__Digital Terrain Models (DTMs) __

- Introduction: Basically, we assume that objects such as the surface of the earth are continuous, not discrete phenomena. As such, to fully model the surface of the earth, we would require an infinite number of points. Unfortunately, this is not feasible, so the question becomes: "how do we represent the earth's surface?"
- Using a GIS, there are three basic methods of doing this: Digital elevation models (DEMs), Triangulated Irregular Networks (TINs), and contour lines.There are also point files, such as those generated from LIDAR data. However, these are usually used to generate DEMs or TINs.
- Contour lines are the simplest and most familiar to most people.
In a computer, they are typically a line with an attached elevation attribute.
In this form, they are of little use except as a static reference.
In short, you cannot do surface analyses on contour lines - they have to
be converted to one of the other digital terrain models (DTMs)
- as a quick side note, a DTM is a generic term which refers to any computerised terrain model. DEMs and TINs refer to specific types of terrain models.....

- Digital Elevation Models (DEMs)
- These are raster representations of the earth's surface. The
assumption is that there is a regular grid of spot heights which represent
the average elevation for each raster cell. As such, there is
a bit of averaging involved in a DEM. The amount depends on the
spatial resolution.
- Coverage can range from worldwide at very low resolution to less than 1 metre resolutions for specific areas.

- DEM Creation:
- Airphotos (stereo pairs)
- Hard photogrammetric methods. Contour following or profiling. Very labor intensive. Analyst can correct for terrain (plant/house) inconsistencies.
- Soft Photogrammetric methods. Much faster. Must scan airphotos first. However, the computer only looks at what's on top for determining elevation - problems in areas of vegetation (treetops) or buildings.

- Satellite Imagery - similar to soft photogrammetric methods. Radar imagery or SPOT imagery. Need stereo images. Radar sees through clouds and vegetation
- Lasers (LIDAR). Multiple returns. Requires considerable post-processing. Can be very high resolution. Human interpretation required remove buildings, etc.

- Airphotos (stereo pairs)

- These are raster representations of the earth's surface. The
assumption is that there is a regular grid of spot heights which represent
the average elevation for each raster cell. As such, there is
a bit of averaging involved in a DEM. The amount depends on the
spatial resolution.
- TINs (Triangulated irregular networks). Irregular network of point elevations connected into triangles.
- As a note, about all you can do with TINs is calculate slope and aspect. Fun modelling, etc is simply not possible.

OK, now you have your DTM, what the heck do you do with it? The following discussion will focus on DEMs, as TINs are limited in their modelling capabilities.

First, we need to worry about basic dem errors (spurious pits, and holes). We discussed methods of correcting these errors.

Slope angle calculations. These are probably the most common calculation from a DEM. They are used for all sorts of applications, however, users tend to just accept what the computer calculates. Even though there are huge differences in the different methods of calculation. If I were you, I'd carefully read the Dunn and Hickey paper (2nd set of readings) prior to the exams, as this is an important topic. We went through, in detail, three different methods for calculating slope: averaging techniques (there are many, we only used one), maximum slope, and maximum downhill slope. If I were you, I would be ready to calculate slope on the final exam. Aspect (flowdirection) calculations. Aspect and flowdirection are often defined the same way. The way I visualise it, you are standing in the middle of a cell and looking directly downhill. That direction is both the aspect of that bit of slope AND the direction in which water will flow. GIS programs often calculate this as a 0 - 360 degrees type answer, however, for any sort of modelling, the answer will be 1 - 8, as those are the maximum number of adjacent cells. As with the slope angle calculations, there are a number of different algorithms for calculating aspect. Note, Flowdirection in Arc works this way. Aspect calculates a 0-360 degree answer that is based upon a 3x3 neighborhood (much as slope is calculated). I have developed code to calculate maximum downhill slope angle which would then correspond to flowdirection.

Slope length calculations: The length of a slope from a ridge to a stream (roughly). These are done as an input to erosion models. Simply put, the farther water flows down a slope, the faster it flows. This is obvious in any roadcut - the gullies are deeper at the bottom of the slope than higher up. The only code currently available for these calculations within Arc/Info or IDRISI is downloadable from my home page. It is important to note that the slope length is often reset where there is a significant decrease in slope angle. This is done because as the slope decreases, flow speeds decrease, and you get deposition rather than erosion. Therefore, the longer slope argument no longer applies....

Other topographic attributes. There are bunches of applications, however, we won't go over them in any sort of detail.Next week, we will discuss slope length and the universal soil loss equation in considerable detail. A=RKLSCP. Be sure you know what all the factors represent, how the computer calculates them (or where you get the data), and the value of the output.