# Simulation of the Textbook Sunset

## Introduction

The green-flash explanation offered in many textbooks, as well as on many Web pages, is that atmospheric dispersion causes the green image to lie slightly above the red image of the Sun at the horizon. (The blue and violet are largely removed by atmospheric scattering; the orange is absorbed by water vapor and ozone; so little more than red and green is left.) Thus, the red Sun sets first, leaving the green image for a second or so. This, the textbooks tell us, is the green flash.

This story is based on observations of the red and green rims when the Sun is a few degrees above the horizon. Unfortunately, quantitative calculations made by Gerhard Dietze in 1955 showed that the green rim is too thin and faint to be visible to the naked eye — not to mention that the details of this process are not in agreement with those actually observed in real green flashes, which usually appear some distance above the horizon, not on it. While the isolated green rim is visible in binoculars or low-power telescopes, it is not the cause of any green flash worthy of the name.

Before we examine these green-rim “textbook” flashes, let's have a look at the overall sunset:

Notice that the Sun is slightly flattened. That's a consequence of the temperature gradient in the U. S. Standard Atmosphere, the model for which this sunset is calculated. This model has a lapse rate (which is what meteorologists call the temperature gradient, apart from a sign change) of 6.5 K/km, which is a good average value through the lower 10 km of the Earth's atmosphere.

Also, the shape hardly changes as the Sun sinks to the horizon. That's because the lapse rate is kept constant through the lower part of this standard model — unlike the real atmosphere, which is full of thermal structure.

If you look closely, there is just a hint at this resolution of the greenish upper rim and reddish lower rim. Mostly, they're buried in aliasing noise.

If you stand back so as to see the Sun at naked-eye scale, there's not much indication of a green flash here. And, bear in mind that the green in this image is almost ten times brighter than the green in a real sunset — an artifact of the need to use colors that most browsers can display correctly. Clearly, Dietze was right: refraction in the Standard Atmosphere cannot produce a green flash the unaided eye can see.

Up close, though, there's a little indication of a wisp of green at the very end. So let's take a closer look.

© 1999 – 2003, 2005, 2006, 2012 Andrew T. Young

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