Modeldescription Interaction between the ENSO and the North-South asymmetry in the eastern
Pacific
1. Introduction
The equatorial climate over the eastern Pacific and Atlantic Oceans is strikingly different from that
over the western Pacific and Indian Oceans. The former regions experience interannual variability
dominated by the well known El Niño-Southern Oscillation (ENSO) and a strong annual cycle despite
semiannual solar forcing near the equator. These regions also exhibits striking asymmetries relative to
the equator both in the time-mean conditions and the seasonal cycle. Regions of maximum sea surface
temperatures (SST) and the ITCZ stay to the north of the equator throughout the year. This is
associated with southerly winds that cross the equator, a cold tongue south of the equator and the
eastward North Equatorial Countercurrent that has no counterpart in the Southern Hemisphere. Thus
although the solar heating is zonally uniform and its mean position is on the equator, the tropical
climate is far from symmetric both in zonal and meridional direction. In the past decade studies
concentrate on the interaction between the east-west asymmetry in the Pacific (i.e., the warm pool-cold
tongue structure) and ENSO (e.g., Jin, 1997 ; Dijkstra and Neelin, 1998 ; Vaart and Dijkstra, 1998). In
this report, the feedbacks responsible for the north-south asymmetry (i.e., cold tongue-ITCZ complex)
are explored as well as its interaction with zonal feedbacks and ENSO.
The different character of the equatorial climate in all cases can, to a large extent, be attributed to
different time-mean conditions. Prevailing easterly trade wind over the Atlantic and Pacific is in the
time-mean balanced by pressure gradients in the upper ocean associated by, e.g., a slope in the
thermocline across the basin. It is the shallowness of the thermocline in the eastern tropical Pacific and
Atlantic that causes the climate to differentiate from other regions over the tropical oceans. The trade
winds also induce the equatorial upwelling which effectively bring water from the subsurface to the
surface layer. This subsurface water is inevitable cold in regions with a shallow thermocline, and these
regions are therefore sensible for changes in both upwelling strength and thermocline depth.
However, when the thermocline is too deep, i.e. in the western pacific and Indian Oceans, neither
changes in upwelling nor in thermocline depth can significantly influence SST. Therefore, oceanatmosphere feedbacks are most effective over the eastern Pacific and Atlantic Oceans because changes
in the winds can readily affect SST and visa versa. Two major feedback are revealed so far: the
thermocline feedback and the surface layer feedback. In the former thermocline displacement
determine sea surface temperature changes while with the later surface Ekman currents and their
divergence causes SST to change. Because zonal SST-gradients are thought to drive to a significant
extent the zonally asymmetric atmosphere circulation (Walker circulation), the initial disturbance is
amplified.
These positive feedback processes, first hypothesed by Bjerkness (1969) offers not only an explanation
for the zonal asymmetry in the time-mean (Dijkstra and Neelin, 1995) but also for the interannual
variability in the Pacific. Vaart and Dijkstra (1998) demonstrated that these coupled feedbacks are
essential to both the time-mean condition and ENSO, and that both climate conditions are ultimately
connected. The warm pool-cold tongue (i.e., the zonal asymmetry) is unstable and bifurcates to an
oscillatory solution. In a bifurcation study with a fully coupled Zebiak -Cane type model they showed
that ENSO essentially can be described by the recharge-discharge mechanism as proposed by Jin
(1996), encompassing both the delayed-oscillator (e.g., Schopf and Suarez, 1988 ; Battisti and Hirst,
1989) and the advective-reflective model (Picaut et al. ,1997).
The eastern Pacific and Atlantic Oceans also exhibits striking north-south asymmetry (cold tongueITCZ). Out of observations Mitchell and Wallace (1992) suggested that again coupled feedbacks are
responsible for this cold tongue-ITCZ complex. Chang and Philander (1994) performed an instability
analysis exploring Mitchell and Wallace (1992) hypotheses that meridional wind and its interaction
with local SST gradient play a crucial role. They found that a positive feedback between SST and
surface layer dynamics can yield to antisymmetric and symmetric unstable SST modes. The most
unstable mode is antisymmetric and zonally constant (wavenumber=0). This feedback only operates
within a frictional characteristic length scale of the equator where linear friction dominates Coriolis
force. In this region “the Ekman drift in the surface layer flows in the direction of the surface winds,
and the winds are, most likely, in the direction of the SST gradients. Under such conditions, an
anomalous southerly wind near the equator generates Ekman divergence to the south of the equator
by intensifying the cross-equatorial Ekman drift and causes cooling of the surface waters. The cooling
in the south enhances the northward temperature gradient near the equator, which in turn amplifies
the southerly wind anomaly”. This feedback in north-south direction is enhanced by the surface-layer
feedback in the zonal direction controlling the unstable zonal time-mean condition (warm pool-cold
tongue and ENSO).
When the Coriolis effect dominates, “the Ekman drift is in a direction perpendicular to the surface
wind stresses. Consequently, it cannot produce Ekman upwelling and the surface cooling required for
the positive feedback mechanism is absent”. Moreover, the Coriolis effect deflects the cross equatorial
wind into a westerly wind between the equator and the positive SST anomaly (SSTA). These
westerlies are stronger than the easterlies at the other side of the equator, so that net the thermocline
on the equator will deepen somewhat and the SSTA is opposed. In this paper we will present another
positive feedback mechanism in regions where Coriolis effect dominates. Both feedbacks can
complement each other in the “real world” causing an asymmetry further away from the equator than
the typical frictional length scale (±2.5°) in Chang and Philander (1994)
2. model description
2.1 Model Ocean
For the warm pool-cold tongue condition and ENSO variability we adapt the coupled two-box model
of Jin (1996). Thus, in the zonal direction the equatorial Pacific is divided into an eastern and a western
half. The thermocline in the later box (hw) varies about a zonal mean H according
Žh w
Žt
= – w h w –  w bLb ex
2
(1)
which describes conceptually the slow dynamically renewal of the warm pool heat content and
encompasses the memory of the ocean. The Sverdrup balance between pressure gradient force and
wind stress over the equator relates thermocline displacements in the east (he) to the west:
h e = h w + bLb ex
(2)
The zonal windstress on the equator, ex is assumed not to differ between the two boxes (Jin, 1996), w
measures the basin width dynamic adjustment rate ((300 days) -1), Lb is the basin size (1.5107 m) and
b measures the efficiency of wind stress in driving the thermocline tilt (41.67 m-1s2).
The SST in the western box (Tw) is assumed to be in radiative-convective equilibrium, which is zonally
e
constant, i.e. Tw=T0(y=0)= T0 . The SST of the well-mixed surface layer in the eastern half of the basin is
controlled by
ŽT
Žt
= –v
ŽT
Žy
– M(w)
T–Tsub
H1
–  Tref U (T–T0 )
(3)
The second term on the right hand side of (3) represent dynamically cooling due to the upwelling of
the cold subsurface water (at Tsub) into the surface layer. Upwelling velocity is denoted by w, H1 is the
mixed surface layer depth (thus the subsurface layer depth is H 2=H-H1) and the function M(w) results
from upstream vertical differencing (M(w)=w if w>0 and 0 if w≤0). The subsurface temperature is
parameterized adopted from Jin (1996).
Tsub = Tr0 + Te0 –Tr0 H h e+z 0
h*
(4)
The last term of (3) is the net heating through the ocean surface which acts as a Newtonian cooling
with a coefficient proportional to the local wind (Xie, 1994) and damps SST towards a zonally uniform
radiative-convective equilibrium T0. The coefficient T = U Tref mimics the effects of evaporation but
is in most model handled as a constant (e.g., Jin, 1996). U is the absolute windspeed which had a
minimum value Umin. This evaporation term might be essential in the maintaining of the north-south
asymmetry at the eastern side (Xie and Philander, 1994). Therefore the eastern half of the basin is split
into three boxes a northern, equatorial and southern box with SST Tn, Te en Ts, respectively. We use
the following staggered grid
s+1
s+1
T0
s+0.5
s
e
n
vs
we
vn
vs+1
n+0.5
n+1
vn+1
Ts
Te
Tn
y=– 
y=0
y= 
n+1
T0
Central differencing is used for the meridional advection (first term on the right hand side of (3)).
Symmetrical boundary conditions are applied: Tn+1 = T0(y=4 ) ; Ts+1 = T0(y=–4 ) and the meridional
dependence of the radiative-convective equilibrium T0
T0 = Te0 + Tp–Te0 y/ 3 106m
2
(5)
is adopted from Xie and Philander (1994).
For the north-south asymmetry the interaction with the atmosphere basically occurs essentially with
the mixed layer, i.e., advection of heat due the geostrophic currents can be neglected (Chang and
Philander, 1994). For the ENSO mode horizontal advection is believed to be secondary and only
thermocline displacements are important (equation (1) and (2), see also Jin, 1996). Thus in this study
the meridional surface current (v) and the upwelling (w) can be approximated by meridional ekman
drift and its divergence, respectively:
v=
H 2
r
w =–
H 2
r
2
2
P1 –
y
x + Ld y
H1
H1
P1 P0 x + y
Žx
Žy
+ P1
2y
Ld
y – Ld
(6)
Žy
Žy
(7)
with Ld=r/, the Ekman spreading lengthscale, r the linear damping coefficient in the mixed surface
-1
2
2
layer and P1 = 1+ y/ Ld
and P0 = P1 1– y/ Ld . In (7) the windstress is assumed to be zonally
constant (like in Jin, 1996 and in Xie and Philander, 1994) which is consistent with the neglection of
zonal ekman drift, i.e., upwelling is determined by ∂v/∂y only.
Box averages are used for the surface heatflux ( U and for the thermocline displacements (he, hw), and
local wind values for the surface currents (v, w).
2.2 Model atmosphere
For the meridional, or Hadley, circulation we use a Gill-Matsuno type of model that neglects zonal
variation (see, e.g., Xie and Philander, 1994). Therefore, the zonal windstress is related to the
meridional component by the following relation
x = yy/ Km
(8)
Gill (1980) already obtained a solution for an asymmetric diabatic heating term Q independent of x.
Since the ITCZ has a very small latitudinal extent, he approximated the atmospheric heating Q by a
delta function situated at a given lattitude y0. For the meridional structure, however, we adopt a
smoother expression closely resembling the numerical solution of a zonally independent Gill model
with a broader heating function (see for example the solutions provided by Xie and Philander, 1994).
–(y- y 0 )
y = sign(y- y 0 ) Q A 0 K m exp
2
2ca
2ca
2
(9)
Km is the atmospheric demping rate, ca the long gravity wave speed for the atmosphere and A0 the
wind stress factor per unit of velocity, i.e., x, y = A0 U, V .At first we adopt the non-linear forcing
term of Xie and Philander (1994): Q=TM(T–Tc).
Using expression (8) the contribution of the linear friction in the meridional Ekman drift (6) dominates
the Coriolis term near the equator where |y|<Ld(Km/r)0.5. This meridional length scale is typically 3°,
whereas the permanent position of the ITCZ and accompanied maximum SST is at about 10°N.
Therefore, at first we neglect the meridional windstress contribution in (6) and (7) and use a  of 5°.
We also neglect off-equatorial upwelling because it is of no relevance for the north-south asymmetry
(e.g., Chang and Philander, 1994) and for ENSO variability (Jin, 1997).
The intensity of the zonal Walker circulation is closely related to zonal contrast of SST (e.g. , Jin 1996)
walker = 1(Te–Tw ) exp –y 2/2 ca
(10)
McWilliams and gent (1978) used a value for the zonal Walker coefficient 1 of 310-8 ms-2K-1. We
assume that the Walker cell falls off in the meridional direction as a parabolic cylinder function of zero
order.
Thus the zonal windstress consists of 1) a Hadley cell contribution (9) whose surface branch is turned
zonally by the Coriolis force (hadley=yy/ K m) ; 2) a direct Walker cell driven by the equatorial zonal
SST contract (walker) and 3) an external contribution generated by the poleward transport of angular
momentum by the large scale atmospheric eddies (ext) which cannot be resolved by a linear Gill’s
model.
x = hadley + walker + ext
(11)
The standard parameter values used are listed in table 1
Table 1 : Value of parameters
Lb
w
(300 days)-1
1.5107 m
Umin 8 ms-1
Tref (Umin*150 days)-1
Hm
50 m
H
150 m
Tr0
18°C
h*
50 m
e
30°C
Tp
22°C
T0
-8
-1
A0
c
5.510 s
30 ms-1
a
b
r
z0
Tc
Km
41.67 m-1s2
(2 days)-1
25 m
27.5°C
(1 day)-1
In the uncoupled situation (ext, T, 1)=0 the only solution is that the SST in all boxes equals the
radiative-convective equilibrium T0 as specified in (5). Continuation method ....AUTO is used
(references)....... starting with the uncoupled solution. Time-integration is performed when multiple
steady states are suspected and the bifurcation study does not reveal them.
3. Mechanism to North-South asymmetry
When the Walker cell contribution is ignored (1=0) the above model reduces to a very simple version
of the Xie and Philander (1994) model. The main differences are that the resolution is reduced to a
three box model, the surface heatflux is written as single expression Tref U (T–T0), and atmosphere
and ocean response is given by (8),(9) and (1), (2) respectively.
Figure 1 presents the bifurcation diagram for ext = –2.210-7 ms-2 (is value if Xie and Philander, 1994)
and Umin=8 ms-1. The external wind component now encompass both the Walker circulation and
eddy momentum transport. At T=6.710-3 m2s-3K-1 the symmetrical double ITCZ structure
bifurcates to an asymmetric one. After a limitpoint at T=5.910-3 a stable asymmetric solution exists
with maximum SST and atmospheric diabatic heating in either of the two off-equatorial boxes. Thus
multiple stable steady states are present in the interval 5.910-3<T<6.710-3, confirming the finding
of Xie and Philander (1994, fig. 7). At T=7.510-3 the two asymmetric solutions bifurcate again to a
stable symmetric one.
Four non-linearities contribute to the bifurcation to north-south asymmetry: surface heatflux,
atmospheric forcing, vertical and meridional advection in the SST equation (3). Experiments reveal
that the primary bifurcation point is not sensitive to the first three nonlinearities. However, when
meridional advection is neglected no bifurcation the asymmetry is found. Assume an asymmetric
positive SST anomaly in one off-equatorial box. The meridional wind is directed to the SSTA but when
the Coriolis effect dominates the anomalous Ekman drift is in a direction perpendicular to the surface
wind stresses. In a symmetric climatological situation with two ITCZ (i.e., T n=Ts>Te) the positive
SSTA is enhanced by the meridional advection through anomalous surface current. The mean surface
current has no significant effect on the SSTA as long as the contribution of the Hadley cell to the mean
Ekman drift is overwhelmed by the external easterlies. When the Hadley circulation is strong enough
also the meridional advection by the mean Ekman drift contribute to the positive feedback. The SST in
the other boxes are hardly effected by both contributions. This climate state is therefore unstable to
off-equatorial anomalies whenever this positive feedback by meridional advection is strong enough to
overcome the restoring rate by the surface heatflux. This is encountered when the Hadley response is
strong, i.e. large value of T and strong SST gradients. This confirms a condition for north-south
asymmetry found by Xie (1994) that the climatological SST in the equatorial box has to be low enough.
He states that cooling by equatorial upwelling is necessary to prevent the ITCZ from forming on the
equator. Moreover, the positive feedback in meridional advection is even absent in this other
symmetric climate state with maximum SST in the equatorial box. When linear friction dominates the
Ekman drift flows in the direction of the surface winds and the SSTA is cooled by meridional
advection (i.e., negative feedback). This effect can counteract the positive feedback proposed by
Chang and Philander (1994) involving upwelling caused by cross-equatorial Ekman drift dominated
by linear fiction.
The condition of a low Te value for asymmetric ITCZ is properly the reason why the asymmetric
climate states cease to exist for too large values of T (figure 1). The equatorial SST warms when T
increases mainly due to deepening of the thermocline. The meridional winds converge onto the ITCZ,
for example in the northern equatorial box. South of the ITCZ southerly winds prevail. In the southern
hemisphere the Coriolis force turn the southerly flow westward but in the northern hemisphere it
induces westerlies. Since the winds are stronger close to the ITCZ, the Hadley circulation produces a
net weak westerly wind over the equatorial box. Therefore, due to thermocline- and upwelling
feedback the equatorial SST increases as the strength of the Hadley circulation increases.
These differences between both hemispheres also induce a strong contrast in total wind since the
prevailing easterlies are strengthened in the southern hemisphere and weakened in the northern. The
stronger winds in the southern box keep SST close to T0 because the surface heatflux increases as total
wind increases. However, this is an essential mechanism for the maintenance of the asymmetric
steady states but not the cause. With a constant coefficient in the surface heatflux the symmetric
climate state still bifurcates but the asymmetric climate is unrealistic. The T-interval where
asymmetric steady states exist decreases as the value of Umin decreases, but the primary bifurcation
point remains unchanged at T=6.710-3 for most values of Umin. But for Umin<6.8 ms-1 no bifurcation
to asymmetric climate states exist. Thus evaporation contributes to the maintenance of the asymmetric
steady states.
Equatorial upwelling induced by strong external easterlies is therefore a necessary condition for
north-south asymmetry to occur. The strong easterlies causes low equatorial SST and are needed for
the asymmetry in the surface heatflux. The Hadley circulation remains strong enough for certain
values to overcome the easterlies such that the mean ekman drift also contributes to the positive
feedback (is dat zo?). The continuation method enables us to follow the limitpoint of figure 1 as
function of ext and T. but bifurcation points need to be determined at each point is space. Figure 2
show both limit- and both bifurcation points in (ext, T) space. It confirms that the bifurcation to
asymmetry ceases to exist when the easterlies become too weak. It is very likely that the lower limit in
both ext and Umin are connected. ....(nog uitwerken of dat zo is?)
Figure 2 suggest also a upper limit in ext. When ext becomes too negative, the SST in the offequatorial boxes has cooled below the critical value Tc of the non-linear atmospheric heating. Thus
continuation of T from a high negative ext value (ext<–2.810-7 for standard parameters) will let
the symmetrical climate state unchanged. Figure 2, however, shows that the limitpoint connected to
the asymmetric state does exist for all values above the lower limit of ext. Continuation starting from
a limitpoint reveals that the second bifurcation point is still present at high negative ext value but that
the primary bifurcation disappers. Figure 3a-b presents the bifurcation diagram at ext=–2.810-7 and
–2.910-7, respectively. The asymmetric steady states are hardly changed at all, but is for ext<–
2.810-7 not connected to the initial symmetric state anymore. This artefact is a result of the nonlinear
heating of the atmosphere. When this is replaced by a linear version Q=T(T–Tc)
the steady state solutions are always connected. This linear heating function is not an alternative in
more complex models since it introduces large negative heating anomalies in off-equatorial regions.
This concludes that the nonlinear atmosphere forcing is not an important nonlinearity in the model,
but that the characteristics of the atmosphere response itself is essential for the positive feedback with
meridional advection. Using a discretized form of the Gill model instead of (9) induces large
truncation errors in this box model and severely effects the bifurcation diagrams. Moreover, the
response of a boundary layer driven atmosphere differs somewhat from a convective heating that
bifurcations to north-south asymmetry does not occur with the former.