بررسی تغییرات بعد فرکتالی و دقت مدلهای فراکتالی توزیع اندازه ذرات در زیرحوضه امام‌زاده ابراهیم گیلان

توزیع اندازه ذرات یکی از مهم‌ترین ویژگی‌های خاک است که معادلات مختلف فراکتالی برای توصیف بهتر آنها در دهه‌های اخیر ارایه شده است. هدف از انجام این مطالعه بررسی تغییرات ابعاد فراکتالی محاسبه شده با معادلات مختلف در در زیرحوضه امام زاده ابراهیم واقع در استان گیلان بود. برای انجام این پژوهش تعداد 93 نمونه خاک از مناطق مختلف حوضه با کاربری، فرسایش و نوع پوشش گیاهی گواناگون جمع‌آوری شد. توزیع اندازه ذرات در نمونه‌ها اندازه‌گیری شد. سه مدل فراکتالی بیرد، پریر-بیرد و تیلور- ویتکرفت بر اطلاعات برازش داده شد. نتایج نشان داد که مدل بیرد، پریر-بیرد نسبت به مدل تیلور- ویتکرفت دارای ریشه میانگین مربعات خطا (rmse) کمتری بودند (rmse برای مدل بیرد-پریر و مدل بیرد برابر 8.3 و برای مدل تیلور-ویتکرفت برابر با 29.3 است). مقدار بعد فراکتالی به دست آمده از مدل بیرد (2.73) نسبت به دو مدل دیگر یعنی مدل پریر- بیرد (2.94) و تیلور-ویتکرفت (2.95) کوچک‌تر بود. نتایج به دست آمده از این پژوهش نشان داد که مدل‌های فراکتالی در خاک‌های مختلف دارای دقت متفاوتی هستند. همچنین نتایج نشان داد که بعد فراکتالی هر سه مدل مورد مطالعه با رس دارای رابطه غیر خطی مثبت و با شن دارای رابطه خطی منفی هستند. به طور کلی نتایج نشان داد توزیع اندازه ذرات و درنتیجه بعد فراکتالی تابعی از نوع خاک، پوشش و کاربری اراضی است و مدل‌های دو پارامتری به دلیل انعطاف‌پذیری بیش‌تر، دارای دقت بیش‌تری برای توصیف توزیع اندازه ذرات خاک هستند.

investigation of changes in fractal dimension and accuracy of fractal models of soil particle size distribution in the imamzadeh ebrahim sub-watershed, guilan

background and objectives: particle size distribution stands out as a crucial physical attribute of soil, shaped by a myriad of intricate processes encompassing geological, physical, chemical, and biological factors. over the past few decades, the significance of particle size distribution in soil has prompted the development of various fractal equations aimed at providing more accurate descriptions. recognizing the significance of particle size distribution in soil erosion, it is crucial to scrutinize its variations and the associated equations. furthermore, to date, there has been no comprehensive study evaluating the accuracy of different fractal models across various land uses. this study aims to investigate variations in fractal dimensions calculated using different equations within the imamzadeh ebrahim sub-watershed located in the guilan province. methodology: to conduct this research, 93 soil samples were gathered from various locations within the basin, each exhibiting distinct land uses, erosion levels, and vegetation types. the areas under study encompass forests (8 samples), good pastures (11 samples), degraded pastures (23 samples), tea gardens (5 samples), paddy fields (7 samples), gully (21 samples), eroded sections on the river wall (4 samples) and sediments deposited in pits and sedimentation points at the outlet of the sub-watershed (14 samples). subsequently, the particle size distribution in these samples was meticulously measured. hydrometer readings were captured at intervals of 30 seconds, 1, 3, 10, 30, 60, 90, 120, 300, 600, 1440, and 2880 minutes. after obtaining hydrometer readings, the contents of the cylinder were discharged onto a 53 µm sieve to isolate sand particles from clay and silt. subsequently, particles within specified diameter ranges very fine sand (0.05 to 0.1 mm), fine sand (0.1 to 0.25 mm), medium sand (0.25 to 0.5 mm), coarse sand (0.5 to 1 mm), and very coarse sand (1 to 2 mm) were separated. furthermore, the number of points on the particle size distribution curve within the diameter range smaller than 0.05 mm was determined at 12 different locations. the data obtained were then subjected to fitting with three fractal models bird, perrier-bird and tyler-wheatcraft. findings: the outcomes indicated that the bird, perrier-bird model exhibited a lower root mean square error (rmse) in comparison to the tyler-wheatcraft model (rmse values for the perrier-bird and bird models were 3.8, while the tyler-wheatcraft model registered 3.29). bird's model yielded a smaller fractal dimension value (2.73) than the other two models, namely perrier-bird (2.94) and tyler-wheatcraft (2.95). the study further revealed that different soils exhibited varying accuracies when subjected to fractal models. the results, illustrating the average rmse changes among the three models examined in various samples, are provided. notably, the tyler-whitcroft model exhibited the lowest rmse value in pasture lands. furthermore, the findings indicate that the tyler-whitcroft model did not exhibit significant differences in forest, paddy, and tea garden applications, displaying lower accuracy in these three scenarios compared to other locations. additionally, the results from the bird and perrier-bird model revealed that the lowest rmse value was observed in eroded soils on the river wall and in pastures. moreover, the results highlighted a positive non-linear correlation between the fractal dimension of all three models and clay content, along with a negative linear relationship with sand content. the fractal dimensions of bird and perrier-bird, with correlation coefficients of 0.936 and 0.631, respectively, exhibit a significantly inverse relationship with sand at the 1% level. additionally, bird's fractal dimension demonstrates an inverse and significant relationship with sand components, ranging from very fine sand to coarse sand. the α coefficient of the perrier-bird equation exhibits an inverse relationship with sand (r = -0.494) and its components. however, this coefficient demonstrates a significant positive correlation with clay (r = 0.443) and silt (r = 0.448). conclusion: in summary, the findings underscored that particle size distribution, and consequently, the fractal dimension, is contingent on soil type, land cover, and land use. two-parameter models were identified as more precise in depicting soil particle size distribution due to their increased flexibility. notably, the performance of bird and perrier-bird models closely paralleled each other and surpassed the accuracy of the tyler-wheatcraft model. the research highlighted the variability in accuracy when applying these fractal models to different soil types. notably, the tyler-whitcroft model demonstrated the lowest rmse in pasture lands, with no significant differences observed in forest, paddy, and tea garden applications. however, its accuracy was comparatively lower in these three scenarios compared to other locations. this superiority can be attributed to the two-parameter nature of bird and perrier-bird models. furthermore, the study revealed that bird and perrier-bird models performed exceptionally well in eroded soils on the river wall and in pastures, as evidenced by the lowest rmse values.