Introduction
For noise assessment purposes, maps are often used for condensed visualization of noise predictions and related themes. Older technical regulations, for instance DIN 45682, primarily apply for maps as paperwork. There is no guidance for the presentation of maps on screens or online.
This paper discusses some cartographical aspects of quality-assured noise mapping, proposing some rules that can help to harmonize noise mapping in order to take advantage from using the sophisticated options of modern visualization technique.
Simplicity versus Accuracy
Using projections to picture the world
Projections of maps are based on defined projections of the earth to a ‚plane sheet of paper‘ because the world is not a flat disc. (Universal Transversal Mercator, Lambert or what have you).
Projections typically show lines of latitude and longitude as curved lines. Projections are never at the same time
- conformal (winkeltreu),
- equidistant (abstandstreu),
- and do not preserve the scale throughout the map (maßstabstreu).
However, projections provide in general a concrete representation of locations (lagetreu).
Therefore, distances and angles should not be taken from projections for quality-assured noise mapping.
Using grids to picture the world
Grids (Kartennetze) are based on conventions. There is always a reliable bi-directional referencing transformation for locations from projections to grids and vice versa, provided the map datum (Kartenbezugssystem) (dimension of the earth ellipsoid, ETRS89 or WGS84 for example) is given. As a matter of fact, it is reasonable to base quality-assured noise mapping on the UTMRefGrid ETRS89 because this is the stipulated system in the EU.
Grids are at the same time
- conformal (winkeltreu),
- equidistant (abstandstreu),
- and do preserve the scale throughout the map (maßstabstreu)
- provide a concrete representation of locations (lagetreu).
As a general rule, distances and angles (bearing) for any geometric calculation algorithms reside in grids. With respect to the grids, i.e. in the flat disc world, these measures are accurate.
However, these measures are per definition not accurate in the spherical real world. Their errors depend on the absolute location in the grid relative to the prime meridian (Bezugsmeridian) and not primarily on their resolution or scale. Professional online map systems will display geodetic or grid coordinates re. a selectable map datum.
Google et al.
In noise assessment, popular online-maps are often used to gather geometric data for a prediction. Google maps, Bing maps or OpenStreetMapuse ‘Spherical Mercator’ that relates to a sphere and not to an ellipsoid. Therefore, they do not apply a typical projection. Showing noise maps on such online maps require an additional re-calculation.
If you want to learn more about these popular map sources, see http://openlayers.org. And if you want to compare Goggle maps, Bing maps and OpenStreetMapsuse http://openlayers.org/dev/examples/spherical-mercator.html
Resolution versus Scaling
Just to define the wording here
Often, noise maps are based on sound prediction calculations for well-defined grid squares. Typical grid widths for example are
- 10 m for traffic noise,
- 50 m for aircraft noise or
- 250 m for shooting noise (large weapons) .
The prediction for the center point is taken as the representative value for the respective grid square. This is not necessarily the only way to do it but often found in noise mapping.
Therefore, the resolution (Auflösung) of the layer ‘noise’ is clear:
It measures something like the information density.
The scale (Maßstab) is also clear: It is the ratio of a distance on the map to the distance on earth (on the flat disc earth of grid maps, not on the geodetic earth). If you zoom in or out in maps you change the scale. And if you do not adapt the resolution, you can hide or discover hidden information.
Is it also necessary to change the resolution of the noise load layer if it comes to zooming?
And if so, how to do it?
Rag Rug versus Merging
The combination of Maps
It is rather a challenge to combine two or more maps or thematic layers if they have either a different resolution or refer to different coordinate systems. Decisions are needed on how to show the information on one map, often on an individual basis.
To give an example: Assume to combine the three conflicts (conflict = rating level – noise limit) due to industrial noise, aircraft noise and shooting noise into one decibel number (total conflict) to indicate the cumulated noise situation and put that information together with the population density on one map, you got the challenge meant here.
We will propose a solution setting up some rules to do it quality-assured and comprehensible.
1. Rule (reference grid)
All calculations are done in a specified zone of the ETRS89, UTM(Ref) grid. (Germany 32U or 33U)
2. Rule (calculation grid origin)
The origins of all calculation grids (Rechenraster) are linked to the lower left corner of a 1 km square grid.
(1 km x 1 km is one native square grid of UTMRef.)
3. Rule (calculation grid width)
Only grid widths w are allowed that meet the condition w = 2^p •1 km
-16 <= p <= 0 or 15 cm <= w <= 1 km
p is called the (Peano)precision level.
As a decisive consequence of rule 3, the change of resolution is a self-similar problem, which makes it rather simple.
Basically, the change of resolution depends on the algorithm to build the layer information. We will use the so-called Peano-Code here
to indicate the cells. Let denote n, m, p, q the Peano-bits.
4. Rule (changing resolution: p = p - 1)
5. Rule (changing the resolution: p = p + 1)
Binary layers (case e) have no numerical criteria to make an automatic decision. It depends on the meaning of the theme whether or not the larger cell should indicate the true or false state.
Brain versus Graphic Card
Controlling picture elements (Pixels)
A picture element means the smallest grid cell of an output device (pixels on screens, dots on printers). If you let it go the software or the graphic card will do its best to present the information sharply and perfectly. This underlying rendering process is improving the presentation taking advantage of the capability of our brain to find edges, distinguish colors and so on. (Its like MP3 for sound for human hearing.)
In general, ‘rendering’ is an excellent and always present tool to optimize outputs on screens and printers.
For quality-assured maps however, this feature needs to be controlled. In some applications of online maps – for example if you pick levels from the given color – it needs to be switched off to reliably get the unbiased data. Thus, the scaling of maps needs to consider the resolution of the output device.
The scale can only change by a factor of two (with respect to a linear axis) to make sure that the content of the picture element can be controlled in the same way the resolution of a layer is controlled. Again, the calculation of the properties of the picture element depends on the principle properties of the layer.
A last rule defines the process:
6. Rule (quantized scaling)
Quality-assured maps are scaled in such a way that 1 or 4 or 16 or 64 or ... 4n Pixels meet the resolution of the map or layer respectively.
Conclusion
- Quality-assured mapping should not replace the existing excellent presentation of noise maps available in professional software.
- Quality-assured mapping should be an additional feature.
- Quality-assured maps can be a reference option to make sure that no information is lost or added to provide a reliable basis for data analysis.
- 6 rules are necessary to control resolution, zoom and scale and the combination of layers.
These rules will be proposed for discussion in the DIN/VDI Working group NA 001-02-03-20 that is about to reconsider the DIN 45682 “Sound ImmissionMaps“ which gives guidance on how to compile and present noise maps in Germany.