Cyclic Aspects of Time

The alternation of day and night is important for most animals. It influences the behavior and use of their habitat. At first it looks straight forward to implement temporal data frames similar to the basic case above for this temporal aspect using a position and width parameter (figure 4.3). As an example it could be the aim to select all observations which occurred at dawn. At a second glance it is more complex than expected. There are three reasons for this:

1. The single temporal data frame is replaced by a large number of data frames. For every day a frame has to be constructed which selects the data within dawn at that day. This means a shift from a single TDF to multiple TDFs.

2. Sunset, sunrise and dawn times and all their related aspects are variable throughout the year and change with the position of the earth on its orbit. Figure 4.4 illustrates this fact. In the northern hemisphere the nights are longest in December and shortest in June. In the southern hemisphere this is reversed.

3. Dawn duration as one example depends on the latitude. This is illustrated in figure 4.5. There are two things worth noticing here. First the duration of dawn is longer the further we are from the equator. Second there are two (!) periods with long dawn durations in the year. In the northern hemisphere they are in December and June, while the shortest dawn durations occur in March and September.

Figure 4.3: Illustration of temporal data frames. A temporal data frame can be used in a cyclic time aspect as for example the daily sun movements (geocentric) or moon movements. It is defined as in the basic form with a position and a width parameter. It selects all data e.g. within dusk, which basically means that multiple data frames are set up at intervals covering all dusk times over the whole observation period.

Figure 4.4: Changes of the sunrise (upper line) and the beginning of the civil twilight (lower line) during the year at a latitude of 40$^{\circ}$ north.

Figure 4.5: Changes in the duration of the twilight during the year. Upper line (blue): latitude: 40$^{\circ}$. Lower line (red): latitude: 0$^{\circ}$. Twilight in the northern hemisphere is shortest in spring and summer. The duration of the twilight is also shorter closer to the equator.

This amount of complexity requires that the necessary calculations are automated and become an inherent part of a temporal data frame. These include coordinate system transformations (e.g. Swiss coordinate system to latitude/longitude), time transformations (UTC to JD) and calculations of the angle of the sun above or below the horizon.

The dawn was chosen as an easily understandable example. It is defined in three versions as the civil, nautical and astronomical twilight. They are defined as the time that starts when the sun is 9$^{\circ}$, 12$^{\circ}$ and 18$^{\circ}$ below the horizon and ends at sunrise. It should be clear that the temporal data frames are not limited to these figures and can be applied at continuous ranges of values. The dawn is only one specific setting of values for a TDF.

I used the examples of sunrise, sunset and dawn above. There are other temporal aspects that are relevant in this context. Aside from solar there are lunar aspects that need to be considered. The lunar altitude, azimuth and its illumination are cyclic phenomena often standing on the wish list of a wildlife researcher for the analysis of his or her data. In most cases it remains a wish due to missing methods for handling these aspects. By introducing the concept of temporal data frames as a new method in the field of exploratory data analysis, it becomes possible to gain insights into animals' responses to such phenomena connected to solar and lunar and possibly other rhythms.