Complexity signatures for short time scales in the atmosphere above Adventdalen, Svalbard

Abstract

Atmospheric parameters from the troposphere above Adventdalen, Svalbard, 78°N, 16°E, are examined for signatures of complexity in their respective stochastic components over time scales from~1 h to 1 year. Several approaches are used, all of which can estimate values of the generalized Hurst exponent, α, which can in turn be compared with each other and with similar independent characterizations, usually via the classic Hurst exponent, H, obtained from location-specific and globally averaged time series. For tropopause altitude, the stochastic component exhibits the signature of a persistent fractional Gaussian noise (fGn) with α ≈ 0.75. For surface air temperature, the indications are for fractional Brownian motion (fBm) with α ≈ 1.4. Using recent high time-resolution data from a single high-latitude location, this identification of fBm is relevant for short-term memory as opposed to findings from many other studies addressing possible long-term memory, which demonstrate fGn with α = H ≈ 0.7. Furthermore, the lack of similarity between the results for surface air temperature and tropopause altitude suggests that different underlying processes are responsible for stochastic variability.

Complexity signatures in the geomagnetic <i>H</i> component recorded by the Tromsø magnetometer (70° N, 19° E) over the last quarter of a century

“…Work by Eichner et al (2003), Lennartz and Bunde (2009), and Kantelhardt et al (2006), for example, has refined the approach. Much attention has been given to oceanographic and meteorological observables, including the recent study by Hall (2014), and more recently solar-related observables, e.g. Scafetta and West (2003) and Rypdal and Rypdal (2011).…”

“…The approach to analysing the geomagnetic field data here is the same as that used by Hall (2014): first, the data are filtered using a boxcar to remove all periodicities less than 1 day, and the result is then subtracted from the original time series, thus producing a residual excluding all preconceived 1052 C. M. Hall: Complexity in the geomagnetic H component at 70 • N, 19 • E (deterministic) periodicities. This is equivalent to "deseasonalization", commonly applied to neutral atmosphere data, for example.…”

“…The relationship is conveniently summarized in Fig. 1 of Hall (2014). Moreover, the fractal or Hausdorff-Besicovich dimension D = 2 − H , but assuming fBm.…”

“…One can see, therefore, that calculating D by, for example, the method of Grassberger and Procaccia (1983) can potentially yield H but not unambiguously provide the same information as α. Following the sequence used by Hall (2014), rather than blindly launching into a determination of α which will almost inevitably yield some result, the data are examined first for indications of non-linearity by inspections of the probability density function (PDF) and quantile-quantile (Q-Q) analyses (Wilk and Gnanadesikan, 1968). A PDF can indicate qualitatively whether the distribution is non-Gaussian.…”

“…Some of the methods used most are described and compared by Delignieres et al (2006), Hartmann et al (2013) and Heneghan and McDarby (2000) (note, however, that these last authors use "α" as the spectral scaling exponent rather than β). Using experience gained from Hall (2014), α is obtained using both spectral analysis (SA) and detrended fluctuation analysis (DFA); while most physicists will feel comfortable with the more intuitive SA, DFA (Peng et al, 1993) is arguably the preferred method in contemporary research when searching for long-term memory in data. For the purposes of SA, since experimental data are under consideration, the time series should be treated as irregularly sampled; data gaps are few but, even so, must be assumed to exist.…”