Available online at www.sciencedirect.com ScienceDirect Advances in Space Research 60 (2017) 1797–1806 www.elsevier.com/locate/asr Height-dependent sunrise and sunset: Effects and implications of the varying times of occurrence for local ionospheric processes and modelling Tobias G.W. Verhulst ⇑, Stanimir M. Stankov Royal Meteorological Institute (RMI), Ringlaan 3, B-1180 Brussels, Belgium Received 29 March 2017; received in revised form 4 May 2017; accepted 29 May 2017 Available online 29 July 2017 Abstract It is well established that the sunrise and sunset periods are of particular importance to ionospheric research and modelling because of the rapid changes in the ionospheric plasma density, temperature, and dynamics. In particular, the sharp increase in the ionisation fol- lowing sunrise results in a quick increase in the ionospheric peak density, N mF 2, and a decrease in the peak height, hmF 2. Changes in plasma temperature, scale height and transport processes add further complexity which makes it difficult to investigate and model the ionospheric behaviour during this transitional period from night to day. One of the aspects contributing to this difficulty is that not all ionospheric altitudes are exposed to the first sunlight of the day at the same time. During sunrise, the upper part of the ionosphere is illuminated prior to the lower part which is still in the dark. The boundary between sunlit and dark regions moves downwards until it reaches the surface of the Earth, which is commonly taken as the moment of sunrise at certain geographical coordinates. This means that the sunrise at surface level does not occur until after the entire ionosphere has been illuminated. During sunset, the same process happens in reverse order. This paper addresses the issue of these altitude-dependent times of sunrise and sunset and reports on our study of some of the effects on the diurnal variations in the ionospheric characteristics. Ó 2017 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Ionospheric modelling; Geometrical astronomy; Sunrise/sunset 1. Introduction usually ignored. The amount of local photoionisation is commonly described by the Chapman production function, The ionisation of the neutral particles in the upper which is well known in the literature—see, for example, atmosphere is primarily the result of photoionisation Schunk and Nagy (2000). This production function caused by solar irradiation. The contribution of transport depends, among other things, on the solar elevation angle. processes to the ion and electron density depends strongly The LIEDR (Local Ionospheric Electron Density profile on altitude. At higher altitudes, transport processes have Reconstruction) model has been developed and used to sufficient influence to maintain of the F layer throughout reconstruct the local electron density profile for the entire the night, while at lower altitudes, in the E and D regions, ionosphere (see Fig. 1), including the topside (Stankov the transport processes are rather insignificant and are et al., 2011). This is a real time model, based on the iono- sonde characteristics automatically scaled from ionograms, as well as GNSS derived total electron content (TEC). In ⇑ Corresponding author. the current work, we use this model to reconstruct the elec- E-mail addresses: [email protected] (T.G.W. Verhulst), s.stan- tron density above the Dourbes ionosphere observatory, [email protected] (S.M. Stankov). http://dx.doi.org/10.1016/j.asr.2017.05.042 0273-1177/Ó 2017 COSPAR. Published by Elsevier Ltd. All rights reserved. 1798 T.G.W. Verhulst, S.M. Stankov / Advances in Space Research 60 (2017) 1797–1806 Fig. 1. Panel (A): Schematic of the vertical ionospheric ion and electron density profiles, indicating key characteristics such as peak density (N mF 2), peak density height (hmF 2), plasma scale height (H sc), and the ionospheric slab thickness. Panel (B): Comparison between vertical density profiles obtained with basic analytical models for a given scale height of 100 km. Panel (C): A sample of five profilograms produced in the course of one hour; each profilogram shows the electron density, N e (colour-coded, logarithmic scale on right) as a function of altitude (vertical axis) and time (horizontal axis). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) located at 50.1°N and 4.6°E. The LIEDR operational results altitudes. In this work we demonstrate a different, but con- can be found on the web-page http://ionosphere.meteo.be/ ceptually similar, approach: we switch between the fixed ionosphere/liedr. At the Dourbes observatory, a Digisonde profiles available in the LIEDR model, but we use different DPS4D digital ionosonde (Reinisch et al., 2009) and a profiles for the parts of the ionosphere which are sunlit NovAtel GPStation-6 GNSS receiver are co-located, pro- and the parts that are in darkness. This means that our viding all the necessary input data for the LIEDR model. method, too, is using different profiles at different altitudes. A major problem for the reconstruction of the complete The main distinction with the methods described in the electron density profile is that, while the ionosonde can be aforementioned literature is that we base our choice of pro- used to obtain the bottom-side characteristics, little infor- file function on the position of the sun alone, instead of his- mation is directly available for the topside ionosphere torical or real-time data. (Fig. 1). The topside TEC can be calculated from the total This paper is organised as follows. First, we derive the GNSS-derived TEC by subtracting the bottom-side TEC relevant mathematical formulas and computational algo- estimated from the bottom-side electron density profile rithms than can be used to calculate which part of the iono- reconstructed from ionosonde measurements. However, sphere is irradiated by the sun at a given time and place. to be able to deduce the topside electron density profile After this, we show various ionosonde observations, and from the topside TEC, a suitable profiler function must discuss their relation to the varying times of sunrise at dif- be chosen. In the LIEDR model, a Chapman profile, Epstein ferent altitudes. Finally, we show how the LIEDR model can profile, and exponential profile are available to model the be improved by adapting the topside profiles to the height topside. The model can switch between different profiler dependent sunrise and sunset. functions depending on various parameters like time of day, season, geomagnetic conditions, etc. (Verhulst and 2. Theoretical considerations Stankov, 2014, 2015). However, at different altitudes, the ionosphere is not 2.1. Height of the permanently sunlit region above a certain only exposed to the solar irradiation at different zenith location angles but is also exposed to the irradiation at different times during the sunrise and sunset periods. Simply switch- At a certain altitude above the Earth’s surface, depend- ing between different, fixed topside profiles for day and ing on the day of year and the latitude, the solar nadir is night might therefore not be sufficient to accurately model above the horizon. If this height (h ) is in the ionosphere, the ionosphere. Some proposed improvements are to use a i.e. below the upper O+/H+ ion transition level (UTL), a combination of various profiles, with different scale heights part of the ionosphere would remain sunlit throughout at different altitudes (Fonda et al., 2005; Kutiev et al., the night. This means that photoionisation, and plasma 2006), or to use a profile with an altitude dependent scale transport, would continue to take place in the ionosphere height (Reinisch et al., 2007; Nsumei et al., 2012). The gen- similarly to the daytime conditions. This is particularly eral idea of those methods is to improve the topside mod- important if h is at (lower) altitudes where the photoion- elling by using a different profile function at different ization becomes more significant. The issue is of T.G.W. Verhulst, S.M. Stankov / Advances in Space Research 60 (2017) 1797–1806 1799 Fig. 2. An observer at point P, at some altitude above the Earth’s surface at latitude u, sees the sun exactly on the horizon (ignoring breaking of light in the atmosphere, which is not very important for the ionising fraction of the spectrum). For an observer at the same latitude at sea level, the sun is below the horizon. importance with regard to modelling the topside iono- 1 À sinðu þ e cosðf Á nÞÞ h ðu; nÞ¼R ð7Þ sphere, since it is the topside ionosphere that remains sinðu þ e cosðf Á nÞÞ exposed to the solar irradiation for much longer periods. At midnight during summer solstice, assuming that the Fig. 3A shows this height as a function of latitude for sunlight arrives at the Earth parallel to the ecliptic and that the summer and winter solstices in the Northern Hemi- sphere. The summer curve reaches an altitude of zero at the Earth is spherical, the height h above the Earth’s sur- ° face can be derived from the following equation: 66.56 , which is indeed the latitude of the polar circle. A slightly more accurate formula can be obtained by not R þ h cos / ¼ R ð1Þ using the above approximation (5) but instead using the following expression for the solar declination d : R / ¼ p À h where is the Earth’s radius and 2 (see Fig. 2). From this equation, it follows that 1 À cos / h ¼ R ð2Þ cos / 1 À sin h ¼ R ð3Þ sin h or, with h ¼ u þ e (where u is the latitude and e ¼ 22:44 ¼ 0:3917 is the obliquity angle): 1 À sinðu þ eÞ h ðuÞ¼R ð4Þ sinðu þ eÞ In order to obtain a formula for days other than at sum- mer solstice, the solar declination d needs to be used instead of the obliquity angle.