The fractal geometry of thermal and chemical time series from the active layer, Alaska

Samuel I. Outcalt and Kenneth M. Hinkel

Permafrost and Periglacial Processes, 1992, vol. 3, issue 4, 315-322

Abstract: Two data sets were used to examine the fractal geometry of constituent time series. Soil temperature and soil water ionic concentration observations were collected in August 1991 at proximal sites at the Caribou‐Poker Creeks Research Watershed near Fairbanks, Alaska. The second data set contains thermal records of the 1984 active layer freezeback from Toolik Lake. Following Fourier transformation, log (variance) was plotted as a function of log (wavelength) and three parameters were generated: the exponent (S) of the power law fit to the variance spectrum, the Hausdorff‐Besicovitch Dimension (Dhb) and the Coefficient of Determination (R2). This procedure measures both the degree of roughness of a time series (Dhb) and the degree to which the time series approaches a ‘pure’ fractal condition (R2 = 1.0). The Caribou‐Poker Creeks data set demonstrates that time series from different microenvironments can be discriminated in (R2, S) space. The thermal records from Toolik Lake show that, during formation of the isothermal ‘zero curtain’ layer, heat transfer is accomplished primarily by non‐conductive processes. The zero‐curtain effect is characterized by a ‘pink noise’ spectrum with strong cyclic elements, an increase in Dhb and a corresponding decrease in R2. The methods were applied here to a single probe, but confirm previous analyses employing apparent thermal diffusivity calculations and spectral comparisons requiring data from multiple levels. La géométrie fractale de deux séries de données temporelles a été étudiée. Des observations de la température du sol et de la concentration ionique de l'eau du sol ont été rassemblées en aoǔt 1991 dans des sites proches du Centre de Recherche des eaux de Caribou‐Polker Creeks près de Fairbanks en Alaska. La seconde série de données consiste dans des enregistrements thermiques au moment du retour du gel dans la couche active en 1984, prés du Lac Toolik. Suivant la transformation de Fourier, le logarithme de la variance, a été reporté comme une fonction du logarithme de la longuer d'onde et 3 paramètres ont été générés: l'exposant (S) loi du puissance adapté au spectre de la variance, la dimension Hausdorff‐Besicovitch (Dhb) et le coefficient de détermination (R2). Cette procédure mesure à la fois le degré d'irrégularit d'une série temporelle et le degré auquel, les séries de temps approachent une condition fractale pure (R2 = 1.0).

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:wly:perpro:v:3:y:1992:i:4:p:315-322

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