Shelf Water Entrainment by Gulf Stream Warm Core Rings

1. Shelf Water Entrainment by Gulf Stream Warm Core Rings By Ayan Chaudhuri

2. Agenda • Overview • Data • Quasi-geostrophic Potential Vorticity Model • Ring Entrainment Model • Results • Future Work

3. Overview • Common Occurrence of Gulf Stream warm-core rings (WCRs) within the western North Atlantic’s Slope Sea (SS) and their role in causing seaward entrainment of outer continental shelf water is well documented. • Most reports concerning WCRs and their associated shelf water entrainments have been based upon single surveys or time-series from individual WCRs. Long term impacts not known. • AIM: Estimate annual shelf water volume entrained into the SS by WCRs and study its interannual variability. Source: John Hopkins Remote Sensing Lab 05/02/98

4. Data • Sea Surface Temperature (SST) observations of WCRs within the Slope Sea from 1978-1999. • Domain 75oW and 50oW • Satellite data were digitized at Bedford Institute of Oceanography (BIO), provided by Ken Drinkwater • Data only has positions of rings • Shelf Slope Front (SSF) and Gulf Stream North Wall (GSNW) also available

5. Quasi-geostrophic Potential Vorticity Model (QGPV) • Proposed by Melvin E. Stern, “Large-Scale Lateral Entrainment and Detrainment at the Edge of a Geostrophic Shear Layer”, JPO, Vol.17, No. 10, 1987 • “The evolution of large-amplitude disturbances at the outer edge of a quasi-geostrophic shear layer depends on the sign of the outward gradient of potential vorticity. Entrainment of ambient water can occur when the gradient of relative vorticity dominates in the potential vorticity, and detrainment from the current can occur when the gradient of isopycnal thickness dominates.”

6. QGPV • Derivation (International Geophysics Series, Vol. 19, M.E. Stern) Geostrophic Equation: fv = 1/r dp/dx; fu = -1/r dp/dy …. (1) Substituting dp = rg dH in (1) we get v = (g/f) dH/dx ; u = -(g/f) dH/dy or V = (g/f) kdH….(2) Integrate (2) over time on a length scale L |V|L = (g/f)[h - Hm] where Hm = mean thickness and h varies over time H-Hm = |V|L f/g …. (3) Dividing both sides of (3) by Hm we get (H-Hm)/Hm = |V|L f/gHm ….. (4) Multiply and divide RHS (4) by fL we get (h-Hm)/Hm = |V|/fL * f2L2/gHm … (5)

7. QGPV (h-Hm)/Hm = |V|/fL * f2L2/gHm … (5) Now |V|/fL= Rossby No. (R) and f2L2/gHm = Burger No. Quasi-geostrophy assumes that Burger No. ~ 1, thus (5) becomes h’/Hm = |V|/fL …. (6) where h’(x,y,t) = h-Hm Now |V|/L = dv/dx - du/dy= z ,thus PV = z/f - h’/Hm …. (7) Quasi-geostrophic equation for Potential Vorticity where z = relative vorticity f = Coriolis parameter h’ (x,y,t) = deviation of thickness from Hm in time Hm = mean thickness

8. QGPV PV = z/f - h’/Hm • PV is dimensionless dPV = dz/df – dh’/Hm … (8) (where d is in space or time) • Ideally df /dx ~ constant b hence important factors are Dz and dh’ • Conservation of PV suggests that dPV =0, thus if z increases, h’ should increase or vice versa if z decreases, h’ should decrease or vice versa (As observed with WCRs, rings decrease in size and slow down with time)

9. QGPV • In reality ideal case does not hold true. Large scale amplitude disturbances cause PV anomalies with predominant effect on dh’ dPV = dz/df – dh’/Hm (8) • Positive anomaly occurs when dz dominates (8) and negative anomaly occurs when dh’ dominates (8) • The shear layer however would want to reach its equilibrium stage (PV=0), hence Positive anomaly caused by dz domination will cause dh’ to increase, leading to ambient water entrainment. Negative anomaly caused by dh’ domination will cause dh’ to decrease, leading to detrainment

10. Ring Entrainment Model PV = z/f - h’/Hm …. (7) • Since no depth data is available for WCRs, thickness at the surface is taken in consideration. Thickness at the surface is governed by radius (R) of the ring. Thus (7) becomes PV = z/f - r’/Rm …. (9) where r’ is deviation from the mean radius Rm of a ring z = V/R + dV/dR …. (10) [Csanady, 1979] for WCRs f = 2W sinf …. (11) • How do we get V and R from WCR dataset ????????

11. REM • Best fit Ellipse Model • Ellipse provides Ring Center, Orientation, and Radius = sqrt(a*b), where a and b are length of semi-major and semi-minor axis lengths • Finite difference scheme was used to calculate swirl velocity as V = f2- f1/(t2-t1) Taylor and Gangopadhyay, 1997

12. REM

13. REM PV = z/f - r’/Rm …. (9) • Taking the mean radius (Rm) of all observations of a single ring and consequently calculating radius anomalies to the mean (r’) would invoke a biased estimate in (9) • Finite differencing chosen to be better estimate, thus PV = z/f – ri’/Ri where ri’ = Ri – Ri-1 …. (12) • Temporal Gradient of PV is calculated using finite differencing assuming that the first observation is in steady state or dPV =0;

14. REM

15. REM • All observations with positive PV anomalies are taken to entrain ambient water based on dPV = dz/df – d ri’/ Ri • The amount of water entrained depends on ri’ Suppose dPV > 0 at somed ri’ = Zobs Ideally dPV ~ 0 , thus d ri’ would want increase to dz/df X Ri= Zcalc Entrained Area (A) = p (Zcalc– Zobs)2 Entrained Area (A) = Streamer Area (Length X Width) Streamer Length = A/ Streamer Width Streamer Width = 12km (Bisagni, 1983)

16. REM • If streamer Length > Observed Distance (Ring Edge and SSF), shelf water entrainment is assumed.

17. RESULTS

18. RESULTS

19. RESULTS

20. Future Work • SHORT TERM - Assign Uncertainties - Verification ????? - Regional correlation with NAO • LONG TERM - Nutrient Fluxes - Why NAO strongly correlates to WCR activity ? Model Results