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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

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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 Gopalakrishnan1, Ibrahim Hoteit2, Bruce D. Cornuelle1

1Scripps Institution of Oceanography, University of California San Diego 2King Abdullah University of Science and Technology, Thuwal, Kingdom of Saudi Arabia

6th WMO Symposium on Data Assimilation, 2013

Ganesh 4DVAR/EnKF GoM State Estimation

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary

Background

Gulf of Mexico Circulation Energetic Loop currents (LC) and eddy shedding LC eddy vacillation and resulting eddy shedding and its westward propagation Forecasting LC evolution and eddy shedding with lead times of one or more weeks

Advising operational decisions of the Oil and Gas industry Ecosystem monitoring and emergency response Supporting Navy and Government’s diverse ocean explorations

Longitude ( o W ) Latitude ( o N ) MITgcm−IAS Domain: ( 1/10o resolution)

−5000 −5000 − 5 −4000 − 4 − 4 − 4 − 3 − 3 −3000 − 3 − 3 −3000 − 3 − 2 5 −2500 − 2 5 − 2 5 − 2 5 − 2 5 −2500 −2500 − 2 5 −2000 −2000 − 2 −2000 −2000 −2000 − 2 − 2 − 1 5 − 1 5 − 1 5 −1500 − 1 5 −1500 − 1 5 − 1 5 − 1 − 1 −1000 − 1 −1000 −1000 − 1 − 1 − 5 −500 − 5 −500 − 5 − 5 −500 − 5 − 5 − 5

Campeche Bank West Florida Shelf Lousiana−Texas Shelf F l

  • r

i d a N W P r

  • v

i d e n c e C h a n n e l O l d B a h a m a C h a n n e l Cuba 95 90 85 80 75 10 12 14 16 18 20 22 24 26 28 30 ( m ) −6000 −5000 −4000 −3000 −2000 −1000 Port−to−port position Averagely−extended position Fully−extended position

Intra Americas Seas showing GoM, LC, and eddy shedding processes (Gopalakrishnan et al. 2013a, 2013b) Ganesh 4DVAR/EnKF GoM State Estimation

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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

  • f 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

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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

  • f 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

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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

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary

−3000 − 3 −3000 − 3 −3000 −3000 −3000 −3000 −3000 − 3 −2000 −2000 −2000 −2000 −2000 −2000 − 2 −2000 −2000 −1000 −1000 − 1 − 1 −1000 − 1 −1000 −1000 −500 −500 −500 −500 −500 −500 −500 −500 −500 −500 −500

Longitude (o E) Latitude (o N) 265 270 275 280 285 10 12 14 16 18 20 22 24 26 28 30 ( cm ) −50 −40 −30 −20 −10 10 20 30 40 50

−3000 − 3 −3000 − 3 −3000 −3000 −3000 −3000 −3000 − 3 −2000 −2000 −2000 −2000 −2000 −2000 − 2 −2000 −2000 −1000 −1000 − 1 − 1 −1000 − 1 −1000 −1000 −500 −500 −500 −500 −500 −500 −500 −500 −500 −500 −500

Longitude (o E) Latitude (o N) 265 270 275 280 285 10 12 14 16 18 20 22 24 26 28 30 ( cm ) −50 −40 −30 −20 −10 10 20 30 40 50

Jason-1 ERS-2

−3000 − 3 −3000 − 3 −3000 −3000 −3000 −3000 −3000 − 3 −2000 −2000 −2000 −2000 −2000 −2000 − 2 −2000 −2000 −1000 −1000 − 1 − 1 −1000 − 1 −1000 −1000 −500 −500 −500 −500 −500 −500 −500 −500 −500 −500 −500

Longitude (o E) Latitude (o N) 265 270 275 280 285 10 12 14 16 18 20 22 24 26 28 30 ( cm ) −50 −40 −30 −20 −10 10 20 30 40 50 Longitude (o E) Latitude (o N)

−3000 −3000 −3000 −3000 −3000 − 3 −3000 − 3 −2000 −2000 −2000 −2000 −2000 −2000 −2000 −2000 −2000 −1000 −1000 −1000 −1000 −1000 −1000 −1000 −500 − 5 −500 −500 −500 −500 − 5 −500 −500 − 5 −500

265 270 275 280 285 10 12 14 16 18 20 22 24 26 28 30 ( o C ) 26 26.5 27 27.5 28 28.5 29 29.5 30 30.5 31

Envisat-1 SST

Ganesh 4DVAR/EnKF GoM State Estimation

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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 (Jdata) plus the weighted sum of squared control adjustments (Jcontrol) between the initial time (t0) and the final time (tf ) of the assimilation window constrained by the non-linear model equations subject to a set of control variables

J(u) =

tf

X

t=t0

[y(t) − Ht(x(t))]T R−1(t)[y(t) − Ht(x(t))] | {z }

Jdata

+

tf

X

t=t0

[u(t) − ub(t)]T Q−1(t)[u(t) − ub(t)] | {z }

Jcontrol

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

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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

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary

MITgcm and DART: EnKF assimilation

Based on the Data Assimilation Research Testbed (DART) package developed by NCAR [Anderson, J. L., 2001, 2003] Employs a variety of stochastic and deterministic EnKFs Allows advanced localization and inflation schemes essential for good behavior of EnKF Present study uses a deterministic Ensemble adjustment Kalman Filter (EaKF, [Anderson, J. L., 2001]) MITgcm is coupled to DART using an interface to exchange the information between the two codes

MITgcm/DART (Hoteit et al. 2013) Ganesh 4DVAR/EnKF GoM State Estimation

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary

MITgcm-EnKF parameters

Ensemble members were based on model EOFs from 2004 − 2008 forward integration Localization scheme based on Gaspari and Cohn (1999) : defined by a smooth function with a cut-off radius which limits the utmost distance that an observation might affect the neighboring grid points A prior multiplicative inflation factor was used Experiments using different ensemble members (25, 50, and 100) were tested, along with varying localization radius and inflation factor A mean DOT based on the difference between DNSCMSS08 and EGM08 (DNSCMSS08-EGM08) was added to along-track SSH anomalies to create total SSH signal A high SST observational error of 10◦C, and SSH error of 5 cm (for Jason1 and Jason2) and 10 cm (for Envisat1 and ERS-2) were used

Ganesh 4DVAR/EnKF GoM State Estimation

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary 265 270 275 280 18 20 22 24 26 28 30 Longitude (o E) Latitude (o N) MIT−A (100−ENS) : 2006−08−29 12:00:00 100 cm/s (a) 265 270 275 280 18 20 22 24 26 28 30 Longitude (o E) Latitude (o N) MIT−F (100−ENS) : 2006−08−29 12:00:00 (b) 265 270 275 280 18 20 22 24 26 28 30 Longitude (o E) Latitude (o N) MIT : 2006−08−29 12:00:00 100 cm/s (c) 265 270 275 280 18 20 22 24 26 28 30 Longitude (o E) Latitude (o N) MIT−REF : 2006−08−29 12:00:00 (d) 265 270 275 280 18 20 22 24 26 28 30 Longitude (o E) Latitude (o N) AVISO : 2006−08−29 12:00:00 (e) 265 270 275 280 18 20 22 24 26 28 30 Longitude (o E) Latitude (o N) HYCOM−GLOBAL : 2006−08−29 12:00:00 (f)

( m )

−0.5 −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 0.5

2006 (Eddy-Yankee): SSH fields at the end of hindcast

Ganesh 4DVAR/EnKF GoM State Estimation

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary 07/01/2006 07/15/2006 08/01/2006 08/15/2006 09/01/2006 09/15/2006 10/01/2006 10/15/200610/28/2006 0.05 0.1 0.15 0.2 Days RMS (m) SSH RMS : AVISO MIT MIT−P MIT−REF HYCOM−GLOBAL 07/01/2006 07/15/2006 08/01/2006 08/15/2006 09/01/2006 09/15/2006 10/01/2006 10/15/200610/28/2006 0.05 0.1 0.15 0.2 Days RMS (m) SSH RMS : AVISO MIT−A (100−ENS) MIT−P MIT−F (100−ENS) HYCOM−GLOBAL

Model-data rmsd for hindcast and forecast with respect to AVISO SSH for 4DVAR (top) and EnKF (bottom)

Ganesh 4DVAR/EnKF GoM State Estimation

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary 265 270 275 280 18 20 22 24 26 28 30 Longitude (o E) Latitude (o N) MIT−ENKF (MEAN STATE) : 2006−09−28 12:00:00 100 cm/s (a) 265 270 275 280 18 20 22 24 26 28 30 Longitude (o E) Latitude (o N) MIT−ENKF (ENS MEAN) : 2006−09−28 12:00:00 100 cm/s (b) 265 270 275 280 18 20 22 24 26 28 30 Longitude (o E) Latitude (o N) MIT−4DVAR : 2006−09−28 12:00:00 100 cm/s (c) 265 270 275 280 18 20 22 24 26 28 30 Longitude (o E) Latitude (o N) MIT−REF : 2006−09−28 12:00:00 (d) 265 270 275 280 18 20 22 24 26 28 30 Longitude (o E) Latitude (o N) AVISO : 2006−09−28 12:00:00 (e) 265 270 275 280 18 20 22 24 26 28 30 Longitude (o E) Latitude (o N) HYCOM−GLOBAL : 2006−09−28 12:00:00 (f)

( m )

−0.5 −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 0.5

SSH fields at the end of first month of model forecast

Ganesh 4DVAR/EnKF GoM State Estimation

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary 08/30/2006 09/15/2006 10/01/2006 10/15/2006 10/28/2006 0.05 0.1 0.15 0.2 Days RMS (m) SSH RMS : AVISO 4DVAR MIT−REF HYCOM−GLOBAL 25−ENS 100−ENS 08/30/2006 09/15/2006 10/01/2006 10/15/2006 10/28/2006 0.05 0.1 0.15 0.2 Days RMS (m) SSH RMS : AVISO 4DVAR MIT−REF HYCOM−GLOBAL 25−ENS 100−ENS

Model-data rmsd for forecast with respect to AVISO SSH. Comparison of ensemble mean forecast (top) Vs mean of ensemble forecast (bottom)

Ganesh 4DVAR/EnKF GoM State Estimation

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary

08/30/2006 09/15/2006 10/01/2006 10/15/2006 10/28/2006 0.05 0.1 0.15 0.2 Days RMS (m) SSH RMS : AVISO MIT (MEAN STATE) MIT (ENS MEAN) MIT−REF HYCOM−GLOBAL ENS

Model-data rmsd for EnKF ensemble forecast with respect to AVISO SSH

Ganesh 4DVAR/EnKF GoM State Estimation

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary

17cm SSH contour : ( 1 − week) Longitude Latitude 268 270 272 274 276 278 21 22 23 24 25 26 27 28 MIT MIT−ENS AVISO ENS 17cm SSH contour : ( 2 − week) Longitude Latitude 268 270 272 274 276 278 21 22 23 24 25 26 27 28 17cm SSH contour : ( 3 − week) Longitude Latitude 268 270 272 274 276 278 21 22 23 24 25 26 27 28 17cm SSH contour : ( 4 − week) Longitude Latitude 268 270 272 274 276 278 21 22 23 24 25 26 27 28

Evolution of LC forecast (SSH contour for 17 cm)

Ganesh 4DVAR/EnKF GoM State Estimation

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary

265 270 275 280 18 20 22 24 26 28 30 1 − week Max = 0.09 Min = 0.01 Ens Forecast Std (SSH) Longitude (o E) Latitude (o N) 265 270 275 280 18 20 22 24 26 28 30 2 − week Max = 0.14 Min = 0.02 Longitude (o E) Latitude (o N) 265 270 275 280 18 20 22 24 26 28 30 3 − week Max = 0.17 Min = 0.02 Longitude (o E) Latitude (o N) 265 270 275 280 18 20 22 24 26 28 30 4 − week Max = 0.26 Min = 0.02 Longitude (o E) Latitude (o N)

( m )

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 265 270 275 280 18 20 22 24 26 28 30 1 − week Max = 0.57 Min = −0.39 Ens Forecast Mean (SSH) Longitude (o E) Latitude (o N) 265 270 275 280 18 20 22 24 26 28 30 2 − week Max = 0.62 Min = −0.35 Longitude (o E) Latitude (o N) 265 270 275 280 18 20 22 24 26 28 30 3 − week Max = 0.63 Min = −0.31 Longitude (o E) Latitude (o N) 265 270 275 280 18 20 22 24 26 28 30 4 − week Max = 0.61 Min = −0.27 Longitude (o E) Latitude (o N)

( m )

−0.5 −0.4 −0.3 −0.2 −0.1 0.1 0.2 0.3 0.4 0.5

Evolution of Standard deviation and Mean of SSH ensemble forecast

Ganesh 4DVAR/EnKF GoM State Estimation

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary 04/30/2010 05/15/2010 06/01/2010 06/15/2010 06/28/2010 0.05 0.1 Days RMS (m) SSH RMS : AVISO 4DVAR MIT−REF HYCOM−GLOBAL 50−ENS 25−ENS

2010 (Eddy-Franklin): Model-data rmsd for forecast with respect to AVISO SSH.

Ganesh 4DVAR/EnKF GoM State Estimation

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary

Summary A 4DVAR and EnKF assimilation system has been developed for the Intra-Americas Seas producing ocean state estimate for analysis and forecasts The assimilation system has been cross-validated by forecasting the LC and eddy shedding events in the GoM including ensemble prediction and forecast uncertainties The skill metrics for the forecast using both methods generally

  • utperformed persistence (keeping the initial state fixed) and reference

(unadjusted) model runs during LC eddy shedding events for a longer forecast horizon of 4 ∼ 8 weeks The 4DVAR has better long-term (longer than 1 month) predictability compared to EnKF, while EnkF is better than 4DVAR for short-term forecasts The EnKF short-term predictability can be enhanced by increasing localization, which enables a better fit with the data

Ganesh 4DVAR/EnKF GoM State Estimation

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary

Acknowledgments

NCAR DAReS Group Several data sources: the Radar Altimetry Database System (RADS), AVISO, NCEP/NCAR Reanalysis-1, the HYCOM consortium, Remote Sensing Systems, Inc, and the ECCO consortium, including MIT, JPL, and the University of Hamburg

Ganesh 4DVAR/EnKF GoM State Estimation

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Background MITgcm-IAS model Observations MITgcm-4DVAR MITgcm-EnKF Results Summary

Thank You

Ganesh 4DVAR/EnKF GoM State Estimation