DEM

Question 1

Define DEM/DTM and explain Slope and its formula and Aspect

Answer 1

DEM: ordered array of numbers hat represent spatial distribution of elevations in a landscape

DTM: ordered array of numbers hat represent spatial distribution of terrain attributes

slope: defined as the elevation gradient:
needed for predicting and measuring flow velocity, runoff rate, precipitation and etc.

FORMULAR: 𝑆𝑙𝑜𝑝𝑒 𝛽 = 𝑡𝑎𝑛 𝛽 = √(𝑑𝑓/𝑑𝑥)2 + (𝑑𝑓/𝑑𝑦)2 where (𝑑𝑓/𝑑𝑥) is slope in x direction and (𝑑𝑓/𝑑𝑦) slope in y direction

• Aspect: slope azimuth (direction to which a hillside faces (north – west) or compass direction that a slope faces) → solar insolation, evapotranspiration, flora and fauna distribution, and abundance.

Aspect = Arctan ((𝑑𝑓/𝑑𝑦) / (𝑑𝑓/𝑑𝑥) where

𝑑𝑓/𝑑𝑥 = (𝑍3 + 𝑍6 + 𝑍9) − (𝑍1 + 𝑍4 + 𝑍7)/6𝑝
𝑑𝑓/𝑑𝑦 = (𝑍1 + 𝑍2 + 𝑍3) − (𝑍7 + 𝑍8 + 𝑍9)/6𝑝

Question 2

Topographic attributes:

Rechnungen für slope, Aspect, upslope area, profile and planar curvature können!!!
Indizes auswendig können?

Answer 2

-primary: elevation, slope , aspect , altitude, catchment area, profile and planar curvature

-secondary/compound: (indices that characterize the spatial variability of specific processes occurring in the landscape:
- soil wetness index,
- sediment transport index,
- stream power index,
- climate attributes,
- climatic characteristics derived from a DEM

Atribute: Definition –> hydrological significance
1. elevation: Altitude –> climate and vegetation
2. upslope height: Mean height of upslope area (total catchment area above a point or short length of contour) → Potential energy.
3. Aspect: Slope azimuth (direction to which a hillside faces (north – west) or compass direction that a slope faces) → solar insolation, evapotranspiration, flora and fauna distribution, and abundance.
- Arctan((df/dy) / (df/dx)
- hier wird ganz normal reihe abgezogen und durch 6p
4. Slope: elevation gradient → flow velocity, runoff rate, precipitation, vegetation,
geomorphology, soil water content, land capability areas.
- Wurzel aus (df/dx)2+(df/dy)2, dann tan
- in x Richtung: - jede zelle in zweiter Reihe
- durch 6p
5. Upslope slope: mean slope of upslope area → runoff velocity.
6. Upslope area: catchment area above a short length of contour. Where does the water comes from the certain pixel? The water from high pixels goes to low pixels. Used to delineate watersheds → runoff volume.
7. Catchment area: area draining to catchment outlet → runoff volume.
8. Specific catchment area: upslope area per unit width of contour → runoff of volume,
steady state runoff rate.
9. Upslope length: mean length of flow paths to a point in the catchment → flow
acceleration, erosion rate.

10. Profile curvature: Slope profile curvature. Perpendicular to the contour lines, water flow is decelerated on the convex forms (A) and accelerated on the concave forms (B). Large impact on erosion → flow acceleration, erosion (deposition).
11. Planar curvature: contour curvature. Perpendicular to the slope. Water flow converges on the concave forms and diverges on the convex forms → flow divergence.
    –> Profile and Planar curvature are the second derivative form the slope

Question 3

window operation on raster data

Answer 3

*Low pass filter, the value at the center of the window is computed as a simple arithmetic average of the values of the other cells –> A 3x3 filter: the mean value is calculated by multiplying each cell value by a weight of 1/9 and adding the results.
*The low pass filter has the effect of removing extremes from the data, producing a smother image.
*The high pass filter is defined as the original surface minus the low pass image. It enhances short–range spatial properties of the continuous surface, enhancing areas of rapid change or complexity.

Question 4

Calculate the flow direction and length of flow:

Answer 4

ÜBEN!!

Question 5

Topographic attributes:

Answer 5

-primary: slope , aspect , altitude, catchment area, profile and planar curvature
-secondary/compound (= Indices that characterize spatial variability of
specific processes occurring in the landscape):
1. soil wetness index (=Magnitude of liquid water residing in a vertical profile observable by satellite image. Quantifies moisture condition at various depths in the soil)
2. sediment transport index (=Sediment transport can be related to the length-slope (LS) factor of the Wischmeier equation),
3. stream power index (=Measures the erosive power of overland flow as a function of local slope and upstream drainage area. Large values are critical.),
4. climate attributes (Potential solar radiation),
5. climatic characteristics derived from a DEM

Question 6

Explain the difference between an elevation matrix and a TIN (Triangular irregularnetwork)

Answer 6

TIN: A triangulated irregular network is a digital data-structure used in a GIS for representation of a surface.
- TINs are a form of vector-based digital geographic data and are constructed by triangulating a set of vertices (points).
-TIN can be generated from a surface source measurement or by converting another functional surface to a TIN surface.

Elevation matrix:
It’s a rectangular grid of cells (raster-based digital data)

Question 7

characterization of raster and Tin surface models

Answer 7

Raster (rectangular grid, elevation matrix)
- sample Z-values of sample feature
- Surface cannot be more accurate than grid solution
- the accuracy is therefore determined by the cell dimension
- For higher accuracy you have to resample raster with higher resolution

Tin:
- digital data structure used in GIS for representation of surfaces
- The vertices (points) are sampled data points with X,Y, an Z values, connected by lines to form delauny. triangles
- Variable point density, so accuracy can be increased by adding mass points, break lines or polygons

Question 8

Advantages, disadvantages of TIN

Answer 8

• points of TiN are distributed variably based on an algorithm that determines which points are necessary to represent the terrain accurately
• fewer data points must be stored and data input is more flexible
• slope and aspect: TIN is less suitable as DEM. A DEM can be interpolated from a TIN

Question 9

delauny triangulation

Answer 9

• one method to triangulate a set of points
• A triangulation is a delauny triangulation, if, and only if the circumcircle of any of its triangles does not contain any other point of its interior.

Question 10

surface feature in A TIN

Answer 10

point surface features
- Mass points represent location and Z-Values (parks)
- delauny tringulation algorithm is applied to create an initial TIN (shape of surface, but not sharp changes in terrain)

Lineare:
- Break lines represent natural features (roads)
- New nodes are created when a break-in is added

** Aerial**:
- Polygons represent features with a constant elevation (lake, ocean)
- TIN has now been refined to model areas of constant elevation and the boundary of interpolation

Question 11

collection of data of digital elevation

Answer 11

• Ground survey (high accuracy, time consuming)
• Photographic data capture: interpretation of aerial photographs to satellite images (minimize data collection effort with maximizing accuracy of DTM)
• Catographic data. sources: Contour maps and profiles. digitized through manual digitizing, semi-automated or raster scanning or vectorization (large areas, problem: not useful as a scheme for numerical surface representation, over and under sampling, cannot be more accurate that original map)
  -radar, laser (LIDAR)