A simple estimation of equatorial Pacific response from windstress to untangle Indian Ocean Dipole and Basin influences on El Niño

Abstract

Sea Surface Temperature (SST) anomalies that develop in spring in the central Pacific are crucial to the El Niño Southern Oscillation (ENSO) development. Here we use a linear, continuously stratified, ocean model, and its impulse response to a typical ENSO wind pattern, to derive a simple equation that relates those SST anomalies to the low frequency evolution of zonal wind stress anomalies τ _x over the preceding months. We show that SST anomalies can be approximated as a “causal” filter of τ _x , τ _x (t − t ₁) − c τ _x (t − t ₂), where t₁ is ~1–2 months, t₂ − t₁ is ~6 months and c ranges between 0 and 1 depending on τ _x location (i.e. SST anomalies are approximately proportional to the wind stress anomalies 1–2 months earlier minus a fraction of the wind stress anomalies 7–8 months earlier). The first term represents the fast oceanic response, while the second one represents the delayed negative feedback associated with wave reflection at both boundaries. This simple approach is then applied to assess the relative influence of the Indian Ocean Dipole (IOD) and of the Indian Ocean Basin-wide warming/cooling (IOB) in favouring the phase transition of ENSO. In agreement with previous studies, Atmospheric General Circulation Model experiments indicate that the equatorial Pacific wind responses to the IOD eastern and (IOB-related) western poles tend to cancel out during autumn. The abrupt demise of the IOD eastern pole thus favours an abrupt development of the IOB-cooling-forced westerly wind anomalies in the western Pacific in winter–spring (vice versa for an IOB warming). As expected from the simple SST equation above, the faster wind change fostered by the IOD enhances the central Pacific SST response as compared to the sole IOB influence. The IOD thereby enhances the IOB tendency to favour ENSO phase transition. As the IOD is more independent of ENSO than the IOB, this external influence could contribute to enhanced ENSO predictability.

Appendix

1.1 Estimating the oceanic response to any equatorial τ _x (x,t)

Equation (4) can also be written for SSH or U anomalies, and for other averaging regions. And the convolution approach can be generalised to the response at any longitude to an equatorial τ _x forcing at any longitude, without loosing too much simplicity. One just needs to take into account the longitudinal variations in the temporal constants used in the equations of causal-filters given in Sect. 3. These longitudinal variations are related to Kelvin and Rossby waves characteristics, propagation speed, attenuation and interference between them for the (mainly) first and second baroclinic modes. To precisely obtain them, one could force the LCS by various spatial pulses distributed along the equatorial Pacific (i.e. formally determining the “Green’s function”), to reconstruct the whole response and to see the sensitivity of the response to longitude. Here the main purpose of this section is simpler: give very simplified equations for the “causal filtering” approximation of the oceanic response at any longitude to any equatorial τ _x (x_f,t) forcing. These crude equations are inferred from the impulse responses of the linear ocean model to western, central-west (described in Sect. 3) and central-east Pacific (not shown) westerlies, and need to be precised in future studies.

So, as a very crude approximation of the oceanic response estimated from the LCS model plus SST equation, we can write a semi-empirical formula for the equatorial linear response of the oceanic field F _eq (x,t) (average over 2°N–2°S) to any τ _x (x_f,t) forcing along the equator:

$$\begin{aligned} F_{eq} \left( {x,t} \right) = & \, C\int_{{x_{f} = x_{w} }}^{{x_{f} = x}} {\left( {\left( {1 - \frac{{x - x_{f} }}{{x_{E} - x_{f} }}} \right) \;\; \tau_{x}^{{ m_{1} }} \left( {x_{f} , t - t_{0} - \frac{{x - x_{f} }}{{c_{K} }}} \right) } \right.} \\ & \left. {{-} \,\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \; \left( {1 - d_{1} \left( {x,x_{f} } \right)} \right) \;\; \tau_{x}^{{ m_{2} }} \left( {x_{f} , t - t_{0} - \frac{{x_{E} - x_{f} }}{{c_{K} }} - \frac{{x_{E} - x}}{{c_{R} }}} \right)} \right)dx_{f} \\ & + C\int_{{x_{f} = x}}^{{x_{f} = x_{E} }} {\left( {\left( {1 - \frac{{x_{f} - x}}{{x_{f} - x_{W} }}} \right) \;\; \tau_{x}^{{ m_{1} }} \left( {x_{f} , t - t_{0} - \frac{{x_{f} - x}}{{c_{R} }}} \right) } \right.} \\ & \left. {{-}\, \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \; \left( {1 - d_{2} \left( {x,x_{f} } \right)} \right) \;\; \tau_{x}^{{ m_{2} }} \left( {x_{f} , t - t_{0} - \frac{{x_{E} - x_{f} }}{{c_{K} }} - \frac{{x_{E} - x}}{{c_{R} }}} \right)} \right)dx_{f} \\ \end{aligned}$$

where the coordinate x _f (unit: °E) is the longitude of the forcing τ _x (x _f ,t), x _W (=130°E) and x _E (=280°E, i.e. 80°W) are the western and eastern boundaries, t is time in months, c _K/R are the first mode Kelvin/Rossby wave speeds in °E per month (with c _R  = c _K /3), τ ^3m _x is the 3 months running mean of τ _x , and:

• if F_eq is the zonal current U_eq: constant C ~ 0.7 m s⁻¹ (N m⁻²)⁻¹ °E⁻¹; t₀ ~ 0.5 months; running mean m₁ = m₂ = 2 months and $d_{1} \left( {x,x_{f} } \right) = d_{2} \left( {x,x_{f} } \right) = \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \frac{{x_{E} - x}}{{x_{E} - x_{W} }}$.

• if F_eq is SST_eq, the formula has a similar form,⁴ with: constant C ~ 1.1 °C (N m⁻²)⁻¹ °E⁻¹; t₀ ~ 1.5 months; running mean m₁ = 3 months and m₂ = 4 months; $d_{1} \left( {x,x_{f} } \right) = \frac{{x - x_{f} }}{{\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} (x_{E} - x_{f} ) }}$ and $d_{2} \left( {x,x_{f} } \right) = \frac{{x_{f} - x}}{{x_{f} - x_{W} }}$.

• if F_eq is SSH_eq, the pattern is a priori more complex (cf. Fig. 3), but if the effect of the reflexion to the east is neglected, we can keep an almost similar form (not shown).

This formula could appear complex at first sight, but can be actually simply interpreted. The two integrals on the right hand side of the equation are of similar form, and physically represent the two cases x _f  < x and x _f  > x. And within each integral, the two terms represent the fast positive response of the ocean to the westerly pulse followed by the delayed negative feedback (cf. Fig. 3).

We emphasize that these formulae are very crude. Their main purpose is to help to physically understand the equatorial oceanic response to various forcing cases.