Chapter 4 - Topography

The topography (or the terrain profile) has two major effects on the propagation of sound and on the calculation of sound propagation:

1. The topography determines the height of sources, of screening objects and of receivers, provided the height has been specified as relative height above the ground. The terrain profile may affect significantly, in particular at short source-receiver distances, the path length difference and thus the sound ray‘s length. The path length difference and the distance determine the screening (=Abar, i.e. the „barrier attenuation“ by terrain), the geometrical divergence and the air absorption.

2. Usually, by evaluating the ray path and the terrain profile, the ground attenuation is calculated from the ray‘s average height and the distance source-receiver. This procedure is used by the majority of ground attenuation models which consider the real terrain profile to calculate the ground attenuation. More sophisticated ground attenuation models do not use distinct rays, but consider the complex ground impedance and add the direct ray and the ray reflected by the ground, respecting the phase information (e.g. Harmonoise HAR-2004) .

Any sound propagation software considering the terrain profile during the calculation evaluates the (absolute) heights of all objects involved in the sound transmission and having relative object heights using the height information available from the input data. In principal, this terrain model may consist of terrain contours, height points, and lines of fault. Moreover, also objects the absolute ground height which has been specified may determine the local terrain profile.

Practical Hints

In practice, often different levels of detail may be discovered with terrain models which are mostly determined by the availability of input data. Since the majority of terrain data are imported and not entered manually this data is mostly used „as is“ without being in the position to adapt the level of detail to the requirements of sound propagation calculation. Therefore, it may be useful - especially at a high level of detail - to reduce the complexity of a terrain model in order to save computation time without loosing accuracy of prediction.

The following points may be relevant when assessing the suitability of an existing terrain model to be used for sound propagation calculation:

Terrain Model from Terrain Contours

In case the terrain model consists of terrain contours, height steps from 1 to 5 m are useful for the purpose of sound propagation calculation. This means, for example, that adjacent terrain contours differ by 1 meter in their absolute height. An even smaller vertical stepping leads - in general - to longer computation times without causing an additional screening effect. A vertical stepping being larger than 5 meters may cause relevant terrain details (such as local cuts or peaks) to be ignored in the calculation of sound propagation.

Examples

3D-Special view of a terrain model with equidistantheight differences between the terrain contour of 1 m

3D-Special view of a terrain model with equidistantheight differences between the terrain contour of 6 m

Terrain Model from Height Points

A terrain model consisting of individual height points may have horizontal distances from 1 to 10 m between the height points. In case such terrain models are imported from data provided by the local or national ordnance survey the height points usually form an equidistant grid. Nevertheless, terrain models may also consist of irregularly distributed heights points (e.g. resulting from aerial surveys (laser dots) or from surveys of road cross section).

Examples

Terrain model of equidistant height points

Terrain model from non-uniformly distributed height points

Terrain Model from Terrain Contours and Height Points

With a mixed case (i.e. the terrain model consists of both, terrain contours as well as height points), it cannot be judged per se, whether the resulting terrain model is useful and not over-determined.

Terrain Model with only a few terrain forming objects

With just a few terrain forming objects - either being terrain contours and/or height points - it must be assessed in each individual case whether the terrain model is suitable and valid and whether it can be used in sound propagation calculation. Remember when having a rough and sketchy terrain model that the triangles generated in the triangulation may be very large and can, consequently, not represent properly the real terrain shape (see DTM Digital Terrain Model Tab). The result will be a terrain model with spatially varying precision representing the real terrain just to a minor extend.

Example

Terrain model with a few, unevenly distributed terrain contours (solid lines) with non-equidistant height differences (2 to 4 m). The triangulation (dashed lines) generates large triangles of terrain with constant slope. In these areas, the digital terrain model represents the terrain‘s real profile only approximately.

Terrain Models and Project Area

Terrain models should extend beyond the actual project area in order to cover also ray paths propagating tangentially along the actual project area (i.e. the area where the sources, the obstacles and the receivers are located). Otherwise ray paths may exist propagating across terrain parts being outside of the actual terrain model. In those cases, the terrain‘s slope and thus the resulting screening effect by the terrain as well as the ray‘s average height (ground attenuation) would be at random in this area and depending on the limit‘s corners (see Limits).

Example

Town model with a terrain model being too small:The rays (in blue color) extending from relevant sources (in this case the road sections on the right) cross terrain without explicit height defined by terrain forming objects (e.g. terrain contours).The resulting screening effect of the triangulated terrain contours (dashed lines)is at random, because it also depends on the location of the project‘s limits.

Software-internal Procedure

In order to assess the required and reasonable level of detail, it is useful to know the software-internal procedure when evaluating digital terrain models in the process of sound propagation calculation. In the following, this processing of height information in CadnaA is described.

• By default, each section of a terrain contour - whether it was entered or whether it results from triangulation - generates a screening edge with this line as the top edge (holds also for lines of fault). This replacing screen stands perpendicular to the reference plane having an absolute height of 0 meters. The entered height of a terrain contour (on dialog Geometry) is always interpreted as an absolute height.
• When the terrain is solely modeled by using height points, these will not provide any screening, but only the terrain contour lines resulting from the triangulation. In this case, ensure that the option „Explicit Edges Only“ on the „DTM“ tab (see DTM Digital Terrain Model Tab) is not activated.
• Lines of fault are superfluous in conjunction with the triangulation, since they can be replaced by two parallel terrain contours. Otherwise, the heights left/right has to be specified and are not automatically derived from the actual terrain model.

Prior to the calculation of propagation CadnaA calculates the absolute heights of all vertices of all objects:

• For objects with specified relative heights, the absolute level of the terrain at the base point and the height above the reference plane are determined using the local terrain height as resulting from the triangulation of the terrain forming objects.
• For objects with absolute heights, this height represents the final height.
• For objects the height of which has been specified using the height attribute option „Height above Roof“ the same procedure as with relative heights applies, while, in addition, the height of the surrounding object is considered when determining the absolute heights.
• For objects that have been entered using the height attribute „absolute Height/Ground at every Point“ just the object‘s height is taken into account by default. In order to respect the ground it requires that the option „Objects with Ground at every Point influence DTM"“ is activated (see DTM Digital Terrain Model Tab).
• The object height is evaluated
  • for line-like objects (i.e. open polygon lines, e.g. line sources, roads, railways, barriers etc.) for each vertex point of the polygon,
  • for area-like objects (i.e. closed polygons, e.g. for area sources, parking lots etc.) for each vertex point of the polygon,
  • for buildings (being a closed polygon) just for the first polygon point. This refers to the first polygon point as listed on the dialog Geometry of the object „Building“ (first point).

Within the calculation of sound propagation a sound ray reaching from the source to the receiver intersects with all intervening terrain contours and lines of fault (and also with all other screening objects). In this course, the path length difference and, consequently, the screening effect caused by terrain edges and other objects is determined. In addition, from the height of the sound ray above the terrain at all intersecting points and from the path lengths between these points the average ray‘s height is calculated by iteration, finally resulting in the ground attenuation. The terrain height at the source and the receiver are also considered.