LdT: A new index of ionospheric activity based on GNSS-derived rates of change in TEC

TL;DR

This paper presents $L_{\mathrm{dT}}$, a novel logarithmic ionospheric activity index derived from GNSS-derived rates of change in TEC ($\delta_{\textrm{EC}}$). It employs a distribution-focused analysis, fitting $P(\delta_{\textrm{EC}})$ with a Gaussian core plus two exponentials and, when data are rich enough, incorporating power-law tails, to robustly characterize ionospheric disturbances while avoiding moments that may diverge. The method includes data processing across global GNSS networks, data partitioning into space-time slices, and two-stage normalisation (path-angle correction and band-pair scaling) driven by quiet-day references, culminating in a wide-area index $L_{\mathrm{dT}} = 2 \log_2(40 W_{\mathrm{dT}})$. The index offers a practical, regionally-resolved, near-real-time metric of ionospheric geoeffectiveness that complements traditional geomagnetic indices and supports space-weather services and GNSS operations. The approach is demonstrated on quiet and storm-day scenarios, and it enables intuitive spatial maps and local-time dependent insights into GNSS propagation disturbances.

Abstract

Many aspects of our societies now depend upon satellite telecommunications, such as those requiring Global Navigation Satellite Systems (GNSS). GNSS is based on radio waves that propagate through the ionosphere and experience complicated propagation effects caused by inhomogeneities in its electron density. The Earth's ionosphere forms part of the solar-terrestrial environment, and its state is determined by the spatial distribution and temporal evolution of its electron density. It varies in response to the "space weather" combination of solar activity and geomagnetic conditions. Notably, the radio waves used in satellite telecommunications suffer due to the dispersive nature of the ionospheric plasma. Scales and indices that summarise the state of the solar-terrestrial environment due to solar activity and geomagnetic conditions already exist. However, the response of the ionosphere to active geomagnetic conditions, its geoeffectiveness, and its likely impact on systems and services are not encapsulated by these. This is due to the ionosphere's intrinsic day-to-day variability, persistent seasonal patterns, and because radio wave measurements of the ionosphere depend upon many factors. Here we develop a novel index that describes the state of the ionosphere during specific space weather conditions. It is based on propagation disturbances in GNSS signals, and is able to characterise the spatio-temporal evolution of ionospheric disturbances in near real time. This new scale encapsulates day-to-day variability, seasonal patterns, and the geo-effective response of the ionosphere to disturbed space weather conditions; and can be applied to data from any GNSS network. It is intended that this new scale will be utilised by agencies providing space weather services, as well as by service operators to appreciate the current conditions in the ionosphere, thus informing their operations.

Figures (14)

• Figure 1: Shows a combination of measurement sampling and categorization into low, medium, and high magnetic latitudes (coloured black, brown, and white respectively), regions where there is no data coverage are dark blue. The magnetic latitude zones are as determined at the altitude of the ionosphere (i.e. not the magnetic latitude at ground level), as based on a sinusoidal approximation to the relevant figure(s) shown at the end of the WMM2015 WMM2015 and WMM2020 WMM2020 reports. We use an ionosphere-altitude demarkation of magnetic latitude, because the signal intersection/interaction is in the ionosphere, and not at ground-level.
• Figure 2: A depiction of the four elements of the G2E fit, as well as the power-law tail, using a logarithmic vertical scale, and with differences exaggerated for clarity: (a) the offset of the central peak from the origin at $\delta_{\textrm{EC}}=0$ is given by the parameter $\alpha_0$; (b) the width and weighting of the gaussian component (cyan parabola) by $\alpha_1$ and $\alpha_2$; (c, d) the decay and weighting of the left hand (negative) and right hand (positive) exponential components (magenta dashed lines) by $\alpha_3, \alpha_4$ and $\alpha_5, \alpha_6$; and (e) the power law components (green dot-dashed lines) cutoff, fall-off exponent, and weighting by $\alpha_7, \alpha_8, \alpha_9$. Example histogram fits can be seen in the the Supplementary Material.
• Figure 3: Histogram plots with different path-angles as different colours, plotted using coloured markers and logarithmic scales to improve visibility. On the left we see data for entirely uncorrected dTEC values and unnormalised histograms, in the centre we see it with normalised histogram data, and on the right with dTEC values additionally scaled by $C^{1.65}$. Over the most likely ranges of log(dTEC), i.e. roughly between 0.01 and 0.3, we see that the histograms for different $C$ are now rather well matched. This data comprises all that from our quiet 006/007 days in 2022, but the same behaviour was also seen for our notional "typical" day 319 in 2022, as well as the active days 113/114 in 2023.
• Figure 4: The globally-aggregated weighted widths $W_{\textup{dT}}$ shown hour-by-hour for the two quiet days in 2022, i.e. 006, 007. In (a) we bin the dTEC events in two-hour slices "D" by UTC, but in (b) we show them by local/solar time two-hour slices "S". Widths are indicated for each magnetic latitude zone individually, and smaller markers indicate widths based on poorer fits to the data.
• Figure 5: The globally-aggregated weighted widths $W_{\textup{dT}}$ shown hour-by-hour for a ten-day period in November 2022. In (a) we bin the dTEC events in two-hour slices by UTC, but in (b) we show them by local/solar time. Although these plots contain a great wealth of detail, here we only intend them to indicate general trends and behaviours. The take-home message here is simply the increased regularity and periodicity of the local time data slices, especially at low latitudes. Widths are indicated for each magnetic latitude zone individually and smaller symbols indicate poorer fits.