Hello! This part of he lesson on digital elevation models is dedicated to the representation of relief and geomorphometry. We first have to outline some definitions concerning digital elevation models. First we have digital surface model or DSM. It is the envelope that covers all of the objects on the surface built objects, vegetation, and waterways. Here, we have a crude model from which we can remove all objects and we will have a digital terrain model. where we only have the ground surface which is shown here. These two terrain and surface models are the family of digital elevation models. The relief is characterized by the shapes and inequalities of the terrestrial surface or in a given territory. It can be described in two ways either quantitatively or qualitatively. Qualitatively, we can describe a territory with some adjectives like flat, hilly, rough, etc.... This is useful for geography books. On the contrary, for our engineering work we must have a quantitative approach that is to say, we will measure elevation of characteristic points. We can also on this map section describe one of these regions for example here with a relatively steady slope. We have in this region, maybe a rougher terrain with the presence of rocks. In the region, we can have an average altitude. We can also find some characteristic elevation points. which are given on this map and the swamp regions that are flatter. Here are some relief interpretations in this region of Simplon. The geomorphometry is the technique that allows for determining variables which will characterize the different landforms. We also have two approaches, the global approach and the local approach. The global approach is the one that will characterize the entire survey area for example, a watershed. In this case, we have a characteristic, which may be the average elevation. For the global approach, it will be the geometric properties like for example, slope, orientation, etc... In this example, my surveying zone is what is outlined in red I can calculate the average elevation or more locally, if I place myself in this region I have a certain slope, as well as an orientation if I have the north of the map here, the region will be oriented northeast. Locally, I have two indicators: the slope and orientation that will characterize this portion of the map. On of the global geomorphometry characteristics is the hypsometric curve. The hypsometric curve is the distribution of the surface of a given zone as a function of elevation. For example, if I confine my perimeter I have a first zone of 500 m with a certain surface, then I have another zone of 1000 m with another surface, etc..., here 1500 m We construct hypsometric curves like in this graph with for example at 2500 m, I find myself at 12% and at 1500 m, I am at 50%. I have 38% between these 2 zones: I have 38% of the surface area between 1500 and 2500 m. This type of curve is useful to characterize a watershed for hydrological studies. Another global characteristic is the roughness. We can look, in a given perimeter, at some statistical values in particular classes of elevation, classes of slopes. These are the values that allow us to get an idea of the terrain roughness. Another way to approach this global variable is already looking at a map where we see regions with a certain steady slope with smooth terrain, flat and more troubled regions like here where this notion of roughness can also be interpreted intuitively. It is even more interesting to see what we call a shaded model made from digital elevation model, in particular laser models. We see on this map that the regions called rough stand out as soon as we have very bumpy relief areas it is apparent on these shaded models. To quantify this relief roughness, we can use the fractal index. We will relate the length of a curve with a fractal dimension like in this small example with the the completly straight line the red curve slightly wavy and the yellow curve very wavy, so in other words very rough. In this small example, we have the sinusoidal character or a curve. In this example, the fractal index, the fractal dimension for the right is 1, for a very wavy curve, D is equal to 2. It is an example for a straight line, we can use a model for surfaces with other fractal dimensions. In geomorphometry, the most important local characteristics are slope and orientation. To illustrate these elements I draw a horizontal reference plane as well as a small surface element that will cut through my horizontal plane at a certain angle. I can draw in the center of my small surface dS the slope vector of this small surface element. From my horizontal plane, I have an angle i, which is the inclination angle or slope that can be expressed in either degrees or %. Then. we must characterize the orientation, ie here the vector from the intersection of my two planes and I can have, in this case, the direction of north on the map which is somewhere here. I will find East and the orientation relative to the cardinal points will be northeast. We can therefore cut the portion of land that interests us in small pixels or small terrain elements, and in each of these elements we can describe these 2 variables, the orientation and the slope. We can then create a complete map with these pieces of information. From the digital elevation models that cover the territory we can create slope maps, orientation maps as we find them in the cartographic shops with the example of the Neuchâtel canton. First, we have here a slope map in this image, with a scale that is not linear. We see here 0 degrees, a relatively flat region between 0 and 2 degrees, and at the other end, very steep slopes as we have here in this valley with rather dark colors. We can quickly interpret this map and see where we have steep areas in this region. The other element, is the orientation. I bring back the little valley with in red the slopes facing west and in green, areas facing east. We can easily see the areas facing north or northeast illustrated here in blue, dark blue. Here are two more local characteristics; convexity and concavity. To explain these 2 parameters, I draw a terrain profile where I will place planes or tangential straight lines. Here for this area here for this region. I have 2 possible scenarios, the first with a tangent plane above the surface. I have here a area called convex for example a bump or I have here an area called concave with a pit. To summarize this part of the lesson on digital elevation models we recall that the digital surface model and the digital terrain model are the main elevation models. Then, the geomorphometry allows us to characterize the different landforms globally or locally. with quantitative or qualitative approaches. And finally, there exists a number of products derived from elevation models that allows for creating slope maps, orientation maps as we find in the different cartographic shops