Environmental Erosion Research

fa استفاده از مدل جاذبه به منظور تهیه مدل رقومی ارتفاع و لندفرم ها با قدرت تفکیک مکانی بیشتر Preparation of landforms with more spatial resolution using gravity model and its relationship with erosion rate روشهای نوین و دقیق در تهیّه نقشه فرسایش (سنجش از دور و سیستم‌های اطلاعات جغرافیایی) پژوهشي Research مطالعات نشان می‌دهد که با افزایش قدرت تفکیک مکانی داده‌ها میتوان جزئیات بیشتری را از منطقه مورد مطالعه بررسی کرد. بنابراین هدف از این مطالعه، تهیه داده‌های با قدرت تفیک بیشتر برای دریافت اطلاعات با جزئیات بیشتر است. با توجه به اهمیت رودخانه‌ها و نقش آنها در فرسایش، استفاده از مدل‌های جدید برای افزایش قدرت تفکیک مکانی مهم است. بنابراین، در این مطالعه از مدل جاذبه برای افزایش قدرت تفکیک مکانی مدل رقومی ارتفاعی سی متر در بخشی از رودخانه کر واقع در جنوب استان خوزستان استفاده شد. در ادامه با استفاده از مدل رقومی ارتفاع تهیه شده با استفاده از مدل جاذبه، نقشه لندفرم‌های منطقه با استفاده از روش شاخص موقعیت توپوگرافی (TPI) تهیه شد. در واقع، در این مطالعه با تهیه نوع لندفرم‌های منطقه با دقت بیشتر می‌توان وضعیت فرسایش یا رسوبگذاری را در منطقه مورد مطالعه حدس زد. در نهایت، نقشه لندفرم‌های تهیه شده با استفاده از مدل رقومی ارتفاع با قدرت تفکیک سی متر، با نقشه لندفرم تهیه شده با قدرت تفکیک مکانی بیشتر مقایسه شد. نتایج نشان داد که شاخص مقیاس ۳ و مدل همسایگی چهارگانه در مدل جاذبه، در افزایش قدرت تفکیک مکانی مدل رقومی ارتفاع و استخراج لندفرمها در منطقه مورد مطالعه بیشترین دقت را داشت. همچنین نتایج حاصل از روش TPI نشان داد که لندفرمهای آبراهه‌ها، زهکشهای شیب میانی، زهکشهای مناطق مرتفع، درّه‌های u شکل، دشت، شیب‌های باز، شیب‌های بالایی، تپه‌های موجود در درّه، تپه‌های کوچک موجود در دشت و قله کوه به ترتیب دارای مساحت 0.001، 32.11، 0.56، 4.28، 0.083، 1.76، 0.004، 1.12، 2.04، 0.014 کیلومتر مربع است. نتایح حاصل از مقایسه لندفرمهای تهیه شده از مدل رقومی ارتفاع با قدرت مکانی بیشتر نسبت به مدل رقومی سی متر نشان داد که میتوان جزئیات بیشتری را از لندفرمهای منطقه بهدست آورد. در پایان با توجه به نتایج لندفرمها مشخص شد که 37 درصد منطقه از زهکش‌های شیب میانی و درّههای U شکل تشکیل شدهاست که استعداد منطقه برای فرسایش را نشان می‌دهد.   1- Introduction In geomorphological studies, it is important to prepare landforms for the study of forms in different regions. In the same vein, with more accurate input data, landform maps are prepared with higher accuracy. Therefore, by using digital elevation model maps with more resolution, more accurate landforms can be extracted (Shayan et al., 2005). Identifying landforms, classifying them, and identifying different geomorphic forms are important in examining the relationships between form and process in the area. By extracting landforms, various information such as climatic characteristics, soil type, and hydrology can be estimated in a watershed. Due to the significance of the issue, it is important to use a digital elevation model with more resolution to prepare landforms with more accuracy. There are several methods to increase the spatial resolution of the digital elevation model. Obtaining more detail from pixels was first proposed by the Gravity Model by Atkinson (1977). In this technique, the pixels are divided into several sub-pixels according to the values of the neighboring pixels. In the gravity method, a large pixel is subdivided into sub-pixels, and a ground cover class is assigned to each sub-pixel. There is a limitation that the total number of sub-pixels of each class is directly proportional to the percentage of canopy coverage of the larger original pixel (Atkinson et al, 1997). In this way, soft input layers can be converted to hard categories with better resolution. The main problem in sub-pixel mapping is determining the location of each land cover class in larger pixels (Verhoeye, 2002). Various methods have been proposed to solve this problem, including the Hopfield network (Tatem et al., 2001; Muad and Foody 2012), the neural network after error propagation (Zhang et al., 2008; Wu et al. 2011, Nigussie et al. , 2011), linear optimization technique (Tatem et al., 2001), spatial gravity model (Mertens et al., 2006; Wang et al., 2011), pixel displacement algorithm (Kasetkasem, 2005), and genetic algorithm (Mertens et al., 2003). 2- Methodology Gravity model In this model, the pixels in the digital model of altitude are named based on their position relative to the upper left pixel, known as P0.0. The same structure is used for subpixels. This means that for a scale equal to 2, it has sub-pixels p0,0, p0,1, p1,0 p1,1. So that a sub-pixel pa, b is placed inside a pixel Pi, j when the following equation is established (Xu et al., 2014): <m:omathpara><m:omathparapr><m:jc m:val="left"></m:jc></m:omathparapr><m:omath><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r>p</m:r></m:e><m:sub><m:r>a</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>;</m:r><m:r>b</m:r></m:sub></m:ssub><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>∈</m:r><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r>P</m:r></m:e><m:sub><m:r>i</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>;</m:r><m:r>j</m:r></m:sub></m:ssub><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>⇔(</m:r><m:f><m:fpr><m:ctrlpr></m:ctrlpr></m:fpr><m:num><m:r>a</m:r></m:num><m:den><m:r>S</m:r></m:den></m:f><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>=</m:r><m:r>i</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>)&and;(</m:r><m:f><m:fpr><m:ctrlpr></m:ctrlpr></m:fpr><m:num><m:r>b</m:r></m:num><m:den><m:r>S</m:r></m:den></m:f><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>=</m:r><m:r>j</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>)</m:r></m:omath></m:omathpara> Where a is the sub-pixel row number, b is the corresponding sub-pixel column number, s is the scale factor, and i is the neighboring pixel row number, and j is the neighboring pixel column number. The neighborhoods defined in the previous step are also defined as follows: <m:omathpara><m:omathparapr><m:jc m:val="left"></m:jc></m:omathparapr><m:omath><m:r>N</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>2</m:r><m:d><m:dpr><m:begchr m:val="["><m:endchr m:val="]"><m:ctrlpr></m:ctrlpr></m:endchr></m:begchr></m:dpr><m:e><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r>p</m:r></m:e><m:sub><m:r>a</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>;</m:r><m:r>b</m:r></m:sub></m:ssub></m:e></m:d><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>=</m:r><m:d><m:dpr><m:begchr m:val="{"><m:endchr m:val="}"><m:ctrlpr></m:ctrlpr></m:endchr></m:begchr></m:dpr><m:e><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r>P</m:r></m:e><m:sub><m:r>i</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>;</m:r><m:r>j</m:r></m:sub></m:ssub><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>|</m:r><m:r>d</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>(</m:r><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r>p</m:r></m:e><m:sub><m:r>a</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>;</m:r><m:r>b</m:r></m:sub></m:ssub><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>.</m:r><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r>P</m:r></m:e><m:sub><m:r>i</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>;</m:r><m:r>j</m:r></m:sub></m:ssub><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>)≤</m:r><m:f><m:fpr><m:ctrlpr></m:ctrlpr></m:fpr><m:num><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>1</m:r></m:num><m:den><m:rad><m:radpr><m:deghide m:val="on"><m:ctrlpr></m:ctrlpr></m:deghide></m:radpr><m:deg></m:deg><m:e><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>2</m:r></m:e></m:rad></m:den></m:f><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>(2</m:r><m:r>S</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>-</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>1)</m:r></m:e></m:d></m:omath></m:omathpara> Where N2 is a quadruple neighborhood model. The distance between each sub-pixel and the surrounding pixel (d) is calculated as follows (Xu et al., 2014): <m:omathpara><m:omathparapr><m:jc m:val="left"></m:jc></m:omathparapr><m:omath><m:r>d</m:r><m:d><m:dpr><m:ctrlpr></m:ctrlpr></m:dpr><m:e><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r>p</m:r></m:e><m:sub><m:r>a</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>;</m:r><m:r>b</m:r></m:sub></m:ssub><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>.</m:r><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r>P</m:r></m:e><m:sub><m:r>i</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>;</m:r><m:r>j</m:r></m:sub></m:ssub></m:e></m:d><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>=</m:r><m:rad><m:radpr><m:deghide m:val="on"><m:ctrlpr></m:ctrlpr></m:deghide></m:radpr><m:deg></m:deg><m:e><m:ssup><m:ssuppr><m:ctrlpr></m:ctrlpr></m:ssuppr><m:e><m:d><m:dpr><m:begchr m:val="["><m:endchr m:val="]"><m:ctrlpr></m:ctrlpr></m:endchr></m:begchr></m:dpr><m:e><m:r>a</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>+0.5-</m:r><m:r>S</m:r><m:d><m:dpr><m:ctrlpr></m:ctrlpr></m:dpr><m:e><m:r>i</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>+0.5</m:r></m:e></m:d></m:e></m:d></m:e><m:sup><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>2</m:r></m:sup></m:ssup><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>+</m:r><m:ssup><m:ssuppr><m:ctrlpr></m:ctrlpr></m:ssuppr><m:e><m:d><m:dpr><m:begchr m:val="["><m:endchr m:val="]"><m:ctrlpr></m:ctrlpr></m:endchr></m:begchr></m:dpr><m:e><m:r>b</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>+0.5-</m:r><m:r>S</m:r><m:d><m:dpr><m:ctrlpr></m:ctrlpr></m:dpr><m:e><m:r>j</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>+0.5</m:r></m:e></m:d></m:e></m:d></m:e><m:sup><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>2</m:r></m:sup></m:ssup></m:e></m:rad></m:omath></m:omathpara> Topographic Position Index (TPI) method for landform extraction In this study, the neighborhood method was used to study and classify landforms. Thus, the topographic position index (TPI) was used to isolate landforms in the region. TPI is the equation of each cell in a digital elevation model with the average height of neighboring cells according to the following equation. At the end of the height, the average decreases from the height in the center (Weiss, 2001). TPIi=Z0-∑n-1Zn/n Z0 is the height of the model point under evaluation, Zn is the height of the grid and n is the total number of surrounding points considered in the evaluation. 3- Results In this study, to increase the spatial resolution of the digital elevation model of southern part of Fars province, the gravity model was studied. First, the gravity model was used to increase the spatial resolution of the 30-meter DEM. In this study, four neighborhoods with different scales 2, 3 and 4 were used to find the best model to increase the spatial resolution. The results showed that the use of quadratic neighborhood (T2) with scale 2 increases the number of sub-pixels and increases the spatial resolution. According to the error values, it is determined that the best model to increase the spatial resolution is the model S = 3 for the digital model of 30 meters height. Therefore, digital elevation (DEM) model S = 3 and T = 2 were used to map the landforms of the region as input data. TPI method was used to extract the landform map of the study area. The results of applying a polynomial distribution function to select the best scale for landforms separation showed that 3 × 3 (minimum scale) and 45 45 45 (maximum scale) windows with the lowest RMSE for TPI mapping and finally landform mapping were the most suitable ones in the study area. The results showed that the TPI values of the study area are between -33 to 46.77 for the 3 3 3 scale and -42.53 to 77.56 for the 45 45 45 scale (Figure 4). Indeed, in high areas such as ridges and hills, near-zero codes indicate flat areas or areas with low slope changes, and negative codes indicate low areas such as valleys and waterways. Each of the categorized landforms covers a part of the area. According to the results, it is clear that the study area includes 10 types of landforms. The results also show that the map of landforms prepared using the gravity model is more accurate. 4- Discussion & Conclusions In this study, gravity model and TPI method were used to study landforms in the south of Fars province. In this study, the resolution of images was increased using the gravity model. The results of this study showed that the gravity model with scale 3 and quadruple neighborhood has a high accuracy to increase the spatial resolution of the digital elevation model. Therefore, by using these maps with high spatial resolution, landform maps can be prepared with high accuracy. Also, by using the type of landforms and their percentage, the erosion rate in the study area can be estimated.   لندفرم, فرسایش, مدل جاذبه, مدل رقومی ارتفاع (DEM). Landform, Erosion, Gravity model, Digital elevation model (DEM). 122 137 http://magazine.hormozgan.ac.ir/browse.php?a_code=A-10-812-1&slc_lang=fa&sid=1 Abbas Sedghamiz عباس صدق آمیز sedghamiz1347@gmail.com 10031947532846007096 10031947532846007096 No Shiraz University, Collage of Agriculture and Natural Resources of Darab, Department of Water Engineering بخش مهندسی آب، دانشکده کشاورزی و منابع طبیعی داراب، دانشگاه شیراز، ایران Marzieh Mokarram مرضیه مکرم m.mokarram@shirazu.ac.ir 10031947532846007097 10031947532846007097 Yes Department of Geography, Faculty of Economics, Management and Social sciences, Shiraz University, Iran بخش جغرافیا، دانشکده اقتصاد، مدیریت و علوم اجتماعی، دانشگاه شیراز، ایران