Twilight Sky Simulations (including Sunrise & Sunset)

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 that lower clouds have a sunset progression from yellow to orange to red as the sun gets more below the horizon (given low aerosol content). Very high clouds have a somewhat different progression, going from yellow to orange to a slight purple color. This purple coloration is due to the presence of ozone absorption preferentially reducing the red light and letting through more blue to illuminate the cloud. Higher clouds have more of a light path going through the stratospheric ozone, relative to the Rayleigh scattering gases more dominant in the troposphere.

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.

Click above images for twilight sequence animations. Polar and cylindrical animations are every 5 minutes and represent clear sky only without clouds. Various aspects of twilight are visible, including the Earth/atmosphere shadow and Belt of Venus opposite the sun shortly before sunrise. Stellar limiting magnitude at the zenith is listed, and assumes a moderate amount of skyglow due to artificial lighting. These are intentionally "underexposed" so we avoid distorting the colors in bright areas due to saturation. It can help to turn up your monitor brightness to see the best view.

Some artifacts that are present from the process of making the animated GIFs can be avoided by looking at the individual cylindrical and polar frames, while others stem from the model grid boxes that are used when clouds are present and crepuscular rays are being simulated.

Effect of Ozone

We can see in the above two images the effect of ozone with the sun 3 degrees above the horizon. Surface pressure is 850mb with no aerosols. Top has no ozone and bottom has 300DU of ozone. Only Rayleigh scattered light is shown so the sun itself and the localized glow around the sun (aureole) are invisible. The overhead sky would turn a paler blue when the sun is near or below the horizon, though ozone saves the evening by keeping the zenith sky a deeper blue. The bottom frame may have too bright of a yellow hue around 3 degrees above the horizon, though this can be reduced by apportioning more of the ozone in the troposphere (not shown). Generally about 10% of the ozone mass is in the troposphere though this could increase in polluted areas. Increasing the spectral resolution in the ray-tracing algorithm might also help.

Volcanic Twilight Sky

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.

More on volcanic twilights is here.

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