Delayed Advective Oscillation of the Atlantic Thermohaline Circulation

1
Delayed Advective Oscillation of the Atlantic
Thermohaline Circulation
Sang-Ki Lee Associate Research Scientist, CIMAS,
UM Collaborators C. Wang (AOML/NOAA) R. J.
Greatbatch (IFM-GEOMAR)

Outline

gt Previous studies on the mechanism of
AMOC variability

gt A simple dynamic model
as a candidate mechanism for the multidecadal
oscillation of the AMOC
gt Other hypotheses in comparison
with the newly proposed mechanism

gt A preliminary
result from a 3D ocean model
2
Observational Evidences of AMOC Variability

• Overflow from the Nordic Seas (e.g., Dickson and
  Brown 1994 Macrander et al. 2005 Eldevik et al.
  2009)
  gt Measurements of transport
  through Denmark Strait suggest interannual and
  longer-period fluctuations
• Great Salinity Anomalies (GSA) of the 1970s,
  1980s and 1990s in the Labrador Sea (e.g.,
  Hakkinen 2002) gt
  May be related to deep water formation
• Direct measurement at 26.5N (Cunningham et al.
  2007 Kenzow et al. 2009)
  gt One
  year data (Mar/2004-Mar/2005) shows a significant
  amplitude of short-term variability of the AMOC
• Atlantic Multidecadal Oscillation (AMO) (e.g.,
  Schlesinger and Ramankutty 1994)
  
  gt AMO is a signature of internal (i.e.,
  unforced) variability

3
Persistent AMOC Oscillation in CGCMs

• Delworth et al. (1993)
  gt Reported
  unforced irregular oscillation of AMOC with an
  average period of about 50 yrs using GFDL model
• Delworth and Mann (2000)
  gt
  SST variability of the past 330 yrs from proxy
  records is consistent with the simulated AMO and
  AMOC variability with about 70 yrs period
• Knight et al. (2005) and others
  
  gt Other climate model
  studies show consistent results with Delworth and
  Mann (2000)

4
Conflict-1 Ocean-Only or Coupled Process?

• It is an ocean-only process
  
  gt Numerous studies have shown
  that ocean-only models can support self-sustained
  interdecadal oscillations of the AMOC (e.g.,
  Marotzke 1990 Weaver and Sarachik 1991
  Greatbatch and Zhang 1995)
• Perhaps, it is affected by the atmosphere
  gt Chen
  and Ghil (1996) and others showed that a large
  thermal (or haline) damping at the surface can
  wipe out the interdecadal oscillation of the AMOC
• It may be a coupled process
  
  gt The ocean component of
  GFDL model used in Delworth et al. (1993) cannot
  support a self-sustained oscillation without an
  active coupling with the atmosphere regardless of
  the surface flux conditions (Weaver and Valcke
  1998)

5
Conflict-1 Ocean-Only or Coupled Process?

• It maybe a forced damped oscillation
  gt
  Delworth and Greatbatch (2000) arrived at a
  somewhat different conclusion from Weaver and
  Valcke (1998) using the same GFDL ocean-only
  model They showed that purely atmospheric
  low-frequency variability (James and James 1989)
  can excite a damped oscillation of the AMOC
• In summary, I think that
  gt It is
  mainly an ocean-only process, but the interaction
  with atmosphere may be crucial Some modeling
  studies try to link the NAO and AMOC by provoking
  a fully coupled atmosphere-ocean feedback (e.g.,
  Saravanan and McWilliams, 1997 Eden et al., 2002)

6
Conflict-2 Self-Sustained or Damped Oscillation?

• It is self-sustained process
  
  gt Many ocean-only models can
  support self-sustained interdecadal oscillations
  of the AMOC (e.g., Weaver and Sarachik 1991
  Greatbatch and Zhang 1995)
• It may be a damped oscillation
  
  gt Some ocean-only models
  suggest that the AMOC is subject to a damped
  oscillation, and thus requires finite amplitude
  of stochastic weather noise from or coupling with
  the atmosphere to sustain its oscillation (e.g.,
  Capotondi and Holland 1997 Winton 1997 Delworth
  and Greatbatch 2000 Eden and Greatbatch 2003)
• I think that
  gt
  This is still an open question But, more recent
  studies suggest that the system is subject to a
  damped oscillation

7
Some clues from model studies

• Greatbatch and Zhang (1995) and others
  gt (1) AMOC ?
  
  gt (2) HT
  from low- to high-latitude ?
  gt (3) Meridional density
  gradient ?
  gt (4) AMOC ?
  
  gt (5) HT from low- to high-latitude ?
  gt (6) Meridional
  density gradient ?
  gt (1) AMOC ?
• If (3) and (4), or (6) and (1) are in phase, the
  anomalies interfere destructively gt no
  oscillation

8
Some clues from model studies

• How does the system become unstable?
  gt Analogy between AMOC
  oscillation and beam balance

Stable System
Oscillatory System
9
Some clues from model studies

• So, it appears that
  
  gt If the meridional density advection by AMOC
  is simply behaves like a Newtonian damping to the
  north-south density gradient, the system is
  always stable.
  gt To ensure an oscillation, the
  meridional density advection by AMOC must
  OVERSHOOT!
  gt The overshoot is possible if there
  is a TIME-LAG between the north-south density
  gradient and AMOC
• What determines the time lag?
  gt Te Raa and
  Dijkstra (2002) concluded that instability of
  AMOC is essentially 3D, and involves westward
  propagating temperature signal
  gt Killworth (1985)
  showed that the first 5 yrs of integrating a
  two-level buoyancy-driven ocean model are
  dominated by the westward passage of a long
  Rossby wave

10
Delayed Advective Oscillator

• Main hypothesis of this study
  
  gt Adjustment of buoyancy-driven baroclinic
  flow is associated with the basin-crossing time
  of long baroclinic Rossby waves ( 10 yrs for
  high-latitude North Atlantic)

11
Delayed Advective Oscillator

• Four-box model

12
Delayed Advective Oscillator

• Governing equations
  gt
  Volume integration of the density conservation
  equation for each box yields

gt Horizontal diffusion is neglected


gt Convection is activated by mixing the upper
and lower boxes when density inversion occurs
13
Delayed Advective Oscillator

• Equation for baroclinic volume transport, V
  
  gt V is proportional to the zonal
  geostrophic baroclinic flow subject to the
  north-south density gradient with a time delay ?

14
Delayed Advective Oscillator

• Non-dimensionalization

15
Delayed Advective Oscillator

• One-equation model

16
Delayed Advective Oscillator

• Equilibrium solution to one-equation model

gt Amplitude of equilibrium solution is
determined by ko, ?, and q


gt Solving for T and S (instead of single
variable ?) will lead to multiple equilibrium
solutions as in Stommel (1961), Rooth (1982) and
others
17
Delayed Advective Oscillator

• Linear stability analysis

gt One-equation model is always stable regardless
of ko, ?, and q
18
Delayed Advective Oscillator

• Numerical solution to four-box model ko0.2
  ?2.0 q0.1

gt For a larger value of ?, the solution
oscillates with a period of about 2??
gt The main result The overshooting requires a
sufficient time-lag between the north-south
density gradient and AMOC
19
Delayed Advective Oscillator

• Mechanism of the oscillation ?20 ko0.2
  ?2.0 q0.1 gt processes affecting
  north-south density gradient

Storage
Advection
Surflux
Dissipation
20
Delayed Advective Oscillator

• Mechanism of the oscillation
  gt (1) A ??avg Adv min ??? gt (2)
  AgtB ()
  gt (3) B ??max Advup ???
  gt (4) BgtC (-)
  gt (5) C ??avg Adv max
  ??? gt (6) CgtD ()
  gt (7) D ??min Adv
  avg ??? gt (8) DgtE (A) (-)
• Unstable mode is
  gt maintained by alternating actions of
  amplification and stabilization, which are
  operated by delayed advective flux divergence in
  response to a north-south density gradient

21
Delayed Advective Oscillator

• Relationships among ??, Adv, and V
  gt ?? Period
  is 2?
  
  gt V V lags ?? by ?
  
  gt Adv Adv leads V by ?/2, and lags ?? by
  ?/2
• Application to North Atlantic
  gt Lx 5?106m
  
  gt Ly2.0?106m
  
  gt gy?
  1.0?10-2m s-1(related to meridional density
  gradient)
  
  gt gz? 0.5?10-2m s-1(related to vertical
  density gradient)
  gt fo
  10-4 s-1
  
  gt ? 2?10-11 m-1 s-1
  
  gt H 2000m
  
  gt Basin crossing time Lx/c
  16 yrs (c g?H?/(2fo2)) gt
  Adjustment time basin crossing time
  gt ? 12.5
  
  gt Period of delayed advective
  oscillator 32 yrs

22
Delayed Advective Oscillator

• Linear Stability Analysis
  gt
  Runge-Kutta 4th order scheme with double
  precision computation to obtain equilibrium
  solutions with ? 0
  
  gt Nonlinear eigenvalue problem is
  solved by using Mullers method gt Convection is
  excluded
• Influences of four parameters
  gt increasing ? destabilizes gt
  increasing ? destabilizes
  gt increasing ko
  stabilizes
  gt impact of q is not monotonic
  gt too large or small value of q can
  stabilizes the system

23
Delayed Advective Oscillator

• Impact of external forcing (only in the
  high-latitude) ?20 ko0.2 ?2.0 q0.1
  
  gt (a) Ice-melting (AGW)
  
  gt (b) Complete shutdown (Heinrich events)
  gt (c) Abrupt cooling
  (Younger Dryas)

24
Delayed Advective Oscillator

• Fresh water flux in high-latitude
  
  gt Slow down AMOC delayed advective oscillation
  is substantially reduced (recovery is slow)
• Complete shutdown
  gt Delayed advective oscillation is completely
  disrupted (recovery is extremely slow)
• Abrupt cooling in high-latitude
  gt Minor impact on AMOC strength
  the delayed advective oscillator is weakened
  (recovery is slow)

25
Delayed Advective Oscillator

• North Atlantic Oscillation (NAO)
  gt High-frequency
  portion of NAO originates from weather noise
  
  gt NAO has a coherent
  spatial structure with a dipole-like meridional
  pattern of the SLP
• Impact of high-frequency forcing ?20 ko0.2
  ?1.2 q0.1 gt High-frequency forcing is
  represented as a random noise surface density
  forcing with anti-symmetric meridional pattern
  (amplitude is set equal to q/2)
  gt (a) with weather noise
  gt (b) without
  weather noise
  gt (c) with both external
  forcing and weather noise

26
Delayed Advective Oscillator

• Impact of weather noise
  gt Without weather noise, the system is
  subject to a damped oscillation (? 1.2 ? 20)
  gt Finite amplitude
  weather noise can sustain a delayed advective
  oscillation of the period 2? and the amplitude
  of up to 36 of the mean AMOC
  gt Finite amplitude weather
  noise can effectively revive the delayed
  advective oscillation once the external forcing
  is removed

27
Delayed Advective Oscillator

• Why the delayed oscillator is excited by weather
  noise? gt Simple stochastic climate
  model of Hasselmann (1976) suggests that random
  weather noise can produces a red noise spectrum
  of ocean temperature via ocean memory gt
  Random noise can produce large amplitude of
  north-south density gradient at low-frequency
  including at the frequency of delayed advective
  oscillator, ? 0.5?-1

28
Other Hypotheses

• Hypothesis-1 Phase-lag between the meridional
  heat and salt advections
  
  gt Griffies and Tziperman (1995) used a
  four-box model to obtain a damped oscillation,
  which caused by the phase-lag between a
  stabilizing effect of heat advection and a
  destabilizing effect of salt advection
  gt Pros This model
  can reproduce some features of Delworth et al.
  (1993)
  gt Cons There are many
  ocean models can support self-sustained
  interdecadal oscillations of the AMOC without
  salinity effect (e.g., Te Raa and Dijkstra 1995)
  gt I vote (Yes) Certainly
  worthwhile to consider

29
Other Hypotheses

• Hypothesis-2 Nonlinearity of the relationship
  between the north-south density gradient and AMOC
  
  gt Riven and Tziperman (1997) modified the
  three-box model of Joyce (1991), by specifying a
  nonlinear relationship between the north-south
  density gradient and AMOC, to obtain a
  self-sustained oscillation
  gt Pros This model suggests that the
  relationship between the north-south density
  gradient and AMOC is critical to the oscillation
  This idea is supported by Lucas et al. (2006)
  
  gt Cons This model
  relies on an ad hoc assumption, which has no
  solid physical background
  gt I vote
  (No) The proposed mechanism is interesting, but
  not so convincing

30
Other Hypotheses

• Hypothesis-3 Time delay of advective heat flux
  caused by a finite transit time from the low- to
  high-latitude
  gt Kurtze and Restrepo (2001)
  considered a low-latitude box connected to a
  high-latitude box through two narrow pipes
  
  gt The time
  delay caused by transit time from the low- to
  high-latitude box, ? V/L can produce a
  self-sustained oscillation of the AMOC
  
  gt The volume transport is not
  delayed The time delay is in the influx
  temperature and salinity
  gt Pros and Cons
  The main idea is very plausible But, the two
  ocean boxes connected through pipes is not so
  appealing
  gt I
  vote (Yes) This mechanism should be explored
  further Perhaps, a proper way is to add a
  mid-latitude box in-between the two ocean boxes)

31
Other Hypotheses

• Hypothesis-4 Out-of-phase relationship between
  the north-south density gradient and AMOC
  gt Huck et al. (1999)
  assumed in a simple box model that the rate of
  change of AMOC is proportional to the north-south
  density gradient to find a purely oscillatory
  solution
  gt Pros This model suggests that
  the phase-lag between the north-south density
  gradient and AMOC is critical to the oscillation
  
  gt Cons This solution has
  no instability mechanism
  
  gt I vote (No) The basic idea is similar
  to the delayed advective oscillator, but some
  critical ingredients are obviously missing

32
Other Hypotheses

• Hypothesis-5 Baroclinic instability of the mean
  state of thermohaline circulation
  
  gt Colin de Verdiere and Huck (1999) performed a
  linear instability analysis of an idealized
  three-layer ocean model to argue that the mean
  state of thermohaline circulation is subject to
  baroclinic instability
  gt Pros No one can
  disagree that the mean state of thermohaline
  circulation is unstable
  gt Cons The classical two-layer model
  of Phillips (1954) does not support multidecadal
  time-scale oscillation
  gt I vote (No) These authors have to come up
  with a more convincing evidence

33
Other Hypotheses

• Hypothesis-6 Te Raa and Dijkstra (2002)

gt A warm anomaly in the north-central part of
the basin causes a positive meridional
perturbation temperature gradient, which induces
a negative zonal overturning perturbation (a).
The anomalous upwelling and downwelling
associated with this zonal overturning are
consistent with westward propagation of the warm
anomaly, while a cold anomaly appears in the east
(b). Due to the westward propagation of the warm
anomaly, the eastwest temperature difference
decreases and becomes negative, inducing a
negative meridional overturning perturbation. The
resulting upwelling and downwelling perturbations
along the northern and southern boundary reduce
the northsouth perturbation temperature
difference, causing the zonal overturning
perturbation to change sign and the second half
of the oscillation starts.
34
Other Hypotheses

• Hypothesis-6 Westward propagating SST anomalies
  gt Te Raa and
  Dijkstra (2002) performed a linear instability
  analysis of an idealized ocean-model to report an
  unstable mode with interdecadal time scale
  gt They
  argued that the instability originates from the
  westward propagating SST anomalies that produce a
  phase-difference between the AMOC and AZOC via
  thermal wind balance
  gt Pros
  The idea is quite clear and very interesting
  gt Cons The proposed mechanism is an
  advanced version of Greatbatch and Zhang (1995)
  It does not explain the instability
  gt I
  vote (Yes) However, I think that the authors
  still need to show why the system is unstable
  Simply saying Hopf bifurcation is not enough

35
Other Hypotheses

• Hypothesis-7 Adjustment of north-south density
  gradient associated with baroclinic Kelvin waves
  gt Greatbatch and
  Peterson (1996) using an ocean-only GCM to argue
  that the baroclinic Kelvin waves in response to
  north-south density gradient are responsible for
  interdecadal oscillation of the AMOC
  gt Pros and Cons
  Many idealized ocean models that filter out
  Kelvin waves by design do produce interdecadal
  oscillation of the AMOC
  gt I vote (No)
  Kelvin waves may play a role, but it is not
  necessary to explain the interdecadal oscillation
  of the AMOC
• Many more hypotheses There are too many
  hypotheses to review them all

36
Conclusions and discussions

• A simple model of delayed advective oscillator
  is proposed as a candidate mechanism for the
  multidecadal oscillation of AMOC
• It relies on alternating actions of () and (-)
  feedbacks operated by a slow adjustment of the 3D
  baroclinic ocean circulation and the associated
  delayed advection
• In plain language, the overshooting of the AMOC
  is possible by its delayed response to the
  north-south density gradient
• There is no observational evidence to prove or
  disprove the proposed hypothesis
• Perhaps, we are still far away from having a
  unified simple model for the multidecadal
  oscillation of AMOC
• Definitely, we need (1) to come up with smarter
  and more systematic ways to monitor the long-term
  evolutions of AMOC in various key locations and
  (2) to use models to fill the gap between the
  reality and hypotheses

37
Planetary-Geostrophic Ocean Model (PGOM)

• 3D picture of the AMOC oscillation
  gt Requires a 3D
  ocean model
• Samelson and Vallis (1997)
  gt A simplified
  numerical ocean model based on thermocline
  equations (e.g., Welander 1971)

38
Planetary-Geostrophic Ocean Model (PGOM)

• Experiment-1
  
  gt 65?65?34 resolutions
  gt surface
  thermal forcing is a linear function of latitude
  (warming in the low-latitude and cooling in the
  high-latitude)
  
  gt no wind
  
  gt Salinity is constant
  gt All
  variables are non-dimensional

39
PGOM EXP-1

• MOC gt lat ? depth

40
PGOM EXP-1

• Depth-integrated density
  gt lon ? lat

41
PGOM EXP-1

• Vertical velocity at z 0.8
  gt lon ? lat

42
Planetary-Geostrophic Ocean Model (PGOM)

• Some thoughts
  
  gt I am wondering if there is analogy
  between the AMOC oscillation and the western
  Pacific oscillator mechanism of Weisberg and Wang
  (1997)
  gt I am also
  wondering if there is any similarity between the
  AMOC oscillation and the Loop current in the Gulf
  of Mexico
• R. J. Greatbatch, Personal communication
  gt Topographic damping
  may be too large to support a self-sustained
  oscillation of the AMOC (Winton 1997)
  gt Therefore, low-frequency variability and the
  spatial coherence of the NAO are required to
  excite a damped oscillation of the AMOC