# Resampling and hydrogeomorphometrical processing of dense Lidar/DEM

Christian Depraetere, Serge Riazanoff, Benoît Deffontaines

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Christian Depraetere, Serge Riazanoff, Benoît Deffontaines. Resampling and hydrogeomorphometrical processing of dense Lidar/DEM. GEOMORPKOMETRY 2023 conference, Jul 2023, Iasi,, Romania. hal-04427094

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# Resampling and hydrogeomorphometrical processing of dense Lidar/DEM: Relationships between landforms and hydrological processes in a Mediterranean peri-alpine catchment basin

(1) Christian Depraetere
Institut de Recherche pour le Développement
UMR Espace-DEV, Maison de la Télédétection
500, rue Jean-François Breton
38000, Montpellier, France
corresponding author: christian.depraetere@ird.fr

(2) Serge Riazanoff,
VisioTerra, Scientific consulting for Earth observation, 14 rue Albert Einstein, 77420 Champs-sur-Marne, France
(3) Benoît Deffontaines,
Université Gustave Eiffel (ex UPEM / UMLV),
5 Bd Descartes, 77454 Marne-la-Vallée, Cedex 2, France

## I. INTRODUCTION

Dense DEM/DTM from LIDAR tend to become an overarching data for environmental sciences particularly those requiring an accurate knowledge of the relationships between landforms and hydrological, so to say hydrogeomorphology. Herein, the focus is on a specific hydrogeomorphological processing of the forthcoming EEA-10 Copernicus DTM covering all EU (Figure 1). For testing purpose, a "pseudo" EEA-10 DTM was generated by undersampling at 10 meters resolution from the RGE ALTI® at 1 meter resolution available all over France (® Institut Géographique National, IGN).

An *ad hoc* method (SEAD) is tested to minimize the smoothing effect of undersampling on the landforms especially along the crest and the talweg lines. Then, an innovative sub surface percolation algorithm (DRAMP) derived from Beven's index is tested with this "RGEAlti-SEAD-10m" on the peri alpine Mediterranean catchment basin of the Duyes in the Southern Alps. A study of the sensitivity of hydrogeomorphological landform depictions (i.e. alluvial fans, gullies, anastomosing channels, scree slopes, etc.) according to resolution shows that 10-meters resolution with decimeter precision suggesting that the forthcoming EEA-10 DTM should be a promising and more accurate product for various environmental issues along the river beds and hazards such as floods and landslides.

<figure><img src="image_1.png" /><figcaption>Figure 1</figcaption></figure>

## II. THE DTM DATA

The DTM under-sampling method SEAD (Sous Echantillonnage ADaptatif [5], adaptative undersampling) from dense to coarser resolution is purposely suitable for hydrogeomorphological applications. Taken a given spatial resolution of µ=1 meter of the RGEALTI® DTM, the aim is to resampled it with µ = 10 meters to simulate a surrogate EEA-10 DTM. Instead of usual resampling methods based on averaging elevations and therefore smoothing the topography, SEAD is
56 "adapting" the elevation at coarse resolution taking into account
57 the topographic pattern at fine resolution. For instance, a summit
58 or a crest should remain as such in the undersampled topography
59 with high elevation compare to their surrounding points and vise-
60 versa for pit, talwegs and valley. This means that it preserve
61 better the major orographic patterns such as crest and talweg
62 lines as well as it minimize the smoothing of hillslopes.

63 Taking the example of a subset of 15 by 15 meshes (μ=1) in
64 Figure 2, the objective is to compute the elevation on the central
65 meshe of a 3x3 undersampled window with (μ=5). For the nine
66 5μ meshes, the min, average and max elevation are calculated
67 from the 15x15 1μ meshes.

<figure><img src="image_2.png" /><figcaption>Figure 2</figcaption></figure>

69 A score S<sub>z</sub> is computed according to the relative elevations of
70 min, average and max of the neighboring meshes compared to
71 the central one.

$$
72 \underline{S_z = S_{\text{minz}} + S_{\text{averz}} + S_{\text{maxz}} \text{ with } S_z \in [0..24]}
$$

73 If S<sub>z</sub>=0, the central part corresponds to a well defined summit
74 and the elevation Z for meshe(i,j) will be equal to MaxZ(i,j).
75 Conversely, a value of 24 for S<sub>z</sub> means that it is clearly a
76 depression area (pit, deep valley, etc.) with elevation Z for
77 meshe(i,j) equal to MaxZ(i,j). In other cases, it comes:

$$
78 \underline{Z[i,j] = MaxZ(i,j) - (S_z/24) \cdot (MaxZ(i,j) - MinZ(i,j))}
79 \text{ with } Z[i,j] \in [\text{MinZ(i,j)}, \text{MaxZ(i,j)}]
$$

81 For instance on the example in Figure 3 corresponding to a
82 valley, the score S<sub>z</sub> is equal to 18. Therefore, the elevation Z[i,j]
83 between MinZ(i,j) and MaxZ(i,j) but closer to the minimum
84 value (Z[i,j]=MaxiZ(i,j)-+(18/24) (MaxZ(i,j)-MinZ(i,j)).

<figure><img src="image_3.png" /><figcaption>Figure 3</figcaption></figure>

86 For comparison purposes, two DTM at 5 metres resolution
87 (μ=5 m) are undersampled with two methods: Z<sub>aver</sub> with the
88 averaged value (AveZ(I,j)), Z<sub>sead</sub> with the method SEAD
89 explained before. The differences of elevation (ΔZ) are given on
90 Map 1B (Resolution 5 m) in the downstream part of the Riou
91 torrent with various hydrogeomorphological landforms as shown
92 on Map 1A (REGALTI® full resolution 1 m).

$$
93 \Delta Z = Z_{\text{sead}} - Z_{\text{aver}}
$$

94 Purposefully with the SEAD method, the elevations of crest
95 and summit tend to be “positively” preserved while the elevation
96 for talweg, creeks and river bed are instead “negatively”
97 maintained.

<figure><img src="image_4.png" /><figcaption>Map 1</figcaption></figure>
### III. SIMULATION OF SUB SURFACE PERCOLATION

The method that is presented is a simplified variant of the Beven's Index ([1][2][9]) and applied on the catchment basin of the Duyes valley (150 km², sedimentary rocks and alluvial deposits, peri alpine Mediterranean climate, Map 2).

This catchment offers a large palette of hydrodynamic landforms such as glacis, upstream reception basins, gullies, alluvial fans, fluvial terraces, scree slopes, stony river beds, etc. developed on geological structural features of the Digne thrust sheet (Map 3).

The Beven's index also is also called the Topographic wetness This catchment offers a large palette of hydrodynamic landforms such as glacis, upstream reception basins, gullies, alluvial fans, fluvial terraces, scree slopes, stony river beds, etc. developed on geological structural features of the Digne thrust sheet.

<figure><img src="image_5.png" /><figcaption>Map 2</figcaption></figure>

The Beven's index, also known as the Topographic wetness index ($I_{tw}=Log(α)/Tan(β)$), states two basic assumptions about sub-surface percolation within pervious substrates:

- It is proportional to the drained surface $Ln(α)$ in the sense of multidirectional drainage weighted for each direction according to the difference in level. It is an estimate of the probability of water flowing through a specific point;

- It is contrary wise proportional to the local slope $Tan(β)$.

In this study, the parameter α will be used without β because the present purpose is the multidirectional sub-surface percolation mapping for hydrogeomorphological applications (Cf. Map 3 with RGEAlti-SEAD-10m DTM) and not for the parametrization of potential saturation of soil (or "source area") as $I_{tw}$ is usually used for distributed and physical based hydrological modelling like TOPMODEL and its variants.

This simplified variant of the Beven's index is called the DRAMP method (DRAinage Multidirectionnel Probabiliste [5], Probabilistic multidirectional drainage). Thus, $I_{dramp} = Log(α)$.

<figure><img src="image_6.png" /><figcaption>Map 3</figcaption></figure>
The computation of $\alpha$ can be explained on the example of Figure 4A. It is more complex than the usual “mono directional” surface flow D8 based on steepest descent as shown in Figure 4B or purpose like methods ([3][7][8][11]). This “oil cloth” D8 flow routing generates only one drainage line from a given point, for instance from the “source” point at 105 m down to the “outlet” point at 1 m. From the same source point with the DRAMP method, many drainage lines are possible as shown on Figure 4C and depending on the slope gradient pattern. This corresponds to a “multi directional” sub-surface flow routing that could assimilated as a “sponge” like superficial reservoir. The amount of water percolating down to the outlet point has a strong probably to be inferior to the infiltrated water into the source point.

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<figure><img src="image_7.png" /><figcaption>Figure 4</figcaption></figure>

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The Figure 5 detailed the probability of percolation from the source point to the outlet point along the steepest descent line as defined in Figure 4B. It comes that only 16% percolates from the source down to the outlet. The other 84% follow others multiple diverging flow lines, some of them not flowing through the outlet. On this example, the value of $\alpha$ will be superior to 16% and inferior to 100 mm. The overall computation with a shifting 3x3 window consider each point as a source and an outlet.

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<figure><img src="image_8.png" /><figcaption>Figure 5</figcaption></figure>

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Starting from the RGE ALTI®, this allows comparing the effect of SEAD undersampling 5, 10 ("pseudo" DEM EEA-10) and 25 meters resolution on sub-surface percolation simulation with the DRAMP algorithm ([5]). A sensitivity analysis of hydrogeomorphometric patterns and textures rendering from the DRAMP method is given in Map 4 on the same area of the lower part of the Riou catchment (cf. Map 1A and Map 3). The percolation patterns are clear at 5 and 10 meters resolution with well-depicted divergent percolations on the alluvial fan and in the torrential river bed. Conversely, the rendering becomes fuzzy at 25 meters resolution with not so well depiction of landform units such as the limit between the main river bed of the Duyes and the alluvial fan of the Riou.

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<figure><img src="image_9.png" /><figcaption>Map 4</figcaption></figure>

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The Map 5 gives a more detailed hydrogeomorphological analysis of the various landforms unit identifiable at 5 meters resolution and still detectable at 10 meters resolution with the “pseudo” COP-EEA-10.

<figure><img src="image_10.png" /></figure>

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<caption>Map 5</caption>

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## IV. CONCLUSIONS

The previous simulation and analysis suggests that the forthcoming Copernicus DEM COP-EEA-10 covering 29 countries of Europe (cf. Map 1) should be an accurate product for mapping and semi-automatic detection of fluvial and torrential landform. This should contribute to a standardization of hydro-geomorphological mapping and parametrization of risk evaluation and mitigation for flooding and landslides hazards at the European scale.

In France, the undersampling of the RGE ALTI® (or LITTO3D on some overseas territories) at 5 or even 10 meters with appropriate method such as SEAD could back up the steady national policy on the integrated management of rivers following the Water Framework Directive (WFD 2000) and its translation into French law (Law on Water and Aquatic Environments, LEMA, 2006).

In the regions of the French Southern Alps, Haute Provence and probably other Mediterranean mountainous area, the ongoing impact of river beds incision due to reforestation and abandonment of agricultural land since many decades ([6][7]) is manifolds: lowering of alluvial water table, erosion of alluvial terraces and undermining of dykes and bridge piers. These facts pledge for an accurate and continuous GIS monitoring of the “The green and blue network” (*trames verte et bleue*) with Lidar data.

The DRAMP method could be one asset for those actions.

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**Keywords:** Dense Lidar/DEM, undersampling of DEM, hydrogeomorphology, subsurface flowpaths, semi-automatic geomorphological mapping.

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## V. ACKNOWLEDGMENTS

The study and field works in the Duyes Valley were conducted in collaboration with the UNESCO Geopark of Haute Provence and the National Taiwan University in Taipei.

The scientific and technical support of VisioTerra, contributed to this work with expertise and remote sensing data. https://www.visioterra.fr

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