Digital Elevation Model Error in Terrain Analysis

Digital elevation models (DEMs) have been an important topic in geography and surveying sciences for decades due to their geomorphological importance as the reference surface for gravita-tion-driven material flow, as well as the wide range of uses and applications. When DEM is used in terrain analysis, for example in automatic drainage basin delineation, errors of the model collect in the analysis results. Investigation of this phenomenon is known as error propagation analysis, which has a direct influence on the decision-making process based on interpretations and applications of terrain analysis. Additionally, it may have an indirect influence on data acquisition and the DEM generation. The focus of the thesis was on the fine toposcale DEMs, which are typically represented in a 5-50m grid and used in the application scale 1:10 000-1:50 000. The thesis presents a three-step framework for investigating error propagation in DEM-based terrain analysis. The framework includes methods for visualising the morphological gross errors of DEMs, exploring the statistical and spatial characteristics of the DEM error, making analytical and simulation-based error propagation analysis and interpreting the error propagation analysis results. The DEM error model was built using geostatistical methods. The results show that appropriate and exhaustive reporting of various aspects of fine toposcale DEM error is a complex task. This is due to the high number of outliers in the error distribution and morphological gross errors, which are detectable with presented visualisation methods. In ad-dition, the use of global characterisation of DEM error is a gross generalisation of reality due to the small extent of the areas in which the decision of stationarity is not violated. This was shown using exhaustive high-quality reference DEM based on airborne laser scanning and local semivariogram analysis. The error propagation analysis revealed that, as expected, an increase in the DEM vertical error will increase the error in surface derivatives. However, contrary to expectations, the spatial au-tocorrelation of the model appears to have varying effects on the error propagation analysis depend-ing on the application. The use of a spatially uncorrelated DEM error model has been considered as a 'worst-case scenario', but this opinion is now challenged because none of the DEM derivatives investigated in the study had maximum variation with spatially uncorrelated random error. Sig-nificant performance improvement was achieved in simulation-based error propagation analysis by applying process convolution in generating realisations of the DEM error model. In addition, typology of uncertainty in drainage basin delineations is presented.Lukuisten käyttötarkoitusten ja sovellusmahdollisuuksien ansioista digitaaliset korkeusmallit, eli maan pinnanmuotoja esittävät numeeriset mallit, ovat olleet tutkimuksen kohteena maantieteen ja maanmittaustieteiden aloilla vuosikymmeniä. Kun korkeusmallia käytetään maastoanalyysissä, esimerkiksi automaattisessa valuma-aluerajauksessa tai tulvavaarakartoituksessa, mallissa olevat virheet kasautuvat analyysin tulokseen. Virheenkasautumisanalyysillä on suora vaikutus maastoanalyysipohjaiseen päätöksentekoon ja lisäksi sen avulla voidaan vaikuttaa epäsuorasti korkeusmallin luontiin tähtäävään tiedonkeruuseen sekä mallin tuottavien laskentamenetelmien käyttöön. Väitöskirja esittää kolmevaiheisen prosessin korkeusmallipohjaisten maastoanalyysien virheenkasautumisen tutkimiseksi. Työssä käytetyissä korkeusmalleissa maanpinnan korkeudet esitettiin 10-30m hilassa tyypillisen sovellusmittakaavan ollessa 1:10 000-1:50 000. Prosessiin kuuluu menetelmiä korkeusmallien karkeiden virheiden visuaaliseen havaitsemiseen, virheen tilastolliseen karakterisointiin ja virhemallin luontiin, analyyttiseen ja simulaatio-pohjaiseen virheenkasautumisanalyysiin sekä virheenkasautumisanalyysin tulosten tulkintaan. Virhemallin luonnissa käytettiin spatiaalisen tilastotieteen menetelmiä. Tulokset osoittivat, että tutkittujen korkeusmallien virheiden kuvaaminen ja mallintaminen kattavasti oli haastavaa. Tämä johtui mallien virhejakauman poikkeavien havaintojen suuresta määrästä sekä morfologisista karkeista virheistä, joiden visuaaliseksi havaitsemiseksi esitetään jakojäännöskarttojen käyttöä. Lisäksi korkeusmallien virheiden globaali karakterisointi osoittautui karkeaksi yleistykseksi todellisuudesta johtuen virheen paikkariippuvuudesta. Tämä osoitettiin empiirisesti käyttäen vertausaineistona koko tutkimusalueen kattavaa topografiseen laserkeilaukseen perustuvaa korkeusmallia. Virheenkasautumisanalyysit osoittivat, että korkeusmallin virheen kasvaessa myös maastoanalyysien virheet kasvoivat ja joissain tapauksissa virheiden kasvu oli huomattavasti ennalta arvioitua suurempaa. Virheen spatiaalisen autokorrelaation vaikutus analyysituloksiin oli sovellusriippuvaa. Spatiaalisesti autokorreloimatonta virhemallia on yleisesti pidetty pahimman tapauksen huomioonottavana mallina, mutta millään työssä käsitellyistä maastoanalyyseistä suurin epävarmuus ei liittynyt autokorreloimattomaan virhemalliin. Simulaatiopohjaisen virheenkasautumisanalyysin toteutuksessa sovellettu prosessikonvoluutiomenetelmä mahdollistaa korkeustiedon epävarmuuden huomioonottavien vuorovaikutteisten paikkatietopalvelujen luomisen. Esimerkkeinä mainittakoon jääpatojen aiheuttama tulvavaarakartoitus ja vaarallisten aineiden kuljetuksiin liittyvät onnettomuudet, joissa nestemäisten kemikaalien leviämisestä ympäristöön on saatava nopeasti luotettava kuva mikrotason valuma-alueanalyysillä

Spectral filtering as a method of visualising and removing striped artefacts in digital elevation data

Spectral filtering was compared with traditional mean spatial filters to assess their ability to identify and remove striped artefacts in digital elevation data. The techniques were applied to two datasets: a 100 m contour derived digital elevation model (DEM) of southern Norway and a 2 m LiDAR DSM of the Lake District, UK. Both datasets contained diagonal data artefacts that were found to propagate into subsequent terrain analysis. Spectral filtering used fast Fourier transformation (FFT) frequency data to identify these data artefacts in both datasets. These were removed from the data by applying a cut filter, prior to the inverse transform. Spectral filtering showed considerable advantages over mean spatial filters, when both the absolute and spatial distribution of elevation changes made were examined. Elevation changes from the spectral filtering were restricted to frequencies removed by the cut filter, were small in magnitude and consequently avoided any global smoothing. Spectral filtering was found to avoid the smoothing of kernel based data editing, and provided a more informative measure of data artefacts present in the FFT frequency domain. Artefacts were found to be heterogeneous through the surfaces, a result of their strong correlations with spatially autocorrelated variables: landcover and landsurface geometry. Spectral filtering performed better on the 100 m DEM, where signal and artefact were clearly distinguishable in the frequency data. Spectrally filtered digital elevation datasets were found to provide a superior and more precise representation of the landsurface and be a more appropriate dataset for any subsequent geomorphological applications

Kinematic analysis of the Pakuashan fault tip fold, west central Taiwan: Shortening rate and age of folding inception

The Pakuashan anticline is an active fault tip fold that constitutes the frontal most zone of deformation along the western piedmont of the Taiwan Range. Assessing seismic hazards associated with this fold and its contribution to crustal shortening across central Taiwan requires some understanding of the fold structure and growth rate. To address this, we surveyed the geometry of several deformed strata and geomorphic surfaces, which recorded different cumulative amounts of shortening. These units were dated to ages ranging from ~19 ka to ~340 ka using optically stimulated luminescence (OSL). We collected shallow seismic profiles and used previously published seismic profiles to constrain the deep structure of the fold. These data show that the anticline has formed as a result of pure shear with subsequent limb rotation. The cumulative shortening along the direction of tectonic transport is estimated to be 1010 ± 160 m. An analytical fold model derived from a sandbox experiment is used to model growth strata. This yields a shortening rate of 16.3 ± 4.1 mm/yr and constrains the time of initiation of deformation to 62.2 ± 9.6 ka. In addition, the kinematic model of Pakuashan is used to assess how uplift, sedimentation, and erosion have sculpted the present-day fold topography and morphology. The fold model, applied here for the first time on a natural example, appears promising in determining the kinematics of fault tip folds in similar contexts and therefore in assessing seismic hazards associated with blind thrust faults

On the uncertainty of stream networks derived from elevation data: the error propagation approach

DEM error propagation methodology is extended to the derivation of vector-based objects (stream networks) using geostatistical simulations. First, point sampled elevations are used to fit a variogram model. Next 100 DEM realizations are generated using conditional sequential Gaussian simulation; the stream network map is extracted for each of these realizations, and the collection of stream networks is analyzed to quantify the error propagation. At each grid cell, the probability of the occurrence of a stream and the propagated error are estimated. The method is illustrated using two small data sets: Baranja hill (30 m grid cell size; 16 512 pixels; 6367 sampled elevations), and Zlatibor (30 m grid cell size; 15 000 pixels; 2051 sampled elevations). All computations are run in the open source software for statistical computing R: package geoR is used to fit variogram; package gstat is used to run sequential Gaussian simulation; streams are extracted using the open source GIS SAGA via the RSAGA library. The resulting stream error map (Information entropy of a Bernoulli trial) clearly depicts areas where the extracted stream network is least precise – usually areas of low local relief and slightly convex (0–10 difference from the mean value). In both cases, significant parts of the study area (17.3% for Baranja Hill; 6.2% for Zlatibor) show high error (H>0.5) of locating streams. By correlating the propagated uncertainty of the derived stream network with various land surface parameters sampling of height measurements can be optimized so that delineated streams satisfy the required accuracy level. Such error propagation tool should become a standard functionality in any modern GIS. Remaining issue to be tackled is the computational burden of geostatistical simulations: this framework is at the moment limited to small data sets with several hundreds of points. Scripts and data sets used in this article are available on-line via the www.geomorphometry.org website and can be easily adopted/adjusted to any similar case study

Modeling seismic wave propagation and amplification in 1D/2D/3D linear and nonlinear unbounded media

To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the finite volume method, etc. All these methods have various advantages and drawbacks. The amplification of seismic waves in surface soil layers is mainly due to the velocity contrast between these layers and, possibly, to topographic effects around crests and hills. The influence of the geometry of alluvial basins on the amplification process is also know to be large. Nevertheless, strong heterogeneities and complex geometries are not easy to take into account with all numerical methods. 2D/3D models are needed in many situations and the efficiency/accuracy of the numerical methods in such cases is in question. Furthermore, the radiation conditions at infinity are not easy to handle with finite differences or finite/spectral elements whereas it is explicitely accounted in the Boundary Element Method. Various absorbing layer methods (e.g. F-PML, M-PML) were recently proposed to attenuate the spurious wave reflections especially in some difficult cases such as shallow numerical models or grazing incidences. Finally, strong earthquakes involve nonlinear effects in surficial soil layers. To model strong ground motion, it is thus necessary to consider the nonlinear dynamic behaviour of soils and simultaneously investigate seismic wave propagation in complex 2D/3D geological structures! Recent advances in numerical formulations and constitutive models in such complex situations are presented and discussed in this paper. A crucial issue is the availability of the field/laboratory data to feed and validate such models.Comment: of International Journal Geomechanics (2010) 1-1

Shape from Shading法を用いた天体表面の斜面推定に関する研究

学位の種別: 修士University of Tokyo(東京大学

Quality Assessment of Hydrogeomorphological Features Derived from Digital Terrain Models

Digital terrain models (DTM) provide a model for representing the continuous earth elevation surface that can contain errors introduced by the main phases of generation and modelling. Uncertainty of the model is rarely considered by users. Assessment of uncertainty require information on the nature, amount and spatial structure of the errors. DTMs of di®erent original resolution were compared in order to assess the quality of derived hydrological and morphological features. SRTM dataset with resolution of 100m, DEM dataset mosaic from various sources with a resolution of 60m and ASTER derived dataset with a resolution of 30m were used. The error propagation was modelled with a stochastic approach. The probabilistic distribution of extracted hydrological features was drawn considering the spatial structure of errors in the datasets. The features considered were stream network and watershed divides net. The distribution of the Strahler order of the features was studied. An analysis of the overall probability of features extracted from variously prepared datasets was carried in order to get information on where is the most probable stream network or watershed divides net.JRC.H.6-Spatial data infrastructure

A finite element framework for modeling internal frictional contact in three-dimensional fractured media using unstructured tetrahedral meshes

AbstractThis paper introduces a three-dimensional finite element (FE) formulation to accurately model the linear elastic deformation of fractured media under compressive loading. The presented method applies the classic Augmented Lagrangian(AL)-Uzawa method, to evaluate the growth of multiple interacting and intersecting discrete fractures. The volume and surfaces are discretized by unstructured quadratic triangle-tetrahedral meshes; quarter-point triangles and tetrahedra are placed around fracture tips. Frictional contact between crack faces for high contact precisions is modeled using isoparametric integration point-to-integration point contact discretization, and a gap-based augmentation procedure. Contact forces are updated by interpolating tractions over elements that are adjacent to fracture tips, and have boundaries that are excluded from the contact region. Stress intensity factors are computed numerically using the methods of displacement correlation and disk-shaped domain integral. A novel square-root singular variation of the penalty parameter near the crack front is proposed to accurately model the contact tractions near the crack front. Tractions and compressive stress intensity factors are validated against analytical solutions. Numerical examples of cubes containing one, two, twenty four and seventy interacting and intersecting fractures are presented