Twilight Sky Simulations

Sunset simulation with solar elevation angle of -0.8 degrees. In the west the mountain wave cloud is bright orange-yellow, while in the east some clouds are redder and somewhat dimmer. Low in the east we can see the Earth's shadow framed on the top by the reddish band of the anti-twilight arch or "Belt of Venus".

Note the Earth's shadow can be a bit higher than expected (even visible just prior to sunset) due to several factors: 1) Instead of the Earth's limb, we are seeing the shadow of the lower atmosphere, clouds, or higher terrain to the west. In this simulation the lower atmospheric extinction is the main factor. 2) One can also see "extra" Earth's shadow when on a more isolated mountain top and the horizon shows up at a depressed angle.

Evening twilight simulation with a solar elevation angle of -3.3 degrees. The ray-tracing algorithm includes the scattering by N2 and O2, as well as absorption by ozone. The ozone contribution adds significantly to the blue sky color near the zenith during early twilight, otherwise it would be more grayish. Later in twilight with the sun lower than this elevation, secondary scattering predominates near the zenith and thus Rayleigh scattering once again has more effect.

The twilight arch is visible with a gradient of intensity and colors as we near the western horizon. Recently in Colorado I've noticed enhanced purple colors in the twilights that seem to be either from a recent volcano or some other type of sulfate pollution. One candidate would be Calbuco that erupted in Chile in April, 2015. This is reminiscent of the volcanic twilights of the 1980s and 1990s though more moderate in intensity. The simulated sky is modeled by considering an additional (mainly) stratospheric aerosol layer from 13-25km high having an optical depth of .026, uniformly distributed within this vertical layer. This reasonably matches my visual impression of recent sunsets, though the all-sky camera has a tendency to wash out the colors. The photo below was taken on the evening of September 20, 2015 with a regular digital camera and shows the volcanic twilight colors more clearly. The mountains cut off the view within about 3 degrees of the horizon.

Click above image for animation of twilight sequence. Animation is every 5 minutes and represents clear sky only without clouds. This is a polar or sky dome view.
Other formats: Polar MP4 , Panoramic MP4