Department of Geography, University at Buffalo—The State University of New York, 105 Wilkeson Quad, Buffalo, NY , USA UNCERTAINTY IN DIGITAL ELEVATION DATA USED FOR GEOPHYSICAL FLOW SIMULATION Laércio M. Namikawa Chris S. Renschler

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

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

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

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Titan2D 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

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Computational Techniques Multi - processor Computing Dynamic Load Balancing Adaptive Grid Cluster computers and distributed memory multicomputers

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Elevation Data First Derivatives First Derivatives Second Derivatives Second Derivatives Small difference in elevation Small difference in elevation Areas with none or low risk turn into high risk areasAreas with none or low risk turn into high risk areas Simulation model Simulation model Hazard maps considering uncertainties in elevation dataHazard maps considering uncertainties in elevation data

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Elevation Uncertainty Global measure Global measure Distributed quantity for every location is also needed Distributed quantity for every location is also needed Required Required A method to define uncertainty in Digital Elevation Model by taking advantage of the existence of more than one data set for same regionA method to define uncertainty in Digital Elevation Model by taking advantage of the existence of more than one data set for same region

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Method to Define Elevation Uncertainty Existence of more than one data set for same region Existence of more than one data set for same region SRTM – For whole globeSRTM – For whole globe Uncertainty analysis Uncertainty analysis Correlation with morphological featureCorrelation with morphological feature Focus on differences between DEMs that are not randomly distributedFocus on differences between DEMs that are not randomly distributed Divide into regions Divide into regions Random distributed differencesRandom distributed differences Clustered high differencesClustered high differences

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Clustering Analysis Descriptive statistics measures of dispersion Descriptive statistics measures of dispersion Coefficient of variationCoefficient of variation Hypothesis Hypothesis If uncertainty in DEM is randomly distributed, measures from descriptive statistics are expected to be similarIf uncertainty in DEM is randomly distributed, measures from descriptive statistics are expected to be similar Cluster detection method Cluster detection method

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Cluster detection method Rogerson method: Rogerson method: Z-score of coefficient of variationZ-score of coefficient of variation Smooth using Gaussian kernel filterSmooth using Gaussian kernel filter Find significant peaks and pitsFind significant peaks and pits

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Gaussian Kernel Filter Standard deviation value Standard deviation value Smooth random differencesSmooth random differences Enhance clustersEnhance clusters Discrete convolution using mask of kernel filter weights Discrete convolution using mask of kernel filter weights Maximum distance Maximum distance Percentage of maximum valuePercentage of maximum value

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Critical Value Approximation Defined: Defined: For 95% significancy Clusters if higher than M* Clusters if higher than M* Valid if Valid if Area smaller than 10,000Area smaller than 10,000 Even if greater Even if greater Only slightly smaller critical valueOnly slightly smaller critical value

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Correlation with Terrain Morphology Slope Slope Hypothesis: Mostly due to positional inaccuracyHypothesis: Mostly due to positional inaccuracy Curvature Curvature Maximum slope directionMaximum slope direction Perpendicular to maximum slope directionPerpendicular to maximum slope direction Hypothesis: Related to resolutionHypothesis: Related to resolution

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Case Study – Colima Volcano DEM DEM Arizona Image ArchiveArizona Image Archive SRTMSRTM

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Available Digital Elevation Models Map references Map references Base maps: 1:50000 scale, UTM projection, ITRF92 datumBase maps: 1:50000 scale, UTM projection, ITRF92 datum ARIADEM: 60m resolution, UTM projection, NAD27 datumARIADEM: 60m resolution, UTM projection, NAD27 datum SRTMDEM: 3-arc second, WGS84 datumSRTMDEM: 3-arc second, WGS84 datum Reproject and resample to a 90 meter resolution UTM grid, ITRF92 Reproject and resample to a 90 meter resolution UTM grid, ITRF92

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

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

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Gaussian Kernel Std. Dev: Std. Dev:2 Distance: Distance:95% Legal program (SPRING) Legal program (SPRING)

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow SimulationClusters M*: M*: 4.739

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Correlation with Terrain Morphology Linear correlation coefficient of variation and terrain morphology Linear correlation coefficient of variation and terrain morphology Terrain Morphology Parameter Correlation Coefficient Correlation t-score, N=95866, Critical t = ±1.98 for 95% significance Slope Profile Curvature Tangential Curvature However… Slopes and coefficient of variation are all positive Curvatures can be positive and negative

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Correlation with Terrain Morphology Correlation in whole grid: coefficients of variation and slope is significant Correlation in whole grid: coefficients of variation and slope is significant

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Correlation with Terrain Morphology Linear correlation difference between two DEMs and terrain morphology Linear correlation difference between two DEMs and terrain morphology All grid cells Correlation in clustered areas Terrain Morphology Parameter Correlation Coefficient Correlation t-score, N=95866, Critical t = ±1.98 for 95% significance Slope Profile Curvature Tangential Curvature

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Correlation with Terrain Morphology Correlation in whole grid: differences in elevation and slope is significant Correlation in whole grid: differences in elevation and slope is significant

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Correlation with Terrain Morphology Linear correlation: mean difference and mean morphology in clusters Linear correlation: mean difference and mean morphology in clusters Only tangential curvature has significant linear correlation Terrain Morphology Parameter Correlation Coefficient Correlation t-score, N=117, Critical t = ±1.98 for 95% significance Slope Profile Curvature Tangential Curvature

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Scatterplot of differences in elevation and tangential curvature

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Differences between predicted and observed differences at clusters

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Discussions Difference in elevation and tangential curvature inside clusters Difference in elevation and tangential curvature inside clusters Significant linear correlationSignificant linear correlation Differences between predicted and observed Differences between predicted and observed Std. deviation: 25.5 mStd. deviation: 25.5 m Greater than 2 std. deviation: 9 clustersGreater than 2 std. deviation: 9 clusters

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Discussions Clusters (2std. dev) Clusters (2std. dev) At edgesAt edges Too smallToo small Close to volcano – erosion and depositionClose to volcano – erosion and deposition Other clusters Other clusters Ridge and valleyRidge and valley

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Summary Uncertainty of DEM can be defined when other data is available Uncertainty of DEM can be defined when other data is available Correlation of uncertainty measure and slope at individual cells: Correlation of uncertainty measure and slope at individual cells: Miss knowledge about DEM parameters that affects uncertaintyMiss knowledge about DEM parameters that affects uncertainty Define significant regions of high uncertainty using a cluster detection method Define significant regions of high uncertainty using a cluster detection method Influence of slope and random variations are diminishedInfluence of slope and random variations are diminished

GeoInfo 2004 Uncertainty in Digital Elevation Data Used for Geophysical Flow Simulation Summary Significant correlation between mean uncertainty and mean terrain tangential curvature Significant correlation between mean uncertainty and mean terrain tangential curvature Extreme tangential curvature values along ridge and valley lines Extreme tangential curvature values along ridge and valley lines DEM can be modified in these regions with additional dataDEM can be modified in these regions with additional data Importance of existence of global coverage DEM - SRTM Importance of existence of global coverage DEM - SRTM