Detecting alluvial fans using quantitative roughness characterization and fuzzy logic analysis Andrea Taramelli [email_address] Third International Workshop on "Geographical Analysis,Urban Modeling, Spatial Statistics" GEOG-AN-MOD 08 The 2008 International Conference on Computational Science and its Applications (ICCSA 2008) June 30th to July 3rd, 2008 Laura Melelli Lamont-Doherty Earth Observatory – Columbia University, New York, USA ICRAM - Marine Sciences Research Institute , Rome Uniersità degli Studi di Perugia – Earth Science Department
Outline of Presentation <ul><li>Investigate the relationship between alluvial fans and the distribution of boundaries </li></ul><ul><li>How satellite remote sensing data helps us </li></ul><ul><ul><li>understand geomorphometric measures from SRTM elevation data </li></ul></ul><ul><li>How results from RS data analysis feed into fuzzy logic analysis </li></ul>
The Study area 1 st case Perugia Gubbio basin Valle Umbra basin
Beijing The Study area 2 nd case The Alashan area
Fundamental question of spatial information in geomorphology: how we can defined alluvial fan with indistinct geographically location? <ul><li>SEMANTIC: a landform is the result of a classification that simplifies the real world </li></ul><ul><li>GEOMETRIC: highlights the geometric characteristics of a feature related to the topographic surface properties </li></ul>Bottom Alluvial part Upper Alluvial part
Does geometric - morphometric analysis directly map alluvial fans? <ul><li>Highlights primary attributes classes (roughness, elevation and curvature) of an alluvial fan </li></ul><ul><li>Investigate the relationship between geomorphic processes and topography </li></ul>The similarity relation model: uses surface derivatives, such as roughness, slope and curvature, as input to a multivariate fuzzy classification which yields the membership values
Methodology <ul><li>Estimating SubPixel Surface Roughness Using the C-band SAR backscatter from SRTM </li></ul><ul><li>Automatic Geometric parameter delineation using SRTM DEM </li></ul><ul><li>Delineation of the alluvial fans: Populating the Similarity Model under fuzzy logic </li></ul>
Surface height variation: Finding Roughness Through Radar Backscatter <ul><li>The surface can be modeled as a stationary random Gaussian height distribution </li></ul><ul><li>Mean and variance of elevation (related to the horizontal length) provide a complete description of statistical properties </li></ul>Relation between normalized radar cross section σº derived from SAR data and protrusion coefficient PC obtained from the POLDER-1 bi-directional reflectance distribution function Both σº and PC relate to surface roughness (Laurent et al., JGR, 2005; Pringent et al., JGR, 2005): z º = a * exp(PC/b),
<ul><li>Radar backscattered power serves as a proxy for “surface roughness” (Taremelli et al., Integration of the advanced remote sensing technologies to investigate the dust storm areas, 8th ICDD Conference, Beijing, 2006) </li></ul><ul><li>“ Smoother” surfaces (such as bare soils) have a smaller surface roughness than “rougher” surfaces (such as alluvial areas) </li></ul>Foligno Valle Umbra The Valle Umbra C-band backscatter power from the February 2000 SRTM mission. Purple -> blue is low; orange -> gray is high.
We processed and analyzed this data, producing roughness maps for the two main basins at full-resolution (90 m) and on a 0.25 degree grid, for comparison with the existing maps of the location of alluvial fans <ul><li>In each 1 degree tile all four SRTM subswaths of backscatter data from trajectories passing through the tile were provided as independent data files, along with corresponding files of radar look angle (nominal incidence angle). </li></ul><ul><li>The data from the subswaths had to be combined, and the given backscatter power at each pixel needed to be corrected to a standard incidence angle </li></ul>Foligno
Geometric parameters delineation using SRTM dem <ul><li>Scheme of the geometric classes of alluvial fans </li></ul><ul><li>The altitude class has a range between H max and H min . </li></ul><ul><li>The convex contour class is highlighted by the direction of the triangles. The cone geometry is evident from the increase in the arc circumference from the segment AA’ to DD’. </li></ul><ul><li>The longitudinal profile (xy) shows a convex-concave radial shape from the top (H max ) to the bottom (H min ). </li></ul>
Landform Delineation Algorithm: Populating the Similarity Model P i is Maximum likelihood probability of attribution to the class. n Number of measurement variables. Ci Covariance matrix of the class considered. Mi Mean vector of the class considered. X Pixel vector. Pr i Prior probability of the class considered defined from the frequency histograms of the training sets. Fr is the pixel count of the class under examination. Frt Is the sum of counts of all the classes.
<ul><li>The first selected parameter is the range of altitude values. </li></ul><ul><li>Within this range of values the second assignment chooses only the convex contour shape. </li></ul><ul><li>As a third boundary the algorithm selects only convex contours with an arc circumference that increases toward lower altitude. </li></ul><ul><li>Finally, as a fourth boundary, convex-concave radial slope values are chosen (roughness) </li></ul>Cluster results for the eight classes in the Gubbio and Valle Umbra intermontane basin
Cluster results 2.5 D and 2D for the Gubbio intermontane basin - an initial negative value of curvature (-6°) represents the upper fan-head trenching because of the linear channel erosion typical of the alluvial fans in our study area due to the recent regional tectonic uplift and the consequent readjustment of the drainage network; - a second positive value of curvature (8°) corresponds to upper and medium parts of the fan where the gravel deposits are present and show a convex longitudinal profile. - a last value (-0.5°) represents the area of the lower fan where lime and clay deposits lay adjacent to flat alluvial sediments.
Radar Backscatter (Feb. 2000) The retrieved roughness thresholds range from – 5 in the sandy deserts (Taklimakan, Badain Jaran, and Tengger Deserts) to up to 2 in the Gobi desert.
SRTM Analysis: Landform Delineation Algorithm The Alashan area
Conclusions <ul><li>The geometric - morphometric analysis does not directly map alluvial fans, but highlights primary attributes classes (roughness, elevation and curvature) of an alluvial fan. </li></ul><ul><li>Delineation of alluvial fans is then identified within an approximate spatial extent together with fuzzy memberships </li></ul><ul><li>Sophisticated coupling of geomorphic and remote sensing processes can be attempted within fuzzy logic, in order to test for feedbacks between geomorphic processes and topography </li></ul>