Selected statistical characteristics of NAO index variation according to Hurell (1864-2019)

Abstract

This article presents the results of several attempts to statistically characterize the short-term (year-to-year) and long-term (>10-year) variability of the NAO Hurrell index in the period 1864 – 2019 and is a complementary continuation of their description presented in the study by Kożuchowski and Wibig (2021). The study used a time series of seasonal averages (DJFM) of the NAO index values according to Hurrell from the period 1864-2019. It was shown that the distribution of the NAO index and changes in the index from year to year do not differ significantly from the normal distribution and the observed frequency of increases or decreases of the index in relation to this value shows good convergence with adequate normal distribution probability (Fig. 2). The symmetry of the normal distribution means that the numbers of year-to-year increases and decreases in the index are equal in the entire index set. The NAO time series shows an above-average association of changes with opposite signs, which constitute more than 2/3 of the total number of all changes and form a negative, significant autocorrelation of the Δ variable (r1= -0.47). As a result, there is a tendency to prefer the change index sequences: decrease/increase and increase/decrease. Such associations of multi-directional changes develop most strongly in the range of the lowest and highest index values, which is confirmed by the significant negative autocovariance of changes. When examining the sequence of successive NAO indices in the time series, the association of the NAOi and NAOi+1 indices was found to be basically random. Frequency distributions of NAOi+1 values depending on NAOi are random – they do not differ significantly from the binomial distribution. However, in the statistics describing the volatility of NAO indices, signals were found that disturbed the symmetrical distribution of the observed changes in the index. They include e.g., repeated in the time series cases of difference between decreases and increases in the index – after significant decreases in the value of the index, its significant increases are characteristic and above average, but after large increases – decreases are not so great and frequent (Fig. 6 and 7). A special peculiarity is the form of volatility c, which means an increase in the index following its decrease and is associated with almost all cases of the index in the range of the 1st decile of the NAO value (Fig. 3). The volatility of the lowest indices (especially in the range of the 1st decile NAO) is much larger than the volatility of higher indices representing the positive NAO phases, the reason for the formation of such volatility asymmetry are different circulation conditions, corresponding to extremely low and moderately high and high NAO indices, i.e., the domination of meridional circulation or zonal circulation. The most significant signs of deviation from the stochastic nature of NAO volatility are revealed in the long-term course of the index. The observed concentration of extremely low and extremely high NAO indices in some decades of the multiannual period (Table 9) is characterized by a negligible probability of occurrence in a random series.

Keywords

• nao index
• temporal variability
• circulation conditions