Inter-decadal change in El Niño-Southern Oscillation examined with Bjerknes stability index analysis

Abstract

Characteristics of El Niño-Southern Oscillation (ENSO) have changed since the late 1970s as it synchronized with the Pacific Decadal Oscillation (PDO). In order to investigate the primary feedback process responsible for the interdecadal change in ENSO characteristics according to the PDO, using the ocean assimilation data (SODA) and the reanalysis data (NCEP/NCAR), we performed Bjerknes linear stability index (BJ index) analysis of two decadal periods: one before the late 1970s (the nPDO period) and the other after the late 1970s (the pPDO period). The BJ index for the pPDO period (−0.07 year⁻¹ for the growth rate of the eastern Pacific SST anomaly) is significantly larger than that for the nPDO period (−0.25 year⁻¹). The larger BJ index value is primarily due to the enhanced zonal advection feedback (ZA; +0.44 year⁻¹), thermocline feedback (TH; +0.33 year⁻¹), and the reduced damping by the mean meridional current (MD; +0.16 year⁻¹). The increases in ZA and TH are mainly attributed to the shoaling of the mean thermocline depth, which increased the sensitivity of the ocean dynamic fields to the wind forcing; and the reduced MD is related to the reduced mean meridional current associated with the weakened trade wind. The enhanced positive feedback is partly compensated by the enhanced thermodynamic damping including the shortwave, sensible heat flux and latent heat flux (collectively, −0.88 year⁻¹). Interestingly, the change in air–sea coupling strength from the nPDO to the pPDO period was small. Without the two extreme El Niño events (1982–1983 and 1997–1998) in the pPDO period (pPDO_noBIG), the difference in BJ index between nPDO and pPDO_noBIG periods became smaller (~0.07 year⁻¹), indicating that the two extreme El Niño events largely contribute to the larger ENSO variability of the pPDO period, possibly due to nonlinear feedback processes. Nevertheless, qualitative similarity in each of the feedback and damping components of BJ index exists between the pPDO and pPDO_noBIG periods, which suggests that the tropical climate states of the pPDO period provided more favorable conditions for the emergence of extreme El Niño events by intensifying the linear feedback processes.

Appendices

Appendix 1: Parameters of the BJ index

$L_{x}$ and $L_{y}$ in the first two terms of Eq. (2) are the zonal and meridional distances in the eastern box; a₁ and a₂ are estimated to reform the zonal and meridional mixed layer advections in partial flux form, i.e., $- \frac{{\partial (\bar{u}T)}}{{\partial {\text{x}}}} - \frac{{\partial (\bar{v}T)}}{{\partial {\text{y}}}},$ respectively, where $\bar{u}$ and $\bar{v}$ represent climatologically averaged mixed layer currents.

The net downward heat flux change in SST anomaly can be written in the following form:

$$\left\langle Q \right\rangle_{E} = - \alpha_{s} \left\langle T \right\rangle_{E} ,$$

(3)

where $\alpha_{s}$ is the thermodynamic damping regression coefficient.

The ocean-to-atmosphere impact is presented by a simple linear relationship between SST and wind stress. The equatorial basin-wide (120°E–80°W) trade wind anomaly can be simply described in linear form using the least-square estimation with respect to the SST anomaly over the eastern box:

$$\left[ {\tau_{x} } \right] = \mu_{a} \left\langle T \right\rangle_{E} ,$$

(4)

where $\mu_{a}$ is wind response to SST forcing.

In the zonal advection feedback term, $- \left\langle \frac{{\partial \bar{T}}}{\partial x} \right\rangle_{E}$ is the zonal temperature gradient of the mean mixed layer temperature, and the zonal mixed-layer current is determined by surface wind stress (i.e., Ekman current) and thermocline depth field (i.e., geostrophic current) as follows:

$$\left\langle u \right\rangle_{E} = \beta_{u} \left[ {\tau_{x} } \right] + \beta_{uh} \left\langle h \right\rangle_{w} ,$$

(5)

where $\left\langle h\right\rangle_{w}$ is an ocean heat content averaged over the western box (vertically integrated ocean temperature from the surface to 300 m depth). The two coefficients $\beta_{u}$ (wind response to SST forcing) and $\beta_{uh}$ (geostrophic current adjusted to thermocline depth) determine the zonal current so that, unlike other equations, the coefficients are estimated using a multiple linear regression.

In the thermocline feedback, $\beta_{h}$ represents the sensitivity of a zonal contrast of heat content between the two boxes to wind stress forcing as follows:

$$\left\langle h \right\rangle_{E} - \left\langle h \right\rangle_{W} = \beta_{h} \left[ {\tau_{x} } \right].$$

(6)

$\alpha_{h}$ represents an effect of thermocline depth changes on ocean subsurface temperatures, $H\left( {\bar{w}} \right)$ is a step function to consider only climatological upwelling from below the subsurface region to the mixed layer as follows:

$$\left\langle {H\left( {\bar{w}} \right)T_{sub} } \right\rangle_{E} = \alpha_{h} \left\langle h \right\rangle_{E} .$$

(7)

In Ekman (upwelling) feedback, $-\left\langle \frac{{\partial \bar{T}}}{\partial z}\right\rangle_{E}$ is the mean vertical temperature gradient within the mixed layer, and the vertical motion forced by the wind stress can be presented in the following form:

$$\left\langle {H\left( {\bar{w}} \right)w} \right\rangle_{E} = - \beta_{w} \left[ {\tau_{x} } \right],$$

(8)

where $\beta_{w}$ is a response of ocean upwelling to wind forcing.

Appendix 2: β _h and β _uh modified by the wind stress pattern

The oceanic Rossby waves are generated by wind stress curl, which is modified by the meridional width of the wind stress. In order to explore the oceanic wave generation against the wind stress pattern, we computed the wind stress curl generated by the simplified wind stress pattern. Suppose a zonal wind stress resembling the zonal wind stress pattern during El Niño is as follows:

$$\tau_{x} = \tau_{M} \left( {y_{0} } \right)e^{{ - \left( {\frac{{y - y_{0} }}{{L_{y} }}} \right)^{2} }} ,$$

(9)

where y is the latitude, $\tau_{M} (y_{0} )$ is the maximum zonal wind stress amplitude at $y_{0} ,\,L_{y}$ is the e-folding scale. Suppose $y_{0} = 0,$ then, wind stress curl (assuming $\tau_{y} = 0$) becomes

$$\nabla \times \tau = \frac{{2\tau_{M} (0)}}{{L_{y}^{2} }}ye^{{ - \left( {\frac{y}{{L_{y} }}} \right)^{2} }} .$$

(10)

Therefore, larger L _y results in smaller wind stress curl. We then computed the latitude of maximum wind stress curl by taking a partial derivative of (10) as follows:

$$\frac{\partial }{\partial y}\nabla \times \tau = \frac{{2\tau_{M} \left( 0 \right)}}{{L_{y}^{2} }}e^{{ - \left( {\frac{y}{{L_{y} }}} \right)^{2} }} \left( {1 - \frac{{2y^{2} }}{{L_{y}^{2} }}} \right),$$

(11)

and the maximum latitude of the wind stress curl is ${\text{y}}_{max} = \pm \frac{{L_{y} }}{\sqrt 2 }.$ Therefore, as L _y increases, i.e., increased meridional width of zonal wind stress, the latitude of maximum wind stress curl increases.

Appendix 3: β _h , β _u , and β _w modified by ocean structure

As in Sect. 3.2:

$$\beta_{u} \approx \frac{{H_{2} }}{{\rho r_{s} HH_{1} }}\quad \left( {{\text{e}} . {\text{g}} . ,\,{\text{Zebiak}}\,{\text{and}}\,{\text{Cane}}\,1987} \right),$$

(12)

$$\beta_{h} \approx \frac{L}{{2\rho g^{{\prime }} H}}\quad \left( {{\text{e}} . {\text{g}} . ,\,{\text{Hirst}}\, 1 9 8 6 ;\,{\text{An}}\,{\text{and}}\,{\text{Cane}}\,2001} \right),$$

(13)

and

$$\beta_{w} \sim\frac{{2H_{2} }}{{\rho r_{s} HL}}\quad \left( {{\text{e}} . {\text{g}} . ,\,{\text{Zebiak}}\,{\text{and}}\,{\text{Cane}}\,1987} \right),$$

(14)

where $g^{{\prime }}$ is reduced gravity; $\rho$ is sea water density; ${\text{L}}$ is Pacific basin length; H, H₁, and H₂ (H = H₁ + H₂) are upper layer depth, mixed layer depth, and lower layer depth, respectively. All three are inversely proportional to H.

H slowly changes in time as follows:

$${\text{H}}\left( {\text{t}} \right) = H_{0} + \tilde{H}\left( t \right),$$

(15)

where $H_{0}$ is a constant, and $\tilde{H}(t)$ is a slowly varying mean thermocline depth. Since $\tilde{H}(t) \ll H_{0} ,$ the slowly varying $\beta_{i}$ (i = u, h, w), $\tilde{\beta }_{i}$ becomes

$$\tilde{\beta }_{i} \left( t \right) \approx \beta_{i} \left( {1 - \frac{{\tilde{H}(t)}}{{H_{0} }}} \right).$$

(16)

Therefore, the deepening of the mean thermocline results in the reduction of sensitivity of $\beta$ to wind forcing, which is opposite for the shoaling of the mean thermocline.

The reduced gravity $g^{{\prime }} = g\frac{{\rho_{2} - \rho_{1} }}{\rho },$ where $\rho_{1}$ and $\rho_{2}$ are the density above and below the thermocline, respectively. Therefore, the warming of the water above the thermocline reduces the density, $\rho_{1} ,$ and thus increases $g^{{\prime }} ,$ which results in decreased $\beta_{h}$.

Appendix 4

A linearized SST equation can be written as

$$\frac{{\partial T^{{\prime }} }}{\partial t} = - \bar{u}\frac{{\partial T^{{\prime }} }}{\partial x} + \cdots - u^{{\prime }} \frac{{\partial T^{{\prime }} }}{\partial x} + \cdots$$

(17)

Where a bar and a prime indicate the time mean and the perturbation from the time mean, respectively. Usually in a linearization, the time mean quantity has a unit dimension, while the prime has the dimension of an epsilon (ε ≪ 1). Therefore, a linear term in (17) (scale = ε) is greater than a nonlinear term (scale = ε²). However, as a system is growing, the perturbation could reaches larger than a unit through a linear feedback, and then the nonlinear term can strongly booster the perturbation to be a big event because the nonlinear term (scale = Ε²) becomes greater than the linear term (scale = Ε, where Ε > 1). Note that this explanation is only valid for a quadratic nonlinearity.