP forced by observed atmosphere (hindcast) Ensemble Assimila.on 48 POP oceans Forced by 48 CAM reanalyses Ocean Sciences Mee.ng 24 Feb

86 Challenges where ocean model is unable, or unwilling, to simulate reality. Example: cross sec.on along Kuroshio; model separates too far north. Hurrell SST 2 4 o N 4 o N 3 o N 3 o N 2 1 Regarded to be accurate. 2 o N 12 o E 132 o E 144 o E 16 o E 168 o E 18 o W POP SST 2 4 o N 4 o N 3 o N 3 o N 2 1 Free run of POP, the warm water is too far North. 2 o N 12 o E 132 o E 144 o E 16 o E 168 o E 18 o W Ocean Sciences Mee.ng 24 Feb

87 Challenges in correc.ng posi.on of Kuroshio. 6- day assimila.on star.ng from model climatology on 1 January 24. Temperature Temperature Temperature.me = days.me = 2days.me = 3days La.tude La.tude La.tude Ini.ally warm water goes too far north. Many observa.ons are rejected (red), but others (blue) move temperature gradient south. Adap.ve infla.on increases ensemble spread as assimila.on struggles to push model towards obs..me = 4days.me = days.me = 6days Ocean Sciences Mee.ng 24 Feb

88 Challenges in correc.ng posi.on of Kuroshio. 6- day assimila.on star.ng from model climatology on 1 January 24. Green dashed line is posterior at previous.me, Blue dashed line is prior at current.me, Ensembles are thin lines. Model forecasts finally fail due Observa.ons keep pulling the warm water to the south; to numerical issues. Black Model forecasts con.nue to quickly move warm water dashes show original model further.me north. = days Infla.on con.nues to.me increase = 2days spread..me = 3days state from January. Temperature Temperature Temperature.me = 4days.me = days.me = 6days La.tude La.tude La.tude Ocean Sciences Mee.ng 24 Feb

89 Challenges in correc.ng posi.on of Kuroshio. 6- day assimila.on star.ng from model climatology on 1 January 24. Assimila.on cannot force model to fit observa.ons. Use of adap.ve infla.on leads to eventual model failure. Reduced adap.ve infla.on can lead to compromise between observa.ons and model..me = days.me = 2days.me = 3days Temperature Temperature Temperature.me = 4days.me = days.me = 6days La.tude La.tude La.tude Ocean Sciences Mee.ng 24 Feb

90 Ensemble DA and UQ for Global Ocean Models Ø Very certain that model predic.ons are different from observa.ons. Ø Very certain that small correla.ons have large errors. Ø Moderately confident that large correla.ons are realis.c. Ø Very uncertain about state in sparse/unobserved regions. Ø Must Calibrate and Validate results (adap.ve infla.on/localiza.on). Ø There may not be enough observa.ons to do this many places. Ø First order of business: Improving models. DA can help with this. Ocean Sciences Mee.ng 24 Feb

91 Code to implement all of the algorithms discussed are freely available from: hpp:// Ocean Sciences Mee.ng 24 Feb