Comparison of 4DVAR and EnKF state estimates and forecasts in the - PowerPoint PPT Presentation

Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary Comparison of 4DVAR and EnKF state estimates and forecasts in the Gulf of Mexico Ganesh Gopalakrishnan 1 , Ibrahim Hoteit 2 , Bruce D. Cornuelle 1 1 Scripps Institution of Oceanography, University of California San Diego 2 King Abdullah University of Science and Technology, Thuwal, Kingdom of Saudi Arabia 6 th WMO Symposium on Data Assimilation, 2013 Ganesh 4DVAR/EnKF GoM State Estimation

Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary Background Gulf of Mexico Circulation Energetic Loop currents (LC) and eddy shedding ( m ) MITgcm−IAS Domain: ( 1/10 o resolution) 0 30 LC eddy vacillation and resulting 0 0 0 West Florida Shelf 1 Lousiana−Texas Shelf − 28 −1000 F eddy shedding and its westward o l − 5 0 0 r −1000 i d a − 2 0 0 0 N W 26 −2500 −3000 P r propagation o v i d e n 0 c e 0 C 5 −2000 h a 1 − − −4000 n n −5000 − 5 0 0 1 − e 5 3 l 24 −2500 0 0 0 0 0 −2000 − 5 0 0 Forecasting LC evolution and eddy O l − 0 Campeche Bank d B −500 1 0 0 − a 5 22 3 1 Cuba h a 0 − 5 0 m 0 0 0 0 −2000 a − C 2 5 −2000 h Latitude ( o N ) a n 0 n e shedding with lead times of one or 0 l 0 −2500 1 −3000 0 − −1500 5 0 20 0 − 2 − 1 0 0 0 0 0 −500 4 −3000 − 0 0 more weeks 0 0 −5000 0 0 −2000 3 0 5 3 0 − − − 2 0 0 − 0 2 − 5 0 0 1 5 − 0 0 − 5 − 1 5 0 0 0 0 0 1 0 0 0 0 18 − 4 0 − − 5 0 0 0 5 0 0 −1000 − 0 5 0 −2000 1 Advising operational decisions of − − 5 0 0 16 5 0 0 − 2 −4000 the Oil and Gas industry 0 0 Port−to−port position 0 2 − 14 − 4 0 0 0 Averagely−extended position Ecosystem monitoring and 0 0 Fully−extended position 5 2 12 0 0 − −5000 − 2 −1000 0 emergency response −1500 −500 0 0 0 10 3 − Supporting Navy and −6000 Government’s diverse ocean 95 90 85 80 75 Longitude ( o W ) explorations Intra Americas Seas showing GoM, LC, and eddy shedding processes ( Gopalakrishnan et al. 2013a, 2013b ) Ganesh 4DVAR/EnKF GoM State Estimation

Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary Main focus of the present study To produce an ocean state estimate by assimilating satellite measurements of SSH and SST over a period of two months using four-dimensional variational (MITgcm-4DVAR) and ensemble Kalman filter (MITgcm-EnKF) assimilation systems for the Gulf of Mexico (GoM) To predict the circulation in the GoM including loop current (LC) evolution and eddy (LCE) shedding To compare the quality of the ocean state estimates and forecasts using both methods including the contribution of the ensemble prediction and forecast uncertainties Assessment of LC predictability with a long forecast horizon of 4 ∼ 8 weeks: Beneficial for public and private stakeholders in the GoM Ganesh 4DVAR/EnKF GoM State Estimation

Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary MITgcm-Intra Americas Seas Model 1/(10 ◦ ) Horizontal resolution 40 vertical z -levels ( ∼ 5m near surface) NCEP/NCAR Reanalysis-1 surface winds/fluxes: bulk formulation [ Large and Pond (1981) ] HYCOM + NCODA global (1 / 12 ◦ ) analysis boundary conditions [ Chassignet et al (2007) ], ( http://hycom.org/dataserver/glb-analysis ) Monthly climatological run-off fluxes MITgcm-4DVAR: SSH and SST data in the GoM were assimilated for a period of two months using HYCOM state as the first guess. MITgcm-EnKF: SSH and SST data in the GoM were assimilated sequentially every 3 days for a period of 60 days using ensemble members based on the model EOFs from 2004 − 2008 forward integration The GoM state estimate obtained using both methods is cross-validated by using it as initial conditions for forecasting the ocean state including LC eddy separation. Ganesh 4DVAR/EnKF GoM State Estimation

Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary Observations Sea Surface Height (SSH) along-track anomalies from the Radar Altimetry Database System (RADS: http://rads.tudelft.nl/rads/index.shtml ). SSH anomalies from satellites: Jason-1 (J1), Jason-2 (J2), Envisat (N1), ans ERS-2 (E2) were used Sea Surface Temperature (SST) data from the daily optimally interpolated product derived from the TMI-AMSRE (TMI-AMSRE OI product with ∼ 25km resolution), produced by the Remote Sensing Systems Inc. ( http://www.remss.com/ ) Used inverted barometer correction ( local - global mean pressure ) and the geoid correction ( DNSC08 mean sea surface ) along with RADS default corrections Used time mean DOT calculated from the difference between DNSCMSS08 [ Andersen and Knudsen (2009) ] and EGM08 (DNSCMSS08-EGM08) Ganesh 4DVAR/EnKF GoM State Estimation

Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary ( cm ) ( cm ) 50 50 30 −2000 30 −2000 − − 1 0 1 0 0 0 40 0 0 40 28 28 −500 −500 −500 −500 30 30 26 −2000 −3000 −1000 26 −2000 −3000 −1000 − 2 − 2 0 0 0 −3000 0 0 0 −3000 24 −500 20 24 −500 20 −3000 −500 −3000 −500 −500 −500 Latitude ( o N) 0 Latitude ( o N) 0 22 0 10 22 0 10 0 0 1 −2000 1 −2000 − −2000 − −2000 −3000 0 −3000 0 0 0 0 0 −1000 3 −1000 3 20 − 20 − 0 0 0 0 0 0 −500 3 0 −1000 −3000 −2000 −500 3 0 −1000 −3000 −2000 − −500 −1000 −500 − −500 −1000 −500 18 −3000 18 −3000 −500 −10 −500 −10 −1000 −1000 16 −500 −2000 16 −500 −2000 −20 −20 −2000 −2000 14 14 0 0 0 −30 0 −30 −3000 3 0 −3000 3 0 − − 12 −2000 12 −2000 0 0 − 1 0 0 − 1 0 0 −500 −500 −40 −40 10 10 −50 −50 265 270 275 280 285 265 270 275 280 285 Longitude ( o E) Longitude ( o E) Jason-1 ERS-2 ( o C ) ( cm ) 50 31 30 −2000 30 − 1 0 0 0 40 30.5 28 28 −500 −500 −500 30 26 −2000 −1000 −2000 30 −3000 26 − 3 0 0 0 − 2 −2000 0 0 0 −3000 24 −500 20 −500 −500 −3000 29.5 24 −1000 −500 −500 −3000 Latitude ( o N) 0 −500 0 22 0 10 Latitude ( o N) −3000 0 0 22 5 −1000 29 1 −2000 − −2000 − −2000 −2000 −2000 −3000 0 0 0 −3000 −1000 3 − 20 − 20 5 −1000 0 0 0 28.5 0 0 0 −500 3 0 −3000 −2000 0 0 −3000 −2000 − −1000 −500 −1000 −500 3 −1000 −500 −1000 −500 − 18 −3000 18 −500 −10 28 −1000 − 5 0 0 −2000 −500 −2000 −1000 16 16 −500 −20 27.5 −2000 −2000 14 14 0 0 −30 27 −3000 3 0 − −3000 12 −2000 12 −2000 0 − 1 0 0 −500 −500 −40 −3000 26.5 10 10 −1000 −50 26 265 270 275 280 285 265 270 275 280 285 Longitude ( o E) Longitude ( o E) Envisat-1 SST Ganesh 4DVAR/EnKF GoM State Estimation

Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary MITgcm and ECCO: 4DVAR assimilation Strong constraint 4DVAR: Based on the Estimating the Circulation and Climate of the Ocean (ECCO) system Minimization of a “cost function” ( J ) penalizing the weighted sum of squared misfits between model and observations ( J data ) plus the weighted sum of squared control adjustments ( J control ) between the initial time ( t 0 ) and the final time ( t f ) of the assimilation window constrained by the non-linear model equations subject to a set of control variables tf tf X [ y ( t ) − H t ( x ( t ))] T R − 1 ( t )[ y ( t ) − H t ( x ( t ))] X [ u ( t ) − u b ( t )] T Q − 1 ( t )[ u ( t ) − u b ( t )] J ( u ) = + t = t 0 t = t 0 | {z } | {z } J data J control The gradient of the cost function obtained by integrating the adjoint of the tangent linear model backward in time [ Le Dimet and Talagrand (1986) ] determines the descent directions toward the minimum of the cost function and is solved iteratively using conjugate-gradient algorithm Ganesh 4DVAR/EnKF GoM State Estimation

Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary MITgcm-4DVAR controls and optimization Model controls Initial conditions for Temperature and Salinity ( T, S ). The adjustments to the starting guess controls were penalized in the cost function. Observation/Background Uncertainties Daily and spatially bin-averaged along-track SSH observations were separated into time mean and anomalies and were separately fit to the model mean SSH and daily mean SSH anomalies, using larger uncertainty for the mean SSH and identical space and time averaging SSH anomaly and geoid uncertainty was assumed to be spatially-invariant: 5 cm for Jason-1 and Jason-2, 10 cm for Envisat and ERS-2, and 10 cm for geoid Used high SST observational uncertainty, especially near the coast Background uncertainties for the Initial condition controls were computed from the standard deviation (over time) of the model variability over 2004 − 2008 forward integration ECCO system enforces 2D and 3D smoothness of control variables following [ Weaver (2003) ] with a horizontal decorrelation scale of 50 km Ganesh 4DVAR/EnKF GoM State Estimation