Reducing stochasticity in the North Atlantic Oscillation index with coupled Langevin equations

We present a critical investigation of the functional relationship between the two pressure time series routinely used to define the index characterizing the North Atlantic Oscillation (NAO), well known to regulate global climate variability and change. First, by a standard Markov analysis we show that the standard NAO index based on the pressure difference is not optimal in the sense of producing sufficiently reliable forecasts because it contains a dominating stochastic term in the corresponding Langevin equation. Then, we introduce a variationally optimized Markov analysis involving two coupled Langevin equations tailored to produce a NAO quasi-index having the desired minimum possible stochasticity. The variationally optimized Markov analysis is very general and can be applied in other physical situations involving two or more time series.