Multiscale analysis of high resolution digital elevation models using the wavelet transform

At the end of the nineties the emergence of high resolution (1 m) digital elevation models (DEMs) settled the context of high precision geomorphological analysis. These new elevation models permitted to reveal structures that remained heretofore undetectable. Earth scientists henceforth benefit from a field of analysis with a textural richness that was never attained before. However, the complexity and the volume of the data reveal a series of questions and problems. The storage size has increased, the computational processes have become heavier, and the visual or digital interpretation has become more complex. Moreover, these new models make it possible to characterize and analyse much smaller phenomena than previously. "Traditional" DEMs with resolutions ranging from 10 m to 90 m can be used to analyse a valley or a hillside. Transposed to a cartographic scale, this corresponds at best to a 1 : 25 000 ratio. As for high resolution DEMs, they show much more detailed structural levels and can be used to analyse geomorphological features of 2 – 3 meters, this corresponding to scales ranging from 1 : 10 000 to 1 : 1 000. Yet, in the abundance offered by this growing resolution, large geomorphological structures are still present, including the finer structures. They are even the actuators of processes relevant to larger cartographic scales. Consequently, high resolution DEMs contain a multitude of structures, which exist throughout their interactions with other structures at other scales. This is the context of the present study. Geomorphometry – the quantitative counterpart of exploratory geomorphology – permits to explore and quantify a wide range of shapes and terrain indicators. At higher resolution however, the methods of this discipline can hardly be used. Geomorphometrical methods are based on a geometric model (a quadratic surface) and few of these methods can be applied it in a multiscale context. Furthermore inappropriate techniques are frequently used, hence the idea to move to a multiscale approach called the wavelet transform. The latter had previously been explored by few researchers within the geomorphometry community, but never thoroughly to micro- and to mesoscales. Due to the non-stationarity of DEMs, the wavelet transform was preferred to the Fourier transform in order to decompose DEMs into multiscale spaces. This facilitates a coherent navigation from scale to scale, but also makes new scale specific phenomena emerge for different frequencies. The wavelet transform is a technique widely used in image analysis. It allows decomposing a signal according to its frequency components, but also according to the position of the frequencies in the signal. Its multi-scale capacity is an effective analytical tool in multiple domains. More particularly in geomorphology, structural components – specific to a specific phenomenon – are well determined in these sub-spaces specific to the scale continuum. Finally an in-depth analysis of the phenomena enabled us to understand processes and their and their phenomenological inter-dependencies. In order to understand the effects and outcomes of the approach we developed an artificial landslide. We then computed some profiles and analysed the autocorrelation, slope attenuation and local fractal indicator. The resulting high-pass information of the wavelet transform has also been analysed and filtered using several types of filters. In a case study we used a real-world landslide to validate the transform and to understand its impact on geological structures. Within this case-study we conducted a web-based survey that allowed the participants to analyse the landslide using wavelet results and to make comments on the potential of the wavelet transform in the field of geomorphometry. Moreover, important contributions of this thesis are new algorithms that allow the illustration of the structural coherence in relation to each subspace. These are based on the theory of vision of Marr and on structure tensors. The results of our studies show a high consistency. The wavelet transform thereby extends the range of tools in geomorphometry. The different structural scale levels show that such these methods are needed to better understand the phenomenology of geomorphological processes.