Elevation at Horizon

Sunrise occurs sooner when standing on top of a mountain looking east over a plain, due to the height of the observer above the horizon.

Optionally, TPE can account for this effect by allowing you to specify the elevation above sea level at the horizon. Either touch the text field to enter a value directly or place the secondary pin (grey) and TPE will find the elevation at that point and enter it into the field for you.

When enabled, the theoretical distance to the visible horizon from the primary location is displayed. This value can be calculated from the difference in elevation together with the curvature of the earth and the effects of atmospheric refraction.

In addition, the dip of the horizon is shown: this is a measure of how much the horizon is depressed because of the observer's elevation above the ground. A positive value, e.g. +1.1° indicates that the horizon is lower than normal by that amount. The higher the observer is above the horizon, the greater the dip of the horizon. The dip of the horizon is used to adjust the altitude at which rise or set is determined to occur. The higher above the horizon you are, the sooner you'll see the sun rise.

If you set elevation at the horizon using the secondary pin, but the distance between the pins is significantly different from the distance to the horizon, you may want to adjust the secondary position to make the distances match more closely for more accurate results.

Once set, times of sun/moon rise/set are adjusted for the height above the horizon implied by the difference in elevation from the primary pin. An overlay is displayed on the map showing the distance to the horizon. Remember that the distance to the horizon will vary based on direction. The distance shown is based on the elevation at the horizon that you have specified.


Let's walk through a worked example. To begin, I set the primary pin at the summit of Longs Peak, the northernmost "fourteener" in Colorado (peaks over 14,000' above sea level). On the selected date, sunrise is shown at 7:19am. That time is accurate for the standard definition of sunrise, but it does not account for the effect of the summit being so far above the surrounding terrain.


To find the time when the sun will actually strike the summit of Longs, we need to adjust for the elevation at the horizon. We can do that fairly easily using the Geodetics function and the secondary map pin.

I enable Geodetics and drag the gray pin along the line of sunrise as shown:


Next, go to the Elevation at Horizon page and enable both "Adjust for height above horizon" and "Use secondary pin":


When "Use secondary pin" is enabled, the app checks if the primary pin lies higher then the secondary, and if it does, it calculates the estimated distance to the horizon implied the elevation difference, and the effective "dip of the horizon". As shown above, in this case, the secondary pin lies some 10,000 feet lower than the summit of Longs.

Returning to the map, we now see a circle indicating the estimated distance to the horizon:


Note: it does not match the grey pin position exactly. In varied terrain, you may need to move the pin back and forth along the sunrise line to establish a reasonable position where the estimated horizon matches the pin position - a little trial and error may be required. Remember: we're using the grey pin as a convenient aid to avoid working out elevation differences in our heads. If you know the area already, you can probably guess roughly where the visible horizon lies. And of course, if you're shooting out over the ocean, it doesn't really matter - the elevation at the horizon is zero, by definition.

If we exit geodetics, we can see the effect of the elevation of Longs Peak above its surrounding terrain on the time of sunrise - it's now 7:09 am, some ten minutes earlier, as expected:


The timeline captions that are affected by the Elevation at the horizon adjustment are shown with titles in italics.


The horizon adjustment is only meaningful when the primary location (red pin) lies above the horizon, i.e. the Elevation at horizon value should be less than the elevation at the primary pin. Examples might include standing on a cliff looking out to sea; or standing on the summit of a mountain looking out over the plains below.

In these circumstances, the observer's height above the horizon results in earlier sunrises and later sunsets, for example, just as you see from an aircraft.

In varied terrain be sure to establish the elevation at the horizon in the direction of the rise or set event you care about. In the Longs Peak example above, the elevation above the horizon is far greater for rise events to the east than it is for set events to the west.

If you are trying to determine the effect of standing in a valley looking at a mountain that is blocking the sun, then use Geodetics instead.

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