Blue twilight in a simple atmosphere

Assuming a curved exponential atmosphere with beam attenuation and isotropic scattering both proportional to density, we model three regimes that each become dominant in turn as the sun sets. This drastic simplification of the earth's real atmosphere both provides insight to guide system design and is able to fit over an irradiance range exceeding nine decades a set of narrowband measurements of blue light intensity made in the natural environment on clear days. The single-scattering regime involves only overall illumination (or cloudiness) as an adjustable parameter and appears especially relevant to animal geolocation based on measurement of diffuse irradiance.