Detecting alluvial fans Detecting alluvial fans using quantitative using quantitative

roughness roughness characterization and fuzzy characterization and fuzzy

logic analysislogic analysisAndrea TaramelliAndrea Taramelli

ataram@ldeo.columbia.edu

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 MelelliLaura 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 PresentationOutline of Presentation

• Investigate the relationship between alluvial fans and the distribution of boundaries

• How satellite remote sensing data helps us– understand geomorphometric measures from

SRTM elevation data

• How results from RS data analysis feed into fuzzy logic analysis

The Study area1st case

Perugia

Gubbio basin

Valle Umbra basin

Beijing

The Study area2nd case

The Alashan area

Fundamental question of spatial information in Fundamental question of spatial information in geomorphology: how we can defined alluvial fan geomorphology: how we can defined alluvial fan

with indistinct geographically location?with indistinct geographically location?

• SEMANTIC: a landform is the result of a classification that simplifies the real world

• GEOMETRIC: highlights the geometric characteristics of a feature related to the topographic surface properties

Bottom Alluvial part

Upper Alluvial part

Does geometric - morphometric Does geometric - morphometric analysis directly map alluvial fans? analysis directly map alluvial fans?

• Highlights primary attributes classes (roughness, elevation and curvature) of an alluvial fan

• Investigate the relationship between geomorphic processes and topography

The similarity relation model: uses surface The similarity relation model: uses surface derivatives, such as roughness, slope and derivatives, such as roughness, slope and curvature, as input to a multivariate fuzzy curvature, as input to a multivariate fuzzy classification which yields the membership classification which yields the membership valuesvalues

MethodologyMethodology

• Estimating SubPixel Surface Roughness Using the C-band SAR backscatter from SRTM

• Automatic Geometric parameter delineation using SRTM DEM

• Delineation of the alluvial fans: Populating the Similarity Model under fuzzy logic

Surface height variation: Finding Roughness Through Radar Backscatter

• The surface can be modeled as a stationary random Gaussian height distribution

• Mean and variance of elevation (related to the horizontal length) provide a complete description of statistical properties

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):

zº = a * exp(PC/b),

• 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)

• “Smoother” surfaces (such as bare soils) have a smaller surface roughness than

“rougher” surfaces (such as alluvial areas)

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

Foligno

• 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).

• 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

Geometric parameters delineationGeometric parameters delineationusing SRTM demusing SRTM dem

Scheme of the geometric classes of alluvial fans

• The altitude class has a range between Hmax and Hmin.

• 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’.

• The longitudinal profile (xy) shows a convex-concave radial shape from the top (Hmax) to the bottom (Hmin).

ieCiPi MiXCMiX Pr||)2( )]()')[(2/1(21

2n-1 1

FrtFri /Pr

Landform Delineation Algorithm: Landform Delineation Algorithm: Populating the Similarity ModelPopulating the Similarity Model

PPii is Maximum likelihood probability of attribution to is Maximum likelihood probability of attribution to the class.the class.n Number of measurement variables.n Number of measurement variables.Ci Covariance matrix of the class considered.Ci Covariance matrix of the class considered.Mi Mean vector of the class considered.Mi Mean vector of the class considered.X Pixel vector.X Pixel vector.PrPrii Prior probability of the class considered defined Prior probability of the class considered defined from the frequency histograms of the training sets.from the frequency histograms of the training sets.

Fr is the pixel count of the Fr is the pixel count of the class under examination.class under examination.Frt Is the sum of counts of all Frt Is the sum of counts of all the classes.the classes.

No.

Input terrain derivative Output fuzzy landform attribute

Description of fuzzy landform attribute

Standard Index

Dispersion index

1 Elevation Near_max Relatively

near maximum elevation

90.0

15.0

2 Elevation Near_min Relatively

near minimum elevation

10.0 15.0

3 Profile Concave_D Relatively

convex profile (down)

10.0 5.0

4 Profile Convex_D Relatively

concave in profile (down)

-10.0

5.0

5 Profile Planar_D Relatively

planar in profile (down)

0.0

5.0

6 Planar Convex_A Relatively

convex in plan (across)

10.0 5.0

7 Planar Concave_A Relatively

concave in profile (across)

-10.0 5.0

8 Planar Planar_A Relatively

planar in profile (across)

0.0 5.0

Cluster results for the eight classes in the Gubbio and Valle Umbra intermontane basin

• The first selected parameter is the range of altitude values.

• Within this range of values the second assignment chooses only the convex contour shape.

• As a third boundary the algorithm selects only convex contours with an arc circumference that increases toward lower altitude.

• Finally, as a fourth boundary, convex-concave radial slope values are chosen (roughness)

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 - 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 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;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 - 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.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 - a last value (-0.5°) represents the area of the lower fan where lime and clay deposits lay adjacent to flat alluvial sediments.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 SRTM Analysis: Landform Delineation AlgorithmDelineation Algorithm

The Alashan area

Conclusions Conclusions

• The geometric - morphometric analysis does not directly map alluvial fans, but highlights primary attributes classes (roughness, elevation and curvature) of an alluvial fan.

• Delineation of alluvial fans is then identified within an approximate spatial extent together with fuzzy memberships

• 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