Estimating Vertical Eddy Viscosity in the Pacific Equatorial Undercurrent Natalia Stefanova Masters Thesis Defense October 31, 2008 UW School of Oceanography

Masters Committee Chair Mike McPhaden (Advisor), NOAA/PMEL and UW Physical Oceanography Masters Committee Members Billy Kessler, NOAA/PMEL, UW Physical Oceanography Jim Murray, UW Chemical Oceanography LuAnne Thompson, UW Physical Oceanography Other collaborators Xuebin Zhang, NOAA/PMEL

Objective: Use TAO data to estimate seasonal to interannual time scale changes in the vertical eddy viscosity in the EUC using an inverse model based on linear dynamics Outline: The Equatorial Undercurrent (EUC) and eddy viscosity Inferring vertical eddy viscosity from large-scale fields Results from the OGCM test Results from TAO buoy and SODA reanalysis data Conclusions OutlineIntroductionMethodsModel TestTAO and SODAConclusions

The Equatorial Pacific Ocean OutlineIntroductionMethodsModel TestTAO and SODAConclusions a very large area: small changes in sea surface temperatures large effect on tropical and global climate: El Niño and La Niña climate models cannot accurately represent ENSO yet USA Today, Aug. 19, 1997 ScienceDaily, Jan. 16, 2008 Surfer Magazine, 1998 EUC

The Equatorial Undercurrent (EUC) OutlineIntroductionMethodsModel TestTAO and SODAConclusions A fast subsurface current along the Equator Flows eastward and upward in the upper thermocline opposite to surface currents and winds Feeds equatorial upwelling and affects SST Varies on seasonal and ENSO timescales dynamics strongly constrained by vertical turbulent mixing Johnson et al 2002 EUC SEC(S)SEC(N) TJ(S)TJ(N) NECC

Introduction: Vertical Eddy Viscosity OutlineIntroductionMethodsModel TestTAO and SODAConclusions Highly variable in both time and space Along the equator turbulent friction is a zero order term in the dynamical balance Hard to measure directly Models have to parameterize it OGCM Turbulent Viscosity (shading) and Zonal Velocity (contour)

Inferring Eddy Viscosity Zonal momentum equation without horizontal diffusion: OutlineIntroductionMethodsModel TestTAO and SODAConclusions We assume the stress is proportional to the shear: Then integrate from a depth -h to the surface to get: lineartimenon-linear

OGCM Output Princeton Ocean Model (POM) Flat-bottom 4000 m deep 29 layers 1˚ zonal and 1/3˚ meridional forced by daily ECMWF-ERA 40 reanalysis data from 1979 to 2002 Pacanowski and Philander 1981, Richardson number vertical mixing Output every 2.5 days OutlineIntroductionMethodsModel TestTAO and SODAConclusions

Eddy Viscosity Profile at 110°W OutlineIntroductionMethodsModel TestTAO and SODAConclusions Depth (m) Eddy viscosity (cm 2 s -1 ) Zonal velocity (cm s -1 ) OGCM Turbulent Viscosity (shading) and Zonal Velocity (contour) Reasonable estimates can be obtained only in the high shear zone above the core OGCM viscosity zonal velocity

Eddy Viscosity Profile at 110°W Reasonable estimates can be obtained only in the high shear zone above the core OGCM viscosity zonal velocity linear+nonlinear+time Depth (m) Eddy viscosity (cm 2 s -1 ) Zonal velocity (cm s -1 ) OGCM Turbulent Viscosity (shading) and Zonal Velocity (contour) OutlineIntroductionMethodsModel TestTAO and SODAConclusions

Eddy Viscosity Profile at 110°W Reasonable estimates can be obtained only in the high shear zone above the core OGCM viscosity zonal velocity linear+nonlinear+time linear Depth (m) Eddy viscosity (cm 2 s -1 ) Zonal velocity (cm s -1 ) OGCM Turbulent Viscosity (shading) and Zonal Velocity (contour) OutlineIntroductionMethodsModel TestTAO and SODAConclusions

Eddy Viscosity at 25m at 110°W Time (years) Eddy viscosity (cm 2 s -1 ) Correlation = linear OGCM OutlineIntroductionMethodsModel TestTAO and SODAConclusions

Eddy Viscosity at 25m at 110°W Time (years) Eddy viscosity (cm 2 s -1 ) Correlation = linear OGCM ‘u dudx’ term ‘v dudy’ term ‘w dudz’ term ‘dudt’ term OutlineIntroductionMethodsModel TestTAO and SODAConclusions

Seasonal Cycle at 25m at 110°W Time (months) Eddy viscosity (cm 2 s -1 ) linear OGCM nonlinear time March: Stratification Ri Mixing OutlineIntroductionMethodsModel TestTAO and SODAConclusions

Anomalies at 25m at 110°W Time (years) Eddy viscosity anomalies (cm 2 s -1 ) linear OGCM OutlineIntroductionMethodsModel TestTAO and SODAConclusions

What happens when we repeat the same calculation with (almost) real data?

Tropical Atmosphere Ocean (TAO) Buoy Array Data TAO ADCP zonal velocity 1990s m vertical resolution, hourly measurements 4 sites: 165°E, 170°W, 140°W, 110°W In this study: monthly means OutlineIntroductionMethodsModel TestTAO and SODAConclusions Images from

SODA Reanalysis Data Simple Ocean Data Assimilation (SODA) vertical layers, 3600 meters depth at the equator 0.5º lat x 0.5º lon resolution forced by ECMWF-ERA 40 ( ) and QuickSCAT satellite ( ) data Large et al K-Profile Parameterization (KPP), bi-harmonic mixing scheme In this study: monthly averages of temperature, salinity, sea surface height, wind stress At the same 4 equatorial sites with emphasis on the Eastern Pacific OutlineIntroductionMethodsModel TestTAO and SODAConclusions Carton et al 2007 and personal communication Black = TAO u Red = SODA u SODA/ TAO Comparisons: zonal velocity u [cm/s] at 0ºN 140ºW

Input: 1. SODA velocity, T, S, sea surface height, wind stress 2. TAO zonal velocity + SODA T, S, sea surface height, wind stress Equation: Output: 1. Vertical eddy viscosity from all SODA 2. Viscosity from TAO and SODA Inferring Eddy Viscosity OutlineIntroductionMethodsModel TestTAO and SODAConclusions lineartime non-linear

Eddy Viscosity Profile at 110°W Reasonable estimates can be obtained only in the high shear zone above the core zonal velocity OGCM viscosity linear OGCM viscosity Depth (m) Eddy viscosity (cm 2 s -1 ) Zonal velocity (cm s -1 ) OGCM Turbulent Viscosity (shading) and Zonal Velocity (contour) OutlineIntroductionMethodsModel TestTAO and SODAConclusions

Eddy Viscosity Profile at 110°W Reasonable estimates can be obtained only in the high shear zone above the core zonal velocity OGCM viscosity linear OGCM viscosity linear SODA viscosity Depth (m) Eddy viscosity (cm 2 s -1 ) Zonal velocity (cm s -1 ) OGCM Turbulent Viscosity (shading) and Zonal Velocity (contour) OutlineIntroductionMethodsModel TestTAO and SODAConclusions

Eddy Viscosity Profile at 110°W Reasonable estimates can be obtained only in the high shear zone above the core zonal velocity OGCM viscosity linear OGCM viscosity linear SODA viscosity linear+time SODA viscosity Depth (m) Eddy viscosity (cm 2 s -1 ) Zonal velocity (cm s -1 ) OGCM Turbulent Viscosity (shading) and Zonal Velocity (contour) OutlineIntroductionMethodsModel TestTAO and SODAConclusions

Eddy Viscosity Profile at 110°W Reasonable estimates can be obtained only in the high shear zone above the core zonal velocity OGCM viscosity linear OGCM viscosity linear SODA viscosity linear+time SODA viscosity linear+nonl+time SODA viscosity Depth (m) Eddy viscosity (cm 2 s -1 ) Zonal velocity (cm s -1 ) OGCM Turbulent Viscosity (shading) and Zonal Velocity (contour) OutlineIntroductionMethodsModel TestTAO and SODAConclusions

Eddy Viscosity Profile at 110°W Depth (m) Eddy viscosity (cm 2 s -1 ) Zonal velocity (cm s -1 ) OGCM Turbulent Viscosity (shading) and Zonal Velocity (contour) OutlineIntroductionMethodsModel TestTAO and SODAConclusions Reasonable estimates can be obtained only in the high shear zone above the core zonal velocity OGCM viscosity linear OGCM viscosity linear SODA viscosity linear+time SODA viscosity linear+nonl+time SODA viscosity linear TAO-SODA viscosity

Eddy Viscosity at 45m at 110ºW OutlineIntroductionMethodsModel TestTAO and SODAConclusions SODA linearSODA with timeSODA with time and nonlinearSODA and TAO linear

Seasonal cycle at 45m at 110ºW OutlineIntroductionMethodsModel TestTAO and SODAConclusions SE ≈ 10% SODA linear SODA all terms SODA-TAO OGCM [cm 2 /s]

Seasonal cycle at 45m at 110ºW OutlineIntroductionMethodsModel TestTAO and SODAConclusions March: Stratification SODA linear SODA all terms SODA-TAO OGCM [cm 2 /s] N2N2 SE ≈ 10%

Seasonal cycle at 45m at 110ºW OutlineIntroductionMethodsModel TestTAO and SODAConclusions March: Stratification SODA linear SODA all terms SODA-TAO OGCM [cm 2 /s] SE ≈ 10% N2N2 shear

Seasonal cycle at 45m at 110°W OutlineIntroductionMethodsModel TestTAO and SODAConclusions March: Warmest season High SST Weakest winds Weak upwelling SODA linear SODA all terms SODA-TAO OGCM [cm 2 /s] SE ≈ 10% March: Stratification Ri Mixing N2N2 shear Ri - 1

Anomalies at 45m at 110W OutlineIntroductionMethodsModel TestTAO and SODAConclusions SODA all terms viscosity

Anomalies at 45m at 110W OutlineIntroductionMethodsModel TestTAO and SODAConclusions SODA all terms viscosityStratification

Anomalies at 45m at 110W OutlineIntroductionMethodsModel TestTAO and SODAConclusions SODA all terms viscosityStratification Shear

Anomalies at 45m at 110W OutlineIntroductionMethodsModel TestTAO and SODAConclusions SODA all terms viscosityStratification ShearRi -1

Conclusion: Vertical Eddy Viscosity The calculation robust only in the high-shear zone above the EUC core: shear larger so the resulting profile is smoother vertical integration error not as big physically, closer to the surface the winds have more effect Qualitatively, the calculation seems to work better in the Eastern Pacific but further analysis is needed to understand why OGCM Turbulent Viscosity (shading) and Zonal Velocity (contour) OutlineIntroductionMethodsModel TestTAO and SODAConclusions

Conclusions: OGCM output test implies that we can use linear dynamics to estimate vertical eddy viscosity above the EUC core only Using TAO and SODA data with the same equation also gives good results only above the EUC core The horizontal pressure gradient, even though problematic to estimate with sparse data, cannot be left out in order to get accurate viscosity Calculating the horizontal pressure gradient over various distances (1 deg, 10 deg, 20 deg, 30 deg) does not have a significant effect on the final result of viscosity, so using observations when available would work well Open Questions: Why does TAO data give different results during the big La Nina? What will the viscosity look like with all “real” (TAO?) data? OutlineIntroductionMethodsModel TestTAO and SODAConclusions

La Nina - cool Pacific Ocean - slower jet stream - faster Earth spin - less time in a day But during La Nina the eddy viscosity is lower than usual So does running out of time imply low eddy viscosity? Or, can low rates of mixing be blamed for lost time?

Thank you!

Inferring eddy viscosity

Pacanowski and Philander mixing scheme (JPO 1981) Mixing processes strongly influenced by the shears of mean currents: vertical eddy viscosity