measure

As we saw last week Google Earth’s measuring tools are actually quite accurate when measuring distances based on latitude and longitude, and can even take altitude into account. However, many people will be measuring distances between objects visible in satellite imagery and will not have the actual latitude and longitude of the objects in question. So, it is important to take into account various issues relating to what we see in satellite imagery, such as alignment issues.

Aligning satellite imagery correctly is complicated. We have created many image overlays (such as this one showing the surface deformation after the Chile earthquake) and we have never managed to get exact alignment between the overlay and the underlying satellite imagery in Google Earth. Even when we are trying to align an image that is already in Google Earth, such as the DigitalGlobe image of Shanghai, China, from this post, exact alignment is not possible. This is because satellite imagery must go through a process known as orthorectification, which uses a model of the terrain and knowledge of the position of the satellite at the time the photo was taken and the angle at which it was taken to adjust the image.

As we can see with the tallest building in the world, the Burj Khalifa, if the satellite takes an image from anywhere other than directly overhead, the top of the building can be quite a long way from the bottom of the building in the resulting image.

The Burj Khalifa is, according to Wikipedia, 829.8m tall. In this image, the top experiences an apparent shift of over half that distance at 482.4m

If you go through historical imagery for the Burj Khalifa, or any city with sky scrapers, you will see that the degree of displacement in the above image due to the satellite not being directly overhead is not that unusual. For sky scrapers or other buildings this is typically left as is and as a user, it is simply a matter of making sure you make your measurements from ground level objects. For mountains and other geographic features, the imagery is orthorectified by moving the top of the mountains the appropriate amount to put it in the right place. For very steep mountains this results in the effect we can see below:

Some steep mountains in the Himalayas show a streaking effect where the slopes of the mountains away from the camera had to be stretched out to get everything in the right place.

The process of orthorectification depends on having an accurate model of the terrain. The accuracy of Google Earth’s terrain model varies from place to place. We also don’t know whether or not the same terrain model is used for orthorectifying the images. What is clear though is that the process is not perfect and some displacement does take place, especially in mountainous regions. Cycling through historical imagery usually shows some movement between images.

Whether caused by this or other alignment issues, a quick check of a location in Cape Town showed differences of up to 30m between historical images. We have not yet done the same test in other locations to see whether there are more extreme variations elsewhere.

We marked the location of a feature on various historical images to see how much the location varies.

So, when making measurements in Google Earth based on objects seen in satellite imagery, keep in mind that the imagery alignment may be off by a significant amount.

In yesterday’s post we mentioned that Google Earth’s measurements did not match ours, which used the Haversine formula. So we decided to investigate a bit more.

The Haversine formula assumes the earth is a perfect sphere and in our case we assumed the radius to be 6,378,137m. The earth is actually closer to an oblate spheroid (a flattened sphere), with the equator bulging slightly relative to the poles. According to Wikipedia Google Earth uses the WGS84 datum as used by GPS, which uses an oblate spheroid that approximates the real shape of the earth. There is a formula known as Vincenty’s formula that can be used to calculate distances for the WGS84 datum. We found some JavaScript code to do this here. We have incorporated it into yesterday’s post, so you now have the option to use either the Haversine formula or Vincenty’s formula.

So, we used our updated code and again compared it with Google Earth’s measurements, and it still doesn’t quite match. Further investigation was needed. We discovered that Google Earth takes altitude into account when displaying the length of a path. When you draw a polygon in Google Earth, it is by default given an absolute altitude of 0. It is also set as ‘clamped to ground’ which means it is drawn on top of the ground surface or at sea level when over the oceans, but we found that whatever the local ground height, it gave the same distance measurements as an absolute altitude of 0. If you give the path an absolute altitude, you can raise or lower the path, and its measurement will change, getting longer as it gets higher. We discovered that to get a match between the results of Vincenty’s formula and Google Earth’s measurements, we had to set the path to an altitude of 80m. This worked at various latitudes. So does Google Earth have a slightly different sea level from the one used for WGS84 or are we missing something? We would love to hear from any of our readers with more expertise in this area.

If you wish to do some testing for yourself, you can download this test KML file, which has three lines at different latitudes, each of which covers exactly one degree of latitude.

For the above lines we got the following measurements in centimetres:

As you can see, the discrepancies we are talking about are only on the 6th significant digit.

See here to learn various ways to measure in Google Earth, and here for some of the extra measurement features found in Google Earth Pro.