Timescales of mesoscale eddy equilibration in the Southern Ocean

Transcription

1 Timescales of mesoscale eddy equilibration in the Southern Ocean Anirban Sinha & Ryan P. Abernathey Columbia University in the City of New York Southern Ocean Workshop, NCAR April 13, 2017 Image courtesy Los Alamos National Lab,

2 Southern Ocean Momentum Balance westerly winds Ekman pumping: steepens isopycnals Eddy restratification Neutral Density Existing Theoretical Framework (Gill et. al. 1974, Marshall & Speer, 2012; Hallberg & Gnanadesikan, 2006; Abernathey & Cessi, 2014): Competition between wind driven upwelling and baroclinic eddies determines mean isopycnal slope, ACC transport, and MOC

3 Meredith & Hogg (2006, GRL) satellite altimetry model SAM EKE 2 ~ 3 yrs 2 ~ 3 yrs 2 ~ 3 yrs Meredith et al. (2012)

4 Power Spectra of Winds NCAR Reanalysis ERA Interim

5 EKE lags wind stress by 2-3 years But why? Wind Stress > APE > EKE Variable Wind forcing at surface Simple model: channel SO wind power input Conversion term d(ap E) = W dt C d(eke) = C dt D Adiabatic Interior C = ZZZ Drag dv w 0 b 0 K GM (rb) 2 N 2

6 Simple model: w/o Eddy feedback dp (t) = f(t) dt cp (t) dk(t) = cp (t) dt rk(t) GM type closure linear bottom drag Transfer Function f = ˆfe i!t = ˆf e i!t+ f P = ˆPe i!t = ˆP e i!t+ P K = ˆKe i!t = ˆK e i!t+ K ˆK ˆf, ˆP ˆf K f, P f c K GM L 2 y 10 9 s 1 (~3 years!)

7 Simple model w/o Eddy feedback dp (t) dt dk(t) dt = f(t) cp (t) = cp (t) rk(t) Same as c, (eddy mixing coeff) with Eddy feedback based on mixing length arguments dp dt = f kpk dk = kpk r dt 1 K general bottom drag linearize and solve for Two conversion terms : c 1, c 2 New term, (eddy feedback) dp 0 dt = f 0 c 1 P 0 c 2 K 0 dk 0 dt = c 1 P 0 + c 2 K 0 rk 0 Sinha & Abernathey (JPO, 2016)

8 Isopycnal GOLD model: (Hallberg & Gnanadesikan, 2001, 2006; Howard et al. 2015) x (3200 km) Reduced gravity model 4 km horizontal resolution Three isopycnal layers Wind forcing only z (4 km) Eight experiments Steady sinusoidal wind jet (0.2 N/m^2) plus oscillations +/- (0.1 N/ m^2), 0.25, 0.5,1, 2, 4, 8, 16 year periods y (1600 km) Diagnostics EKE APE Wind Energy input Sinha & Abernathey (JPO, 2016)

9 Spectral Analysis energy input: same power, different frequency response: different amplitudes Sinha & Abernathey (JPO, 2016)

10 Composite Analysis

11 Composite Analysis Sinha & Abernathey (JPO, 2016)

12 Compare Analytic & Numerical Model dp 0 dt = f 0 c 1 P 0 c 2 K 0 dk 0 dt = c 1 P 0 + c 2 K 0 rk 0 weak eddy feedback c 1 = f/p ; c 2 = f/2k ~560 days ~157 days strong eddy feedback c 1 = f/p ; c 2 = f/k ~560 days ~78 days Sinha & Abernathey (JPO, 2016)

13 Discussions Eddy generation and dissipation - non-local in time Eddy memory effect - Time dependent eddy parameterization

14 Eddy Feedback vs Eddy Memory Eddy Feedback Southern Ocean (Sinha and Abernathey, 2016 JPO) Eddy Memory Beaufort Gyre (Manucharyan et al. in press)

15 Discussions Eddy generation and dissipation - non-local in time Eddy memory effect - Time dependent eddy parameterization Used in conjunction with multiple timescale response to thermodynamic forcing (Ferreira et al 2014 )(sea ice, ozone depletion etc.) - more complete theory for SO response, baroclinic eddy equilibration

16 Summary Two limits : Fast vs Slow - Transient response to changing winds Analytical model: Energy Budget - wind power, APE, EKE with and without eddy feedback smooth transfer function, complex phase and amplitude response to changing winds: Regime shift Numerical simulations with idealized model mechanistic description of the eddy equilibration process with purely dynamic forcing

17 Thank you.

18 Appendix

19 Simple model: Energy pathway wind work ZZ da u W K m C Km!P m P m = W C Pm!P t dissipation D K t C Pt!K t P t EKE steady-state balance = C APE wind power input d(ap E) dt d(eke) dt C = Conversion term = W C = C D Drag term ZZZ dv w 0 b 0 K GM (rb) 2 N 2

20 Meredith & Hogg (2006, GRL) Simple model: channel SO SAM EKE Variable Wind forcing at surface 2 ~ 3 yrs Wind Stress > APE > EKE Adiabatic Interior Simple model: Energy pathway d(ap E) = W dt C d(eke) = C dt D wind power input Conversion term Drag term C = ZZZ w 0 b 0 dv K GM (rb) 2 N 2

21 Simple model with Eddy Feedback

22 Spectral Amplitude Response

23 Transport Spectra

24 Amplitude and Phase from Composite

25 Composite Transport