The result of 2.5D representation of noise levels is shown in Figure 6. Although current noise simulation models predict noise levels in 3D, the output of the models, being a point data set with computed noise levels, cannot be used directly for meaningful 3D visualisation or 3D analyses. In order to utilize the 3D information of noise software output, noise levels need to be visualised understandably using the third dimension of the observation points. From Figure 7 it can be seen that the 2.5D approach is able to add this extra dimension to the output of noise models. The 2.5D representation offers insight into the effect of noise at any particular height on the terrain surface and on façades of buildings: high noise levels occur on road surfaces and low noise levels occur on top and backside of buildings.

For this 2.5D representation, different interpolation methods were applied and compared to conclude on the best suitable method for generating 2.5D noise representation. In our research, TIN (Triangulated Irregular Network) was indicated as the most suitable method for the generation of 2.5D noise representations. The explanation for this is that TIN can deal very well with the irregular distribution of observation points as present in our point data set when looking from above (Figure 5). More triangles with relative small sizes are generated at locations with higher point density. The other methods considered in our research (Inversed Distance Weighted interpolation, Natural Neighbourhood Method and Kriging) are all based on a weighted-average method resulting in a grid structure with equal cell sizes for the whole area. However, more trials with different approaches for point densities should be made to be able to draw thorough conclusions.

The 3D noise representation is a solid model representing attribute values in the form of 3D grid cells, called voxels. These attribute values are the result of spatial interpolation in three dimensions based on the calculated values on the observation points. Currently very few commercial GIS software provide tools for 3D interpolation for 3D point data. Most existing tools are for hydrology, geochemical, geophysical, geotechnical or lithology studies and they are based on borehole data. Examples are GOCAD, Environmental Visualization Systems (EVS), Rockworks, and GRASS. Only the FIELDS software (Field Environmental Decision Support tools, extension of ArcView 3.5; FIELDS, 2007) was applied successfully in our research. GRASS can also be used for interpolation of 3D point data but had a limitation concerning amount of input points.

In the 3D IDW method implemented in FIELDS, the searching ellipsoid-body is used to find the known points that will contribute to the interpolated value. The true, 3D distance between points is used to determine the weights of the known points. The user has to define parameter values to define the shape and size of the ellipsoid-body. It is obvious that compared to 2D it requires more expertise to guide the 3D IDW process.

The result of the 3D interpolation is presented in Figure 7. Due to limitation of software it was not possible to display the 3D city model together with the 3D solid noise model. However, it was possible to clip the model using the polygon layer of roads. Figure 8 shows that noise levels on the main as well as on the interior roads can be analysed in 3D using the solid model. This representation clearly shows the pattern of noise levels above the road surface in all directions. It shows high noise levels at the middle of the road and gradually reducing noise levels with increasing 3D distance from the centre line of road.

From our experiments we can conclude that true 3D interpolation looks promising, since it reflects the three dimensional character of noise. Therefore the 3D model offers good possibilities for noise experts to improve insight into 3D noise propagation and the way this behaviour is implemented in current noise computer models.

However, 3D modelling of attribute values is still in developing stage. For example, the following are the limitations in the FIELDS software:

- The software does not have tools for spatial analysis. It is difficult to identify noise levels at a particular height.
- It is not possible to generate 3D contours.
- The 3D noise representation cannot be presented together with the 3D city model. Consequently, it is difficult to locate and orient oneself.
- The solid model requires specific interaction functionalities (e.g. slicing) to be able to analyse the values at all locations.

Although these findings indicate limitations specific to this software, the last three can be indicated as more general limitations that currently apply to solid models representing at-tribute values in 3D.

In our research, the possible benefits of a 2.5D approach compared to 2D noise maps were tested by applying it to the

assessment of the reduction of noise levels by noise barriers.
Figure 8 shows the effect of seven different noise barriers varying in height, width and distance from the road. The details of the different barriers are shown in the bottom left corner of the figure.

The first three barriers (a), (b), (c) are of height 3 m and located at a distance of 3 m, 6 m, and 9m, respectively, from the edge of the road. As can be seen in Figure 13, the effect of the barrier reduces when the distance of the barrier to the road increases. Furthermore, it shows that there is no effect of the barriers on higher floors.

The next three barriers (d), (e), (f) are of different heights (2 m, 3 m, and 4 m respectively) and located at an equal distance of 5 m from the edge of the road. Figure 13 shows that noise reduction due to the noise barriers increases when the height of the barrier increases. Still no effect of the noise barrier is found at the higher floors.

Barrier (g) is located where there is no building. Barrier (g) shows therefore the effect on the ground surface.

This case study shows that a noise barrier should be high enough and sufficiently close to the road to have a reducing effect for all floors. A 2D map representing the noise level for only one height (close to the surface) cannot provide this information. Noise levels on lower floors could be overestimated and on higher floors underestimated.

As can be concluded from this paper, 2.5D noise representations offer many improvements compared to traditional 2D noise maps. A 2.5D representation provides insight into noise behaviour with respect to height. As a result, more accurate assessment of noise impact is possible in particular when different floors of a building or noise barriers are concerned. Since 2.5D representation is easy to 'understand' they are beneficial for communication purposes in city planning processes with the broad public.

The study presented in this article showed that general available 2D interpolation methods in combination with 3D GIS can be used to produce 2.5D representations of noise levels.

An advantage of a 3D noise representation is that even more accurate information can be given on the three dimensional character of noise which is the propagation of noise in all directions. However the studied 3D software do not provide the desired performance. The software could not handle the large number of observation points that are common as output of noise simulation models and could not provide the required integrated visualisation of noise levels and contours with the 3D city model. In addition, 3D spatial analysis functionalities were lacking. Further development of functionalities is needed concerning 3D interpolation, 3D visualisation of continuous data and 3D analysis. If major progresses in these areas are achieved, 3D representations provide more thorough understanding of noise propagation and 3D noise effects.

Improvement in visualisation suggests an improvement in accuracy. Although this article shows that this is certainly the case in studying noise on different floors or behind a noise barrier, a warning is appropriate. The accuracy of noise models is dependent on the whole noise modelling process starting from available data. Accuracy is influenced at each operation such as during generation of observation points, spacing of points, noise calculation, spatial interpolation and analysis. Ambitions for further improvement of visualisation are obviously supported by the authors but not without emphasising the need for error assessment and presentation of the uncertainties.

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