DEM Lecture

8/10/2019 DEM Lecture

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Digital Elevation Model (DEM)Digital Elevation Model (DEM)

ProcessingProcessing

Advanced Remote Sensing for Department of Mineral Resources of Thailand

Organized by GIS Application Center, AIT

18-19 September 2003

Dr. HONDA Kiyoshi

[email protected]

Space Technology Applications and Research, School of Advanced TSpace Technology Applications and Research, School of Advanced Technologiesechnologies

Asian Institute of Technology (AIT), Bangkok, ThailandAsian Institute of Technology (AIT), Bangkok, Thailand

IntroductionIntroduction

Digital Elevation Models orDigital Elevation Models or DEMsDEMs are increasingly becomingare increasingly becoming

the focus of attention within the larger realm of digitalthe focus of attention within the larger realm of digital

topographic data due to the fundamental nature of the data,topographic data due to the fundamental nature of the data,

and knowledge to the data they represent. The precision ofand knowledge to the data they represent. The precision of

DEM in simulating the true terrestrial parameters of elevation,DEM in simulating the true terrestrial parameters of elevation,slope and aspect improved significantly the quality and caliberslope and aspect improved significantly the quality and caliber

of knowledge in numerous applications in earth, environmentalof knowledge in numerous applications in earth, environmental

and engineering sciences.and engineering sciences.

Researches/applications where quality topographic data areResearches/applications where quality topographic data are

needed benefited so much on the data thatneeded benefited so much on the data that DEMsDEMs havehave

provided in the past, and still, in the future as DEM accuracyprovided in the past, and still, in the future as DEM accuracy

and acquisition techniques are further improved, and becomeand acquisition techniques are further improved, and become

cheaply available for the scientific and engineering community.cheaply available for the scientific and engineering community.


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Lecture OutlineLecture Outline

1.1. Overview of DEMOverview of DEM

Why DEM is important

DEM Applications

Structure of DEM

How to produce DEM

ASTER DEM

2.2. DEM ProcessingDEM Processing

Removing sinks

Calculation of slope

Slope direction (Aspect)

Lecture OutlineLecture Outline

Grid/Flow Accumulation

Stream Order

3.3. Application to floodApplication to flood

Runoff models, Lumped, Distributed

Unit hydrograph and its applications

Rationale Approach for peak runoff rate

Curve Number (CN) Method for runoff volume

4.4. DiscussionsDiscussions


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1. Overview of DEM1. Overview of DEM

What is a DEM?What is a DEM?

A DEM provides a digital representation of a portion of theA DEM provides a digital representation of a portion of the

earthearths surface terrain over a two dimensional surfaces surface terrain over a two dimensional surface

(UNEP/GRID)(UNEP/GRID)

A DEM is an ordered array of numbers that represents theA DEM is an ordered array of numbers that represents thespatial distribution of elevations above some arbitraryspatial distribution of elevations above some arbitrary

datumsdatums in the landscapein the landscape ((MeijerinkMeijerink et al., 1994)et al., 1994)

A DEM is a digital file consisting of terrain elevations forA DEM is a digital file consisting of terrain elevations for

ground positions at regularly spaced horizontal intervalsground positions at regularly spaced horizontal intervals

(USGS definition)(USGS definition)

Keyword: only elevation dataKeyword: only elevation data


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DEM vs. DTMDEM vs. DTM

Digital Terrain Model (DTM) is a representation of terrainDigital Terrain Model (DTM) is a representation of terrain

information using discrete sampled digital values, likeinformation using discrete sampled digital values, likeslope, aspect, etc.slope, aspect, etc.

DEM only represents the elevation data.DEM only represents the elevation data.

Aerial PhotographAerial Photograph


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Sample of DEMSample of DEM

Contour Lines

Digital Elevation Model

Watershed

Why DEM is important?Why DEM is important?

DEM provides the basis in modeling and analysis ofDEM provides the basis in modeling and analysis of

spatiospatio--topographictopographic information.information.

INPUTINPUT OUTPUTOUTPUTSYSTEMSYSTEMINPUTINPUT OUTPUTOUTPUTSYSTEMSYSTEM

QQ

TT

MODELMODEL

RESULTSRESULTS


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DEM ApplicationsDEM Applications

Civil Engineering:Civil Engineering: cut and fill in road design, site planning,cut and fill in road design, site planning,

volumetric calculations in dams and reservoirs etc.volumetric calculations in dams and reservoirs etc.

Earth Sciences:Earth Sciences: for modeling, analysis and interpretationfor modeling, analysis and interpretation

of terrain morphology e.g. drainage basin delineation,of terrain morphology e.g. drainage basin delineation,

hydrological runhydrological run--off modeling,off modeling, geomorphologicalgeomorphological

simulation and classification, geological mapping etc.simulation and classification, geological mapping etc.

Planning and resource management:Planning and resource management: site location,site location,

support of image classification in RS, geometric andsupport of image classification in RS, geometric and

radiometric correction in RS images, erosion potentialradiometric correction in RS images, erosion potential

models, crop suitability studies, pollution dispersionmodels, crop suitability studies, pollution dispersion

modeling etc.modeling etc.

Surveying andSurveying and PhotogrammetryPhotogrammetry:: in building high qualityin building high quality

contours, used in survey orcontours, used in survey or photogrammetricphotogrammetric data capturedata capture

and subsequent editing,and subsequent editing, orthophotoorthophoto production, dataproduction, data

quality assessment and topographic mapping.quality assessment and topographic mapping.

Military Applications:Military Applications: intervisibilityintervisibility analysis for battlefieldanalysis for battlefield

management, 3management, 3--D display for weapons guidance systemsD display for weapons guidance systems

and flight simulation, and radar line of sight analysesand flight simulation, and radar line of sight analyses


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3D Example for Military or Airline3D Example for Military or Airline

Industry ApplicationsIndustry Applications

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

GRID structureGRID structure=>elevation data are stored in an array of grids.=>elevation data are stored in an array of grids.

Data structure of a GRID shares much similarity with the fileData structure of a GRID shares much similarity with the filestructure of computers: as two dimensional array (every point castructure of computers: as two dimensional array (every point cannbe assign to a row and column). This similarity of storagebe assign to a row and column). This similarity of storagestructures, the topological relations between the data points arstructures, the topological relations between the data points areerecorded implicitly. THIS streamlines information processing anrecorded implicitly. THIS streamlines information processing anddalgorithm developmentalgorithm development (see example)(see example)

Triangulated Irregular Network (TIN)Triangulated Irregular Network (TIN)=>a network of interconnected=>a network of interconnectedtriangles with irregularly spaced nodes or observation points witriangles with irregularly spaced nodes or observation points withthx,y coordinates and z values. Advantage over GRID is its abilitx,y coordinates and z values. Advantage over GRID is its ability toy togenerate more information in areas of complex relief, and avoidigenerate more information in areas of complex relief, and avoidingngthe problem of gathering a lot o redundant data from areas ofthe problem of gathering a lot o redundant data from areas of

simple reliefsimple relief (see example)(see example)

Structure of DEMStructure of DEM


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Contour LinesContour Lines

Grid DEMGrid DEM


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TIN DEMTIN DEM

DelauneyDelauney TriangulationTriangulation

How to produce DEM?How to produce DEM?

Existing Contour MapExisting Contour Map


SatelliteSatellite

Optical Remote SensingOptical Remote Sensing

SARSAR Synthetic Aperture Radar (Synthetic Aperture Radar (InterferometryInterferometry))


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Existing ContoursExisting Contours

ProcedureProcedure

DigitizeDigitize

ScanScan

Label the contour linesLabel the contour lines

Assign contour IDAssign contour ID

Label contour line by elevationLabel contour line by elevation

Create TIN: by triangulationCreate TIN: by triangulation

Create GRID/lattice: by interpolation, e.g.Create GRID/lattice: by interpolation, e.g. splinespline,,

krigingkriging etc.etc.


ByBy photogrammetricphotogrammetric methods based onmethods based on stereo aerialstereo aerial

photography:photography:

Using the relation between stereo parallax and objectUsing the relation between stereo parallax and object

elevation in the scene for orthogonal and centralelevation in the scene for orthogonal and centralprojection imagery.projection imagery.


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Relation between stereo parallax and object elevationRelation between stereo parallax and object elevation

B

hB

h

p1p2

A

B

pa pbhA

f

parallaxp

ppfBhhh

p

fBh

ab

AB

:

11

==

=

Stereo aerial photographStereo aerial photograph


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Optical Satellite Remote SensingOptical Satellite Remote Sensing

SatelliteSatellite STEREO PAIRSTEREO PAIR

A stereo pair is a set of two images of the same terrainA stereo pair is a set of two images of the same terrain

acquired from two different view angles. The view angles areacquired from two different view angles. The view angles are

optimally adjusted to get maximum overlap.The reliefoptimally adjusted to get maximum overlap.The relief

displacement from the stereo pair is used to extract thirddisplacement from the stereo pair is used to extract third

dimension . This is done through computational based parallaxdimension . This is done through computational based parallax

error between the images. Therefore the images should noterror between the images. Therefore the images should not

have undergone any manipulations such as geometrichave undergone any manipulations such as geometric

corrections. Height information derived from stereo pairs iscorrections. Height information derived from stereo pairs is

more detailed than that derived from contour map.more detailed than that derived from contour map.

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


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

SARSAR -- InterferometryInterferometry


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RADAR MeasurementRADAR Measurement

Geometry ofGeometry ofInterferometricInterferometric SARSAR


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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 modelhttp://www.geo.unizh.ch/rsl/fringe96/papers/herland/

Example, MappingExample, Mapping MayonMayon Volcano,Volcano,

AlbayAlbay, Philippines, Philippines


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Interferogram 1996

0 2

Flattened Interferogram 1996

0 2

Phase unwrapped image 1996 INSAR DEM with 160-meter cycle


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3D image view using INSAR DEM

Shuttle RadarShuttle Radar

TopographyTopographyMission (SRTM)Mission (SRTM)

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


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Topographic data improvementTopographic data improvement


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Somewhere in JapanSomewhere in Japan

Somewhere in JapanSomewhere in Japan


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ASTER DEMASTER DEM

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 without

ground 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 aspect

which 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 Name

ASTER Digital Elevation Model

Granule Shortname

AST14DEM

Data Set Characteristics

Area = ~60 km x 60 km

Image Dimensions = 2500 rows x 2500 columns

Input Image Resolution: 15 meters

Output Image Resolution: 30 meters

File Size = ~25 MB

Data Type = 32-bit real

Valid Ranges = (-)2,147,483,648 to (+)2,147,483,648

Vgroup Data Fields = 1

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

Sample of ASTER DEMSample of ASTER DEM

Adapted from Terrainmap.com


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2. DEM Processing2. DEM Processing

DEM ProcessingDEM Processing

Removing SinksRemoving Sinks

Calculation of SlopeCalculation of Slope

Slope Direction (Aspect)Slope Direction (Aspect)

GRID Accumulation (Flow Accumulation)GRID Accumulation (Flow Accumulation)

Stream OrderStream Order


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SinkSink

Sinks are potholes in DEM. They can be natural in occurrence suSinks are potholes in DEM. They can be natural in occurrence such asch as

ravine etc in the landscape but most likely they are errors in iravine etc in the landscape but most likely they are errors in interpolationnterpolation

or data preparation/acquisitionor data preparation/acquisition

SINKSINK

Filled SINKFilled SINK

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

Slope of a surfaceSlope of a surface

x

yz

( )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 0

y z 0

za

x

zb

y

=

=

=

=

z zn , ,1

x y

=

r

z n z n cos = uur r r r

222

22

1 cos z z 1tan 1 1

cos x y z z1

x y

= = + + + +

22

z n 1cos

z n z z1

x y

= =

+ +

rur

uurr

22

22

22

z z

x yz z1

x y z z1

x y

+ = + + + +

THEREFORETHEREFORE22

Surfacez z

Slopex y

= +


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SlopeSlope

ihg

fed

cba

x

y

z

Slope in x

Slopeiny ResultantSlope

x

zSlope

x

=

y

zSlope

y

= ( ) ( )

22

R x ySlope Slope Slope= +

182420

253022

252010

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

z 25 10 25 22 18 20/ 3 0.0889

x 60 60 60

= + + =

30 m

z 10 20 20 24 25 18/ 3 0.0389

y 60 60 60

= + + =

( ) ( )2 2

eSlope 0.0889 0.0389 0.0967= + =


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Example of slopeExample of slope

AspectAspect

Aspect is expressed in degrees from north, clockwise, from 0 toAspect is expressed in degrees from north, clockwise, from 0 to 360. Due360. Due

north is 0, due east is 90, 180 is due south and 270 is due westnorth is 0, due east is 90, 180 is due south and 270 is due west. 361 is. 361 is

used to define flat surfaces such as water bodies.used to define flat surfaces such as water bodies.

x

y nr

a

b 1

a xtan

b y

x 180tan

y

= =

=

if x and y = 0, then the aspect is flat,

otherwise, aspect=180+ .

z


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Example of aspectExample of aspect

Slope/flow directionSlope/flow direction

12

3

4

56

7

8

Determine the steepest descent fromDetermine the steepest descent from

the 8 possible directionsthe 8 possible directions


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Example flow directionExample flow direction

Flow accumulationFlow accumulation

712

511

121

watershedwatershed

Flow directionFlow direction

vectorvector


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Example flow accumulationExample flow accumulation

Example delineated watershedExample delineated watershed


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Stream OrderStream Order

StrahlerStrahlerOrderingOrdering

1

11

2

1

2

2

11

21

2

3

Example of Stream NetworkExample of Stream Network


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2. Applications to Flood2. Applications to Flood

Application to FloodApplication to Flood

The Hydrologic Cycle and RunoffThe Hydrologic Cycle and Runoff

RainfallRainfall--Runoff ModelsRunoff Models

Lumped, Distributed ModelLumped, Distributed Model

Rationale Approach for peak runoff ratesRationale Approach for peak runoff rates

CN Method for runoff volumeCN Method for runoff volume

Unit hydrograph, definitions and applicationsUnit hydrograph, definitions and applications


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Hydrologic CycleHydrologic CycleFrom Maidment (1993)

Hyetograph and hydrographHyetograph and hydrograph

From Chow et al. (1988)


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INPUTINPUT OUTPUTOUTPUTSYSTEMSYSTEMINPUTINPUT OUTPUTOUTPUTSYSTEMSYSTEM

QQ

TT

MODELMODEL

RESULTSRESULTS

MODEL of a SYSTEMMODEL of a SYSTEM

RAINFALLRAINFALL--RUNOFF MODELSRUNOFF MODELS

Lumped ModelLumped Modele.g. CN Methode.g. CN Method

Distributed ModelDistributed Model

2D (e.g. Mike 21)2D (e.g. Mike 21)

3D (e.g. Mike SHE)3D (e.g. Mike SHE)

average slopeaverage slope

average CN valueaverage CN value etc.etc.

2D2D3D3D

Advantages/DisadvantagesAdvantages/Disadvantages

LumpedLumped

-- easy to calculateeasy to calculate

-- cancant evaluate all possiblet evaluate all possible

scenariosscenariosDistributedDistributed

-- powerful in scenario analyses e.gpowerful in scenario analyses e.g

setting of boundarysetting of boundary conditions etc.conditions etc.

-- computational time is highcomputational time is high

-- parameterization is difficultparameterization is difficult


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Peak Runoff RatePeak Runoff Rate

Rational MethodRational Method

Rateofrainfallandrunoff

Rateofrainfallandrunoff

TimeTime

Rainfall rate, i

D

I

Q

Tc

C=q/i

Peakrunoffrate

Peakrunoffrate

q 0.0028CiA=

qq -- the peak runoff rate, mthe peak runoff rate, m33/s/s

CC runoff coefficientrunoff coefficient

ii rainfall intensity, mm/hrainfall intensity, mm/h

AA watershed area, hawatershed area, ha

0.77 0.385

c gT 0.0195L S =

TTcc time of concentration, mintime of concentration, min

LL maximum length of flow, mmaximum length of flow, m

SSgg watershed gradient, m/mwatershed gradient, m/m

Curve Number (CN) MethodCurve Number (CN) Method

Rainfall

Rainfall

AbstractionAbstraction

ExcessExcessrainfallrainfall RunoffRunoff

f(CN)f(CN)

CN=f(CN=f(landuselanduse, AMC), AMC)

PP

IIaa

FFaaSS

PPee

Deep infiltrationDeep infiltration

PPee = P= P IIaa FFaa


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Runoff VolumeRunoff Volume

Precipitationrate

Precipitationrate

TimeTime

IIaa FFaa

PPee

a e

a

F P

S P I=

e a aP P I F= + +

The hypothesis of theThe hypothesis of the

SCS method is that theSCS method is that the

ratios of the two actualratios of the two actual

((FFaa

,, PPee

) and the potential) and the potential

quantities (S,quantities (S, PP--IIaa) are) are

equalequal

ContinuityContinuity

EquationEquation

PP total precipitationtotal precipitation

PPee excess rainfallexcess rainfall

IIaa initial abstractioninitial abstraction

FFaa continuing abstractioncontinuing abstraction

SS potential maximum retentionpotential maximum retention

SCSSCS--CN MethodCN Method

( )2

a

e

a

P IP

P I S

=

+

aI 0.2S=

( )2

a

e

P IP

P 0.8S

=

+

Depth of RunoffDepth of Runoff

Therefore:Therefore:


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Graphical Solution of the SCS runoff EquationGraphical Solution of the SCS runoff Equation

CN=100CN=100

impervious andimpervious and

water surfaceswater surfaces

GoodForest

Urban

1

00%

Cumulative Rainfall (in)

Cumulativedirect

Runoff(in)

Group A: Deep sand, deep loess, aggregated siltsGroup A: Deep sand, deep loess, aggregated silts

Group B: Shallow loess, sandy loamGroup B: Shallow loess, sandy loam

Group C: Clay loams, shallow sandy loam, soils low in organicGroup C: Clay loams, shallow sandy loam, soils low in organiccontent and soils usually high in claycontent and soils usually high in clay

Group D: Soils that swell significantly when wet, heavy plasticGroup D: Soils that swell significantly when wet, heavy plastic claysclays

and certain saline soils.and certain saline soils.

CN(II)CN(II)


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1000S 10

CN(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 1.4II 0.5-1.1 1.4-2.1III Over 1.1 Over 2.1

Classification of antecedent moisture classes for theClassification of antecedent moisture classes for the

SCSSCS--CN methodCN method

DEMDEM

Forest, 55%Forest, 55%

CN=77CN=77Agriculture,Agriculture,

30%30%

CN=88CN=88Residential,Residential,

15%15%

CN=79CN=79

From RSFrom RS

CNCNWatershedWatershed=80.6=80.6

S=(1000/80.6)-

10=2.41 inches

Precipitation=4.5 inchesPrecipitation=4.5 inches

PPee=(4.5=(4.5--

0.2*2.41)0.2*2.41)22/(4.5+0.8*2.41)/(4.5+0.8*2.41)

==2.51 inches2.51 inches

IIaa

=0.2*2.41==0.2*2.41=0.4820.482 inchinch


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Time Distribution of SCS AbstractionTime Distribution of SCS Abstraction

( )aa

a

S P IF P I S

= +aP I

( )

2

a

2

a

dF S dP dt

dt P I S=

+

Differentiating and noting thatDifferentiating and noting that IIaa and S are constantsand S are constants

dPdP//dtdt rainfall intensityrainfall intensity

Column 1Time(h)

2CumulativeRainfall, P(in)

3CumulativeAbstractions(in), Ia

4CumulativeAbstractions(in), Fa

5Cumulativeexcessrainfall,Pe(in)

6Excessrainfallhyetograph(in)

0 0 0 - 0

0

1 0.20 0.20 - 0

0.06

2 0.90 0.50 0.34 0.06

0.123 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,CN=80, S=2.50, IIaa=0.5=0.5

All abstractedAll abstracted

( )aa

a

S P IF

P I S

=

+

Col2Col2--col3col3--col4col4


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Unit HydrographUnit Hydrograph

The unit hydrograph is the unit pulse response functionThe unit hydrograph is the unit pulse response function

of a linear hydrologic system.of a linear hydrologic system.The unit hydrograph of a watershed is defined as theThe unit hydrograph of a watershed is defined as the

direct runoff hydrograph (DRH) resulting from 1 inchdirect runoff hydrograph (DRH) resulting from 1 inch

(usually taken as 1 cm in SI units) of excess rainfall(usually taken as 1 cm in SI units) of excess rainfall

generated over the drainage area at a constant rate forgenerated over the drainage area at a constant rate for

an effective duration.an effective duration.


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Discrete Time Convolution Equation of a LinearDiscrete Time Convolution Equation of a Linear

SystemSystem

n M

n m n m 1m 1

Q P U

+=

=

Direct runoffDirect runoffPulsePulse

(rainfall)(rainfall)

unitunithydrographhydrograph

ordinateordinate

nn index for timeindex for time

mm index for pulseindex for pulse

MM no. of pulseno. of pulse


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UU11=Q=Q11/P/P11

UU22=(Q=(Q22--PP22UU11)/P)/P11

ALSOALSO

Unit hydrograph

ordinate

0

20

40

60

80100

120

140

160

180

200

1 2 3 4 5 6 7 8 9 10 11

Time (every 0.5 hr)

Rainfall,mm

0

50

100

150

200

250

300

UH,m

3hr-1mm

-1o

rQ,m

3s-1

UnitUnit

hydrographhydrograph

DirectDirect

runoffrunoff

hydrographhydrograph

RainfallRainfall

pulsepulse

Unit hydrograph applicationUnit hydrograph application


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D Water Discharge Model

Water Discharge Model

Motion Equation of Water


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Surface Information + DEM Processing

Forest Classification

Ground Water

Saturation

Red 12 hr

Green 18 hr

Blue 24 hr


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Debris Flow SimulationDebris Flow Simulation

CONCLUSIONCONCLUSION

DEM has numerous applications in researchDEM has numerous applications in research

and practice.and practice.

DEM from RS are potentially easier toDEM from RS are potentially easier to

acquire and use for terrain modeling,acquire and use for terrain modeling,

hydrological modeling etc.hydrological modeling etc.

Spatial Functions in GIS add more value toSpatial Functions in GIS add more value to

DEM for modeling purposes.DEM for modeling purposes.

Let us use DEMLet us use DEM


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THANK YOU VERY MUCHTHANK YOU VERY MUCH

DEM Lecture

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