Wind Stress Curl and ENSO Discharge/Recharge in the Equatorial Pacific
Authors: Clarke Allan J. , Van Gorder Stephen , Colantuono Giuseppe 
Published: May 2007

Abstract
Discharge and recharge of the warm water volume (WWV) above the 20°C isotherm in an equatorial Pacific Ocean box extending across the Pacific from 156°E to the eastern ocean boundary between latitudes 5°S and 5°N are key variables in ENSO dynamics. A formula linking WWV anomalies, zonally integrated wind stress curl anomalies along the northern and southern edges of the box, and flow into the western end of the box is derived and tested using monthly data since 1993. Consistent with previous work, a WWV balance can only be achieved if the 20°C isotherm surface is not a material surface; that is, warm water can pass through it. For example, during El Niño, part of the WWV anomaly entering the box is cooled so that it is less than 20°C and therefore passes out of the bottom of the box, the 20°C isotherm surface. The observations suggest that the anomalous volume passing through the 20°C isotherm is approximately the same as T ′W, the anomalous WWV entering the western end of the box. Therefore the observed WWV anomaly can be regarded as being driven by the anomalous wind stress curl along the northern and southern edges of the box. The curl anomaly changes the WWV both by divergent meridional flow at the edges of the box and vortex stretching; that is, the Sverdrup balance does not hold in the upper ocean. A typical amplitude for the rate of change of WWV for the 5°S–5°N box is 9.6 Sv (Sv ≡ 106 m3 s−1). The wind stress curl anomaly and the transport anomaly into the western end of the box are highly correlated with the El Niño index Niño-3.4 [the average sea surface temperature anomaly (SSTA) over the region 5°S–5°N, 170°–120°W] and Niño-3.4 leads minus the WWV anomaly by one-quarter of a cycle. Based on the preceding results, a simple discharge/recharge coupled ENSO model is derived. Only water warmer than about 27.5°–28°C can give rise to deep atmospheric convection, so, unlike past discharge/recharge oscillator models, the west-central rather than eastern equatorial SSTAs are emphasized. The model consists of two variables: T ′, the SSTA averaged over the region of strong ENSO air–sea interaction in the west-central Pacific equatorial strip 5°S–5°N, 156°E–140°W and D′, the 20°C isotherm depth anomaly averaged over the same region. As in the observations, T ′ lags D′ by one-quarter of a cycle; that is, ∂T ′/∂t = νD′ for some positive constant ν. Physically, when D′ &gt; 0, the thermocline is deeper and warmer water is entrained through the base of the mixed layer, the anomalous heat flux causing ∂T ′/∂t &gt; 0. Also, when D′ &gt; 0, the eastward current anomaly is greater than zero and warm water is advected into the region, again causing ∂T ′/∂t &gt; 0. Opposite effects occur for D′ &lt; 0. A second relationship between T ′ and D′ results because the water is warm enough that T ′ causes deep atmospheric convection anomalies that drive the wind stress curl anomalies that change the heat storage ∂D′/∂t. The atmosphere responds essentially instantly to the T ′ forcing and the curl causes a discharge of WWV during El Niño (T ′ &gt; 0) and recharge during La Niña (T ′ &lt; 0), so ∂D′/∂t = −μT ′ for some positive constant μ. The two relationships between T ′ and D′ result in a harmonic oscillator with period 2π/νμ ≈ 51 months.