Department of Geography, University at Buffalo—The State University of New York, 105 Wilkeson Quad, Buffalo, NY 14261-0023, USA UNCERTAINTY IN DIGITAL

Department of Geography, University at Buffalo—The State University of Department of Geography, University at Buffalo—The State University of New York, 105 Wilkeson Quad, Buffalo, NY 14261-0023, USANew York, 105 Wilkeson Quad, Buffalo, NY 14261-0023, USA

UNCERTAINTY IN DIGITAL UNCERTAINTY IN DIGITAL ELEVATION DATA USED FOR ELEVATION DATA USED FOR

GEOPHYSICAL FLOW GEOPHYSICAL FLOW SIMULATION SIMULATION

Laércio M. NamikawaLaércio M. NamikawaChris S. Renschler Chris S. Renschler

GeoInfo 2004GeoInfo 2004Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation

Geophysical FlowGeophysical FlowBlock and AshBlock and Ash


Geophysical FlowGeophysical FlowMudslide - LaharMudslide - Lahar



Titan2DTitan2D

Parallel adaptive numerical simulation of dry avalanches over natural terrain

Depth-averaged granular flows governed by Coulomb-type interactions

Adaptive grid second-order Godunov solver

Large-scale simulations Direct connection to GIS databases

• Material – Bed Friction Angle• Elevation


Computational Techniques

•Multi -processor Computing

•Dynamic Load Balancing

• Adaptive Grid

Cluster computers and distributed memory multicomputers

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Elevation DataElevation Data

First DerivativesFirst Derivatives Second DerivativesSecond Derivatives Small difference in elevationSmall difference in elevation

• Areas with none or low risk turn Areas with none or low risk turn into high risk areasinto high risk areas

Simulation modelSimulation model• Hazard maps considering Hazard maps considering

uncertainties in elevation data uncertainties in elevation data


Elevation Uncertainty Elevation Uncertainty

Global measureGlobal measure Distributed quantity for every Distributed quantity for every

location is also neededlocation is also needed RequiredRequired

• A method to define uncertainty in Digital A method to define uncertainty in Digital Elevation Model by taking advantage of Elevation Model by taking advantage of the existence of more than one data set the existence of more than one data set for same regionfor same region


Method to Define Elevation Method to Define Elevation Uncertainty Uncertainty

Existence of more than one data set for Existence of more than one data set for same regionsame region• SRTM – For whole globeSRTM – For whole globe

Uncertainty analysisUncertainty analysis• Correlation with morphological featureCorrelation with morphological feature• Focus on differences between DEMs that are Focus on differences between DEMs that are

not randomly distributednot randomly distributed Divide into regionsDivide into regions

• Random distributed differencesRandom distributed differences• Clustered high differencesClustered high differences


Clustering AnalysisClustering Analysis

Descriptive statistics measures of Descriptive statistics measures of dispersiondispersion• Coefficient of variationCoefficient of variation

HypothesisHypothesis• If uncertainty in DEM is randomly If uncertainty in DEM is randomly

distributed, measures from descriptive distributed, measures from descriptive statistics are expected to be similarstatistics are expected to be similar

Cluster detection method Cluster detection method


Cluster detection method Cluster detection method

Rogerson Rogerson method:method:• Z-score of Z-score of

coefficient of coefficient of variationvariation

• Smooth using Smooth using Gaussian kernel Gaussian kernel filterfilter

• Find significant Find significant peaks and pitspeaks and pits


Gaussian Kernel FilterGaussian Kernel Filter

Standard deviation vStandard deviation valuealue• Smooth random differencesSmooth random differences• Enhance clusters Enhance clusters

Discrete convolution using mask of Discrete convolution using mask of kernel filter weightskernel filter weights

Maximum distanceMaximum distance• Percentage of maximum valuePercentage of maximum value


Critical Value ApproximationCritical Value Approximation

Defined:Defined:

For 95% significancyFor 95% significancy Clusters if higher Clusters if higher than than M*M* Valid ifValid if

• Area smaller than 10,000Area smaller than 10,000 Even if greaterEven if greater

• Only slightly smaller critical value Only slightly smaller critical value

AM

281.14ln


Correlation with Terrain Correlation with Terrain MorphologyMorphology

SlopeSlope• Hypothesis: Mostly due to positional Hypothesis: Mostly due to positional

inaccuracyinaccuracy CurvatureCurvature

• Maximum slope direction Maximum slope direction • Perpendicular to maximum slope Perpendicular to maximum slope

directiondirection• Hypothesis: Related to resolutionHypothesis: Related to resolution


Case Study – Colima VolcanoCase Study – Colima Volcano

DEMDEM• Arizona Arizona

Image Image ArchiveArchive

• SRTMSRTM


Available Digital Elevation ModelsAvailable Digital Elevation Models

Map referencesMap references• Base maps: 1:50000 scale, UTM Base maps: 1:50000 scale, UTM

projection, ITRF92 datumprojection, ITRF92 datum• ARIADEM: 60m resolution, UTM ARIADEM: 60m resolution, UTM

projection, NAD27 datumprojection, NAD27 datum• SRTMDEM: 3-arc second, WGS84 datumSRTMDEM: 3-arc second, WGS84 datum

Reproject and resample to a 90 Reproject and resample to a 90 meter resolution UTM grid, ITRF92 meter resolution UTM grid, ITRF92


SRTM ARIA DifferenceSRTM ARIA Difference


Coefficient of VariationCoefficient of Variation


Gaussian KernelGaussian Kernel

Std. Dev: Std. Dev: 22

Distance: Distance:

95%95% Legal Legal

program program (SPRING)(SPRING)


ClustersClusters

M*: M*: 4.7394.739



Linear correlation coefficient of Linear correlation coefficient of variation and terrain morphology variation and terrain morphology

Terrain MorphologyParameter

Correlation Coefficient

Correlation t-score, N=95866,Critical t = ±1.98 for 95% significance

Slope 0.1739 54.70

Profile Curvature 0.0613 19.02

Tangential Curvature -0.0131 -4.067

• However… • Slopes and coefficient of variation are all positive • Curvatures can be positive and negative



Correlation in whole grid: coefficients Correlation in whole grid: coefficients of variation and slope is significantof variation and slope is significant



Linear correlation difference between Linear correlation difference between two DEMs and terrain morphology two DEMs and terrain morphology

• All grid cells• Correlation in clustered areas




Slope -0.1284 -40.11

Profile Curvature -0.0486 -15.08

Tangential Curvature 0.0738 22.93



Correlation in whole grid: differences Correlation in whole grid: differences in elevation and slope is significantin elevation and slope is significant



Linear correlation: mean difference Linear correlation: mean difference and mean morphology in clustersand mean morphology in clusters

• Only tangential curvature has significant linear correlation




Slope -0.1175 -1.269

Profile Curvature -0.1096 -1.183

Tangential Curvature 0.3622 4.168


Scatterplot of differences in Scatterplot of differences in elevation and tangential curvature elevation and tangential curvature

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-0.002 -0.001 0 0.001 0.002

33*23020 tkDiff


Differences between predicted and Differences between predicted and observed differences at clusters observed differences at clusters


DiscussionsDiscussions

Difference in elevation and Difference in elevation and tangential curvature inside clusterstangential curvature inside clusters• Significant linear correlationSignificant linear correlation

Differences between predicted and Differences between predicted and observedobserved• Std. deviation: 25.5 mStd. deviation: 25.5 m• Greater than 2 std. deviation: 9 clusters Greater than 2 std. deviation: 9 clusters


DiscussionsDiscussions Clusters Clusters

(2std. dev)(2std. dev)• At edgesAt edges• Too smallToo small• Close to Close to

volcano – volcano – erosion and erosion and depositiondeposition

Other Other clustersclusters• Ridge and Ridge and

valleyvalley


SummarySummary Uncertainty of DEM can be defined Uncertainty of DEM can be defined

when other data is availablewhen other data is available Correlation of uncertainty measure Correlation of uncertainty measure

and slope at individual cells:and slope at individual cells:• Miss knowledge about DEM parameters Miss knowledge about DEM parameters

that affects uncertainty that affects uncertainty Define significant regions of high Define significant regions of high

uncertainty using a cluster detection uncertainty using a cluster detection methodmethod• Influence of slope and random variations Influence of slope and random variations

are diminished are diminished


SummarySummary Significant correlation between mean Significant correlation between mean

uncertainty and mean terrain uncertainty and mean terrain tangential curvaturetangential curvature

Extreme tangential curvature values Extreme tangential curvature values along ridge and valley linesalong ridge and valley lines• DEM can be modified in these regions DEM can be modified in these regions

with additional data with additional data Importance of existence of global Importance of existence of global

coverage DEM - SRTMcoverage DEM - SRTM

Documents

Department of Geography, University at Buffalo—The State University of New York, 105 Wilkeson Quad, Buffalo, NY 14261-0023, USA UNCERTAINTY IN DIGITAL