Interannual Variability of Shelf Water Entrainment to the Slope Sea by Gulf Stream Warm Core Rings in response to the North Atlantic Oscillation Ph.D. Dissertation Proposal by Ayan Chaudhuri

Agenda Overview Overview Scientific Background Scientific Background Preliminary Work Preliminary Work Hypothesis and Study Objectives Hypothesis and Study Objectives Data and Methods Data and Methods Summary Summary

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. 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. 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. Source: John Hopkins Remote Sensing Lab 05/16/97

Overview The proposed work will investigate the impact of shelf water entrainment into the SS by WCRs in the WNA between 75° and 50°W during a 22 year period from 1978 to The proposed work will investigate the impact of shelf water entrainment into the SS by WCRs in the WNA between 75° and 50°W during a 22 year period from 1978 to Preliminary results suggest a significant response of WCR activity to climate variability related to the state of the North Atlantic Oscillation (NAO). Preliminary results suggest a significant response of WCR activity to climate variability related to the state of the North Atlantic Oscillation (NAO). Source: John Hopkins Remote Sensing Lab 05/16/97

Scientific Background The Gulf Stream (GS) forms large amplitude meanders downstream of Cape Hatteras from baroclinic and barotropic instability processes. Individual meander crests, if large enough (surface radii of 2-4 times the internal Rossby radius) can separate from the main GS current, loop back onto themselves and form WCRs [Saunders 1971, Csanady 1979]. The Gulf Stream (GS) forms large amplitude meanders downstream of Cape Hatteras from baroclinic and barotropic instability processes. Individual meander crests, if large enough (surface radii of 2-4 times the internal Rossby radius) can separate from the main GS current, loop back onto themselves and form WCRs [Saunders 1971, Csanady 1979]. WCRs transport active and passive substances that have a significant impact on the biogeochemistry within the Slope Sea region. WCRs transport active and passive substances that have a significant impact on the biogeochemistry within the Slope Sea region. An important mechanism is the horizontal stirring associated with streamers off the continental shelf and GS waters that these rings entrain into the SS. [ Olson 2001, Ryan et al. 2001, Schollaert et al., 2004]. An important mechanism is the horizontal stirring associated with streamers off the continental shelf and GS waters that these rings entrain into the SS. [ Olson 2001, Ryan et al. 2001, Schollaert et al., 2004].

Scientific Background The Gulf Stream North Wall (GSNW) and the Shelf Slope Front (SSF) have been shown to exhibit considerable inter- annual variability (IAV) in their mean position on the order of km. ( Halliwell and Mooers [1979], Drinkwater [1994]) The Gulf Stream North Wall (GSNW) and the Shelf Slope Front (SSF) have been shown to exhibit considerable inter- annual variability (IAV) in their mean position on the order of km. ( Halliwell and Mooers [1979], Drinkwater [1994]) Given that WCRs originate from the meandering of the GS, does GSNW position IAV have implications on WCR activity over annual or decadal timescales? Given that WCRs originate from the meandering of the GS, does GSNW position IAV have implications on WCR activity over annual or decadal timescales?

Scientific Background The North Atlantic Oscillation (NAO) may be driving the IAV observed in the mean position of the GS [ Taylor and Stephens, 1998, Rossby and Benway, 2000] at an observed lag of 1-2 years. The North Atlantic Oscillation (NAO) may be driving the IAV observed in the mean position of the GS [ Taylor and Stephens, 1998, Rossby and Benway, 2000] at an observed lag of 1-2 years. Given that the state of NAOWI is known to co-vary with the GSNW position, does the NAO have any influence on WCR activity over annual or decadal timescales? Given that the state of NAOWI is known to co-vary with the GSNW position, does the NAO have any influence on WCR activity over annual or decadal timescales?

Preliminary Work Data consists of hand digitized weekly frontal charts produced from satellite-derived sea surface temperature (SST) and charts produced by NOAA and U.S. Navy. ([ Drinkwater et al. 1994]) Data consists of hand digitized weekly frontal charts produced from satellite-derived sea surface temperature (SST) and charts produced by NOAA and U.S. Navy. ([ Drinkwater et al. 1994]) Data were binned at each longitude between o W to obtain monthly mean GSNW and SSF positions. Data were binned at each longitude between o W to obtain monthly mean GSNW and SSF positions. The positions of all observed WCR interfaces located in the SS during and between 75° and 50°W were also obtained The positions of all observed WCR interfaces located in the SS during and between 75° and 50°W were also obtained

Preliminary Work Long term SSF and GSNW mean positions are calculated by averaging data from all months at each of the 26 longitudes (75-50 o W) Long term SSF and GSNW mean positions are calculated by averaging data from all months at each of the 26 longitudes (75-50 o W) A line mid-way between the mean positions of both fronts assumed to be a position where neither the SSF (in its extreme seaward position) nor the GSNW (in its extreme shoreward position) crosses at any point in time. A line mid-way between the mean positions of both fronts assumed to be a position where neither the SSF (in its extreme seaward position) nor the GSNW (in its extreme shoreward position) crosses at any point in time.

Preliminary Work Area anomalies bounded by the SS mid line and the annual mean position for each individual year are calculated for both the GSNW and SSF and differenced subsequently from respective long term mean areas bounded by each front’s long term mean position and the mid-line term SSF and GSNW mean positions are calculated by averaging data from all months at each of the 26 longitudes (75-50 o W) Area anomalies bounded by the SS mid line and the annual mean position for each individual year are calculated for both the GSNW and SSF and differenced subsequently from respective long term mean areas bounded by each front’s long term mean position and the mid-line term SSF and GSNW mean positions are calculated by averaging data from all months at each of the 26 longitudes (75-50 o W)

Preliminary Work Does GSNW position IAV have implications on WCR activity over annual or decadal timescales? The lateral movement of the GS is most likely not forcing the rate of baroclinic instability of the GS and hence rate of WCR formation. Does GSNW position IAV have implications on WCR activity over annual or decadal timescales? The lateral movement of the GS is most likely not forcing the rate of baroclinic instability of the GS and hence rate of WCR formation. Does the NAO have any influence on WCR activity over annual or decadal timescales? The NAOWI is observed to be significantly correlated to WCR activity at a lag of under a year and maybe forcing WCR formation by means different from GS movement. Does the NAO have any influence on WCR activity over annual or decadal timescales? The NAOWI is observed to be significantly correlated to WCR activity at a lag of under a year and maybe forcing WCR formation by means different from GS movement.

Hypothesis Preliminary results suggest that a positive (negative) NAOWI will correspond to more (less) WCRs and consequently high NAO decades will see more (less) ring activity. Preliminary results suggest that a positive (negative) NAOWI will correspond to more (less) WCRs and consequently high NAO decades will see more (less) ring activity. Higher numbers of WCRs generated during positive NAO years would increase the probability of entrainment events and result in higher fluxes of shelf water being advected into the SS. Higher numbers of WCRs generated during positive NAO years would increase the probability of entrainment events and result in higher fluxes of shelf water being advected into the SS. HYP(I): Volume fluxes of shelf water into the SS due to WCR entrainment vary over inter-annual and inter- decadal timescales with higher (lower) fluxes in years when the NAO is positive (negative) supported by increased (decreased) WCR activity. HYP(I): Volume fluxes of shelf water into the SS due to WCR entrainment vary over inter-annual and inter- decadal timescales with higher (lower) fluxes in years when the NAO is positive (negative) supported by increased (decreased) WCR activity. The objective of HYP(I) will be to examine the importance of water fluxes entrained by WCRs to the transport balance between the SS and the continental slope. The objective of HYP(I) will be to examine the importance of water fluxes entrained by WCRs to the transport balance between the SS and the continental slope.

Hypothesis The entrainment of nutrient rich waters from the outer continental shelf by WCRs to the SS may significantly influence the nutrient budgets of both the shelf and slope regions. The entrainment of nutrient rich waters from the outer continental shelf by WCRs to the SS may significantly influence the nutrient budgets of both the shelf and slope regions. The variability and availability of macro nutrients in WNA have significant impacts on all trophic levels. The variability and availability of macro nutrients in WNA have significant impacts on all trophic levels. HYP(II): Fluxes of nitrate (NO) 3 and silicate (Si(OH) 4 ) transported by shelf waters entrained into the SS by WCRs vary interannually with higher advective (lower) fluxes in years when the NAO is positive (negative) augmented by increased (decreased) volume transport. HYP(II): Fluxes of nitrate (NO) 3 and silicate (Si(OH) 4 ) transported by shelf waters entrained into the SS by WCRs vary interannually with higher advective (lower) fluxes in years when the NAO is positive (negative) augmented by increased (decreased) volume transport. The objective of HYP(II) will be to provide bounds for the potential nutrient fluxes from the shelf to the SS assuming steady-state dynamics and neglecting losses due to diffusion, dissipation, mixing and uptake. The objective of HYP(II) will be to provide bounds for the potential nutrient fluxes from the shelf to the SS assuming steady-state dynamics and neglecting losses due to diffusion, dissipation, mixing and uptake.

Hypothesis Since the lateral movement of the Gulf Stream forced by the NAO does not show significant impact on WCR formation, other forcing mechanisms need to be addressed. Since the lateral movement of the Gulf Stream forced by the NAO does not show significant impact on WCR formation, other forcing mechanisms need to be addressed. Recent studies ( Penduff et al. 2004, Brachet et al. 2004, Volkov 2005) have shown the eddy kinetic energy (EKE) varying interannually over the North Atlantic in phase with the NAO index. Recent studies ( Penduff et al. 2004, Brachet et al. 2004, Volkov 2005) have shown the eddy kinetic energy (EKE) varying interannually over the North Atlantic in phase with the NAO index. Instability processes from the mean flow generate excess energy and is the source of EKE and lead to the formation of eddies and rings [ Gill et al. 1974, Stammer 1998]. Instability processes from the mean flow generate excess energy and is the source of EKE and lead to the formation of eddies and rings [ Gill et al. 1974, Stammer 1998]. Stammer [1998] has verified that baroclinic instability is a major eddy source term throughout the ocean, especially for the western boundary currents like GS. Stammer [1998] has verified that baroclinic instability is a major eddy source term throughout the ocean, especially for the western boundary currents like GS. HYP(III): NAO induced variability of wind stress and net heat flux to the WNA significantly affects the EKE distribution of the GS. GS EKE co-varies interannually with the NAOWI such that high (low) EKE distributions are found when the NAO is positive (negative) resulting in the production of more (fewer) WCRs. HYP(III): NAO induced variability of wind stress and net heat flux to the WNA significantly affects the EKE distribution of the GS. GS EKE co-varies interannually with the NAOWI such that high (low) EKE distributions are found when the NAO is positive (negative) resulting in the production of more (fewer) WCRs.

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

QGPV Derivation (International Geophysics Series, Vol. 19, M.E. Stern) Derivation (International Geophysics Series, Vol. 19, M.E. Stern) Geostrophic Equation: fv = 1/  dp/dx; fu = -1/  dp/dy …. (1) Substituting dp =  g dH in (1) we get v = (g/f) dH/dx ; u = -(g/f) dH/dy or V = (g/f) k  ….(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 * f 2 L 2 /gHm … (5)

QGPV Now |V|/fL = Rossby No. (R) and f 2 L 2 /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 =  v/  x -  u/  y=  thus PV =  f - h’/Hm …. (7) Quasi-geostrophic equation for Potential Vorticity where  relative vorticity f = Coriolis parameter f = Coriolis parameter h’ (x,y,t) = deviation of thickness from Hm in time h’ (x,y,t) = deviation of thickness from Hm in time Hm = mean thickness Hm = mean thickness

QGPV PV =  f - h’/Hm PV is dimensionless PV is dimensionless  PV =  f –  h’/Hm … (8) (where  is in space or time) Ideally  f /  x ~ constant  hence important factors are Ideally  f /  x ~ constant  hence important factors are  and  h’ Conservation of PV suggests that  PV =0, thus Conservation of PV suggests that  PV =0, thus if  increases, h’ should increase or vice versa if  decreases, h’ should decrease or vice versa (As observed with WCRs, rings decrease in size and slow down with time)

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

Ring Entrainment Model PV =  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. 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 =  f - r’/Rm …. (9) where r’ is deviation from the mean radius Rm of a ring  = V/R + dV/dR …. (10) [Csanady, 1979] for WCRs f =  sin  …. (11) How do we get V and R from WCR dataset ???????? How do we get V and R from WCR dataset ????????

REM Best fit Ellipse Model Best fit Ellipse Model Ellipse provides Ring Center, Orientation, and Radius = sqrt(a*b), 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 Finite difference scheme was used to calculate swirl velocity as V =  2 -  1  t 2 -t 1  Taylor and Gangopadhyay, 1997

REM PV =  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) 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 Finite differencing chosen to be better estimate, thus PV =  f – r i ’/R i where r i ’ = R i – R i-1 …. (12) Temporal Gradient of PV is calculated using finite differencing assuming that the first observation is in steady state or  PV =0; Temporal Gradient of PV is calculated using finite differencing assuming that the first observation is in steady state or  PV =0;

REM All observations with positive PV anomalies are taken to entrain ambient water based on All observations with positive PV anomalies are taken to entrain ambient water based on  PV =  f –  r i ’/ R i The amount of water entrained depends on r i ’ The amount of water entrained depends on r i ’ Suppose  PV > 0 at some  r i ’ = Z obs Ideally  PV ~ 0, thus  r i ’ would want increase to  f X R i = Z calc Entrained Area (A) =  Z calc  – Z obs ) 2 Entrained Area (A) = Streamer Area (Length X Width) Streamer Length = A/ Streamer Width Streamer Width = 12km (Bisagni, 1983)

RESULTS

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