The El Niño stochastic oscillator

Abstract A stochastic model is fitted to the observed NINO3.4 time series between 1951–1995. The model is nothing more than the complex version of a first-order autoregressive process. The autocorrelation of this stochastic oscillator model is an exponentially decaying cosine, specified by three parameters: a period, a decay time, and a phase shift. It fits the observed NINO3.4 autocorrelation quite well. Anomalies during an El Niño can be characterized to a large extent by a single, irregularly oscillating, index. Equatorial wave dynamics and delayed-oscillator models have been used to explain this behaviour, and it has been suggested that El Niño might be a stable phenomenon excited by weather noise. Assuming this is the case, the stochastic oscillator has a direct physical interpretation: the parameters of the oscillation can be linked to dynamical models of the delayed-oscillator type, and the noise terms represent random influences, such as intraseasonal oscillations. Long Monte Carlo simulations with the stochastic oscillator show substantial decadal variability and variation in predictability. The observed decadal variability is comparable, except for the rather large rise in the long-term mean around 1980. The observed seasonal dependence of El Niño behaviour is not compatible with the natural variability of a stationary stochastic oscillator. Formulating the model in terms of standardized anomalies takes into account some of the seasonal dependence. A stochastic oscillator forecast model has a skill approaching that of more comprehensive statistical models and may thus serve as an appropriate baseline for the skill of El Niño forecasting systems.

[1]  Ocean Wave Dynamics and El Niño , 1995 .

[2]  Ka-Ming Lau.  Elements of a Stochastic-Dynamical Theory of the Long-Term Variability of the El Niño/Southern Oscillation , 1985 .

[3]  M. Cane,et al.  A Model El Niñ–Southern Oscillation , 1987 .

[4]  Eli Tziperman,et al.  A Linear Thermohaline Oscillator Driven by Stochastic Atmospheric Forcing , 1995, ao-sci/9502002.

[5]  Anthony C. Hirst,et al.  Interannual variability in a tropical atmosphere−ocean model: influence of the basic state, ocean geometry and nonlinearity , 1989 .

[6]  Prashant D. Sardeshmukh,et al.  The Optimal Growth of Tropical Sea Surface Temperature Anomalies , 1995 .

[7]  E. Maier‐Reimer,et al.  Decadal Oscillations in a Simple Coupled Model , 1998 .

[8]  T. Barnett,et al.  ENSO and ENSO-related Predictability. Part I: Prediction of Equatorial Pacific Sea Surface Temperature with a Hybrid Coupled Ocean–Atmosphere Model , 1993 .

[9]  Mojib Latif,et al.  Tropical Ocean circulation experiments , 1987 .

[10]  R. Kleeman.  On the Dependence of Hindcast Skill on Ocean Thermodynamics in a Coupled Ocean-Atmosphere Model , 1993 .

[11]  A. Hirst.  Unstable and Damped Equatorial Modes in Simple Coupled Ocean-Atmosphere Models , 1986 .

[12]  M. Flügel,et al.  Impact of dynamical and stochastic processes on the predictability of ENSO , 1996 .

[13]  Eli Tziperman,et al.  El Ni�o Chaos: Overlapping of Resonances Between the Seasonal Cycle and the Pacific Ocean-Atmosphere Oscillator , 1994, Science.

[14]  R. Balescu.  Equilibrium and Nonequilibrium Statistical Mechanics , 1991 .

[15]  Mojib Latif,et al.  Predictability of a Stochastically Forced Hybrid Coupled Model of El Niño , 1997 .

[16]  T. Barnett,et al.  Long-Lead Seasonal ForecastsWhere Do We Stand? , 1994 .

[17]  P. Chang,et al.  A decadal climate variation in the tropical Atlantic Ocean from thermodynamic air-sea interactions , 1997, Nature.

[18]  Ming Ji,et al.  Coupled Model Predictions of ENSO during the 1980s and the 1990s at the National Centers for Environmental Prediction. , 1996 .

[19]  S. Philander,et al.  Interdecadal Climate Fluctuations That Depend on Exchanges Between the Tropics and Extratropics , 1997, Science.

[20]  Stephen M. Griffies,et al.  Predictability of North Atlantic Multidecadal Climate Variability , 1997, Science.

[21]  Mechanisms of Seasonal – ENSO Interaction , 1995, ao-sci/9508001.

[22]  Thomas M. Smith,et al.  Improved Global Sea Surface Temperature Analyses Using Optimum Interpolation , 1994 .

[23]  M. Balmaseda,et al.  ENSO prediction using a dynamical ocean model coupled to statistical atmospheres , 1994 .

[24]  Aperiodic Variability in the Zebiak-Cane Coupled Ocean-Atmosphere Model: Air-Sea Interactions in the Western Equatorial Pacific , 1995 .