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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
Rel
ativ
e Fr
eqen
cy D_A_LP
D_I_LP
0
0.05
0.1
0.15
0.2
0.25
Rel
ativ
e Fr
eque
ncy
D_I_LP
D_US_LP
0
0.05
0.1
0.15
0.2
0.25
Rel
ativ
e Fr
eque
ncy D_US_LP
D_NC_LP
0
0.05
0.1
0.15
0.2
0.25
Rel
ativ
e Fr
eque
ncy
D_NC_LP
PD_A_LP
0
0.1
0.2
0.3
0.4
0.5
Rel
ativ
e Fr
eque
ncy
PD_A_LP
PD_I_LP
0
0.2
0.4
0.6
0.8
1
Rel
ativ
e Fr
eque
ncy
PD_I_LP
PD_US_LP
0
0.1
0.2
0.3
0.4
0.5
0.6
Rel
ativ
e Fr
eque
ncy
PD_US_LP
PD_NC_LP
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Rel
ativ
e Fr
eque
ncy
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