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Geofísica internacional

versión impresa ISSN 0016-7169

Geofís. Intl vol.48 no.4 Ciudad de México oct./dic. 2009




The relationship between Pacific Decadal and Southern Oscillations: Implications for the climate of northwestern Baja California


E. G. Pavia*


Centro de Investigación Científica y Educación Superior de Ensenada, km 107 Carretera Tijuana Ensenada, 22800, A. Postal 360, Ensenada, Baja California, México. *Corresponding author:


Received: September 3, 2008
Accepted: May 18, 2009



La relación entre la Oscilación Austral (SO) y la Oscilación Decenal del Pacífico (PDO) es analizada por medio de modelos forzados y de predicción secundaria de la PDO. Estos modelos son construidos con los mismos índices comunmente asociados a diferentes aspectos del clima del noroeste de Baja California, es decir el índice de Oscilación del Sur (SOI) y el índice de la Oscilación Decenal del Pacífico (PDOI). El modelo secundario explica alrededor del 40% de la variabilidad anual de la PDO, mientras que el modelo forzado explica alrededor del 60% de la variabilidad anual más la variabilidad decenal de la PDO. Estos resultados verifican que el fenómeno de El Niño–Oscilación del Sur (ENSO) fuerza a la PDO; por lo tanto también sugieren que las variabilidades interanual y decenal del Pacífico, así como sus impactos climatológicos en el noroeste de Baja California, son principalmente generados por el ENSO. Por lo que se espera que en tanto mejoren los pronósticos del ENSO, mejoraran las predicciones climatológicas en esta región así como los pronósticos de la PDO.

Palabras clave: ENSO, PDO, clima, predicción, Baja California.



The relationship between the Southern Oscillation (SO) and the Pacific Decadal Oscillation (PDO) is studied by means of forced and secondary forecast models of the PDO. These models are constructed with the same indices frequently associated to different aspects of the climate of northwestern Baja California, namely the Southern Oscillation Index and the Pacific Decadal Oscillation Index (SOI and PDOI). The secondary forecast model explains about 40% of the interannual variability of the PDO while the forced model explains about 60% of PDO interannual plus decadal variability. These results confirm that El Niño–Southern Oscillation (ENSO) forces the PDO. Thus interannual and decadal variabilities in the Pacific Ocean, and related climatological impacts in northwestern Baja California, may be mainly ENSO–generated. As ENSO forecasts improve, PDO forecast and climatological predictions in this region should also improve.

Key words: ENSO, PDO, climate, predictions, Baja California.



The El Niño–Southern Oscillation (ENSO) phenomenon dominates tropical Pacific variability (Philander et al, 1984). The Pacific Decadal Oscillation (PDO) is the leading mode of sea surface temperature (SST) anomalies in the North Pacific (Mantua et al., 1997). Both are believed to play a prominent role in the climate of USA and Mexico (Bove and O'Brien, 2000, Pavia et al., 2006). Constructive interference of these two signals may significantly modify precipitation regimes in southwestern California (Gershunov and Barnett, 1998) and in northwestern Baja California (Reyes–Coca and Troncoso–Gaytan, 2004; Pavia et al., 2006). Warm phases of both ENSO and PDO seem to favor higher than average wintertime precipitations in this region. However, Newman et al. (2003) and Schneider and Cornuelle (2005), extended the stochastic forcing paradigm (Hasselmann, 1976; Frankignoul and Hasselmann, 1977), and suggested that the PDO is dependent on ENSO on both interannual and decadal time scales. This dependence must be taken into account for forecasts of decadal climatic variability in northwestern Baja California (e.g. Reyes–Coca and Troncoso–Gaytan, 2004), where ENSO seems to modulate precipitation (Pavia and Badan, 1998). Similarly it has been suggested that for northwestern Baja California ENSO effects seem to be better represented by an atmospheric index, rather than an oceanic index, at annual and lower–frequency scales (Campos, 1999). Nevertheless previous forced models have been based on oceanic El Niño indices (e.g. Newman et al., 2003).

Pacific decadal variability is an "ENSO–like" variability (Zhang et al., 1997). It is also related to PDO (Mantua et al., 1997); but recently this ENSO–like variability and PDO have been treated as different phenomena (Vimont, 2005). A major problem to identify the physical processes that generate tropical Pacific decadal variability is the lack of long observational records. Progress in understanding this variability has been achieved lately (Timmermann and Jin, 2002; Liu et al., 2002; Newman et al., 2003; Miller and Schneider, 2000). More recently, some aspects of its spatial structure have been explained by relating the pattern of tropical Pacific decadal variability to patterns associated to interannual ENSO variability (Vimont, 2005; Alexander et al., 2002). It has been suggested that ENSO, through an atmospheric bridge and the reemergence of SST anomalies, is an important component of PDO (Newman et al., 2003). Furthermore, it has been suggested also that PDO may result from the superposition of SST fluctuations of different dynamical origins (Schneider and Cornuelle, 2005). These contributions suggest that ENSO may generate north Pacific low–frequency variability. And, since our emphasis is on the potential implications for northwestern Baja California climate, we use the same SOI and PDOI as in Reyes–Coca and Troncoso–Gaytan (2004) and Pavia et al. (2006) to construct an ENSO–forced PDO model.


Data and methods

For the tropical Pacific decadal variability we use the PDOI data from latest, and for ENSO we use the negative of the SOI available at NOAA's climate prediction center at We use the data for 1933 to 2008, the longest available record without gaps.

Working indices for PDO and SO are constructed by averaging 12 monthly values from September to August of the next year, centering on the wintertime (Pavia and Badan, 1998). We compute standardized indices as annual values minus the 74–year annual mean divided by the standard deviation. This procedure results in statistical zero–mean and unit standard deviation for two 74–year–long time series (Pn and Sn; =1, 2, ..., 74).

The forced model (Newman et al., 2003), based on Hasselmann (1976), is:

where Pn is the forecast PDO index at year n, Pn–1 is the PDO index at year n–1, similarly Sn is the ENSO index at year n, Nn is white noise at year n, and n is time in years. As in Newman et al. (2003) the parameter β = 0.61 is obtained by the regression of P onto S using a least–squares method; and the parameter α = 0.76 is similarly obtained by regressing the residual ε = (Pnβ × Sn) onto the previous year's PDO index: Pn–1 (see Fig. 1). The first step may be similar to a secondary forecast model (Pavia, 2000) replacing n by n+1:

(see Fig. 2).



The main results are:

(1) Sn values perform similarly at forcing Pn as in previous models (e.g. Newman et al., 2003); for example the correlation between "forecast" and observed Pn is r= 0.76 (see Fig. 1).

(2) The relatively successful linear model Pn= 0.61 Sn shows the importance of ENSO as a component of the PDO (see Fig. 2); for example the complementing model Sn= 0.47 Pn is not nearly as good.

(3) The conspicuous low frequency of the residual e (see Fig. 3) indicates that Sn is not directly accountable for the variance, σ2(Pn), which corresponds to the decadal variability of the PDO.

(4) The Gaussian character of the selected working indices shows that the non–autoregressive term (β × Sn) of the forced model may even serve as an undemanding secondary forecast for Pn (see Fig. 4).


Discussion and conclusions

We find that the Sn–forced model explains 57% of σ2(Pn) (r= 0.76) of which 39% may be explained by the term β × Sn. The remaining 43% of σ2(Pn) must be explained by other mechanisms which may generate the rest of the PDO variability. These may be partially ENSO generated (see, for example, Timmermann and Jin, 2002) or non–ENSO generated (see Liu et al., 2002). Or yet combinations of ENSO generated and non–ENSO generated processes, for example direct ENSO forcing, physical re–emergence of SST anomalies, white noise atmospheric forcing (Newman et al., 2003); or ENSO, zonal advection in the Kuroshio–Oyashio extension, anomalies of the Aleutian Low (Schneider and Cornuelle, 2005). Our analysis supports a contribution of ENSO to the north Pacific variability. Thus the reddening of Sn is responsible for a large amount of σ2(Pn); the SO forces the PDO and not the opposite, as suggested in northwestern Baja California winter precipitation studies (Reyes–Coca and Troncoso–Gaytan, 2004). Independently of the indices used, while SO may not contribute directly to PDO variability, its stochastic forcing does, by forcing processes generating decadal variability (Fig. 1). Therefore ENSO explains around 60% of PDO variance. The remaining 40% of the total variance may be accounted for by other physical mechanisms. Due to the Gaussian character of the working indices, a secondary forecast model may serve as a simple Pn forecast tool; for example, assuming a perfect primary Sn forecast, a Pn "hindcast" of the last ten years showed a remarkable 9/10 skill (Fig. 4); recall that theoretical and cross–validated skill is just 2/3. Thus better ENSO predictions should improve PDO forecasts and related annual and lower–frequency climate predictions.

In conclusion the expanded null hypothesis for the PDO is corroborated. Variability in the north Pacific on annual to decadal time scales is due to reddening of both white noise and ENSO. This contradicts the idea that PDO may regulate decadal climate variability in northwestern Baja California as well as ENSO.



My research is funded by the CONACYT System. I thank Federico Graef for early discussions on this topic, and two anonymous reviewers plus a technical editor for excellent suggestions.



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