Viewsheds are useful layers that allow us to model visibility of features on the surface of the earth.  In this post we look at the effect of the curvature of the earth on these raster layers

With due homage to The Who, this post goes out to all those who adhere to the crazy idea that we live on a spheroidical planet – flat earthers need read no further.  Well, they’re welcome to but I suspect it will only lead to lots of tears.

We’ve been talking about viewsheds in the GIS courses recently.  I usually focus on the Lyttelton Timeball to illustrate this but this time I started with the Auckland Sky Tower:

At 328 m in height, it’s the tallest structure in the southern hemisphere.  With an observation level at 220 m above ground level, it provides a good opportunity to show the effect of the curvature of the earth on viewsheds.

Roughly speaking, when the average person is standing at sea level, looking out to sea, the visible horizon is just under five kilometres away, i.e. that’s about as far as you can see with the naked eye.  The attraction in going up in things like the Sky Tower, or climbing mountains for that matter, is the enhanced view you get, the new perspective on the world.  With viewsheds we can determine and map the areas visible from a point (or points) a given distance above the ground.  I’ll use ArcGIS Pro for this post and we’ll also use two different elevation layers: the 25 m North Island DEM and a 1 m DSM (Digital Surface Model).  The difference between a DEM and a DSM is that the former shows us the “bare earth” with no trees or buildings, while the DSM does.  Let’s first look at your standard viewshed.

First, we need a point to give us the location of the Sky Tower:

To take into account the elevation of the observation deck, I’ve added a new integer field to my attribute table called OffsetA and added the value of 220 for that point’s record.  Now to the Viewshed tool:

My input raster is nidem, the 25 m North Island DEM

The input point is my Sky Tower point (I can also use lines as an input – the line vertices will be used by the tool)

My output is called VS252D

Note the tick box at the bottom – leaving it unchecked means the curvature of the earth won’t be taken into account – the whole of the North Island will be one big flat fish of Maui.

Unlike ArcMap, Pro has a “Run” button at the bottom of the tool to get it going – here’s the result:

So in this image, all the blue areas are visible from the Sky Tower.

Quite expansive!  The north slopes of Mounts Taranaki and Ruapehu are visible.  For those with keen eyesight, they may even be able to see the Tararuas!

I didn’t include the South Island DEM in this viewshed but I’d be pretty confident that Mount Cook would also shown in blue as well.

Here’s another angle on this (with apologies to the flat earthers [ed. not really]):

Now we’ll rerun the tool with the same inputs but tick the box for earth curvature corrections:

We’ve got a new parameter to deal with here: Refractivity coefficient.  This takes into account the effect of visible light being deflected in air – the default value is 0.13.  Clicking Run gets us this:

Here the orangey areas are visible taking into account curvature – this is the full extent of this layer.  The image below shows both viewsheds together:

Here we can see the areas that get cut off due to curvature.  And another 3D view:

Quite a difference!  In terms of area the flat viewshed covers approximately 2,608 square kilometers while the curvature viewshed is only 872 square kilometers.

One last thing we’ll do is use a high resolution viewshed.  Looking on, I found a 1 m DSM for Auckland based on LiDAR data.  This takes into account features on the earth’s surface like trees, buildings and Lime scooters (okay, it might not pick up a Lime scooter).  It’s quite a big beast so I had to corp it to get it down to a manageable download size – even still it’s 3.5 Gb:

(Side note – when downloading this, what I got was 2,917 separate DEMs. each roughly 480 m x 525 m, that needed to be merged into a mosaic dataset so I could work with them). On my map it looks like this:

If we zoom into the CBD and play with the symbology a bit, we get this:

(I cheated here – had to do this in ArcMap).  We get some very nice detail from this, eh?  In the image below I’ve overlain the viewshed from the Sky Tower in purple with a bit of transparency:

It’s a bit of a mess but if you look closely you can see the “shadows” of areas not visible behind buildings and lots of visibility corridors emanating out from the Sky Tower (blue dot at centre bottom).  For such a small area, the curvature of the earth really doesn’t come in to play, but I hope you can see how when larger areas are considered, it’s an important thing to take into account.

This post has mainly been about the effect of the curvature of the earth on viewsheds but also gave us a chance to see how using high resolution DSMs can produce more realistic results, especially in urban areas.  Now, back to The Who