1. Introduction
Over the last decades, the Global Navigation Satellite System (GNSS) has become a valuable tool for remote sensing of the ionosphere. Using dual-frequency measurements, one of the most important ionospheric quantities, the total electron content (TEC), may be obtained. This ionospheric TEC is usually provided in the IONosphere EXchange format (IONEX) in the form of global ionosphere maps (GIMs). Currently, seven Ionosphere Associated Analysis Centers (IAACs) of the International GNSS Service (IGS) generate their own GIMs [
1]. These ionospheric products are commonly used in many practical and scientific applications, like precise positioning or space weather studies. For example, GNSS users require ionospheric corrections to improve their position estimates [
2,
3,
4,
5]. Moreover, space weather and geophysical studies are often based on GIM data [
6,
7,
8].
Since there is a wide range of the above-mentioned engineering and geophysical applications of GIMs, it is essential to validate empirical accuracy of the ionospheric products. So far, several studies have been published in the context of the GIMs performance. This kind of research is based on the comparison of the TEC derived from the IAAC models with selected reference TEC values. Given that GIMs are global products, two complementary methods are recommended to investigate their quality: (1) direct comparison to relative slant TEC (STEC) from dual-frequency GNSS observations, and (2) comparison to vertical TEC (VTEC) derived from dual-frequency satellite altimeter measurements above the oceans [
9]. As is well-known, the ionosphere is primarily driven by solar and geomagnetic conditions. Therefore, GIM performance is generally studied in relation to different solar activity levels as well as under different geomagnetic conditions [
10,
11,
12]. Since the ionosphere is characterized by spatial variability, the assessment of GIM often divides the Earth into a few latitude-dependent regions [
13].
It should be noted that ionosphere temporal variability may have a noticeable impact on GIM accuracy. In the beginning of the IGS Ionosphere Working Group activity, all contributing IAACs produced GIMs at a 120-min interval. Over the years, some of the centers have started to provide products with higher temporal resolution. Currently, the IAACs provide GIMs with intervals ranging from 30 to 120 min. Besides the IGS products, the Ion-SAT group from the Polytechnic University of Catalonia (UPC) generates GIM (UQRG) with a very high resolution of 15 min [
14]. However, the relation of GIMs interval to their accuracy is still under-researched. One of the recent studies on GIM performance that includes GIM interval analysis was published by Roma-Dollase et al. [
15]. This analysis, based on UPC GIMs, was performed in relation to VTEC altimeter data. Liu et al. [
16] presented the study focusing entirely on the influence of the temporal resolution, however again only UPC GIMs were analyzed. Besides these two well-known investigations, the studies on GIM performance usually do not consider their temporal resolution. Therefore, we propose a comprehensive study focused on the influence of GIM interval on performance of IAAC final ionospheric products. In our study, IAAC GIMs and UQRG GIM were assessed with GNSS and altimetry-derived TEC during selected low and high solar activity periods, as well as during geomagnetic storms, and also over different geomagnetic latitudes.
2. Materials and Methods
To analyze GIMs under different solar and geomagnetic conditions, we selected four periods:
Year 2014, representing high solar activity period (F10.7 index ranged from 89 to 253 sfu);
Year 2018, representing low solar activity period (F10.7 index ranged from 65 to 85 sfu);
the first case study during geomagnetic storm on 19 February 2014 (max Kp = 6+);
the second case study during the St. Patrick’s Day geomagnetic storm on 17 March 2015 (max Kp = 8−).
In each of these periods, GIMs were also analyzed with respect to three distinctive geographic regions. The analysis was performed for (1) low geomagnetic latitudes covering equatorial region (from 30°S to 30°N), (2) mid-latitude region (from 30° to 60° in both hemispheres), and (3) high latitudes covering polar and auroral zones (from 60° to 90° in both hemispheres). For the investigation, we chose the final GIMs, providing grids of VTEC values with spatial resolution of 2.5° × 5° in the latitude and longitude, respectively. In our study, we tested three IAAC GIMs and also UQRG GIM, since these GIMs are available with higher temporal resolution than standard 120 min (see
Table 1). Each product was analyzed with its nominal temporal resolution, and additionally with resolution reduced to 60 and 120 min.
In order to comprehensively evaluate the analyzed models, we made a comparison of GIM-derived TEC with two independent reference TEC data sources: STEC from ground GNSS observations (GNSS-STEC) and VTEC from altimeter measurements (Alt-VTEC) over the oceans. The former reference data are based on the precise carrier phase L1 and L2 observables. These observables form the geometry-free linear combination (
) that is used to extract STEC data along phase continuous data arc between receiver
i and satellite
k. This is the most precise evaluation method often called self-consistency analysis, and according to Feltens et al. [
20] its accuracy is of about 0.1 TECU. In this study, we used the approach published by Krypiak-Gregorczyk et al. [
21], where GNSS geometry-free data are fitted into GIM-derived STEC, and post-fit residuals (RMS) are analyzed (
Figure 1). Namely, (1)
combination is created for each continuous data arc cleaned from gaps and cycle slips, (2) STEC from GIMs is calculated for the same data arc at ionosphere piercing points (IPP), (3)
is fitted into GIM-derived STEC resulting in GNSS-STEC, (4) post-fit residuals are created, and (5) their RMS is calculated as a GIMs accuracy metric. As IPP locations change with every observational epoch, this approach allows for testing GIMs in both space and time.
For this approach, 18 globally distributed stations were selected (
Figure 2). The calculations were carried out using the GPS data with 30-s intervals and 25° elevation cut-off. In the case of GIMs data, VTEC values were interpolated using a method recommended by Schaer et al. [
22]. This approach is based on linear interpolation, and it is a function of latitude, longitude and time. Then the resulting VTEC was converted to STEC using the standard single layer model (SLM) mapping function (h = 450 km and α = 1, [
18]).
The latter data source uses altimeter measurements for GIM evaluation. Dual-frequency altimeters enable the determination of reference VTEC, which is a unique and independent source of TEC data, as it provides VTEC directly with no mapping function need [
9]. This data are limited to sea/ocean regions (
Figure 3), hence allowing GIM evaluation in areas far from the GNSS stations. In this study, we selected data from Jason-2 and Jason-3 satellites. More detailed description of VTEC data extraction from altimeter measurement can be found in Imel [
23]. One should keep in mind that altimetry-derived VTEC needs to be preprocessed (filtered and smoothed) to serve as a reference for GIM evaluation. Therefore, we used the median with a window of 80 s, which filters altimetry VTEC in low-pass mode, removing high-frequency noise and making it more comparable to the upper frequencies of GIMs. Applying this process results in Alt-VTEC accuracy of about 1 TECU [
9]. To achieve consistency with GIM VTEC, altimetry data were complemented with remaining plasmaspheric VTEC above the satellite orbital height (over ~1300 km). For this reason, we used model-derived plasmaspheric VTEC from the NeQuick-2 empirical model [
24]. Our earlier study shows that the application of plasmaspheric VTEC improved the comparison results by even 11% [
12]. Moreover, VTEC data are also affected by unknown instrumental bias. To reduce this bias, our analysis was based on standard deviation (STD) of differences between Alt-VTEC and GIM VTEC.
4. Conclusions
This study confirmed the influence of GIMs temporal resolution on TEC accuracy. Indeed, based on GNSS-STEC and Alt-VTEC analysis, this influence is clearly correlated with the phenomena that drive the ionosphere, such as solar and geomagnetic conditions. It can be observed that the accuracy degradation is the highest for the 120-min interval. In addition, the influence of temporal resolution is the most clearly visible in low-latitude region. This may indicate that higher TEC and its gradients existing over the equatorial anomaly require higher temporal resolution to be properly represented by GIMs. Moreover, the degradation of accuracy with increased map interval is even more evident during the geomagnetic storms. Looking at the results obtained for UQRG, it can be concluded that the more severe storm, the greater influence of the temporal resolution on GIMs accuracy.
In general, the interval of 60 min seems to be a good compromise between maps’ temporal resolution and their resulting accuracy and may be recommended in ionosphere GNSS remote sensing applications. This confirms suggestions presented by Liu et al. [
16], who showed that temporal resolution higher than 1 h had a significant impact on accuracy degradation. Note, however, that this conclusion concerns the final IAAC products only. The quality of the real-time GIMs is still worse, even though they are provided with higher temporal resolutions [
26].
Specific results show that the highest accuracy is obtained for the high-resolution UQRG15 maps, which are based on stochastic technique (kriging). It is interesting that in the case of CASG maps the interval has a lesser influence on the accuracy in comparison to other GIMs. This may suggest that the intrinsic interval of the underlying model is longer than 30 min.