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

• Published in: Permafrost and Periglacial Processes
• Main Authors: Outcalt, Samuel I., Hinkel, Kenneth M.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Wiley 1992
• Subjects: Fairbanks; Caribou-Poker Creeks Research Watershed; Permafrost and Periglacial Processes; Alaska
• Online Access: http://dx.doi.org/10.1002/ppp.3430030405; https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fppp.3430030405; https://onlinelibrary.wiley.com/doi/pdf/10.1002/ppp.3430030405

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 ( D hb ) and the Coefficient of Determination ( R 2 ). This procedure measures both the degree of roughness of a time series ( D hb ) and the degree to which the time series approaches a ‘pure’ fractal condition ( R 2 = 1.0). The Caribou‐Poker Creeks data set demonstrates that time series from different microenvironments can be discriminated in ( R 2 , 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 D hb and a corresponding decrease in R 2 . 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.