Adjusting Highway Mileage in 3-D Adjusting Highway Mileage in 3-D Using LIDARUsing LIDAR

ByByHubo CaiHubo Cai

August 4August 4thth, 2004, 2004

OrganizationOrganization

IntroductionIntroduction Research ObjectivesResearch Objectives 3-D Models and 3-D Distance Prediction3-D Models and 3-D Distance Prediction Computational ImplementationsComputational Implementations Case StudyCase Study

Accuracy Evaluation and Sensitivity AnalysisAccuracy Evaluation and Sensitivity Analysis Significant FactorsSignificant Factors

Conclusions and RecommendationsConclusions and Recommendations

IntroductionIntroduction Why adjust highway mileage?Why adjust highway mileage?

Location is Critical in TransportationLocation is Critical in Transportation Events Are Located via Distances along Roads to Events Are Located via Distances along Roads to

Reference PointsReference Points Errors and Inconsistencies in Distance Measures Errors and Inconsistencies in Distance Measures

in Transportation Spatial Databasesin Transportation Spatial Databases Why use GIS?Why use GIS?

Other methodsOther methods Design Drawings Design Drawings Ground SurveyingGround Surveying GPSGPS Distance Measurement Instrument (DMI)Distance Measurement Instrument (DMI)

Time-consuming and labor intensiveTime-consuming and labor intensive GIS-based approach is efficientGIS-based approach is efficient

Introduction (Continued)Introduction (Continued)

Why in 3-D?Why in 3-D? Real World Objects ---- Three DimensionalReal World Objects ---- Three Dimensional Using 2-D LengthUsing 2-D Length

Why LIDAR?Why LIDAR? 3-D approach (the introduction of elevation)3-D approach (the introduction of elevation) Highly accurateHighly accurate AvailabilityAvailability

Main concernsMain concerns How?How? Accuracy and error propagationAccuracy and error propagation

Research ObjectivesResearch Objectives

Adjust highway mileage in 3-D using LIDARAdjust highway mileage in 3-D using LIDAR Evaluate its accuracy via a case study Evaluate its accuracy via a case study Evaluate its sensitivity to the use of LIDAR Evaluate its sensitivity to the use of LIDAR

versus NEDversus NED Identify significant factorsIdentify significant factors

3-D Models3-D Models

3-D Point Model and Its Variants3-D Point Model and Its Variants 3-D Distance Prediction3-D Distance Prediction

3-D Point Model

A B CD

EF

G

X

A

B CD E

F GSpecified by Z = f1 (X, Y) and Y = f1(X)

Specified by Y = f1 (X)Y

Z Specified by Z = f2 (X, Y) and Y = f2(X)

Specified by Z = f31 (X, Y) and Y = f3(X)

Specified by Y = f2 (X)

Specified by Y = f3 (X)

3-D Point Model – Variant 1, LRS-Based

Distance

X

Y

LRS

Z/Elevation

2-D Line

AB C E

G

F

D

A

B

C D E

GF

Specified by Z = f1 (Distance)

Specified by Z = f2 (Distance) Specified by Z = f3 (Distance)

3-D Point Model – Variant 2, LRS-Based

Distance

X

Y

LRS

Z/Elevation

2-D Line

AB C E

G

F

D

A

B C D E

GF

Straight Line Segments

3-D Distance Prediction

Horizon

Vertical Profile

Horizontal Projection

Difference in Elevation--d

Planimetric Length--pl

Surface Length = sqrt (d*d + pl*pl)

Required Source DataRequired Source Data Elevation DatasetElevation Dataset

LIDARLIDAR USGS NEDUSGS NED

Planimetric Line DatasetPlanimetric Line Dataset

LIDARLIDAR General InformationGeneral Information

A LIDAR operates in the Ultraviolet, Visible, and Infrared Region of A LIDAR operates in the Ultraviolet, Visible, and Infrared Region of the Electromagnetic Spectrumthe Electromagnetic Spectrum

A LIDAR consists of GPS, INS/IMU, and Laser Range FinderA LIDAR consists of GPS, INS/IMU, and Laser Range Finder Last “return” for Bare Earth DataLast “return” for Bare Earth Data Raw Data – Mass Point DataRaw Data – Mass Point Data

End Products GenerationEnd Products Generation Post ProcessingPost Processing Comma-Delimited ASCII File in X/Y/Z Format Comma-Delimited ASCII File in X/Y/Z Format DEMsDEMs

AccuracyAccuracy A Typical 6-Inch Error Budget in Elevations and PositionsA Typical 6-Inch Error Budget in Elevations and Positions The Guaranteed Best Vertical Accuracy -- ± 6 Inches (± 15 The Guaranteed Best Vertical Accuracy -- ± 6 Inches (± 15

Centimeters)Centimeters) No Better than 4 InchesNo Better than 4 Inches Market Models – Range from 10 – 30 cm (Vertical RMSE)Market Models – Range from 10 – 30 cm (Vertical RMSE)

DEMsDEMs A DEM is a digital file consisting of terrain A DEM is a digital file consisting of terrain

elevations for ground positions at elevations for ground positions at regularlyregularly spaced horizontal intervals spaced horizontal intervals

Grid SurfaceGrid Surface0 1 2 3 4 5

0

1

2

3

4

X, Y coordinates are (4, 3)

Row

Column

NEDNED Future Direction of USGS DEM DataFuture Direction of USGS DEM Data Merge the Highest-Resolution, Best-Quality Merge the Highest-Resolution, Best-Quality

Elevation Data Available across the US into a Elevation Data Available across the US into a Seamless Raster Format Seamless Raster Format

Source Data Selected According to the Source Data Selected According to the Following Criteria (Ordered from First to Last): Following Criteria (Ordered from First to Last): 10-Meter DEM, 30-Meter Level-2 DEM, 30-10-Meter DEM, 30-Meter Level-2 DEM, 30-Meter Level-1 DEM, 2-Arc-Second DEM, 3-Arc-Meter Level-1 DEM, 2-Arc-Second DEM, 3-Arc-Second DEM Second DEM

AccuracyAccuracy Varies with Source DataVaries with Source Data Systematic Evaluation under ProcessingSystematic Evaluation under Processing ““Inherits” the Accuracy of the Source DataInherits” the Accuracy of the Source Data

Level 1 DEMs (Max RMSE 15 m, Desired RMSE 7 m)Level 1 DEMs (Max RMSE 15 m, Desired RMSE 7 m) Level 2 DEMs (Max RMSE One-half Contour Interval)Level 2 DEMs (Max RMSE One-half Contour Interval) Level 3 DEMs (Max RMSE One-third Contour Interval)Level 3 DEMs (Max RMSE One-third Contour Interval)

Computational ImplementationsComputational Implementations

Development EnvironmentsDevelopment Environments ArcGIS 8.2ArcGIS 8.2 ArcObjectsArcObjects Visual Basic for ApplicationsVisual Basic for Applications

Key ---- Obtaining 3-D PointsKey ---- Obtaining 3-D Points Obtaining Planimetric Positions (Depending Obtaining Planimetric Positions (Depending

on the Format of Input Elevation Data)on the Format of Input Elevation Data) Obtaining ElevationsObtaining Elevations

Obtaining 3-D Points ---- Working Obtaining 3-D Points ---- Working with LIDAR Pointswith LIDAR Points

Working with LIDAR Point DataWorking with LIDAR Point Data Depending on the Point Elevation DataDepending on the Point Elevation Data Interpolation ApproachInterpolation Approach Approximation ApproachApproximation Approach DiscussionsDiscussions

Interpolation Approach

• Apply A Buffer• Identify All Points in the Buffer• Group Points into 3 Groups• Use Group C Points Directly• Identify Point Pairs for Group

A and Group B Points• Create Points from Each Point

Pair by Linear Interpolation• Deal with Start and End Points

Group A points

Group B points

Group C points

P

QO

Elevation for point O is linearly interpolated from points P and Q

Approximation Approach

• Developed based on Road Geometry• Apply A Buffer• Identify All Points in the Buffer• Points on Line for Direct Use• Snap Points to the Line• Deal with Start and End Points

Discussion• Errors due to Approximation

– Typical Lane Width (12 ft for Interstate and US Roads, 10 ft for NC Routes)

– Typical Cross-Sectional Slope (2%)– Maximum Errors based on the typical

slope (0.24 ft ( 7.31cm) and 0.2 ft (6.10 cm))

• Prerequisite– Lines in Correct Positions– High-Density LIDAR Points

• LIDAR Point Density– 18.6 ft (Average Distance between Two

Neighboring LIDAR Points)• Discussion

– Approximation Approach Results in Almost Double the Number of 3-D Points

– Snapping Provides At Least Equal Accuracy, If Not Better

Vertical error due to approximation

Vertical error due to interpolation

Corresponding point on road centerline C

LIDAR point B A

B

C

A

B

LIDAR point A

Points after Snapping

Obtaining 3-D Points ---- Working with LIDAR DEMs and NED

• Planimetric Position (2-D Point) ---- Uniform Interval (full cell-size and half cell-size)

• Elevation– For A Given Point, Its

Elevation Is Interpolated from Elevations of the Four Surrounding Cells

– Two Steps (Intermediate Points and the Target Point)

1035 1048

1041 1060

A

B C

DE

30m

30m

22.4m

22.25m

A

B C

D

EG

F

1039.49 1052.46 1056.98

A

B

C

D

d

d

d

Case Study ---- Study Scope• Limited by LIDAR Availability• Considered Sample Size and Variety• Interstate Highways in 9 Counties and US and NC Routes in Johnston

County

Study Scope

Legend

NEUSE

TAR-PAMLICO

River BasinCountyCounties in Study ScopeInterstate HighwaysUS RoutesNC Routes

Map produced by Hubo Cai, August 2003

Case Study Information SourcesCase Study Information Sources

Digital Road Centerline DataDigital Road Centerline Data Elevation DataElevation Data

LIDAR Point DataLIDAR Point Data LIDAR DEMs (20 and 50 ft resolutions)LIDAR DEMs (20 and 50 ft resolutions) NED (30 m resolution)NED (30 m resolution)

Reference Data (DMI Data)Reference Data (DMI Data)

Digital Road Centerline Data• Digitized from

DOQQs ---- 93 B/W and 98 CIR

• Data Description– Link-Node Format– County by County– Stateplane Coordinate

System– Datum: NAD83– Units: foot

Elevation Data – LIDAR DataElevation Data – LIDAR Data Data Collection and DescriptionData Collection and Description

Downloaded from Downloaded from www.ncfloodmaps.comwww.ncfloodmaps.com Tile by Tile (10,000 ft * 10, 000 ft)Tile by Tile (10,000 ft * 10, 000 ft) Bare Earth Point Data, 20-ft DEMs, and 50-ft DEMs Bare Earth Point Data, 20-ft DEMs, and 50-ft DEMs

(ASCII Files)(ASCII Files) Datum: NAD83 and NAVD 88Datum: NAD83 and NAVD 88 Units: FootUnits: Foot

AccuracyAccuracy Coastal Counties (95% RMSE, 20 cm)Coastal Counties (95% RMSE, 20 cm) Inland Counties (95% RMSE, 25 cm)Inland Counties (95% RMSE, 25 cm) Metadata States: 2 m Horizontal, 25 cm VerticalMetadata States: 2 m Horizontal, 25 cm Vertical

Elevation Data -- NEDElevation Data -- NED Data Collection and DescriptionData Collection and Description

Downloaded from North Carolina State University Downloaded from North Carolina State University Spatial Information Lab (Spatial Information Lab (http://www.precisionag.ncsu.edu/http://www.precisionag.ncsu.edu/))

County by CountyCounty by County Interchange Files (.e00 Files)Interchange Files (.e00 Files) Stateplane Coordinate SystemStateplane Coordinate System Datums: NAD83 and NAVD88Datums: NAD83 and NAVD88 Units: Foot (Horizontal), Meter (Vertical)Units: Foot (Horizontal), Meter (Vertical) Resolution: 1-arc-second (approximately 30-Meter or Resolution: 1-arc-second (approximately 30-Meter or

92.02-Feet)92.02-Feet) Errors and AccuracyErrors and Accuracy

Inherits the Accuracy of the Source DEMsInherits the Accuracy of the Source DEMs Metadata States Source DEMs Are Level 1 DEMsMetadata States Source DEMs Are Level 1 DEMs Vertical RMSE: 7-Meter (Desired), 15-Meter (Maximum)Vertical RMSE: 7-Meter (Desired), 15-Meter (Maximum)

Modeling Road Centerlines in 3-DModeling Road Centerlines in 3-D Using LIDAR Point DataUsing LIDAR Point Data

Intermediate Points (Buffering and Snapping)Intermediate Points (Buffering and Snapping) Start and End Points (Interpolation, Extrapolation, and Start and End Points (Interpolation, Extrapolation, and

Weighted Average)Weighted Average) Using LIDAR DEMsUsing LIDAR DEMs

Uniformly Distributed PointsUniformly Distributed Points IntervalsIntervals

20-ft and 10-ft with 20-ft DEMs20-ft and 10-ft with 20-ft DEMs 50-ft and 25-ft with 50-ft DEMs50-ft and 25-ft with 50-ft DEMs

Using NEDUsing NED Same as Using LIDAR DEMsSame as Using LIDAR DEMs Different Intervals (30-meter and 15-meter)Different Intervals (30-meter and 15-meter)

Quality Control

NC Route FTSeg 6 (Elevation vs. Planimetric Distance to the Start Point along the Road Centerline)

200.00

220.00

240.00

260.00

280.00

300.00

320.00

340.00

360.00

0.00 2000.00 4000.00 6000.00 8000.00 10000.00 12000.00 14000.00

D_TO_S

Z

3-D Points

NC Route FTSeg 37 (Elevation vs. Planimetric Distance to the Start Point along the Road Centerline)

190.00

195.00

200.00

205.00

210.00

215.00

220.00

0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00

D_TO_S

Z

3-D Points

Points do not Follow the general trend

A Typical Scenario

F1 F2

F4

F3

Buffer

Buffer

Buffer Buffer

Buffer Buffer

Buffer

Buffer

Bridge

Bridge

L1

L2

L3

L4

D1 D2

D3

D4

E1

E2

E3

E4

D5 D6

P1/P2

Improvement

• An Averaging Procedure

• Averaging Criteria– Based on Average

Densities– 3 ft for Interstate and

US FTSegs (average density 9.69 ft)

– 4 ft for NC FTSegs (average density 10.92 ft)

D1

D3

D4

D2

L1

L3

L4L2

A1

A2

Sample 3-D Point Data Attribute TableSample 3-D Point Data Attribute Table

XX YY ZZ D_TO_SD_TO_S DIST2DDIST2D ROUTEROUTE MERGEMERGE

2131875.522131875.52 595999.45595999.45 263.49263.49 0.000.00 58.3458.34 3000002730000027 11

2131883.712131883.71 595995.14595995.14 263.62263.62 9.269.26 58.3458.34 3000002730000027 11

2131887.122131887.12 595993.34595993.34 263.07263.07 13.1113.11 58.3458.34 3000002730000027 11

2131903.742131903.74 595984.59595984.59 263.39263.39 31.8931.89 58.3458.34 3000002730000027 11

2131907.132131907.13 595982.80595982.80 262.59262.59 35.7335.73 58.3458.34 3000002730000027 11

2131923.572131923.57 595974.13595974.13 263.02263.02 54.3154.31 58.3458.34 3000002730000027 11

2131927.142131927.14 595972.26595972.26 262.24262.24 58.3458.34 58.3458.34 3000002730000027 11

ResultsResults Each Road Segment Has 8 DistancesEach Road Segment Has 8 Distances

Predicted 3-D DistancePredicted 3-D Distance From the Use of LIDAR Point DataFrom the Use of LIDAR Point Data From the Use of LIDAR 20-ft DEMs and A 10-ft IntervalFrom the Use of LIDAR 20-ft DEMs and A 10-ft Interval From the Use of LIDAR 20-ft DEMs and A 20-ft IntervalFrom the Use of LIDAR 20-ft DEMs and A 20-ft Interval From the Use of LIDAR 50-ft DEMs and A 25-ft IntervalFrom the Use of LIDAR 50-ft DEMs and A 25-ft Interval From the Use of LIDAR 50-ft DEMs and A 50-ft IntervalFrom the Use of LIDAR 50-ft DEMs and A 50-ft Interval From the Use of NED and A 15-m IntervalFrom the Use of NED and A 15-m Interval From the Use of NED and A 30-m IntervalFrom the Use of NED and A 30-m Interval

Reference DistanceReference Distance DMI Measured DistanceDMI Measured Distance

Accuracy EvaluationAccuracy Evaluation Error(Difference) and Proportional Error Error(Difference) and Proportional Error

(Proportional Difference)(Proportional Difference) Evaluation MethodsEvaluation Methods

Descriptive Statistics (Describing Samples)Descriptive Statistics (Describing Samples) Distribution HistogramsDistribution Histograms Statistical InferencesStatistical Inferences Frequency AnalysisFrequency Analysis 100% and 95% RMSEs100% and 95% RMSEs

Sensitivity AnalysisSensitivity Analysis Analysis of Variance (ANOVA)Analysis of Variance (ANOVA) Comparison of Means, Medians, Absolute Means, Comparison of Means, Medians, Absolute Means,

Frequencies, and RMSEsFrequencies, and RMSEs

Accuracy Evaluation Results ---- Descriptive Statistics I

Error Format Road TypeLIDAR Point Data

Mean Median Standard Deviation Skew

Differences

All -8.43 -4.94 24.28 -0.30

Inter -9.93 -5.53 22.76 -0.39

US -10.81 -8.68 26.29 -0.19

NC 2.86 5.29 24.21 -0.41

Proportional Differences

All -6.48 -0.72 50.12 -1.71

Inter -1.17 -0.69 32.14 -1.20

US -15.02 -1.63 62.36 -3.02

NC -12.92 0.36 78.83 0.50

Error Format Road TypeNED, 15-m Interval NED, 30-m Interval

Mean Median Standard Deviation Skew Mean Median Standard Deviation Skew

Differences

All -18.63 -10.89 30.31 -0.72 -18.92 -11.21 30.38 -0.72

Inter -21.56 -13.34 29.46 -0.69 -22.01 -13.89 29.62 -0.69

US -18.97 -9.83 33.96 -0.64 -18.87 -9.82 33.84 -0.63

NC -5.14 -5.14 22.49 -0.82 -5.41 -5.55 22.46 -0.84

Proportional Differences

All -7.48 -1.56 50.22 -1.66 -7.49 -1.58 50.22 -1.66

Inter -2.11 -1.26 32.32 -1.08 -2.14 -1.29 32.32 -1.07

US -16.42 -3.35 62.45 -2.96 -16.41 -3.35 62.45 -2.96

NC -13.36 -0.24 78.80 0.51 -13.38 -0.26 78.79 0.51

Accuracy Evaluation Results ---- Distribution Histograms ID_A_LP

0

0.05

0.1

0.15

0.2

0.25

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ativ

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eqen

cy D_A_LP

D_I_LP

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0.15

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0.25

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eque

ncy

D_I_LP

D_US_LP

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ativ

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eque

ncy D_US_LP

D_NC_LP

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0.15

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0.25

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ativ

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eque

ncy

D_NC_LP

PD_A_LP

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PD_I_LP

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PD_US_LP

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PD_US_LP

PD_NC_LP

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PD_NC_LP

Accuracy Evaluation Results ---- Hypothesis Tests and Confidence Intervals

SampleHypothesis

Statistic Critical Value(s) Reject or Accept at α = 5%Confidence Interval

H0 H1

D_A_LP

μ ≤ 0 μ > 0 -5.6509 1.6476 A*

-8.43 ± 2.94μ ≥ 0 μ < 0 -5.6509 -1.6476 R**

μ = 0 μ ≠ 0 -5.6509 ±1.9642 R

D_I_LP

μ ≤ 0 μ > 0 -5.4826 1.6558 A

-9.93 ± 3.58μ ≥ 0 μ < 0 -5.4826 -1.6558 R

μ = 0 μ ≠ 0 -5.4826 ±1.9771 R

D_US_LP

μ ≤ 0 μ > 0 -3.4651 1.6691 A

-10.81 ± 6.22μ ≥ 0 μ < 0 -3.4651 -1.6691 R

μ = 0 μ ≠ 0 -3.4651 ±1.9979 R

D_NC_LP

μ ≤ 0 μ > 0 0.7088 1.6906 A

2.86 ± 8.19μ ≥ 0 μ < 0 0.7088 -1.6906 A

μ = 0 μ ≠ 0 0.7088 ±2.0317 A

PD_A_LP

μ ≤ 0 μ > 0 -2.1033 1.6476 A

-6.48 ± 6.06μ ≥ 0 μ < 0 -2.1033 -1.6476 R

μ = 0 μ ≠ 0 -2.1033 ±1.9642 R

PD_I_LP

μ ≤ 0 μ > 0 -0.4562 1.6558 A

-1.17 ± 5.05μ ≥ 0 μ < 0 -0.4562 -1.6558 A

μ = 0 μ ≠ 0 -0.4562 ±1.9771 A

PD_US_LP

μ ≤ 0 μ > 0 -2.0295 1.6691 A

-15.02 ± 14.76μ ≥ 0 μ < 0 -2.0295 -1.6691 R

μ = 0 μ ≠ 0 -2.0295 ±1.9979 R

PD_NC_LP

μ ≤ 0 μ > 0 -0.9836 1.6906 A

-12.92 ± 26.67μ ≥ 0 μ < 0 -0.9836 -1.6906 A

μ = 0 μ ≠ 0 -0.9836 ±2.0317 A

Accuracy Evaluation Results ---- RMSEs (LIDAR Point Data)

Error Format Road Type

100% 95%

RMSE Reported Accuracy # of Outliers RMSEReported

Accuracy# of Outliers

Differences

All 25.65 50.27 0 22.48 44.06 0

Inter 24.76 48.53 0 21.39 41.92 0

US 28.26 55.39 0 25.28 49.55 0

NC 24.04 47.12 0 21.32 41.79 0

Proportional Differences

All 50.44 98.86 7 24.90 48.80 6

Inter 32.06 62.84 5 18.19 35.65 6

US 63.72 124.89 2 35.47 69.52 1

NC 78.80 154.45 1 51.93 101.78 1

Accuracy Evaluation Results ---- Frequency Analysis (LIDAR Point Data)

Error Format GroupsAll FTSegs Interstate FTSegs US FTSegs NC FTSegs

# % # % # % # %

Differences

[-5, 5] 52 19.62% 33 20.89% 13 18.31% 6 16.67%

[-10, 10] 97 36.60% 68 43.04% 20 28.17% 9 25.00%

[-20, 20] 151 56.98% 98 62.03% 35 49.30% 18 50.00%

[-30, 30] 205 77.36% 122 77.22% 52 73.24% 31 86.11%

[-50, 50] 249 93.96% 150 94.94% 65 91.55% 34 94.44%

(-∞, -50) and (50, +∞) 16 6.04% 8 5.06% 6 8.45% 2 5.56%

ProportionalDifferences

[-1, 1] 64 24.15% 49 31.01% 4 5.63% 11 30.56%

[-5, 5] 153 57.74% 107 67.72% 25 35.21% 21 58.33%

[-10, 10] 177 66.79% 118 74.68% 35 49.30% 24 66.67%

[-20, 20] 201 75.85% 129 81.65% 46 64.79% 26 72.22%

[-30, 30] 211 79.62% 133 84.18% 51 71.83% 27 75.00%

[-50, 50] 228 86.04% 140 88.61% 60 84.51% 28 77.78%

[-100, 100] 250 94.34% 153 96.84% 65 91.55% 32 88.89%

(-∞, -100) and (100, +∞) 15 5.66% 15 9.49% 6 8.45% 4 11.11%

Sensitivity Analysis ---- ANOVA

Sample 1 Sample 2 F Fc Accept or Reject

D_A_LP

D_A_L20_10 11.3710 3.8591 Reject

D_A_L20_20 12.8832 3.8591 Reject

D_A_L50_25 11.7030 3.8591 Reject

D_A_L50_50 3.5764 3.8591 Accept

D_A_N_15 18.3042 3.8591 Reject

D_A_N_30 19.2777 3.8591 Reject

D_A_L20_10

D_A_L20_20 0.0448 3.8591 Accept

D_A_L50_25 34.0175 3.8591 Reject

D_A_L50_50 21.3379 3.8591 Reject

D_A_N_15 0.8327 3.8591 Accept

D_A_N_30 1.0411 3.8591 Accept

D_A_L20_20

D_A_L50_25 35.9627 3.8591 Reject

D_A_L50_50 23.0558 3.8591 Reject

D_A_N_15 0.4933 3.8591 Accept

D_A_N_30 0.6562 3.8591 Accept

D_A_L50_25

D_A_L50_50 2.3418 3.8591 Accept

D_A_N_15 42.4625 3.8591 Reject

D_A_N_30 43.5995 3.8591 Reject

D_A_L50_50D_A_N_15 28.9469 3.8591 Reject

D_A_N_30 29.9824 3.8591 Reject

D_A_N_15 D_A_N_30 0.0114 3.8591 Accept

Difference: F > Fc, Proportional Difference: F < Fc

Sensitivity Analysis ---- Comparison of RMSEs

Comparisons of 100% RMSEs of Differences

20

22

24

26

28

30

32

34

36

38

40

LPL20/10

L20/20L50/25

L50/50 N15 N30

Elevation Dataset and Interval

RM

SE

All FTSegs

Interstate FTSegs

US FTSegs

NC FTSegs

Comparisons of 100% RMSEs of Proportional Differences

30

35

40

45

50

55

60

65

70

75

80

LPL20/10

L20/20L50/25

L50/50 N15 N30

Elevation Dataset and Interval

RM

SE

All FTSegs

Interstate FTSegs

US FTSegs

NC FTSegs

Comparisons of 95% RMSEs of Differences

15

20

25

30

35

LPL20/10

L20/20L50/25

L50/50 N15 N30

Elevation Dataset and Interval

RM

SE

All FTSegs

Interstate FTSegs

US FTSegs

NC FTSegs

Comparisons of 95% RMSEs of Proportional Differences

15

20

25

30

35

40

45

50

55

Elevation Dataset and Interval

RM

SE

All FTSegs

Interstate FTSegs

US FTSegs

NC FTSegs

Comparison Based on RMSEs

Elevation Dataset

100% RMSE 95% RMSE

RMSE Improvement RMSE Improvement

Difference

LIDAR Point 25.65 28% 22.48 25%

LIDAR DEM (20FT) 33.52 6% 27.83 7%

LIDAR DEM(50FT) 34.03 5% 27.71 8%

NED 35.64 ---- 30.06 ----

Proportional Difference

LIDAR Point 50.44 ---- 24.90 ----

Conclusions ---- Accuracy Evaluation and Conclusions ---- Accuracy Evaluation and Sensitivity AnalysisSensitivity Analysis

Errors of the predicted 3-D distances are not normally Errors of the predicted 3-D distances are not normally distributed.distributed.

The higher the accuracy of the elevation dataset being The higher the accuracy of the elevation dataset being used, the higher the accuracy of the predicted 3-D used, the higher the accuracy of the predicted 3-D distances.distances.

Using the same elevation dataset, the accuracy of the Using the same elevation dataset, the accuracy of the predicted 3-D distance is not dependent on intervals, predicted 3-D distance is not dependent on intervals, given these intervals are less than or equal to the cell given these intervals are less than or equal to the cell size.size.

3-D distances predicted using LIDAR point data with the 3-D distances predicted using LIDAR point data with the snapping approach have the best accuracy.snapping approach have the best accuracy.

From the aspect of differences using the 100% RMSE as the From the aspect of differences using the 100% RMSE as the measure of the accuracy, the use of LIDAR point data improves measure of the accuracy, the use of LIDAR point data improves the accuracy by 28% compared to the use of NED data. The use the accuracy by 28% compared to the use of NED data. The use of LIDAR DEMs improves the accuracy by 6% compared to the of LIDAR DEMs improves the accuracy by 6% compared to the use of NED data.use of NED data.

From the aspect of differences using the 95% RMSE as the From the aspect of differences using the 95% RMSE as the measure of the accuracy, the use of LIDAR point data improves measure of the accuracy, the use of LIDAR point data improves the accuracy by 25% compared to the use of NED data. The use the accuracy by 25% compared to the use of NED data. The use of LIDAR DEMs improves the accuracy by 8% compared to the of LIDAR DEMs improves the accuracy by 8% compared to the use of NED data.use of NED data.

From the aspect of proportional differences, the improvements From the aspect of proportional differences, the improvements due to the use of higher accurate elevation datasets are not due to the use of higher accurate elevation datasets are not significant (the majority (53%) of the road segments in this case significant (the majority (53%) of the road segments in this case study are longer than 5,000 ft, 73% are longer than 1,000 ft, and study are longer than 5,000 ft, 73% are longer than 1,000 ft, and 43% are longer than 10,000 ft).43% are longer than 10,000 ft).

Conclusions ---- Accuracy Evaluation and Conclusions ---- Accuracy Evaluation and Sensitivity Analysis (Continued)Sensitivity Analysis (Continued)

Significant FactorsSignificant Factors GoalGoal

Evaluate the relationship between a geometric property and the Evaluate the relationship between a geometric property and the accuracy of the GIS calculated distanceaccuracy of the GIS calculated distance

Factors under ConsiderationFactors under Consideration DistanceDistance Average Slope and Weighted SlopeAverage Slope and Weighted Slope Average Slope Change and Weighted Slope ChangeAverage Slope Change and Weighted Slope Change Number of 3-D Points and Average Density of 3-D PointsNumber of 3-D Points and Average Density of 3-D Points

Evaluation Methods AppliedEvaluation Methods Applied Sample Correlation Coefficient and Sample Coefficient of Sample Correlation Coefficient and Sample Coefficient of

DeterminationDetermination Grouping and ComparisonGrouping and Comparison

BenefitsBenefits Cautions to be paid to certain linear featuresCautions to be paid to certain linear features

Calculation of Factors• Distance = D1 + D2 (DMI measured)• Average Slope = (Abs(S1) + Abs(S2))/2• Weighted Slope = (Abs(S1) * D1 + Abs(S2) * D2)/(D1 + D2)• Average Slope Change = (Abs(S1 – 0) + Abs(S2 – S1))/2• Weighted Slope Change = (Abs(S1 – 0) * D1 + Abs(S2 – S1) *

D2)/(D1 + D2)• Number of 3-D Points = 3• Average Density = (D1 + D2)/2

PD1 PD2

E1

E2

D1

D2

S1

S2

Evaluation Result I: Distance vs. Difference and Absolute Difference

FTSegType

LIDAR Point Data

LIDAR 20-ft DEM LIDAR 50-ft DEM NED

10-ft Interval 20-ft Interval 25-ft Interval 50-ft Interval 15-m Interval 30-m Interval

rxy r2xy rxy r2xy rxy r2xy rxy r2xy rxy r2xy rxy r2xy rxy r2xy

All -0.07 0.00 -0.34 0.12 -0.36 0.13 0.16 0.03 0.06 0.00 -0.35 0.13 -0.37 0.13

Inter -0.11 0.01 -0.37 0.14 -0.39 0.15 0.27 0.07 0.16 0.03 -0.38 0.14 -0.39 0.16

US -0.44 0.19 -0.65 0.42 -0.65 0.42 -0.54 0.29 -0.58 0.34 -0.67 0.44 -0.66 0.44

NC 0.42 0.17 0.08 0.01 0.06 0.00 0.28 0.08 0.22 0.05 0.06 0.00 0.05 0.00

FTSegType

LIDAR Point Data

LIDAR 20-ft DEM LIDAR 50-ft DEM NED

10-ft Interval 20-ft Interval 25-ft Interval 50-ft Interval 15-m Interval 30-m Interval

rxy r2xy rxy r2xy rxy r2xy rxy r2xy rxy r2xy rxy r2xy rxy r2xy

All 0.31 0.10 0.36 0.13 0.37 0.14 0.35 0.12 0.34 0.11 0.40 0.16 0.41 0.16

Inter 0.29 0.09 0.38 0.14 0.39 0.15 0.37 0.14 0.36 0.13 0.42 0.18 0.43 0.19

US 0.49 0.24 0.71 0.50 0.71 0.51 0.59 0.35 0.63 0.40 0.73 0.53 0.72 0.52

NC 0.37 0.14 0.05 0.00 0.04 0.00 0.15 0.02 0.08 0.01 0.05 0.00 0.06 0.00

Distance vs. Difference

Distance vs. Absolute Difference

Grouping and Analysis I: Difference, Groups Based on Distance

Group Distance Range (ft) Number of FTSegs

Percentage

Group 1 (0, 100] 46 17.36%

Group 2 (100, 1,000] 26 9.81%

Group 3 (1,000, 5,000] 52 19.62%

Group 4 (5,000, 10,000] 28 10.57%

Group 5 (10,000, 20,000] 38 14.34%

Group 6 (20,000, 30,000] 32 12.08%

Group 7 (30,000, +∞) 43 16.23%

Total -- 265 100%

GroupLIDAR Point

Data

LIDAR 20-ft DEM LIDAR 50-ft DEM NED

10-ft Interval 20-ft Interval 25-ft Interval 50-ft Interval 15-m Interval 30-m Interval

Group 1 6.75 6.84 6.84 6.78 6.78 6.77 6.77

Group 2 14.10 16.11 16.12 16.06 16.07 16.03 16.04

Group 3 26.73 32.80 32.93 31.56 31.63 33.39 33.42

Group 4 28.15 32.56 32.71 29.45 29.70 34.48 34.53

Group 5 27.76 32.19 32.62 37.92 31.69 37.95 38.10

Group 6 32.52 44.51 45.30 65.97 52.60 47.93 48.29

Group 7 32.23 47.40 48.24 56.33 47.48 49.72 50.20

Comparisons of RMSEs of Differences Grouped Based on the Distance

5

10

15

20

25

30

35

40

45

50

55

60

65

70

Group Based on the Distance

RM

SE

LIDAR PointLIDAR 20-ft DEM, 10-ft IntervalLIDAR 20-ft DEM, 20-ft IntervalLIDAR 50-ft DEM, 25-ft IntervalLIDAR 50-ft DEM, 50-ft IntervalNED, 15-m IntervalNED, 30-m Interval

GroupLIDAR Point

Data

LIDAR 20-ft DEM LIDAR 50-ft DEM NED

10-ft Interval 20-ft Interval 25-ft Interval 50-ft Interval 15-m Interval 30-m Interval

Group 1 116.40 117.94 117.90 116.96 116.92 116.61 116.61

Group 2 41.30 43.25 43.19 42.00 41.83 42.27 42.27

Group 3 10.54 11.83 11.84 11.87 11.86 11.95 11.96

Group 4 4.23 5.06 5.09 4.46 4.61 5.40 5.41

Group 5 1.95 2.27 2.29 2.60 2.22 2.62 2.63

Group 6 1.32 1.76 1.79 2.51 1.98 1.92 1.93

Group 7 0.80 1.22 1.24 1.35 1.17 1.23 1.24Comparisons of RMSEs of Proportional Differences Grouped Based on the Distance

0

10

20

30

40

50

60

70

80

90

100

110

120

Group Based on the Distance

RM

SE LIDAR Point

LIDAR 20-ft DEM, 10-ft IntervalLIDAR 20-ft DEM, 20-ft IntervalLIDAR 50-ft DEM, 25-ft IntervalLIDAR 50-ft DEM, 50-ft IntervalNED, 15-m IntervalNED, 30-m Interval

Grouping and Analysis II: Proportional Difference, Groups Based on Distance

Significant Factor ---- ConclusionsSignificant Factor ---- Conclusions

Conclusions Based on Sample Correlation CoefficientsConclusions Based on Sample Correlation Coefficients The Factors under Consideration are all significant to the The Factors under Consideration are all significant to the

accuracy of the predicted 3-D Distance when compared to the accuracy of the predicted 3-D Distance when compared to the DMI measured distance.DMI measured distance.

Positive Linear Association between the error of the predicted Positive Linear Association between the error of the predicted 3-D distance and a factor under consideration.3-D distance and a factor under consideration.

Negative Linear Association between the proportional error of Negative Linear Association between the proportional error of the predicted 3-D distance and a factor under considerationthe predicted 3-D distance and a factor under consideration

Conclusions Based on Grouping and AnalysisConclusions Based on Grouping and Analysis Confirms the significance of these factorsConfirms the significance of these factors Confirms the general linear associationsConfirms the general linear associations Reveals the existence of thresholdsReveals the existence of thresholds

It is technically feasible to model linear objects in a 3-D It is technically feasible to model linear objects in a 3-D space with existing datasets.space with existing datasets.

The buffering and snapping approach is a creative way The buffering and snapping approach is a creative way in using LIDAR point data.in using LIDAR point data.

Two datasets (elevation and line) are required to adopt Two datasets (elevation and line) are required to adopt the model developed.the model developed.

The prerequisite to adopt the developed 3-D model is The prerequisite to adopt the developed 3-D model is that lines are in correct positions.that lines are in correct positions.

Using the proposed 3-D approach, geometric properties Using the proposed 3-D approach, geometric properties other than 3-D distance could be calculated.other than 3-D distance could be calculated.

Conclusions regarding accuracy and sensitivity.Conclusions regarding accuracy and sensitivity. Conclusions regarding significant factors.Conclusions regarding significant factors.

ConclusionsConclusions

RecommendationsRecommendations Adopt the 3-D approach developed in this research to Adopt the 3-D approach developed in this research to

calculate 3-D distance and other geometric properties.calculate 3-D distance and other geometric properties. Linear objects other than road centerlines could also Linear objects other than road centerlines could also

adopt the 3-D model developed in this research.adopt the 3-D model developed in this research. Spatially correct all line (road) data.Spatially correct all line (road) data. The buffering and snapping approach developed in this The buffering and snapping approach developed in this

research is based on road characteristics. If to be used research is based on road characteristics. If to be used for other linear objects, the appropriateness needs to be for other linear objects, the appropriateness needs to be evaluated.evaluated.

Extra caution should be paid to certain linear objects Extra caution should be paid to certain linear objects (significant factors).(significant factors).

Key BenefitsKey Benefits

3-D Road Centerline3-D Road Centerline Computed 3-D GeometriesComputed 3-D Geometries

No more need for field workNo more need for field work Savings on time, labor, and costSavings on time, labor, and cost

Readily Customizable Programs Readily Customizable Programs Useful to Other ApplicationsUseful to Other Applications

Use of the Model to Assess Highway Flooding• Objective ---- Test the Usefulness of Developed

3-D Model in Assessing Highway Flooding• Flooding Scenario• Two Tasks

– Flood Extent and Depth Determination– Flooded Road Segment Identification

Normal Water Level

Flooded Water Level

Area A

Area BSurface

Line

Road Profile

Segments Flooded

Segments Not FloodedFlooded Water Level

Flood Extent and Depth DeterminationFlood Extent and Depth Determination Traditional ApproachTraditional Approach

Water Level SurfaceWater Level Surface Terrain SurfaceTerrain Surface

Approach Taken in This StudyApproach Taken in This Study Assumption 1: Water Bodies Are Represented As Assumption 1: Water Bodies Are Represented As

PolylinesPolylines Assumption 2: Elevations along Water Lines Are Assumption 2: Elevations along Water Lines Are

Water Surface LevelsWater Surface Levels Assumption 3: Given Flood LevelAssumption 3: Given Flood Level Business Rule 1: Elevations along Water Lines Are Business Rule 1: Elevations along Water Lines Are

Lower Than Surrounding AreasLower Than Surrounding Areas Business Rule 2: Water flows from Higher Water Business Rule 2: Water flows from Higher Water

Levels to Lower Water LevelsLevels to Lower Water Levels

S

E

Water Surface after Flood

Water Surface before Flood

Planimetric View Cross-Sectional View

Flood Extent and Depth Determination (Continued)

Flood Depth

Flooded Road Segment Identification

Flooded Water LevelRoad Segments Not Flooded

Road Segments Flooded

Road Segment outside Flood Extent

Road Segment outside Flood Extent

S1 S2

T1

T2

P2

T3

T4 T5

T6

Test Area

Test Results ---- Flood Extent and Depth

Test Results ---- Flooded Road Segment Identification

Legend

Flood ExtentFlooded Road SegmentInterstate Highway

Legend

Flood ExtentFlooded Road SegmentInterstate Highway

Test Results ---- Flooded Road Segment

Identification (Continued)

LegendInterstate HighwayFlooded Road Segment

Flood Extent