magdalena.naparus@epfl.ch

Magdalena Năpăruş1,2, François Golay1, Mihai-Sorin Stupariu2, Ileana Pătru-Stupariu2

1LaSIG EPFL, 2CeLTIS - University of Bucharest

ongoing Swiss-Romanian research project (2013-2015), aiming to connect wind, terrain and vegetation modeling

cross-disciplinary approach consisting in coupling 3 tracks:

1. Large Eddy Simulation techniques

2. 3D digital terrain representations

3. Landscape models and vegetation patterns

1. Evaluating the response of the multi-resolution digital

elevation models within wavelets analysis

2. Triangulated Irregular Network vs. regular grid:

pros and cons for 3D analyses

3. Assessing and mapping of wind potential over

complex terrains

Wavelets: Mallat (1989) was defining and developping the current wavelet

transform; Datcu et al. (1996) used wavelets to estimate the fractal dimension of DEM; Beyer (2003) and Lashermes et al. (2007) extracted geomorphometric indicators (terrain inclination, curvature) from wavelet coefficients

DEM grid wavelets: Kalbermatten et al. (2010) realized a multi-scale analysis

of topographic features by using the wavelet transform

WTIN: Wu & Amaratunga (2003) introduced a new multi-resolution data

representation: the Wavelet Triangulated Irregular Network (WTIN). The model is based on second generation of wavelet theory (lifting schemes) and it is specially designed for geographical height field data

Defining the framework scale-driven processes

hierarchy of topographical features

Wavelets analysis – a tool for non-stationary signals comparing cell-based DEM format and TIN

constraints on input data availability and altgoritms

similar results ?

comparing study: Travers landslide from Swiss Jura Sample data processed both as regular grid and TIN

Regular matrix of interpolated

elevation data

Three different components:

Nodes – computational model

Mesh – network connection of nodes

Grid - representations with cells

First generation of wavelets transform

(Kalbermatten, 2011)

* Hereafter DEM grid

Relevant surface analysis layers to be used in the wavelet transform

LAS file

Plan curvature

Curvature DEM grid

Profile curvature

Slope

Finite set of points stored together with their elevation

No point pattern and point density could varie over domain

Any point will lie on a vertex, edge or in a triangle of the triangulation

Wavelet TIN (WTIN) – second generation of wavelets (lifting schemes)

(van Kreveld, 1997)

Relevant surface analysis layers to be used in the wavelet transform

Las file

Slope

TIN

curvature?????

TIN Curvature (van Kreveld, 1997)

TIN does not distinguish between plan and profile curvature…

v= convex curvature c = concave curvature f = flat

Every edge of TIN can be defined as convex, concave or flat: e.g. convex region: all incident ridges are convex saddle: incident triangles are different

Similar region are erased to obtain terrain partition

Delaunay polygons

The necessary condition for a perfect reconstruction of the original signal (DEM grid, TIN) Offer hierarchical classification of information depending on scale

Continuous WT- using a function with zero mean (Mallat, 2000)

WT= two dimensional signal (on each X, Y dimension the transform will be applied and it will result in 4 signals) Original DEM 1m res -> 2nd decomposition level -> DEM 4m res

Hurst coefficient

Hammond's landform classification

Geomorphological features extraction

DEM grid TIN

Suitable for direct use in scalable distributed GIS

May loose terrain accuracy and may change the related terrain attributes

(slope , curbature, aspect...) (Deng et al., 2006)

not suitable for direct use in scalable distributed GIS services because it does not have a natural multi-resolution structure

need althgoritms to efficient edge collapse/vertex split

(Yang et al, 2005)

1. Statistical analyses:

• Point-wise elements – based on elevation (compute mean, median, maximum, standard deviation)

- Challenge: slope, curvature

• Surface roughness – based on elevation, slope (Hurst coefficient)

- Challenge: slope, curvature

• Profile-based analyses – based on elevation (compute mean, median, maximum, standard deviation)

- Challenge: slope, curvature

2. Global autocorrelation:

• Moran’s coefficient, Geary’s ratio– based on elevation

- Challenge: slope, curvature

3. Slope to elevation distribution

• Bi-variate distribution of slope-elevation – (weighted linear regression)

- Challenge: other pairs: slope - curvature?

Characteristics DEM grid TIN

Variable resolution X Ѵ

X, Y location for surface details X Ѵ

Fast transform (linear filter) Ѵ Ѵ

Multi-resolution capability Ѵ Ѵ

Easy compression Ѵ Ѵ

Interpolation scheme suitable for GIS applications Ѵ Ѵ

Wavelet- based 3D geometric modeling technique X Ѵ

System resources Ѵ X

Developing a conceptual multi-resolution analysis framework for numerical experiments over complex terrains

Building TIN and DEM based on LiDAR data processing for two areas in Switzerland and Romania

Integrating land cover models / meteorological measurements into WTIN

WindLand project framework, 2013-2015

To create an unique modeling framework for DEM grid and TIN based on the previous research works

To identify all constraints and differences between the two terrain models

To integrate other types of data (land cover and meteorological measurements) in order to assess and map wind modeling over complex terrains (WindLand project)

Beyer, G. 2003. Terrain inclination and curvature from wavelet coefficients. Approximation formulae for the relief, Journal of Geodesy, 76:557-568.

Datcu, M., Luca, D., Seidel, K. 1996. Wavelet-based digital elevation model analysis, Proceedings of the 16th EARSeL Symposium: Integrated Applications for Risk Assessment and Disaster Prevention for the Mediterranean, Malta, pp. 283–290.

Deng, Y., Wilson, J. and Bauer, B. 2007. DEM resolution dependencies of terrain attributes across a landscape. International Journal of Geographical Information Science, 21(2): 187–213.

Dikau R. 1989.The application of a digital relief model to landform analysis in geomorphology. In: Raper, J. (Ed.): Three dimensional application in Geographic Information Systems, Taylor & Francis, p.51-77.

Kalbermatten, M., Van De Ville, D., Turberg, P., Tuia, D., and Joost, S., 2011. Multiscale analysis of geomorphological and geological features in high resolution digital elevation models using the wavelet transform. Geomorphology, 138(1):352-363.

Lashermes, B., Foufoula-Georgiou, E., Dietrich, W.E. 2007. Channel network extraction from high resolution topography using wavelets, Geophysical Research Letters 34.

Mallat, S. 1989. A theory for multiresolutional signal decomposition:The wavelet representation, IEEE Trans. Pattern Analysis And Machine Intelligence, vol. 31, No.7, pp. 674-693.

Stupariu, M.S., Patru-Stupariu, I., Cuculici R. 2010. Geometric approaches to computing 3D landscape metrics. Landscape Online 24:1-12.

Unser, M., Blu, T., 1999. Construction of fractional spline wavelet bases. Proceedings of the Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing, VII, pp. 551–560.

van Kreveld, M. 1997. Digital elevation models and TIN algorithms, Algorithmic Foundations of Geographic Information Systems, 37-78,Springer Berlin Heidelberg.

Wu, J., and Amaratunga, K., 2003. Wavelet triangulated irregular networks. International Journal of Geographical Information Science, 17:273-289.

Yang, B., Shi, W. and Li, Q. 2005. An integrated TIN and Grid method for constructing multi-resolution digital terrain models. International Journal of geographical Information Science, 19(10): 1019-1038.

Project collaborators and partners: FERNANDO PORTÉ-AGEL (WIRE) ALEXANDRE BUTTLER (ECOS) ALEXANDER PERINGER (ECOS)