Using Airborne Laser Scanning for Improved HydraulicModels

Mandlburger, G. and C. Briese

Christian Doppler Laboratory ”Spatial Data from Laser Scanning and Remote Sensing”at the Institute of Photogrammetry and Remote Sensing, Vienna University of Technology, Austria.

E-Mail: gm@ipf.tuwien.ac.at

Keywords: Airborne laser scanning, DTM generation, DTM data reduction, CFD models, mesh generation

EXTENDED ABSTRACT

Due to recent flood events, risk assessment hasbecome a topic of highest public interest. Thedefinition of endangered or vulnerable areas isbased on numerical models of the water flow.The most influential input for such models is thetopography provided as a Digital Terrain Model of theWatercourse (DTM-W).

For capturing terrain data of inundation areasAirborne Laser Scanning (ALS) has become the primedata source. It combines cost efficiency, high degreeof automation, high point density of typically 1-10points per m2 and good height accuracy of less than15cm. For all these reasons ALS is particularlysuitable for deriving precise DTMs as basis forComputational Fluid Dynamic (CFD) models. Thequality of such models depends crucially on howwell vegetation or other off-terrain objects have beenremoved in the DTM generation process.

The task of removing off-terrain points from theALS measurements is commonly referred to asfiltering. Traditional laser scanners only supplyrange measurements to the reflecting objects and,thus, the filtering process has to rely on geometriccriteria. The latest generation of ALS systemsrecord the full backscattered waveform, from whichphysical quantities like echo width and backscattercross section can be derived. An advanced filteringtechnique based on the well established method ofrobust interpolation is presented exploiting the echowidth for a more robust and reliable classificationof the point cloud into ground and off-terrain pointsresulting in a more precise DTM-W. Besides filtering,exact sensor calibration, fine adjustment of ALS-stripdata, proper fusion of ALS and additional river beddata as well as elimination of random measurementerrors are important issues for generating a preciseDTM-W based on the ALS point cloud.

The higher DTM resolution provided by modernsensors comes along with an increased amount ofdata. Thus, a direct use of the high resolutionDTM-W as the geometric basis for CFD models is

impossible. Currently available mesh generators forCFD models basically focus on physical parametersof the calculation grid like angle criterion, aspectratio and expansion ratio. The detailed shape ofthe terrain as provided by modern ALS systems isoften neglected. A DTM data reduction approachis presented, considering both the physical aspectsmentioned above as well as the preservation ofrelevant terrain details. The method starts with aninitial TIN-approximation of the DTM comprisingstructure lines and a coarse grid. The TIN issubsequently refined by adding additional grid pointsuntil a certain height tolerance is met. A spatiallyadaptive data density, where terrain parts beingsensitive for the CFD model are mapped with moredetails than parts of minor importance, can beachieved by introducing individual height tolerancesin the iterative refinement process. In order to obtaina high quality computation grid the resulting surfaceapproximation is professionally conditioned to meetspecific hydraulic requirements.

Finally, practical results of CFD models based on dif-ferent geometry variants are presented and discussed.It will be shown that a very detailed description of thetopography can indeed be established in CFD models,resulting in more realistic flow simulations and moreprecise boundaries of potential flooding areas. Anexample is shown in Figure 1.

Figure 1. Digital flood risk map of the riverDrau (Carinthia/Austria) resulting from a 2D-CFD-simulation based on a high resolution ALS-DTM

1 INTRODUCTION

ALS has become the prime data source for capturingtopographic data in the last years. It combines costefficiency, high degree of automation, remarkableheight precision and high point density. ALS isespecially well suited for capturing inundation areasas well as river banks under low flow conditions andis therefore widely used as data basis for CFD modelstoday.

However, the application of ALS poses problems aswell. Contrary to traditional manual data acquisitiontechniques like stereo-photogrammetry or tachymetry,ALS comprise both ground points and off-terrainpoints on buildings, vegetation, power lines, etc.The quality of the derived DTM and, consequently,the quality of subsequent CFD modeling dependscrucially on how well off-terrain points have beeneliminated within the filtering process. Standard ALSsystems provide only range measurements (typicallyfirst and last echo per pulse) and therefore the filteringhas to rely on geometric criteria only. In addition, therecent generation of laser scanners also provides thefull backscattered waveform, which allows to deductphysical quantities like amplitude, echo width andbackscatter cross section per echo. The combinationof geometric criteria and physical echo parametersimproves the reliability of the filtering (Doneus et al.2007) and, thus, enhances the DTM. Another issuebesides filtering is the fusion of ALS and river beddata. This involves the interpolation of river bed crosssections, the determination of a water surface modeland the derivation of the water-land-boundary.

Nowadays, most CFD models are solved using afinite element or finite volume approach on the basisof unstructured geometries, i.e. a computation gridbased on irregularly distributed points. Many meshgenerators are available which build up a networkof nodes, edges and polygonal faces covering theentire project area. These mesh generators considerhydraulic parameters like angle criterion and aspectratio, but normally disregard the detailed topography.The heights are mapped to the hydraulic grid aposteriori. On the other hand, the direct use of thehigh resolution ALS-DTM as computation grid isimpossible due to the enormous amount of data.

Therefore, the ultimate goal of this work is to derivea high quality computation grid considering hydraulicrequirements as well as geometric details. In a firststep the DTM is thinned out based on a maximumheight threshold using an adaptive TIN-refinementapproach. The algorithm preserves surface details inrough areas and removes as much points as possiblein flat areas. The approximating TIN is analyzedin a subsequent data conditioning step, where theadherence of certain mesh quality parameters like

aspect and expansion ratio but also the alignment ofthe mesh with respect to the principal flow directionare verified. As necessary, additional nodes areadded to the TIN resulting in a grid, which fulfillsthe requirements of a good hydraulic computationgrid additionally preserving surface details. In thatsense the work at hand has to be regarded asinterdisciplinary between the fields of geodesy andhydraulics.

This paper is structured as follows. In section 2 somebasic terms necessary for the general understandingare introduced. Section 3 describes the applieddata processing methods (DTM-W generation, datareduction and data conditioning). In section 4 someexamples of practical CFD simulations are presentedand the results using different variants of computationgrids are discussed. Finally, the basic findings of thework are summarized in section 5.

2 DEFINITIONS

Since this paper addresses readers from differentfields, a short introduction of the terms used is givenin this section.

The processing described in this work starts withthe ALS point cloud from which a DTM is derived.The DTM is regarded as a continuous descriptionof the earth’s surface, mathematically expressedas bivariate function z = f(x, y). Traditionaldata acquisition methods like terrestrial surveying(Kahmen and Faig 1988) or photogrammetry (Kraus2007) provide rather few discrete points or lines onthe ground. ALS data sets, in contrast, contain upto 10 points per m2, some of which are reflectedfrom the bare ground but others from natural orartificial objects (vegetation, buildings, power lines,etc.). Thus, the point cloud needs to be classifiedinto terrain and off-terrain points which is oftenreferred to as filtering. To derive the height at anydesired location, spatial interpolation techniques areemployed. Among a variety of approaches, the linearprediction (Kraus 2000) or the equivalent methodof Kriging (Journel and Huijbregts 1978) have tobe highlighted since random measurement errors areminimized during the interpolation based on statisticaldata properties. DTMs are most commonly storedas regular grids or TINs respectively. In contrast,a hybrid DTM structure based on a regular gridwith intermeshed break lines and spot heights (Kostliand Sigle 1986) combining the advantages of directaccess (grid) and flexibility (TIN) is favored in thiswork. This structure has proven to be well suitedfor storage of even countrywide DTMs (Warriner andMandlburger 2005). For applying in CFD models aspecialized DTM variant is necessary, namely the so-called watercourse DTM (DTM-W). It contains theinundation area, the banks, the river bed and all flow

Figure 2. Hybrid DTM-W of the river Saar (Germany)at Schoden derived from ALS points, echo soundercross sections and data of the power station

prohibiting buildings (Mandlburger and Brockmann2001). Since the near infrared signal typically used bylaser scanners does not penetrate water, it is necessaryto combine the ALS data with river bed data from echosounding or terrestrial surveying to get a DTM-W asit is shown in Figure 2.

As mentioned before, the DTM-W is the geometricbasis for CFD models describing the water flow.The mathematical and physical background ofsuch models are the momentum equations (Navier-Stokes differential equations), which are solved byaid of other physical fundamentals (energy andcontinuity equation) and empirical flow formulae(e.g. Manning-Strickler) using a finite element orfinite volume approach respectively. Therefore, theentire project area is approximated by a polygonalcomputation grid. Unstructured grids (i.e. mesheswith irregularly distributed nodes) are nowadayspreferred to structured grids, because the former allowbetter consideration of the topography. However,several criteria have to be fulfilled by the grid inorder to ensure both good computation performanceand physically reliable results. According to Ferzigerand Peric (2002) these are: angle criterion, aspectratio and expansion ratio. In a nutshell, small angles<10◦ should be avoided, the cells should be alignedto the principal flow direction, the aspect ratio shouldnot exceed 10 (optimum <3) and the expansion ratiomust not be greater than 3 (optimum <1.2). Besidesgeometry, the spatially varying flow resistances areanother input for hydraulic models. They are typicallyconsidered by applying certain roughness coefficientsto each grid cell. In practical flow simulations theCFD model is calibrated by adjusting the roughnesscoefficients until a satisfactory coincidence of modelresults and reality is achieved. It can often be observedthat a lack of geometric details in the hydraulicgrid is compensated by adaption of the roughnesscoefficients. Therefore, the next section describes amethod for constructing a high quality hydraulic grid,which considers topographic details as provided byALS-DTMs.

3 METHOD

3.1 DTM-W generation

The first step towards a topography-based hydraulicgrid is the determination of a precise DTM-W fromthe given ALS and river bed data. This impliesthe following steps: Modeling of break lines (Briese2004), filtering of the ALS point cloud, derivationof the water-land-boundary to split aquatic fromnon-aquatic domain (Mandlburger and Brockmann2001) and densification of river bed cross sectionsconsidering the curved progression of the river axis(Mandlburger 2000). Not all the mentioned topicscan be discussed in this paper in detail but thecomplete process is described in the author’s Ph.D.(Mandlburger 2006).

In the following, the filtering of the ALS pointcloud is focused on since the removal of vegetationand other off-terrain points is crucial for the qualityof subsequent hydraulic modeling. In the past,many different solutions for filtering ALS datawere published (Sithole and Vosselman 2003). Allthese approaches have in common that they relyonly upon geometric criteria (typically the heightrelation of adjacent points) for the elimination ofoff-terrain points. The recent generation of laserscanners, however, provides the full waveform of thebackscattered signal (c.f. Figure 3) and enables thederivation of additional attributes per echo like theamplitude or the echo width in the postprocessingafter the flight mission (Wagner et al. 2006).The robust interpolation approach (Kraus and Pfeifer1998) developed at the Institute of Photogrammetryand Remote Sensing, Vienna, allows a smartconsideration of these additional echo attributes inthe filtering process. The principal idea of robust

Figure 3. Recorded waveform (black dots) and echoattributes derived by Gaussian decomposition; Echoparameters: distance Ri, amplitude Ai and the echowidth EWi

Figure 4. : DTM generation by robust interpolationwith a-priori weights determined from the echo widthdemonstrated by means of a profile; Black dots:Last echo point cloud, Red surface: DTM withoutconsidering individual a-priori weights. Greensurface: Improved DTM by robust interpolation withecho width dependent a-priori weights

interpolation is to start with a surface to which allALS points contribute equally, i.e. all points have thesame weight. Subsequently the weight of each pointis adapted according to its vertical distance form theaveraged surface, where points above the surface getsmaller weights. The additional echo attributes fromfull waveform signal processing can now be used toassign a-priori point weights, thus, speeding up theiterative filtering process and increasing the reliabilityof the classification (Mandlburger et al. 2007). Figure4 shows the result of such an advanced robust filteringfor a terrain profile using the echo width (EW ) forthe determination of a-priori point weights. The echowidth describes the height variation of different targets(e.g. different branches of a tree) contributing to asingle echo. In vegetation areas a widening of the echowidth can be observed. Thus, points with a small echowidth should get higher a-priori weights than pointswith a high echo width. This is achieved by applyingthe weight function w(EW ) = 1

1+a EW b , wherethe coefficients a and b define how fast the weightfunction drops to zero. As can be seen in Figure4, the DTM determined without a-priori weights istoo high in areas covered by low vegetation due tothe fact that the last echo is a mixture of reflectionsof small objects at different ranges above the DTMsurface. Using robust interpolation with echo widthdependent a-priori weights leads to a more reliableDTM, especially near the road in the middle of theprofile. It is less affected by reflections in lowvegetation.

3.2 Data reduction

Most implementations of CFD models are restrictedwith respect to the maximum number of cells in thehydraulic grid (usually <500.000). By contrast, ALS-DTMs typically consist of millions of points andtherefore surface simplification becomes inevitable.

According to Heckbert and Garland (1997) mainlyregular grid algorithms, decimation and refinementtechniques are in use. The regular grid approaches arewidespread, simple and fast, but they are not adaptiveand produce poor approximation results. Betterapproximation quality can be achieved by applyingdecimation and refinement methods based on generaltriangulation algorithms like Delaunay triangulation.Decimation methods work from fine-to-coarse andare not suited for processing large high resolutionALS-DTMs since they require a triangulation of theentire point set. Refinement methods represent acoarse-to-fine approach starting with a minimal initialapproximation. In each subsequent pass one or morepoints are added as vertices to the triangulation untilthe desired approximation tolerance is met or thedesired number of vertices is used.

The performance of DTM data reduction is highlyinfluenced by the existence of systematic andrandom measurement errors. Therefore, refinementapproaches as described above based on the originalALS point cloud directly are not the first choice.Systematic errors have to be removed first by exactsensor calibration and fine adjustment of the ALS-strip data. Furthermore, random measurement errorsof the ALS points should be minimized by applying aDTM interpolation strategy with measurement noisefiltering capabilities. Good results can be achievedusing linear prediction or Kriging respectively. Highreduction rates can only be obtained for DTMs free ofsystematic and random errors.

In contrast to the previously mentioned refinementapproach, which relies on the original point cloud,the subsequently presented refinement frameworkuses the filtered hybrid DTM (regular grid withbreak lines, structure lines and spot heights) asinput (Mandlburger 2006). The basic parameters forthe data reduction are a maximum height tolerance∆zmax and a maximum planimetric point distance∆xymax. The latter avoids triangles with too longedges and narrow angles. The algorithm starts withan initial approximation of the DTM comprisingall line information and a coarse regular grid (cellsize=∆xymax=∆0), which are triangulated using aconstrained Delaunay triangulation. Each ∆0-cell issubsequently refined by iteratively inserting additionalDTM grid points until the height tolerance ∆zmax ismet. These additional vertices can either be insertedhierarchically or irregularly. In case of hierarchicaldivision, the grid cell is divided into four parts in eachpass, if a single grid point within the regarded areaexceeds the maximum tolerance ∆zmax resulting ina quadtree-like data structure. By contrast only thegrid point with the maximum deviation is insertedwhen using irregular division. Higher compressionrates (up to 99% in flat areas) can be achieved withirregular point insertion, whereas the hierarchical

(a) Original hybrid DTM-W, grid width: 2m

(b) Adaptive TIN, hierarchic division, ∆zmax=0.25m,compression rate: 83%

(c) Adaptive TIN, irregular division, ∆zmax=0.25m,compression rate: 94%

Figure 5. DTM-W of the river Drau(Carinthia/Austria); High resolution DTM-W (a)and approximating TINs (b) and (c)

mode is characterized by a more homogeneous datadistribution. Using the terms of hydraulics, thehierarchic division produces an adaptive cartesian gridwhereas irregular division yields an unstructured grid.

Furthermore, the described framework is flexibleconcerning the reduction criterion. The decisionto insert a point can be based on the analysis oflocal surface slope and curvature derived from theDTM or on the vertical distance between the DTMpoint and the approximating TIN. A comparisonof an original high resolution DTM-W with itsapproximating adaptive TIN variants using hierarchicand irregular division is shown in Figure 5.

3.3 Data conditioning

What has been achieved so far is an approximationof the DTM with respect to geometric criteria only.However, the resulting TIN is not an appropriatecomputation grid for hydraulic modeling since nophysical requirements have been considered.

Therefore, the next step is to condition the grid andto adapt the data distribution for special zones ofinterest. From a modeling point of view the followingzones can be differentiated: River bed, river bank,surrounding and extended inundation area. The riverbed is characterized by a permanent flow of water.The flow direction - approximated by the progressionof the river axis - is the predominant direction offorce. Thus, to achieve physically reliable results,the cells of the computation grid have to be alignedalongside the current within the domain of the riverbed. Quadrilateral cells with the longer sides in andthe shorter ones perpendicular to the flow directionproportional 3:1 (optimum aspect ratio) have turnedout to produce good modeling results. The sameapplies for the river bank.

Beyond the embankment the water flow is no longerstrictly parallel, thus, irregular data distribution asdescribed in the previous subsection is appropriate.However, the river bank surroundings should bemodeled in more detail than remote or elevatedareas since they are more endangered by potentialflood events. Height approximation errors of afew centimeters can well have severe effects onthe adjacent estates, which may be of particularimportance for residential areas. With increasingdistance from or height above the river bankthe influence of the topography on the resultsof the CFD model decreases, thus, allowing acoarser approximation of the terrain. Within thedata reduction process the different demand ofapproximation precision can be controlled by spatiallyvariable maximum height tolerances. Mathematicallythis can be expressed as ∆zmax = f(x, y). Distancesfrom the river bank or relative height differencesrespectively can be used to control the tolerances, buta simple zonal model has turned out to be best suited.The delineation of the different accuracy zones can bederived from a pilot survey (e.g. a preliminary 1D-CFD simulation), from DTM visualizations like hillshadings, from existing maps or the like.

That way, a computation grid with a spatially adapteddata distribution and approximation accuracy isderived from the high resolution ALS-DTM accordingto the needs for hydraulic modeling. For the resultingTIN the adherence of the quality criteria (angle, aspectand expansion ratio) has to be checked in a last step.Several tests with real-world data have shown, thatthe angle criterion and the aspect ratio are within

Figure 6. Hydraulic grid derived from a highresolution ALS-DTM considering both geometric andphysical requirements

the valid range in the majority of cases using thedescribed method. However, expansion ratios of >3can be observed occasionally. From a geometric pointof view this is a desired property of the reductionalgorithm since it demonstrates a rapid transition fromflat to rough terrain parts within the approximatedsurface. This shows clearly that it is necessary tocombine geometric as well as physical aspects in orderto obtain a high quality computation grid. A smallsection of a final hydraulic grid is shown in Figure 6.

4 RESULTS

Based on the methods described in the previoussection computation grids were derived for a sectionof the river Lainsitz in Lower Austria (ordinal number5 according to Horton-Strahler, average slope 0.25%,meandering river type). The last echoes of an ALSflight campaign (point density: 1 pt/m2) and riverbed cross sections measured with terrestrial dGPS(profile distance: 100 m) were used to derive a highresolution DTM-W (grid width: 1 m) as described insection 3.1. Additionally, break lines (bridge piers)were integrated in the DTM-W and the data reductionand conditioning techniques explained in sections 3.2and 3.3 were applied to the DTM-W. The resultingcomputation grid was used as the geometric basisfor subsequent CFD modeling. The results of flowsimulations based on two different geometry variantsare shown in Figure 7, where the parts to the north ofthe river are of special interest.

The water levels presented in Figure 7a were obtainedusing a very simple regular grid reduction of theALS-DTM. However, the application of such poorreduction techniques is still popular. It can clearly beseen that the detailed shape of the topography (c.f. theunderlying hill shading) is insufficiently representedin the computation grid. Relevant flow prohibiting orflow enabling features like the roadway and the ditch

are not represented in the surface approximation and,thus, the estimated water levels are incorrect, as AreaA is flood-affected rather than the correct Area B. Bycontrast, the results shown in Figure 7b are based onan elaborately reduced and conditioned computationgrid as described in sections 3.2 and 3.3. As in theformer example, the river bed and the embankment aremodeled using elongated quadrilaterals aligned to theriver axis. Furthermore, the surrounding river forelandincluding the roadway and the ditch is approximatedvery detailed (∆zmax=10 cm) and less geometricdetails are provided in more distant and elevated areas.Figure 7b shows that the roadway acts as an exact flowbarrier whereas a confined run-off is enabled throughthe narrow ditch. The availability of geometric detailsallows a more realistic simulation of the water flowand consequently a more precise determination ofinundated areas.

Besides the water depth, CFD models also provideadditional flow parameters like flow velocity and flowdirection. Figure 8 shows a comparison of these

Area A

Area B

flow d

irectio

n

roadway

ditch

ditch

water depth [m]:

0.01

3.00

1.00

2.00

(a) regular 16m-grid, river bed: cells aligned to the flowdirection

roadway

ditch

ditch

water depth [m]:

0.01

3.00

1.00

2.00

(b) adaptive TIN, ∆zmax=variable=zone-dependent, riverbed: cells aligned to the flow direction

Figure 7. Water depths for high flow conditions (HQ5,30m3/s) resulting from a 2D-CFD-simulation basedon the geometry variants (a) and (b); Data: riverLainsitz (Lower Austria)

flow velocity [m/s]:

0.01

0.30

0.60

0.90

1.50

1.20

(a) adaptive TIN, ∆zmax=const=20cm, no additional dataconditioning

flow velocity [m/s]:

0.01

0.30

0.60

0.90

1.50

1.20

(b) adaptive TIN, ∆zmax=variable=zone-dependent, riverbed: cells aligned to flow direction

Figure 8. Flow vectors and velocity distribution formean flow conditions (MQ, 2.2m3/s) resulting froma 2D-CFD-simulation based on the geometry variants(a) and (b); Data: river Lainsitz (Lower Austria)

parameters again based on two different geometryvariants for a small section of the river Lainsitz. Thecomputation grid shown in Figure 8a was deductedfrom the ALS-DTM using the data reduction approachdescribed in section 3.2. It represents a correctapproximation of the high resolution DTM-W withrespect to a maximum vertical tolerance of 20cm.However, the cells are not aligned to the directionof the water flow resulting in an artificial geometricroughness. Consequently, the calculated flow vectorsand velocity distribution are implausible. In otherwords, to obtain a high quality hydraulic grid it isinsufficient to apply geometric criteria only. By farbetter results can be obtained using cell elementsaligned to the principal flow direction within the riverbed and embankment as can be seen in Figure 8b.

5 CONCLUSIONS

This paper has presented the potential of highresolution DTMs for improved hydraulic models. The

main goal of exploiting the full information providedby ALS can only be achieved by establishing acomplete processing chain from the raw ALS pointcloud, via a precise DTM to the well-conditionedhydraulic grid. The basic input for CFD modelsis a precise DTM of the watercourse free of anysystematic and random errors. This requires thoroughorientation of ALS-strip data, proper filtering of off-terrain points, correct fusion of ALS and additionalriver bed data and, finally, DTM interpolationincluding elimination of random measurement errors.An advanced approach for filtering ALS point cloudsbased on robust interpolation combining geometriccriteria and additional echo attributes derived fromfull waveform data analysis has been presented. Bymeans of the echo width it was shown that additionalecho attributes can very well be used to improve thereliability of the classification and the quality of theDTM especially in low vegetation areas.

Due to the enormous amount of data, the highresolution DTM-W cannot be directly used asgeometric basis for hydraulic modeling. A methodfor DTM data reduction by adaptive TIN-refinementwas presented, which preserves topographic detailsin rough areas and removes redundant points inflat terrain parts. Depending on the terrain typecompression rates of up to 99% can be achieved.In order to obtain a high quality computationgrid for CFD modeling special zones of hydraulicinterest and additional physical requirements (anglecriterion, aspect and expansion ratio) have to beconsidered. Thus, the preliminary TIN approximationis further improved by aligning the cells to theprincipal flow direction within the river bed andthe bank and by establishing a spatially adapteddata distribution within the inundation area in asubsequent conditioning step. That way, computationgrids considering both geometric details provided byhigh resolution ALS data and physical requirementscan be generated and successfully applied in CFDmodels. This result should be the initiation of a deepercollaboration between geodesists and hydrologists inorder to integrate the knowledge of both disciplinesfor an improved flood risk assessment.

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