Fractal geometry is a quantitative tool for studying and modeling a majority of complex natural phenomena. Considering the profound impact of geological variables on the nature and activity of drainage networks, this study investigated the role of lithology and geological formations in quantifying the drainage network of the Yazd–Ardakan catchment. The numerical values of the fractal dimension of the drainage network were obtained for the three geological formations in the studied catchment. A mean fractal dimension of 1.149, 1.161, and 1.207 was respectively for the Taft limestone, Shirkuh granite, and Kahar formations. one-way analysis of variance (ANOVA) showed a significant difference between the mean fractal dimension of the drainage network in the three geological formations at a confidence level of 0.99. The results also showed significant relationships between the fractal dimensions of the drainage network and morphometric indices (drainage density, number of ranks, average length of rank, and rank frequency). The highest correlation coefficient was observed for the regression correlation between the drainage density and fractal dimension (at a confidence level of 0.99). The validation results of the fractal dimension efficiency of the drainage network in classifying and separating geological formations revealed that the fractal dimension effectively separated the Kahar formation with a probability of 93% and the Taft limestone and Shirkuh granite formations, respectively with a probability of 78% and 75%. The fractal dimension more effectively identified the drainage network on the Kahar Formation more effectively than the Shirkuh granite and Taft limestone formations.

This study is organized into the following five sections. 1) In this section, 1:100000 geological maps of the catchment were prepared (Geological Survey & Mineral Explorations of Iran, 2014). Among the geological formations of Yazd–Ardakan catchment, the Kahar, Shirkuh granite, and Taft limestone formations were selected to study their erosion susceptibility under arid to cold semi-arid climates. To this end, PSIAC (Committee PSIAC, 1968), Feyznia (Feiznia, 1995), and Selby (Selby, 1980) methods were used to estimate the erosion susceptibility in each formation. It is noteworthy that the estimated drainage network in the geological formations was extracted from the topographical maps. To this end, data and nine 1:25000 digital topographical maps in Naein (Block 69), Ardakan (Block 70), Abadeh (Block 79), and Yazd (Block 80) blocks were used (NCC National Cartographic Center, 2014). The reason behind selecting these three formations was the lack of spatial expansion and scattering allowing random sampling in a large homogeneous area. Sampling in each formation was carried out using 1 ×1 km² plots to achieve a more exact mean of the fractal dimension of the drainage network, considering the extent of geological formations in the study area. Larger plots may cause the elimination of geological maps and inaccurate evaluation of the drainage network. Moreover, plots smaller than 1 km×1 km do not allow the evaluation of all stream degrees and a full picture of a stream network. To this end, a 1 ×1 km² plot was selected and 33 plots were randomly considered for each formation to calculate the fractal dimension of the drainage network. 2) In the second section, the fractal dimension was calculated for thirty-three 1×1 km² plots in the Kahar, Shirkuh granite, and Taft limestone formations. In each geological formation, the fractal dimension was calculated using the box-counting method with the help of Fractalyse. The number of plots required for each formation was obtained graphically (Fakhar Izadi et al., 2016). First, the mean fractal dimensions were calculated for the two plots. The mean value for different pairs was calculated up to the point at which the mean fractal dimension remained unchanged. After plotting the diagram, the point where the slope changes (the inflection point) appears and the diagram lacks fluctuation is considered as the number of plots required in each formation. After determining the number of plots required for each formation, the mean fractal dimension was calculated. 3) In this section, morphometric indices (Horton, 1932), including the drainage density, number of ranks, average length of rank, and rank frequency in each plot are calculated. The Fractal features of drainage networks on geological formations can be examined using morphometric indices. To this end, the correlation between the morphometric indices and fractal dimensions of the drainage network was obtained. 4) The last section concerns the validation of the fractal dimension efficiency in classifying and separating geological formations.

Researchers should cite this work as follows:

• Mojdeh Mohammadi Khoshoui; Mohammad Reza Ekhtesasi; Ali Talebi (2021), "Application of Fractal Dimension in Erosion Susceptibility Analysis of Geological Formations in Arid Areas," https://mygeohub.org/resources/1549.

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1. fractal dimension