نوع مقاله : مقاله پژوهشی
نویسندگان
1 گروه مدیریت مناطق بیابانی، دانشکده منابع طبیعی، دانشگاه یزد، شهر یزد
2 گروه مدیریت مناطق بیابانی، دانشکده منابع طبیعی، دانشگاه یزد،
3 گروه مدیریت آبخیزداری، دانشکده منابع طبیعی، دانشگاه یزد، شهر یزد
4 گروه ریاضی، دانشکده علوم، دانشگاه یزد، شهر یزد
چکیده
کلیدواژهها
موضوعات
عنوان مقاله [English]
نویسندگان [English]
Introduction
Analysis of land surfaces and plains plays a crucial role in natural resource studies. From a geomorphological perspective, landforms are generally classified into three major units: mountains, plains, and playas. Pediment plains are further subdivided into three types: bare pediment, coalescing pediment, and concealed pediment. Traditionally, field surveys, visual interpretation, and boundary delineation using Google Earth have been employed to identify pediment types. In this study, a novel approach based on fractal geometry techniques was applied. According to Mandelbrot, fractal geometry is grounded in the concept of objects exhibiting self-similar and repetitive patterns across different scales. The objective of this research is to apply fractal analysis in order to characterize the hydrographic networks of different pediment geomorphological types in desert environments.
Research Methodology
The study area covers 1,441.91 km² in the Yazd-Ardakan plain, located within Zone 40. Satellite imagery from the Advanced Land Observing Satellite (ALOS) PALSAR was selected through the Earthdata Search portal (earthdata.nasa.gov) due to its high-resolution Digital Elevation Model (DEM) capabilities.
Using the Hydrology Toolbox in ArcGIS, the hydrographic network was extracted from the DEM. Random plots of varying sizes were selected on the hydrographic network. Fractalyse software was employed to compute the fractal dimension of plots measuring 1, 4, 9, 16, and 64 km² at a scale of 1:50,000 using the box-counting method. The mean and variance of the fractal dimension across plots in each pediment type were calculated, and diagrams were generated to determine the minimum sampling area.
For validation, 10 observed plots and 10 estimated plots were compared within a 9 km² plot (the minimum sample area) in each pediment type. The Kolmogorov–Smirnov test and independent t-test were conducted at the 99% confidence level using SPSS software. Model performance was further evaluated using the Root Mean Square Error (RMSE), Nash–Sutcliffe Efficiency (NSE), Pearson’s correlation coefficient (r), scatter plots, regression equations, slope coefficients, and the coefficient of determination (r²).
Results
Table 1. Number and distribution of sampling plots based on size and type of pediment plain
Plot side length (km)
Plot area (km2)
Total number of plots
Number of plots in each pediment
Bare pediment
Coalescing pediment
Concealed
pediment
1
1
190
51
84
55
2
4
111
33
44
34
3
9
62
20
22
20
4
16
34
12
12
10
8
64
16
5
5
6
Table 2. Mean fractal dimension of hydrographic networks across plots with different areas.
Plot area (km2)
Bare pediment
Coalescing pediment
Concealed
pediment
1
1.168
1.178
1.119
4
1.273
1.277
1.269
9
1.418
1.409
1.363
16
1.427
1.409
1.396
64
1.508
1.499
1.489
Discussion and conclusion
The point at which the variance diagrams of the fractal dimension become linear and stabilized—referred to as the turning point of the diagram—indicates the minimum sampling area, which in this study was identified as 9 km² plots. From this threshold onward, the fractal dimension of the hydrographic networks consistently decreased from erosional pediments toward covered pediments. According to the diagrams, the minimum number of samples required for erosional pediments, alluvial fan pediments, and covered pediments is 15, 17, and 18 plots, respectively. The Kolmogorov–Smirnov test confirmed the normality of the data (p > 0.05), while the independent t‑test showed no significant differences between observed and estimated data (p > 0.05) at the 99% confidence level. The RMSE and NSE indices indicated low model error and high predictive accuracy for bare pediment and coalescing pediment. In concealed pediment, RMSE values were close to zero, confirming highly accurate predictions, while NSE also demonstrated acceptable model performance. The results of Pearson's correlation coefficient (r), regression coefficient, and coefficient of determination (r²) for all three pediment types indicate a strong positive correlation between observed and estimated data, reflecting very good model performance. Overall, for the 9 km² plots—identified as the minimum sampling area—the fractal dimensions of bare pediment, coalescing pediment, and concealed pediment were 1.418, 1.409, and 1.363, respectively. These results highlight the effectiveness of the fractal geometry technique in geomorphological characterization and hydrographic network analysis in arid regions.
کلیدواژهها [English]
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