Variability of the western Pacific warm pool structure associated with El Niño

Abstract

Sea surface temperature (SST) structure inside the western Pacific warm pool (WPWP) is usually overlooked because of its distinct homogeneity, but in fact it possesses a clear meridional high–low–high pattern. Here we show that the SST low in the WPWP is significantly intensified in July–October of El Niño years (especially extreme El Niño years) and splits the 28.5 °C-isotherm-defined WPWP (WPWP split for simplification). Composite analysis and heat budget analysis indicate that the enhanced upwelling due to positive wind stress curl anomaly and western propagating upwelling Rossby waves account for the WPWP split. Zonal advection at the eastern edge of split region plays a secondary role in the formation of the WPWP split. Composite analysis and results from a Matsuno–Gill model with an asymmetric cooling forcing imply that the WPWP split seems to give rise to significant anomalous westerly winds and intensify the following El Niño event. Lead-lag correlation shows that the WPWP split slightly leads the Niño 3.4 index.

Appendix: Atmospheric responses to an asymmetric forcing

To study atmospheric responses to steady-state forcing, the advection term is neglected and the dissipative process is included in the model (Matsuno 1966; Gill 1980):

$$ \varepsilon u - \frac{1}{2}yv = - \frac{\partial p}{\partial x} $$

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$$ \varepsilon v + \frac{1}{2}yu = - \frac{\partial p}{\partial y} $$

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$$ \varepsilon p + \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = - Q $$

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$$ w = \varepsilon p + Q $$

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In these equations (x, y) is non-dimensional distance with x eastwards and y measured northwards from the equator, (u, v) is proportional to horizontal velocity and p is proportional to the pressure perturbation. Q is proportional to the heating rate, $u{\raise0.7ex\hbox{${\partial T}$} \!\mathord{\left/ {\vphantom {{\partial T} {\partial x}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\partial x}$}}_{160E} + v{\raise0.7ex\hbox{${\partial T}$} \!\mathord{\left/ {\vphantom {{\partial T} {\partial y}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\partial y}$}}_{12N} - v{\raise0.7ex\hbox{${\partial T}$} \!\mathord{\left/ {\vphantom {{\partial T} {\partial y}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\partial y}$}}_{EQ}$ is the decay factor.

For a given equatorial asymmetric forcing Q, it could expand in the form of parabolic cylinder functions (Xing et al. 2014)

$$ Q\left( {x,y} \right) = Ag\left( x \right)\exp \left( { - \frac{1}{4}\left( {y + d} \right)^{2} } \right), $$

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$$ g\left( x \right) = \left\{ {\begin{array}{*{20}l} {\cos kx\quad \left| x \right| \le L} \hfill \\ {0\quad \left| x \right| > L} \hfill \\ \end{array} ,\quad k = \frac{\pi }{2L}} \right., $$

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$$ Q = Q_{n} \left( {x,y} \right) = AF_{n} \left( x \right)D_{n} \left( y \right), $$

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where

$$ F_{n} \left( x \right) = c_{n} \left( x \right) = \left( { - 1} \right)^{n} \frac{1}{n!}\left( {\frac{d}{2}} \right)^{n} \exp \left( { - \frac{1}{8}d^{2} } \right)g\left( x \right). $$

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Parabolic cylinder functions $u{\raise0.7ex\hbox{${\partial T}$} \!\mathord{\left/ {\vphantom {{\partial T} {\partial x}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\partial x}$}}_{160E} + v{\raise0.7ex\hbox{${\partial T}$} \!\mathord{\left/ {\vphantom {{\partial T} {\partial y}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\partial y}$}}_{12N} - v{\raise0.7ex\hbox{${\partial T}$} \!\mathord{\left/ {\vphantom {{\partial T} {\partial y}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\partial y}$}}_{EQ}$ are given by

$$ \left\{ \begin{aligned} D_{0} \left( y \right) = \exp \left( { - \frac{1}{4}y^{2} } \right) \hfill \\ D_{1} \left( y \right) = y\exp \left( { - \frac{1}{4}y^{2} } \right) \hfill \\ D_{2} \left( y \right) = \left( {y^{2} - 1} \right)\exp \left( { - \frac{1}{4}y^{2} } \right) \hfill \\ D_{3} \left( y \right) = \left( {y^{3} - 3y} \right)\exp \left( { - \frac{1}{4}y^{2} } \right) \hfill \\ \cdots \cdots \hfill \\ \end{aligned} \right.. $$

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To solve the above equations, Gill (1980) first introduced two new variables q and r to replace p and u, where q = p+u, r = p−u, and assumed that solutions of the equations can be expanded in the form of parabolic cylinder functions $D_{n} \left( y \right)$, where $q = \sum\nolimits_{n = 0}^{\infty } {q_{n} \left( x \right)} D_{n} \left( y \right)$. The Rossby wave and Kelvin wave parts of the detailed solutions for the first two terms of expansion forcing source Q are given by Eq. (4.3), Eq. (4.8), Eq. (5.2) and Eq. (5.6) (Gill 1980). General solutions for the rest expansion terms (n ≥ 2) are as follows (Xing et al. 2014):

$$ I = \exp \left( {\frac{1}{8}d^{2} } \right) \cdot \left( {A\left( { - 1} \right)^{n} \frac{1}{n!}\left( {\frac{d}{2}} \right)^{n} } \right)^{ - 1} , $$

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$$ \left\{ {\begin{array}{*{20}l} {\left( {\left( {2n + 3} \right)^{2} \varepsilon^{2} + k^{2} } \right)Iq_{n + 2} = - k\left( {1 + \exp \left( { - 2\left( {2n + 3} \right)\varepsilon L} \right)} \right)\exp \left( {\left( {2n + 3} \right)\varepsilon \left( {x + L} \right)} \right),} \hfill & {x < - L} \hfill \\ {\left( {\left( {2n + 3} \right)^{2} \varepsilon^{2} + k^{2} } \right)Iq_{n + 2} = - \left( {2n + 3} \right)\varepsilon \cos kx + k\left( {\sin kx - \exp \left( {\left( {2n + 3} \right)\varepsilon \left( {x - L} \right)} \right)} \right),} \hfill & {\left| x \right| \le L} \hfill \\ {\left( {\left( {2n + 3} \right)^{2} \varepsilon^{2} + k^{2} } \right)Iq_{n + 2} = 0,} \hfill & {x > L} \hfill \\ \end{array} ,} \right. $$

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$$ \left\{ {\begin{array}{*{20}l} {p = \frac{1}{2}q_{n + 2} \left( x \right)D_{n + 2} \left( y \right) + \frac{1}{2}\left( {n + 2} \right)q_{n + 2} \left( x \right)D_{n} \left( y \right)} \hfill \\ {u = \frac{1}{2}q_{n + 2} \left( x \right)D_{n + 2} \left( y \right) - \frac{1}{2}\left( {n + 2} \right)q_{n + 2} \left( x \right)D_{n} \left( y \right)} \hfill \\ {v = 2\left( {n + 2} \right)\varepsilon q_{n + 2} \left( x \right)D_{n + 1} \left( y \right) + Q_{n} \left( {x,y} \right)} \hfill \\ {w = \varepsilon p + Q_{n} \left( {x,y} \right)} \hfill \\ \end{array} } \right.. $$

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