## Introduction

This article describes the various times of day that have some solar significance. During the course of any normal day, the Sun rises from the East in the morning, passes in an arc across the sky during the day, and then sets in the West in the evening. This daily process is characterised by periods where there is no available skylight (night time), a gradual increase in skylight until sunrise (dawn twilight), then a more rapid increase in both skylight and sunlight after the Sun rises which continues through the day (day time), then a rapid decrease in the evening until there is no longer any sunlight (sunset), but still some skylight which then gradually decreases back to nothing (dusk twilight).

## Local and Solar Noon

Solar noon at any particular location occurs when the Sun reaches the maximum altitude that it will attain during that day. Solar noon is different from local noon because local clock time is governed by the timezone used at each location. Timezones are a way of synchronising clocks over large geographical areas such as countries or regions. However, solar time is location specific, and also varies throughout the year as a result of the Equation of Time.

Thus, for most timezones, solar noon will occur within an hour or so of local noon, and will be exactly half-way between sunrise and sunset. Exactly when solar noon occurs is affected by where the actual location is relative to the longitude that defines the local timezone, and the day of the year as the Equation of Time varies significantly depending on where the Earth is in its orbit around the Sun.

## Sunrise and Sunset

What we refer to as sunrise and sunset are the times of day when the Sun appears at the horizon, either when rising from below it in the morning or setting from above it in the evening. Both these values are given as precise times usually to within the nearest minute. However, the technical definition of exactly when these times occur is often different from our own real-life perception of when the Sun actually rises or sets. This is because the real world is full of undulating terrain, trees and forests that obscure the horizon, and all sorts of weird atmospheric conditions.

For example, if you are at the bottom of a deep valley, the Sun will appear to rise much later and set much earlier than if you were at the top of a hill. Also, if you happen to be in an aeroplane high over the sea, the Sun will appear to rise slightly earlier and set slightly later than if you were on a boat immediately beneath it due to the curvature of the Earth’s surface.

Additionally, dark clouds at the horizon can act to obscure where exactly the horizon occurs and make it seem that the Sun has risen later or set earlier. Under certain conditions the atmosphere can refract light around the horizon even more in line with the curvature of the Earth, making the Sun appear to linger there slightly longer or appear in separate layers above the horizon for a time.

Also, the arc of the Sun through the sky at the Equator is pretty well at right angles to the horizon, so it is pretty easy to discern when the Sun passes over it. However, the arc of the Sun at higher latitudes is much lower, to the point where it is virtually parallel at the poles. Thus, visually determining exactly when the Sun has risen or set becomes much less obvious with increasing latitude as the effects of atmospheric refraction, observer height and local topography are increasingly magnified.

### Technical Definition

To avoid the influences of local topography and temporal atmospheric effects, the technical definition is that sunrise and sunset occur when the upper edge of the Sun aligns exactly with the apparent unobstructed horizon of an observer at sea level. This accounts for the average apparent radius of the solar disk being 0.26667° (16 arcminutes) and an average atmospheric refraction of 0.56667° (34 arcminutes) at the horizon (ref: US Naval Observatory).

Thus, sunrise and sunset are deemed to occur at sea level when the geometric center of the Sun is at an altitude of -0.83334° from the horizon, or 90.83334° from the Zenith of the sky. The apparent unobstructed horizon will be different for observers above or below sea level, which can be accommodated by applying the equation immediately below (ref: 1).

$$Z_{angle} = 90 + 0.83334 + (0.0347 \times \sqrt{H})$$

Where:

• Zangle = The angle of the center of the Sun from the zenith of the sky, in degrees.
• H = The elevation of the observer above sea level, in metres.

For most solar calculations, the relative variation due to local elevation changes are numerically insignificant compared to the radius of the Earth and distance to the Sun, so site elevation above sea level is rarely a required input parameter. In situations where that level of detail was required, a topographical or digital elevation model which includes the local terrain and apparent solar horizon would typically be used to derive the highly accurate shading values required.

## Twilight

Even well before sunrise and well after sunset there is still some natural light available from the sky due to refraction within the upper atmosphere. This is known as twilight and varies with the Sun’s altitude below the horizon. The twilight time before sunrise is typically known as dawn and the twilight time after sunset as dusk.

There are three defined categories of twilight based on the relative amount of skylight available and the activities that this light would typically allow. Obviously actual light availability is hugely affected by factors such as cloudiness and other local weather effects, so they are necessarily approximate but still useful and convenient definitions.

### Civil Twilight

Civil twilight occurs when the zenith angle of the center of the Sun is less than 96° (6° below the horizon) and the available skylight is still typically sufficient for most civilian outdoor activities. The apparent horizon is still clearly visible against the glowing sky and only the brightest of stars are beginning to show.

### Nautical Twilight

Nautical twilight occurs when the zenith angle of the center of the Sun is less than 102° (12° below the horizon) and the available skylight is no longer sufficient for detailed outdoor activities. However, the outline of the apparent horizon, as well as most large topographical features, are still distinguishable and the key stars used for navigational purposes have all typically become visible.

### Astronomical Twilight

Astronomical twilight occurs when the zenith angle of the center of the Sun is less than 108° (18° below the horizon) and the available skylight is effectively imperceptible compared to moonlight and starlight. Beyond this angle there is no longer any discernible atmospheric refraction so the time after astronomical twilight is basically night.

## References

1. Muneer, T. (2004), Solar Radiation and Daylight Models. Elsevier, ISBN 0 7506 5974 2. (View online)