Lecture Outline Digital Elevation Model (DEM) Processing 3...

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Advanced RS; Honda Kiyoshi; 2. DEM

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Digital Elevation Model (DEM)Processing

Dr. HONDA [email protected]

Space Technology Applications and Research, School of Advanced TechnologiesAsian Institute of Technology (AIT), Bangkok, Thailand


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Introduction

Digital Elevation Models or DEMs are increasingly becoming the focus of attention within the larger realm of digital topographic data due to the fundamental nature of the data, and knowledge to the data they represent. The precision of DEM in simulating the true terrestrial parameters of elevation, slope and aspect improved significantly the quality and caliber of knowledge in numerous applications in earth, environmental and engineering sciences.

Researches/applications where quality topographic data are needed benefited so much on the data that DEMs have provided in the past, and still, in the future as DEM accuracy and acquisition techniques are further improved, and become cheaply available for the scientific and engineering community.


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Lecture Outline

1. Overview of DEMWhy DEM is importantDEM ApplicationsStructure of DEMHow to produce DEMASTER DEM

2. DEM ProcessingRemoving sinksCalculation of slopeSlope direction (Aspect)


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Lecture Outline

Grid/Flow AccumulationStream Order

3. Application to floodRunoff models, Lumped, DistributedUnit hydrograph and its applicationsRationale Approach for peak runoff rateCurve Number (CN) Method for runoff volume

4. Discussions


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1. Overview of DEM


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What is a DEM?

A DEM provides a digital representation of a portion of the earth’s surface terrain over a two dimensional surface (UNEP/GRID)

A DEM is an ordered array of numbers that represents the spatial distribution of elevations above some arbitrary datums in the landscape (Meijerink et al., 1994)

A DEM is a digital file consisting of terrain elevations for ground positions at regularly spaced horizontal intervals (USGS definition)

Keyword: only elevation data

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DEM vs. DTM

Digital Terrain Model (DTM) is a representation of terrain information using discrete sampled digital values, like slope, aspect, etc.

DEM only represents the elevation data.


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Aerial Photograph


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Sample of DEM

Contour Lines

Digital Elevation Model

Watershed


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Why DEM is important?

DEM provides the basis in modeling and analysis of spatio-topographic information.

INPUTINPUT OUTPUTOUTPUTSYSTEMSYSTEMINPUTINPUT OUTPUTOUTPUTSYSTEMSYSTEM

Q

T

MODELRESULTS


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DEM Applications

Civil Engineering: cut and fill in road design, site planning, volumetric calculations in dams and reservoirs etc.

Earth Sciences: for modeling, analysis and interpretation of terrain morphology e.g. drainage basin delineation, hydrological run-off modeling, geomorphologicalsimulation and classification, geological mapping etc.

Planning and resource management: site location, support of image classification in RS, geometric and radiometric correction in RS images, erosion potential models, crop suitability studies, pollution dispersion modeling etc.


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Surveying and Photogrammetry: in building high quality contours, used in survey or photogrammetric data capture and subsequent editing, orthophoto production, data quality assessment and topographic mapping.

Military Applications: intervisibility analysis for battlefield management, 3-D display for weapons guidance systems and flight simulation, and radar line of sight analyses

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3D Example for Military or Airline Industry Applications


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• Line model => describes the elevation of terrain by contours (stored as digital line graphs, DGLs), the x,y coordinate pairs along each contours of specified elevation (see example)

• GRID structure=>elevation data are stored in an array of grids. Data structure of a GRID shares much similarity with the file structure of computers: as two dimensional array (every point can be assign to a row and column). This similarity of storage structures, the topological relations between the data points are recorded implicitly. THIS streamlines information processing and algorithm development (see example)

• Triangulated Irregular Network (TIN)=>a network of interconnected triangles with irregularly spaced nodes or observation points with x,y coordinates and z values. Advantage over GRID is its ability to generate more information in areas of complex relief, and avoiding the problem of gathering a lot o redundant data from areas of simple relief (see example)

Structure of DEM


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Contour Lines


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Grid DEM


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TIN DEM

Delauney Triangulation


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How to produce DEM?

• Existing Contour Map

• Aerial Photograph

• Satellite• Optical Remote Sensing• SAR – Synthetic Aperture Radar (Interferometry)

• Laser Scaner

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Existing Contours

• Procedure• Digitize• Scan

• Label the contour lines• Assign contour ID• Label contour line by elevation

• Create TIN: by triangulation• Create GRID/lattice: by interpolation, e.g. spline,

kriging etc.


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Aerial Photograph

By photogrammetric methods based on stereo aerial photography:

Using the relation between stereo parallax and object elevation in the scene for orthogonal and central projection imagery.


22Relation between stereo parallax and object elevation

B

hB

h∆

p1p2

A

B

papbhA

f

parallaxppp

fBhhh

pfBh

abAB

:

11

−×=−=∆

×=


23Stereo aerial photograph


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Optical Satellite Remote Sensing

Satellite STEREO PAIR

A stereo pair is a set of two images of the same terrain acquired from two different view angles. The view angles are optimally adjusted to get maximum overlap.The relief displacement from the stereo pair is used to extract third dimension . This is done through computational based parallax error between the images. Therefore the images should not have undergone any manipulations such as geometric corrections. Height information derived from stereo pairs is more detailed than that derived from contour map.

http://www.nrsa.gov.in/engnrsa/services/stereo1.html


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27http://www.nrsa.gov.in/engnrsa/services/stereo1.html


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SAR - Interferometry


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RADAR Measurement


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RADAR Interferometry


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Geometry of Interferometric SAR


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Processing chain for generation of interferometric fringes and coherence

Example of interferometric fringes with average coherence 0.5.

Filtered interferometric fringes

Synthetic interferometric fringes

Rectified height model

Existing height model http://www.geo.unizh.ch/rsl/fringe96/papers/herland/

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Example, Mapping Mayon Volcano, Albay, Philippines


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Interferogram 1996

0 2

Flattened Interferogram 1996

0 2


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Phase unwrapped image 1996 INSAR DEM with 160-meter cycle


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3D image view using INSAR DEM


37http://www-radar.jpl.nasa.gov/srtm/index.html


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44Topographic data improvement


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Somewhere in Japan

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Somewhere in Japan


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ASTER DEM


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Product Description

The ASTER Digital Elevation Model is a product that is generated from a pair of ASTER Level 1A images. This Level 1A input includes bands 3N (nadir) and 3B (aft-viewing) from the Visible Near Infra-Red telescope's along-track stereo data that is acquired in the spectral range of 0.78 to 0.86 microns. ASTER DEMs can be generated either with or withoutground control points (GCPs). An Absolute DEM is created with GCPs that are supplied by an end-user who has requested the product. These DEMs have an absolute horizontal and vertical accuracy of up to 7 meters with appropriate GCPs and up to 10 meters without GCPs. Alternatively, a Relative DEM can also be generated without GCPs. These DEMs can be used to derive absolute slope and slope aspectwhich is good up to 5 degrees over a horizontal distance of over 100 meters. ASTER DEMs are expected to meet map accuracy standards for scales from 1:50,000 to 1:250,000.These ASTER DEMs are produced upon customer requests made through the On Demand Processing Request form(http://e0ins02u.ecs.nasa.gov:10800). ASTER DEMs are unique in that they are the only on-demand product that are archived in ECS. You may search and order all previously requested DEM products through the EOS Data Gateway (http://edcimswww.cr.usgs.gov/pub/imswelcome/).

http://edcdaac.usgs.gov/aster/ast14dem.html


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EDG Data Set NameASTER Digital Elevation Model

Granule ShortnameAST14DEM

Data Set CharacteristicsArea = ~60 km x 60 kmImage Dimensions = 2500 rows x 2500 columnsInput Image Resolution: 15 metersOutput Image Resolution: 30 metersFile Size = ~25 MBData Type = 32-bit realValid Ranges = (-)2,147,483,648 to (+)2,147,483,648Vgroup Data Fields = 1

http://edcdaac.usgs.gov/aster/ast14dem.html


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Sample of ASTER DEM

Adapted from Terrainmap.com

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2. DEM Processing


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DEM Processing

• Removing Sinks

• Calculation of Slope

• Slope Direction (Aspect)

• GRID Accumulation (Flow Accumulation)

• Stream Order


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SinkSinks are potholes in DEM. They can be natural in occurrence such as ravine etc in the landscape but most likely they are errors in interpolation or data preparation/acquisition

SINK

Filled SINK

There are many algorithms available to fill the sink, e.g. Honda (1992)


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Slope of a surface

x∆

y∆z−∆

θ

( )y 0, y, z= ∆ −∆r

( )x x,0, z= ∆ −∆r

( )n a,b,1=r

( )z 0,0,1=r

n x 0

n y 0

⋅ =

⋅ =

r r

r r

a x z 0b y z 0

zaxzby

∆ −∆ =∆ −∆ =

∆=∆∆

=∆

z zn , ,1x y

∆ ∆∴ = ∆ ∆

r

z n z n cos⋅ = ⋅ ⋅ θuurr r r

222

221 cos z z 1tan 1 1

cos x y z z 1x y

− θ ∆ ∆ θ = = + + − θ ∆ ∆ ∆ ∆ + + ∆ ∆

22

z n 1cosz n z z 1

x y

⋅θ = =

⋅ ∆ ∆ + + ∆ ∆

rur

uurr

2222

22

z zx yz z 1

x y z z 1x y

∆ ∆ + ∆ ∆ ∆ ∆ = + + ∆ ∆ ∆ ∆ + + ∆ ∆

THEREFORE22

Surfacez zSlopex y

∆ ∆ = + ∆ ∆


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Slope

ihgfedcba

x

y

zSlope in x

Slop

e in

y Resultant Slope

x

zSlopex

∆=∆

y

zSlopey

∆=∆

( ) ( )22

R x ySlope Slope Slope= +


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182420

253022

252010

For 3 x 3 pixels, the slope at the center pixel is calculated as:

z 25 10 25 22 18 20 /3 0.0889x 60 60 60

∆ − − − = + + = ∆

30 m

z 10 20 20 24 25 18 /3 0.0389y 60 60 60

∆ − − − = + + = − ∆

( ) ( )2 2

eSlope 0.0889 0.0389 0.0967= + − =

10


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Example of slope


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AspectAspect is expressed in degrees from north, clockwise, from 0 to 360. Due north is 0, due east is 90, 180 is due south and 270 is due west. 361 is used to define flat surfaces such as water bodies.

⊗ x

ynr

θ

a

b 1

a xtanb y

x 180tany

−

∆θ = =

∆

∆θ = ∆ π

if x and y = 0, then the aspect is flat, otherwise, aspect=180+ .∆ ∆

θ

z


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Slope/flow direction

12

3

45

6

7

8

Determine the steepest descent from the 8 possible directions


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Example flow direction


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Flow accumulation

712

511

121

watershed

Flow direction vector


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Example flow accumulation

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Example of Stream Network


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Example delineated watershed


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Stream Order

Strahler Ordering

1

11

21

2

2

11

21

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DEM Utilization Sample

• Debris Flow Simulation

http://www.star.ait.ac.th/~honda

2. Global DEM Fly Through

http://mission.base.com/theearth/bot.html

3. Visualization

http://www.kashmir3d.com/index-e.html

http://www.visualizationsoftware.com/3dem.html

4. SRTM DEM

http://www2.jpl.nasa.gov/srtm/

ftp://edcsgs9.cr.usgs.gov/pub/data/srtm/


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2. Applications to Flood


71Hydrologic Cycle

From Maidment (1993)

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72Hyetograph and hydrograph

From Chow et al. (1988)


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INPUTINPUT OUTPUTOUTPUTSYSTEMSYSTEMINPUTINPUT OUTPUTOUTPUTSYSTEMSYSTEM

Q

T

MODELRESULTS

MODEL of a SYSTEM

RAINFALL-RUNOFF MODELS

• Lumped Model

e.g. CN Method

• Distributed Model

• 2D (e.g. Mike 21)

• 3D (e.g. Mike SHE)

• average slope• average CN value• etc.

2D 3D


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Advantages/Disadvantages

Lumped- easy to calculate- can’t evaluate all possible scenarios

Distributed- powerful in scenario analyses e.g setting of boundary conditions etc.- computational time is high- parameterization is difficult


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Peak Runoff Rate

Rational Method

Rat

e of

rain

fall

and

runo

ff

Time

Rainfall rate, i

D

I

Q

Tc

C=q/i

Peak

runo

ff ra

te

q 0.0028CiA=

q - the peak runoff rate, m3/sC – runoff coefficienti – rainfall intensity, mm/hA – watershed area, ha

0.77 0.385c gT 0.0195L S −=

Tc – time of concentration, minL – maximum length of flow, mSg – watershed gradient, m/m


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Curve Number (CN) MethodR

ainf

all

Abstraction

Excess rainfall Runoff

f(CN)

CN=f(landuse, AMC)

PIa

FaS

Pe

Deep infiltration

Pe = P – Ia – Fa


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Runoff Volume

Pre

cipi

tatio

n ra

te

Time

Ia Fa

Pe

a e

a

F PS P I=

−

e a aP P I F= + +

The hypothesis of the SCS method is that the ratios of the two actual (Fa, Pe) and the potential quantities (S, P-Ia) are equal

Continuity Equation

P – total precipitationPe – excess rainfallIa – initial abstractionFa – continuing abstractionS – potential maximum retention

SCS-CN Method

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( )2

ae

a

P IP

P I S−

=− +

aI 0.2S=

( )2

ae

P IP

P 0.8S−

=+

Depth of Runoff

Therefore:


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Graphical Solution of the SCS runoff Equation

CN=100 –impervious and water surfaces

Good Forest

Urban100%

Cumulative Rainfall (in)

Cum

ulat

ive

dire

ct R

unof

f (in

)


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Group A: Deep sand, deep loess, aggregated silts

Group B: Shallow loess, sandy loam

Group C: Clay loams, shallow sandy loam, soils low in organic content and soils usually high in clay

Group D: Soils that swell significantly when wet, heavy plastic clays and certain saline soils.

CN(II)


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1000S 10CN(II)

= − (inches)

4.2CN(II)CN(I)10 0.058CN(II)

=−

23CN(II)CN(III)10 0.13CN(II)

=+

Total 5-day antecedent rainfall (in) AMC Group Dormant Season Growing Season I Less than 0.5 Less than 1.4 II 0.5-1.1 1.4-2.1 III Over 1.1 Over 2.1

Classification of antecedent moisture classes for the SCS-CN method


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DEM

Forest, 55%

CN=77Agriculture,30%

CN=88Residential,15%

CN=79

From RS

CNWatershed=80.6

S=(1000/80.6)-10=2.41 inches

Precipitation=4.5 inches

Pe=(4.5-0.2*2.41)2/(4.5+0.8*2.41)=2.51 inches

Ia=0.2*2.41=0.482 inch


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Time Distribution of SCS Abstraction

( )aa

a

S P IF

P I S−

=− + aP I≥

( )

2a

2

a

dF S dP dtdt P I S

=− +

Differentiating and noting that Ia and S are constants

dP/dt – rainfall intensity

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Column 1 Time(h)

2 Cumulative Rainfall, P (in)

3 Cumulative Abstractions (in), Ia

4 Cumulative Abstractions (in), Fa

5 Cumulative excess rainfall, Pe(in)

6 Excess rainfall hyetograph (in)

0 0 0 - 0 0 1 0.20 0.20 - 0 0.06 2 0.90 0.50 0.34 0.06 0.12 3 1.27 0.50 0.59 0.18 0.58 4 2.31 0.50 1.05 0.76 1.83 5 4.65 0.50 1.56 2.59 0.56 6 5.29 0.50 1.64 3.15 0.06 7 5.36 0.50 1.65 3.21

CN=80, S=2.50, Ia=0.5

All abstracted

( )aa

a

S P IF

P I S−

=− +

Col2-col3-col4


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Unit Hydrograph

The unit hydrograph is the unit pulse response function of a linear hydrologic system.

The unit hydrograph of a watershed is defined as the direct runoff hydrograph (DRH) resulting from 1 inch (usually taken as 1 cm in SI units) of excess rainfall generated over the drainage area at a constant rate for an effective duration.


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Discrete Time Convolution Equation of a Linear System

n M

n m n m 1m 1

Q P U≤

− +=

= ∑

Direct runoff Pulse (rainfall)

unit hydrograph ordinate

n – index for time

m – index for pulse

M – no. of pulse


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U1=Q1/P1

U2=(Q2-P2U1)/P1 …

ALSOUnit hydrograph ordinate

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90

020406080

100120140160180200

1 2 3 4 5 6 7 8 9 10 11

Time (every 0.5 hr)

Rain

fall,

mm

0

50

100

150

200

250

300

UH, m

3 hr-1

mm

-1 o

r Q, m

3 s-1

Unit hydrograph

Direct runoff hydrograph

Rainfall pulse

Unit hydrograph application

3D Water Discharge Model

Water Discharge Model

Motion Equation of Water

Surface Information + DEM Processing

Forest Classification

Ground WaterSaturationRed 12 hrGreen 18 hrBlue 24 hr


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Debris Flow Simulation

flx_118_91_saido_15sph.mov

River Saido h

Debris Flow

High Density

High Speed

High Power to destroy everything ( houses, roads, bridges )

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Mt. Mayon Volcano Comprehensive Disaster Prevention Master Plan

• GIS Data Development for Planner

• Historical River planform Change by lava, pyroclastic flow, lahar

• Sediment Production Estimation for river structure planning


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Lava Deposit of Mr. Mayon(Pawa Burabod riverbed)


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Estimation of Lava Deposit Height using SAR InterferometryINSAR result Topographic difference

Volcanic Activity

INTRODUCTION

Lava flow Pyroclastic flow

Volcano Activity MapLandscape photo

Monitoring During Eruption

Lava Location, Movement

Ground based digital image -> continuous monitoring

3D View

3D Graphics

DEM

Ortho-view

3D view

Orthophoto from Ground Digital Camera Image1st Image – 2min, 2nd and later image 3sec.

METHODOLOGY (Rectification)

Skyline Matching

Rectified Image

Reference Edge

Overview of Skyline Matching

Reference

OriginalOriginal Edge

Sobel Filter

Sobel Filter

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METHODOLOGY (Rectification)

Reference

Rectified Image

Overlaid Reference and Rectified mage

Rectified ImageShift X: -51 　　Shift Y: 111 　　Rotation: 1.4°

Orthophoto from Ground Digital Camera Image1st Image – 2min, 2nd and later image 3sec.

Orthophoto from Thermography Image (night time )


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CONCLUSION

DEM has numerous applications in research and practice.

DEM from RS are potentially easier to acquire and use for terrain modeling, hydrological modeling etc.

Spatial Functions in GIS add more value to DEM for modeling purposes.

Let us use DEM…

Lecture Outline Digital Elevation Model (DEM) Processing 3...

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