Detection of heat-mass transfer regime transitions in the active layer using fractal geometric parameters

Abstract

Hourly time series of temperature and a surrogate measure of the soil water ionic (solute) concentration were obtained in the upper 50 cm at a site in central Alaska from August 1991 through May 1992. The site is located over a body of permafrost. A strong “zero curtain” develops in winter and persists for three months; maintenance of this isothermal layer is associated with water advection and vapor movement within the unfrozen zone. Warming of the active layer in spring occurs nearly instantaneously and results from infiltration of snowpack meltwater. Analysis of the time series is facilitated by use of spectral techniques. Fourier transform yields variance spectra from which fractal geometric parameters are calculated. Variations in the time- and depth-dependent fractal parameters are related to dominant heat-transfer regimes determined from previous analyses. The time series were also analyzed using Hurst rescaling. Rescaled trace minima and maxima, taken from the top, middle, and base of the active layer, self-model transitions in seasonal heat-mass transfer mechanisms. The Hurst Exponent, calculated from thermal and solute time series, exhibits process-dependent patterns. In theory, the fractal dimension and Hurst Exponent are linearly related. However, when the fractal dimension is calculated using the variance spectra method, the relationship is not linear as anticipated.