Open AccessArticle

The Movement of GPS Positioning Discrepancy Clouds at a Mid-Latitude Region in March 2015

Janis Balodis

^1,*

Madara Normand

^1,2 and

Ansis Zarins

Institute of Geodesy and Geoinformatics, University of Latvia, LV-1586 Riga, Latvia

Department of Geomatics, Riga Technical University, LV-1048 Riga, Latvia

Author to whom correspondence should be addressed.

Remote Sens. 2023, 15(8), 2032; https://doi.org/10.3390/rs15082032

Submission received: 28 March 2023 / Accepted: 7 April 2023 / Published: 12 April 2023

(This article belongs to the Special Issue Applications of Remote Sensing in Monitoring Ionospheric Physics and Ionospheric Weather Forecasting)

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Figure 1
A schematic map of the Latvian CORS networks. "> Figure 2
Plot of subsets of Formula (9). "> Figure 3
Time of maximum intensity (count of disturbed sites) of regular disturbances. Average change of maximum time was 4 min 8 s per day. "> Figure 4
The time series of 30 sites involved at sequential time moments (with 1.5 min steps) on the latitude–longitude coordinate plane. "> Figure 5
Dependency of number of disturbed sites on time (UT) for 5, 6, and 17 March. "> Figure 6
Count of faulty solutions of each station in subsets <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <mo>∈</mo> <mi>B</mi> <mo> </mo> </mrow> </semantics></math> for 17 March (STORM) and in subsets <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <mo>∈</mo> <mi>B</mi> </mrow> </semantics></math> on other days in March 2015 (OTHER). "> Figure 7
Mean discrepancies for ‘calm’ days (MEAN C) and for storm day, 17 March (MEAN S). "> Figure 8
Standard deviation for ‘calm’ days (STD C) and for storm day on 17 March (STD S). "> Figure 9
Pearson’s correlation coefficients in relation to discrepancies and ROTI for all 36 peak subsets. "> Figure 10
Pearson’s correlation coefficients in relation to the peak discrepancies on 1 March and the peaks on other days. "> Figure 11
The percentage of coincidence of subsets in the intersection of the peak cloud on March 1, with peak clouds on other days (subsets ∊ P) in March (in blue), and a summary of the intersection of all five-cloud subsets on 1 March, with five-cloud subsets on other days (subsets sets ∊ P′) (in red). "> Figure 12
Count of common stations inside the five-cloud subsets intersection in each group (<math display="inline"><semantics> <mrow> <msup> <mi>P</mi> <mo>′</mo> </msup> </mrow> </semantics></math>). "> Figure 13
Center coordinate variations for 36 peak clouds in March 2015 (on the left side <math display="inline"><semantics> <mi>P</mi> </semantics></math>, see <a href="#app1-remotesensing-15-02032" class="html-app">Supplementary Files, Figure S5</a>) and 149 clouds during the geomagnetic storm on 17 March (on the right side <math display="inline"><semantics> <mi>B</mi> </semantics></math>, see <a href="#app1-remotesensing-15-02032" class="html-app">Supplementary Files, Figure S6</a>), where the last peak batch of 17 March is not included. "> Figure 14
Latvian CORS stations and their respective loss-of-lock start times and durations in minutes (B). "> Figure 15
All faulty events and a count of faulty solutions on 16–18 March 2015, in the set of RIMS station solutions GVLA and GVLB, LAPA and LAPB, and WRSA and WRSB. "> Figure 16
RIMS stations and their respective loss-of-lock start times and durations in minutes. "> Figure 17
Typical plot of 90 s sequential discrepancies of RIMS station, GVLB N (blue), E (orange), Up (red). No. of sequential 90 s events on the x-axes. Event No. 64 in <a href="#app1-remotesensing-15-02032" class="html-app">Tables S13 and S14</a>, correspondingly. No. of sequential recurrence of loss of lock on x-axes. ">

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Abstract

The geomagnetic storm on 17 March 2015 had a strong impact on the global navigation satellite systems (GNSS) positioning results in many GNSS Continuously Operating Reference Stations (CORS) in Europe. The analysis of global positioning system (GPS) observations in Latvian CORS stations discovered a strong impact of this space weather event over the whole country. The impact appeared as a moving cloud of positioning discrepancies across the country. However, the analysis of the days before 17 March revealed other smaller duration ionospheric scintillation events. The objective was to analyze the GPS positioning discrepancy cloud movement, total electron content (TEC), and rate of change of the TEC index (ROTI) relationships, as well as discrepancy statistics. The area of analysis on 16–18 March was increased by including the EGNOS ground-based Ranging and Integrity Monitoring Stations (RIMS): GVLA and GVLB, LAPA and LAPB, and WRSA and WRSB. The conclusion of the study is that each “shot” after 90 s gives a completely new cloud with a new impacted station subset, its configuration, and completely irregular discrepancy values.

Keywords:

ionosphere; ionospheric irregularities; space weather; GPS discrepancy clouds; RIMS

1. Introduction

The objective of this study was to discover the ionospheric scintillation events as a result of space weather in a time series of reduction results of observations in March 2015. The results that were analyzed were obtained in a reduction of Latvian Continuously Operating Reference Stations CORS GPS observation data using Bernese GNSS Software v5.2 [1] at the Institute of Geodesy and Geoinformatics, University of Latvia (LU GGI) [2]. Latvia is located in a mid-latitude region with magnetic latitude from 52° to 54°N. In this article, the cases of degraded results were searched in suspicion of a space weather impact on GPS observation results in the entire observation series in March 2015.

Space weather impact plays an important role in GNSS positioning, navigation, and timing tasks. In order to avoid space weather impact, many research groups around the world are conducting research on the development of precise ionosphere products. A number of linear and nonlinear variables have been observed in the ionosphere on GNSS group delay and phase advance in carrier wave phenomena, which effect radio wave communication and navigation signals, Faraday polarization, refraction, Doppler shift, scintillation, etc. The temporal and spatial variations included periodic variations such as daily, monthly, seasonal, and annual variation, and momentary disturbances [3].

In [4], space weather is defined, and the primary phenomena that produce a potential space weather impact on GNSS applications in particular are described: the introduction of large gradients in the ionospheric total electron content (TEC); the rapid variation of a signal’s amplitude and/or phase (scintillation); and/or the sudden increase in background noise.

Global ionosphere maps (GIMs) representing ionospheric total electron content (TEC) are applicable in many scientific and engineering applications and are generated with different temporal resolutions and using different modeling techniques. The Ionosphere Working Group of the International GNSS Service (IGS) is represented by four internationally well-known analysis centers: CODE, ESA/ESOC, JPL, and UPC. The results are available online in NASA’s CDDIS Archive of Space Geodesy database. The TEC routine generation of combined ionosphere maps has been available since 1998. Today, three types of TEC maps are produced: final, rapid, and predicted (NASA’s CDDIS Archive of Space Geodesy Data). The IGS produces the global ionospheric TEC maps described in [5]. The near real-time TEC maps using GPS observations are produced by the Royal Observatory of Belgium with a coverage of every 15 min on 0.5 × 0.5 grids [6]. Near real-time and forecast TEC maps are also produced by the IGS and the European Space Agency (ESA) and NASA. The online TEC global maps of the MIT Haystack Observatory are additionally useful [7].

The approach for regional ionosphere modeling based on undifferenced multi-GNSS carrier phase data for TEC estimation, and thin plate splines for TEC interpolation, is described in [8]. An analysis of the ionospheric corrections required to obtain a significant improvement in PPP-RTK performance, in order to improve position precision, is presented in [9]. Space weather impact on RTK positioning precision in Latvian CORS environment was studied by [10,11].

Satellite laser ranging (SLR) tests show that the impact of higher-order ionospheric (HOI) delay correction can improve the inner and outer coincidence precision of a low earth orbiter (LEO) satellite’s precise orbit determination (POD) and that the improvement decreases gradually with increasing LEO satellite orbit altitude. In summary, the impact of HOI delay on the POD precision of LEO satellites is at the submillimeter level [12]. HOI is not applicable for ground-based GNSS observations.

The GPS-based rate of change of the total electron content index (ROTI) values are more sensitive for events that lead to loss of lock, as evidenced by jumps in the L1 phase values [13]. The use of ROTI as a scintillation index allows observation of TEC fluctuations, which can be used as an estimate of the likelihood of the ionospheric amplitude scintillation. Usually, ROTI > 0.5 in TEC units (TECU)/min indicates the presence of ionospheric irregularities at a length of a few kilometers [13].

The most significant space weather event in the recent past was the St. Patrick’s Day geomagnetic storm on 17 March 2015. Many authors have discussed this event [14,15,16,17,18,19,20]. In space weather research, the investigations of ionospheric storm effects are of fundamental importance [21]. The impact is more severe at high latitudes, while at low latitudes the impact is associated with different types of ionospheric disturbance. By contrast, midlatitude irregularities are less severe, and they are usually attributed to expansion of auroral and/or equatorial irregularities under disturbed conditions [21]. GPS data at a sampling rate of 30 s from 5500 + GNSS stations were processed to characterize ionospheric disturbances and solve kinematic PPP solutions for 17–18 March 2015 by [21]. The St. Patrick’s Day storm in 2015 was the first super geomagnetic storm during the 24th Solar Cycle, and it has gained the attention of many researchers [22].

The high-latitude ionosphere dynamics were studied by [23]. Arrays of ground-based instruments were used, including GPS receivers, HF radars, ionosondes, riometers, and magnetometers [23].

The space weather was very complicated during March 2015; many M-class solar flares occurred in the lead up to the St. Patrick’s super magnetic storm. The X-ray irradiance was active; one X-class flare on 11 March was exactly X2.2, and there were several M-class flares between 2 and 18 March and many C-class flares. After 18 March, there were only C-class solar flares [22]. The space weather before the St. Patrick’s magnetic storm was much more disturbed than after the St. Patrick’s storm, and it reached the most disturbed conditions on St. Patrick’s Day. In the period between 9 and 18 March, there was at least one M-class flare each day, while the Kp, Dst, and AE indexes showed an absence of anomalies before 17 March [22]. During the main phase of the St. Patrick’s magnetic storm (17 and 18 March), there were also jumps for ROTI, but the amplitude was much smaller than the days before in this study. After analyzing the ROTI series in Hong Kong from 9 to 16 March, strong ionospheric scintillation events were observed [22].

The same was observed in Riga (see Tables S1 and S2 in the supplementary files, published online alongside the manuscript).

The St. Patrick’s Day storm was analyzed by [24]. The Global Ionospheric Model (GIM) CODG120 daily STD was 6.47 TECU, with changes during the day of 6.1% in low latitude regions [24]. Their study confirmed the influence of the GIM’s temporal resolution on TEC accuracy.

The GPS observation reduction for Latvian Continuously Operating GNSS Stations (CORS) revealed the ionospheric scintillation in Latvian CORS on a daily basis, similar to on 18 March 2015, as mentioned by [14]. The positioning degradation was not as effective as on March 17; however, ionospheric scintillation for a short period of time continued daily for the whole month of March. GPS observations are mostly used in navigation devices [25], contrary to other GNSS. A schematic map (Figure 1) represents the coverage of Latvian CORS stations in the country (LatPos network [26]) ref. [27] and in the city of Riga (EUPOS^®-RIGA network). The International GPS/GNSS Service (IGS)/European Permanent Network (EPN) station RIGA 1084 [27,28], which is located in the city of Riga, was also included in data analysis. The Latvian CORS observation reduction was performed in 2019, and TEC values were extracted from CODE’s European ionosphere information files [29].

The analysis of space weather’s impact on Latvian CORS stations was performed for both the day of the geomagnetic storm and for the so-called ‘calm’ days in March.

Daily RINEX observations (30 s sampling rate) for the full set of Latvian CORS and six selected RIMS stations (just for 16–18 March) were used by dividing log data into 90 s sessions (90 s) for both CORS and RIMS station coordinate computation. Selective daily GPS observation data, post-processed with Bernese GNSS Software v5.2 in a double-difference (DD) mode, was used to identify the disturbed results in March 2015. The data of EPN reference stations LAMA, METS, VIS0, and VLNS were used. Analysis of the 90 s GPS observation kinematic solution results was performed. The results of the analysis of post-processing data are described in this article.

The term “evil waveform” is used to denote the disturbed information for navigation in some areas caused by the GPS clock error [30]. Astronomers, in the case of interplanetary magnetic field (IMF) movement in space, use the term of the movement of molecular clouds [31]. In this article, the term “GPS positioning discrepancy clouds” was used when analyzing the nature of irregularities of the ionospheric scintillation’s disturbed positioning results.

In the framework of this article, the discrepancy clouds were analyzed. The discrepancies’ distribution and correlation analysis in discrepancy peaks, as well as the correlation with ROTI instead of TEC because the bins of ROTI information were much smaller than the max TEC values per day, were applied in Bernese GNSS Software v5.2 solutions. The whole set of disturbed solutions/stations with associated subsets of discrepancies and ROTI values for analysis was divided into three analyzed subsets.

The conclusion we drew was that the ionospheric scintillation events occurred each night in the post-midnight/predawn time in March 2015 alongside the St. Patrick’s Day storm degradation of positioning results. The size of individual disturbances was not predictable.

2. Data and Methodology

First, the post-processing of the selected dataset in the Bernese GNSS Software v5.2 [1] was carried out during the contract work in 2020. Computing strategy parameters included a kinematic double-difference network solution, ionosphere-free linear combination, CODE products, and four IGS/EPN network stations (LAMA (Olsztyn, Poland), METS (Metsahovi, Finland), VIS0 (Visby, Sweden), VLNS (Vilnius, Lithuania)) as reference stations. GPS observation data with an elevation cut-off angle of 15° were used for 90 s (sampling data 30 s) intervals of kinematic post-processing. The FES2004 ocean tidal model was used, along with correction of the solid Earth tide effect. The dry global mapping function (DRY-GMF) was used for the tropospheric delay modeling. The maximum size of accepted cycle slip corrections was 10.

For the analysis of the post-processed data, we used software programs in Fortran g95, C++, and Phyton programming languages, developed at LU GGI.

The Bernese GNSS Software v5.2 post-processed data solutions were validated. The positioning results with discrepancies of >10 cm were compared with filtrated average monthly station coordinates. The obtained solutions were considered faulty solutions if the values of discrepancies differed by more than the threshold of ±10 cm (Northing, Easting, Up, or summarized sqrt (dN² + dE² + dh²)). The analysis methodology using the software developed by the authors of this article is described below.

The analysis of space weather impacts on GPS positioning in Latvian CORS stations found strong degradation during the St. Patrick’s Day geomagnetic storm on 17 March 2015. However, the less degraded results were fixed daily in post-midnight/predawn ionospheric scintillations for the whole month of March 2015. In this article, the sets of simultaneously occurring discrepancies over the network of CORS stations that were formed by a subset of CORS stations were named discrepancy clouds due to the electron density irregularity in the ionosphere, which can also be considered the electron cloud, similar to molecular clouds in [31].

For data analysis and the data structure statement, Formulas (1)–(8) were formed in the expressions of mathematical logic and set theory on the basis of [32]. The whole set of obtained information was denoted by set T. The subset

S

of Latvian CORS stations was denoted by their DOME names

(s_{j}),

where the count of stations (cardinality of set

S

) was 30 for March 2015 (Formula (1)).

S : = \{‹ s_{j}, φ_{j}, λ_{j} › : 1 \leq j \leq 30\}

(1)

Here, the station’s name (DOME) is s, latitude is φ, and longitude is λ.

The faulty solution data samples for demonstration are presented in several tables in the supplementary files. The records (subsets) with numerical indexing, date, and time in Table S4 present stations where the various size discrepancies occurred simultaneously. In Table S5, discrepancy values for the same events as in Table S4, with numerical indexing, date, time, and additional discrepancies (Northing, Easting, Up, and summary error), as well as the ROTI for each S4 record (subset) station, are given. The ROTI value was in the magnetic local time for a fixed station site [33]. Discrepancies greater than 10 cm are denoted by the symbol “d”, without separation of the coordinate component and ROTI.

In each Day

D_{i}

(31 days in March), there were various counts of records (subsets of stations symbolically named as discrepancy clouds), and various counts of stations in each record as well (Formula (2)). The clouds (subset of stations where discrepancies occurred simultaneously) are denoted by

p_{i}

and the subset of discrepancies and ROTI by

w_{i}

(Equation (3)). For CORS observations in March, a total of 892,800 Bernese GNSS Software v5.2 90-sec solutions were generated. The count of space weather-impacted solutions as of March 2015 was 9587 (1.1%), which in view of the station names (DOMEs) is depicted in subsets of stations in 1584 rows (records) in Table S4. The GPS positioning discrepancies, which occurred simultaneously in several stations, were considered in further analysis.

Each subset

p_{i}

(1 ≤ i ≤ 1584), denoted as a discrepancy cloud, is described as a subset in Formula (3). The cardinality of the whole set of clouds in March was 1584.

p_{i} : = \{‹ s_{i j} › : j \in ‹ D_{i}, t_{i} ›, n_{i} \in ‹ D_{i}, t_{i} ›, 1 \leq j \leq n_{i}\}

(2)

The sample of the subset

w_{i}

(Formula (3)) describing data content is depicted in Table S5. The union (4) of all 1584 discrepancy subsets represents the information of the positioning-degraded results.

w_{i} : = \{‹ k_{i}, D_{i}, t_{i}, s_{i j}, d_{i j}, r_{i j} › : j \in ‹ D_{i}, t_{i} ›, n_{i} \in ‹ D_{i}, t_{i} ›, 1 \leq j \leq n_{i}\}

(3)

W : = \cup \{w_{i}, 1 \leq i \leq 1584\}

(4)

The symbol

n_{i}

defined in Formula (5) denotes the cardinality of selected subsets described in Formulas (2) and (3).

N : = \{n_{i} : n_{i} \in | p_{i} |, 1 \leq i \leq 1584\}

(5)

Both the cloud (or subset of stations)

p_{i}

and cloud discrepancy information

w_{i}

are connected with a corresponding record number

k_{i}

, date, time

t_{i}

, and count of stations in each subset

p_{i}

(see Tables S4 and S5).

The peaks of the station count of simultaneously occurring discrepancies (Table S4) were selected for each day in March. These subsets of

p_{i}

are shown in Table S6, including seven peaks from St. Patrick’s Day (March 17) to those defined for each day (excluding less intensive ionospheric disturbances on March 12). Seven peaks were selected on March 17 (day of ‘storm’). The count of selected subsets was then 36. Formula (5) describes the cardinality of the selected subsets. Subset P of Formula (6) denotes the union of all 36 peak subsets. On each day

D_{i}

, there was one subset with max station cardinality (Formula (6)). The max occurrence subsets were different for each day of the month.

P : = \cup \{‹ k_{i}, D_{i}, t_{i}, p_{i}, d_{i j}, r_{i j} › : j \in ‹ D_{i}, t_{i} ›, j \leq n_{i}, n_{i} = \max \in D_{i}\}

(6)

The daily peak subsets for each ‘calm’ day in March were very similar to each other, occurring approximately after midnight in predawn time, except for 17 March. The subsets

p_{i}

contained the site names of stations

s_{i j}

, where faulty positioning solutions occurred with discrepancies

d_{i j}

(summary error) and ROTI values

r_{i j}

for these exact sites at this exact event time

t_{i}

. For correlation analysis, Table S6 was designed.

On each day, there were occasions where several clouds followed each other every 90 s (1.5 min). The subset of adjacent clouds in this article were named batches and denoted by

b_{i}

for each day “i”. In each batch

b_{i}

(Formula (7)), there were various numbers of clouds described by Formulas (3)–(5).

However, on the day of the geomagnetic storms, there was more than one batch; therefore, on this day, instead of one batch, a group of batches was considered. The group of batches was just on 17 March. The subsets

b_{i}

(batches of clouds) contained subsets (records)

p_{i j}

with numerical auxiliary

k_{j i}

on the fixed date

D_{i}

, time events

t_{j j}

, and discrepancies

d_{i j}

, which are subsets

b_{i} \in B

(Formula (7)). The batches were counted only in situations when the adjacent subsets

p_{i j}

occurred simultaneously in three or more stations.

b_{i} : = \cup \{‹ k_{i j}, D_{i}, t_{k_{i j}}, p_{k_{i j}}, w_{k_{i j}} › : \exists k_{i j} \in D_{i}, \exists t_{k_{i j}} \in D_{i}, \exists t_{k_{i j} + 1} \in D_{i}, (t_{k_{i j} + 1} - t_{k_{i j}}) \leq 90 s e c, n_{i k_{i j}} \geq 3\}

(7)

For each day “i” subset

b_{i}

is the union of subsets of various sizes containing cloud information of corresponding days, resulting in cardinality

|b_{i}|

. There were 32 batches of clouds in March 2015, and two of them on 17 March. The union of batches (8) was denoted by B.

B : = \cup \{b_{i}, 1 \leq i \leq 32\}

(8)

For example, in subset

b_{5}

, Table S4 gives the records from 256 to 272 with names of DOMEs belonging to subsets

p_{256}, p_{257}, \dots, p_{272}

of Day 5, time from 22:55:30 to 23:19:30 with a step of 90 s; in Table S5, the discrepancies and ROTI belonging to subsets

w_{256}, \dots, w_{272}

are depicted. In Table S5, records 258–266 are given in order to use this data to understand Figure 2. In each of these records in Tables S4 and S5, no less than three CORS stations (DOMEs) were considered.

In order to analyze the movement of discrepancy clouds over the territory of Latvia, the subset

P^{'}

of the groups of five adjacent clouds (Table S8), as a part of the daily cloud batch, were selected from set

B

. These were chosen as two subsets before the peak and two after the peak (in addition to the peak subset) to study the movement of adjacent discrepancy clouds within each day.

Further analysis was performed in three data divisions: cloud batches (subsets

B \in T

), 36 selected peak clouds (

subsets P \in T)

, and 36 subsets of adjacent 5-cloud groups (

P^{'} \in T

), where the peak cloud was the central one. These groups were denoted by

B

P

, and

P^{'}

. The subset relationships are described by Formula (9).

P \subset P^{'} \subset B \subset T

(9)

The plot of subsets of Formula (9) is depicted in Figure 2 (see Table S7 in supplementary files). The subsets’ discrepancies and ROTI related to corresponding subsets were then analyzed further.

The analysis procedures were performed as follows:

For selected batches $b_{i}$ , the discrepancy scatter plots for Table S5’s sample subsets with a discrepancy size proportional to the logarithm of the Up component discrepancies were designed in order to validate the discrepancies’ distribution in adjacent 90 s (1.5 min) time events $t_{k}$ (Figure 3).
For peak subsets $P$ , Pearson’s correlation coefficient was computed to find the relationship between discrepancies (subset $d_{i j}$ ) and the ROTI (subset $r_{i j}$ ) by using $d_{i j}$ , $r_{i j}$ instead of $x_{j}$ , $y_{j}$ in Equation (10) [34].

R_{x y} = \frac{\sum_{j = 1}^{n} (x_{j} - \bar{x}) (y_{j} - \bar{y})}{\sqrt{\sum_{j = 1}^{n} {(x_{j} - \bar{x})}^{2} \sum_{j = 1}^{n} {(y_{j} - \bar{y})}^{2}}}

(10)

For peak subsets of $P$ , the intersection of the peak on 1 March (subset $p_{1}$ ) with 35 other peaks was performed in order to find the commonly impacted stations. The intersection is described by Formula (11). The intersection result is shown in Table S8.

c_{v} : = \{‹ s_{1 j} › \cap ‹ s_{v l} › : \exists s_{1 j} \in p_{1}, \exists s_{v l} \in p_{v}, 1 \leq j \leq n_{1}, 1 \leq l \leq n_{v}, 2 \leq v \leq 36\}

(11)

From batch subsets $B$ , Pearson’s coefficients were computed (Equation (10)) for the relationship between $d_{1 j} \in w_{1}$ and $d_{v j}$ $\in w_{v}$ for subsets of all stations $s_{v j} \in c_{v}$ from Formula (11).
For subset $B$ stations, the monthly mean discrepancies and standard deviations were computed for each station in two groups: (1) of all peak subsets on ‘calm’ days (C) and (2) ‘storm’ day (S), correspondingly. The count of faulty solutions for each station in both situations was performed.
For cloud groups of subset $P^{'}$ , the five adjacent clouds (Table S8), as a part of the daily cloud batches, were selected from the set $T^{'}$ . These were chosen as two subsets before the peak and two after the peak (in addition to the peak subset) to study the movement of adjacent discrepancy clouds within each day.
For the group of subset $P^{'}$ , the intersection was performed for subsets of stations within each of group (Table S10).
The cloud center coordinates were computed by computing the mean geographical coordinates for a subset of stations in various combinations.

The GPS data on 18 March 2015 from EGNOS ground-based RIMS stations GVLA, GVLB, LAPA, LAPB, WRSA, and WRSB were analyzed as well.

3. Results and Discussion

In March 2015, during the ‘calm’ days, the positioning disturbance clouds of the 90 s-long observation data of Latvian CORS stations (

T^{'}

\in T

), in 20–30 min cloud batches (groups), were collected, with one batch for each day (Table S4). The ionospheric scintillation maximum was assumed to be the maximum count of impacted stations. Each daily intensity maximum appeared about 4 min 8 s earlier than the previous day. The maximum time dependency on the date is shown in Figure 3. Such regularity might indicate an inertial (not rotating together with the Earth) location of the source of disturbances, with a corresponding position of a zero-meridian plane close to 150° East for 1 March. However, the source clearly was not of a cosmological origin—the daily time shift was 12 s, which is too long for the exact compensation of the Earth’s rotation. Right ascension is slowly changing, decreasing at a rate of about 18 degrees per year (full rotation in 20 years).

3.1. Discrepancy Distribution inside Clouds

Figure 4 shows the time series of the 30 sites involved at sequential time moments (with 1.5 min steps) on the latitude–longitude coordinate plane. The sites with disturbances are represented by blue dots with a size proportional to the logarithm of the Up deviation value. Other (not disturbed) sites are shown by fixed-sized dots in red. All regular disturbance batches (Tables S4 and S5) exhibited a fairly similar picture: the onset occurred within 5–10 min, all territory was affected simultaneously, and no noticeable signs of motion were present in the affected area. The maximum number of disturbed sites occurred a few minutes after the maximum disturbance intensity; it is likely some sites were able to withstand the disturbing factors longer than others. The duration of a strong disturbance did not exceed 5 min. On 17 March, in addition to the regular disturbance batch, a second, much longer (3 h), but weaker disturbance wave was present (Figure 4 and Figure 5). Presumably, it was connected to a geomagnetic storm. The onset was gradual and took almost an hour. After that, a stable high level of disturbance continued for about 2 h. The distribution of affected sites was similar to the regular batches.

In Figure 5, the location of sites on the latitude–longitude coordinate grid per sequential time moments on 5, 6, and 17 March are depicted. The disturbed sites are shown in blue, and the size of a dot is proportional to the logarithm of the Up component deviation. Undisturbed sites are in red. Time (UT) is shown on each graph. The right-side column shows the irregular event (geomagnetic storm) on 17 March. In both the middle and left columns, regular batches are selected based on daily occurrence time. In these plots, the discrepancy size irregularities are clearly visible on each of the adjacent 90 s time events.

3.2. Discrepancy Coverage Parameters

The analysis of subset B’s discrepancy clouds included the St. Patrick’s geomagnetic storm (STORM) situation and ionospheric scintillation discrepancy clouds on other days of March (OTHER). A summary of each station’s participation in subsets

p_{i} \in B

(Formula (6)) is depicted in Figure 6.

The mean discrepancies (Figure 7) and standard deviations (Figure 8) were computed from Table S11 for each station from all peak subsets on ‘calm’ days (C) and from all peak subsets on the STORM day (S). The discrepancy data were collected from the set W (sample in Table S5). During the geomagnetic storm on 17 March, loss of lock occurred in 20 stations. In 10 irregularly spread sites, loss of lock did not occur.

The fluctuation of the discrepancies during the St. Patrick’s Day geomagnetic storm in meters were as follows for Northing [−130.511; 106.922], Easting [−74.896; 120.517], and Up [−531.624; 154.625].

According to Figure 8, stations IRBE, RIGA, and VANG had the largest positioning errors during the geomagnetic storm. The stations LUNI, VAIV, KREI, SALP, and JEK1 were also erroneous. Stations LUNI, VANG, RIGA, and LVRD were most affected on ‘calm’ days.

Pearson’s correlation coefficients (Equation (1), Table S6) were obtained in relation to discrepancies and ROTI in peak subsets

p_{i}

\in B

. All correlation coefficients were less than 0.4 or below zero (Figure 9). This meant that the correlation of discrepancies with ROTI was weak. There was no reason to compute the relationship between discrepancies and TEC because only one TEC max value for the area of Latvia (Table S3) was introduced in the computation with Bernese GNSS Software v5.2.

Pearson’s coefficients were calculated (Equation (1), data in Table S6) in relation to the peak subset between

d_{1 j} \in w_{1}

and

d_{v j} \in w_{v}

for common stations

s_{k j} \in c_{v}

(Table S6) from Equation (1). The Pearson’s correlation results are depicted in Figure 10.

In 14 cases (40%), Pearson’s correlation coefficient for the peak discrepancies was >0.4, i.e., the relationship was good. In 19 cases (55%), the relationship was weak (<0.4), and only in two cases (5%) was the relationship negative.

The groups of five cloud subsets were selected in Table S7 (and additionally two subsets before the peak and two after the peak from set

B

) in order to study the similarity of positioning discrepancy clouds. The intersection of subsets of stations was performed for the five-cloud group subsets on 1 March with 35 other corresponding five-cloud group subsets (Formula (11)). Two types of intersection results were required: (a) cardinality of intersection of the peak subset on March 1 and other peak subsets where the third subset of each group was a peak subset; (b) a percentage of the summarized resulting cardinality compared to the summarized cardinality of 1 March. The results are presented in Table S9 (with source data in Table S8) and the sample is shown below in Table 1.

3.3. Cloud Movement Analysis

The percentage results are depicted in Figure 11 (in blue) for peak subsets. A summary of the results of the intersection of all five clouds (Table S6) on 1 March with the corresponding clouds on other days is shown in Table S8 and represented in Figure 11 (in red).

The comparison of discrepancy clouds on March 1 with the seven clouds on March 17 revealed that the percentage of common stations was <50% at the beginning of March 17 (Table S9). However, the count of common stations in the peak cloud, by the end of the day, reached 100%, which fits the trend of the peak event time series (Figure 11 and Table 2) for the whole month of March.

However, the results were quite different when the intersection was performed on five clouds inside each group. The results are depicted in Table S10 and in Figure 12, which demonstrates that cloud subsets in each group on ‘calm’ days were moving and/or disappearing faster than cloud subsets on the day of the geomagnetic storm, 17 March.

The mean values of the subsets of station coordinates were computed assuming a geometrical center of station sites in the whole peak subsets. The mean coordinates and other parameters are presented in Table 3 and Table S11.

Variations of the center of the coordinates for various cloud selections is depicted in Figure 13 and Figures S1–S6.

The mean coordinates of adjacent cloud subsets differed significantly within the framework of its batches (Figures S1–S4). This was confirmed by Figure 12 and standard deviations shown in Table 3. It was based on changes of the cloud configuration (Figure 11).

3.4. Loss-of-Lock Situations

The first shocking loss-of-lock situation caused continuous discrepancies in station IRBE. This station was out of normal operation for 4 h starting from 14:00:00 UT on 17 March (see Figure 14). After 30 min, the loss-of-lock situation occurred in 13 more stations and lasted for 3.5 h, until approximately 18 h UT. This means that the first six out of seven groups of peaks (starting from

b_{16} \in B

) expressed the log error of station operation. They described the damage to the CORS network caused by the St. Patrick’s geomagnetic storm.

3.5. EGNOS Ground-Based RIMS Stations

The GPS data on 16–18 March 2015 from RIMS stations GVLA and GVLB, LAPA and LAPB, and WRSA and WRSB were analyzed. The mean coordinates for each RIMS station were computed in several iterations using GPS data from March 16 and 18. Data from the day of the St. Patrick’s geomagnetic storm, 17 March, were not included in the station mean coordinate computation. The filtration of gross errors was performed in the mean coordinate computation.

Positioning discrepancies were computed with a threshold of 10 cm from the mean coordinate values. All obtained discrepancies are listed in Table S12. The faulty solutions for a certain day and time were counted, and all events and the count of simultaneously impacted stations are depicted in Figure 15.

From all the 57,600 90 s solutions which were performed in the six RIMS stations, the total count of faulty solutions on 16–18 March was 3269, i.e., 5.7% of faulty solutions occurred on a geomagnetic storm impact day. The results of the GVLA and GVLB stations were computed only for 17–18 March. The count of faulty solutions for each RIMS station is given in Table 4.

The loss-of-lock situation for RIMS stations is depicted in Figure 16. The discrepancy values in Northing, Easting, and Up for each loss-of-lock event for each station are listed in Table S13.

Station GVLA was in a loss of lock for almost 7 h, starting from 13:39:00, LAPA ~5 h, GVLB ~10 h, LAPB ~2 h, and WRSA ~1.5 h from ~16:15:00, GVLA ~3.5 h from 20:45, LAPA ~2 h from 20:45, and LAPB ~2 h from 22:19:30. This means that during the St. Patrick’s geomagnetic storm, the data of these RIMS ground-based stations were strongly affected by the geomagnetic storm. The duration of loss of lock for the RIMS stations was much longer compared to the Latvian CORS stations. The exceptions were the WRSA and WRSB stations, probably due to the differences in geomagnetic latitude. Samples of positioning discrepancies during the loss of lock are depicted in Figure 17. Numerical values on related sequential recurrences of discrepancies are depicted in both Tables S13 and S14.

In [14], the performance degradation of the onboard GPS receivers with a loss of lock of all tracked GPS satellites was analyzed when the Swarm satellite was tandem traversing through the PPEF-induced EPBs and plasma bite-outs. However, this failure was likely an issue for Swarm GPS receivers related to this particular receiver issue of bandwidth setting limitations [14]. Dense ground-based GNSS observations can provide a clue as to the geolocation and spatial extension of the EPB structures [14].

Taking time events from Table 2 and searching for these time events in Table S12, the presence of peak clouds was visible for RIMS stations, similar to the discrepancy clouds of the Latvian CORS.

4. Conclusions

The impact of space weather on GPS positioning quality was measured with stepwise 90 s discrete measurements of positioning precision, expressed as positioning discrepancy clouds. The primary objective was to determine the movement parameters of discrepancy clouds. Following analysis of the positioning discrepancy clouds of Latvian CORS, the results revealed were as follows:

In plots of time series of sequentially disturbed solutions, the discrepancy size distribution was irregular and could not be predicted;
In the count of faulty solutions per station, the mean per month was 221 on 30 ‘calm’ days, and it was 319 per station on one day of the storm;
The mean discrepancy for ‘calm’ days was 0.92 m, and it was 4.52 m for the day of the storm;
The standard deviation of the discrepancy of ‘calm’ days was 3.39 m, and it was 12.75 m for the storm day;
The fluctuation of discrepancies during the geomagnetic storm in meters for Northing was [−130.511; 106.922], Easting [−74.896; 120.517], and Up [−531.624; 154.625].
Pearson’s correlation computed between discrepancies and ROTI values appeared weak;
Pearson’s correlation computed between discrepancies of monthly peak subsets was moderate;
We can infer from Figure 11 and Table 2 that the last peak subset on 17 March belonged to the subset of peaks of ‘calm’ days (contrary to the standpoint of [14] on “an unusual and unexpected event”); however, on 17 March, the batch was much longer;
The fluctuation of sites in discrepancy clouds was more intense on ‘calm’ days. During the storm, the boundaries of adjacent clouds were more stable;
The centers of discrepancy clouds were more scattered on ‘calm’ days, and they were denser during the storm;
The duration of loss of lock was long for Latvian CORS stations up to 4 thousand for EGNOS ground-based RIMS stations up to 10 h.

Each “shot” after 90 s gave a completely new cloud, with a new impacted station subset, its configuration, and completely irregular discrepancy values. In a geographical area as small as Latvia, it is not possible to detect the movement of a plasma bubble somewhere in space by using only ground-based GPS positioning measurements. The positioning measurements were destroyed during the St. Patrick’s geomagnetic storm, when most of the stations experienced a loss-of-lock situation. The size of individual station ionospheric disturbances was not predictable. They had a sporadic, random, and occasional character.

The St. Patrick’s Day geomagnetic storm impacted GPS receivers of various producers in space and on the ground. The three-day analysis of EGNOS ground-based RIMS station data is too short to make any conclusions. However, a 10-h loss of lock of the RIMS station in comparison with a 4-h loss of lock of the Latvian CORS network station elicits interest in looking at the behavior of RIMS stations on ‘calm’ days as well.

Supplementary Materials

The following are available online at: https://www.mdpi.com/article/10.3390/rs15082032/s1. Figures S1–S6: movement of clouds; Tables S1 and S2: monthly max ROTI; Table S1: ROTI max values per day and (per each hour ROTI*1.e04); N—count of faulty solutions; C—count of cycle slips; Table S2: discrepancy (m) max values per day and per hour; N—count of faulty solutions (degraded GPS observations); C—count of cycle slips; Table S3: solar events, TEC, cycle slips (CSLP), and count of daily faulty solutions (>10 cm); Table S4: subsets T. Subsets of stations where faulty positioning solutions simultaneously occurred in March 2015; Table S5: discrepancy samples related to Figure 4 (subset W); Table S6: peak subsets (domes, summary discrepancy, ROTI); Table S7: ionospheric scintillation duration exposed by subsets B, P’, P (according to Figure 2); Table S8: list of clouds from Table S4 in groups: (8.1) subsets of cloud stations belonging to each group of five-clouds, (8.2) subsets of stations belonging to each group of five-clouds 9 subset P prim); Table S9: clouds of March 1 group and results of intersection with corresponding clouds of other groups; Table S10: intersection results of cloud subsets within each subset group; Table S11: characteristics of individual station discrepancies; Table S12: EGNOS RIMS ground-based station discrepancies SUBSET w); Table S13: registration of the sequentially occurred discrepancies; Table S14: discrepancies (m) of individual RIMS stations in loss-of-lock situations.

Author Contributions

Conceptualization, J.B., M.N. and A.Z.; methodology, J.B. and A.Z.; software, J.B. and A.Z.; validation, J.B. and M.N.; formal analysis, M.N.; investigation, J.B. and M.N.; resources, J.B. and M.N.; data curation, J.B. and M.N.; writing—original draft preparation, J.B., M.N. and A.Z.; writing—review and editing, J.B., M.N. and A.Z.; visualization, J.B., M.N. and A.Z.; supervision, J.B.; project administration, J.B.; funding acquisition, J.B., M.N. and A.Z. All authors have read and agreed to the published version of the manuscript.

Funding

Part of this research was funded by the Programme for European Cooperating States (PECS), European Space Agency Contract No: 4000128661/19/NL/SC, project “Ionospheric characterization by statistical analysis of Latvian GBAS 11-year selective daily observations”. The views expressed in this publication can in no way be taken to reflect the official opinion of the European Space Agency. The APC was funded by the University of Latvia. The current analysis presented in this article was funded by the University of Latvia. Contract No. ZDA 2022/24.

Data Availability Statement

Some of the data presented in this study are available in a Microsoft Office 365 OneDrive account provided by the LU GGI. RIMS data in EDAS archive.

Acknowledgments

The authors would like to express gratitude to Inese Vārna and to Irīna Baltmane for their support and assistance in the GNSS data processing with the Bernese GNSS Software v5.2.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. A schematic map of the Latvian CORS networks.

Figure 2. Plot of subsets of Formula (9).

Figure 3. Time of maximum intensity (count of disturbed sites) of regular disturbances. Average change of maximum time was 4 min 8 s per day.

Figure 4. The time series of 30 sites involved at sequential time moments (with 1.5 min steps) on the latitude–longitude coordinate plane.

Figure 5. Dependency of number of disturbed sites on time (UT) for 5, 6, and 17 March.

Figure 6. Count of faulty solutions of each station in subsets

p_{i}

\in B

for 17 March (STORM) and in subsets

p_{i}

\in B

on other days in March 2015 (OTHER).

Figure 6. Count of faulty solutions of each station in subsets

p_{i}

\in B

for 17 March (STORM) and in subsets

p_{i}

\in B

on other days in March 2015 (OTHER).

Figure 7. Mean discrepancies for ‘calm’ days (MEAN C) and for storm day, 17 March (MEAN S).

Figure 8. Standard deviation for ‘calm’ days (STD C) and for storm day on 17 March (STD S).

Figure 9. Pearson’s correlation coefficients in relation to discrepancies and ROTI for all 36 peak subsets.

Figure 10. Pearson’s correlation coefficients in relation to the peak discrepancies on 1 March and the peaks on other days.

Figure 11. The percentage of coincidence of subsets in the intersection of the peak cloud on March 1, with peak clouds on other days (subsets ∊ P) in March (in blue), and a summary of the intersection of all five-cloud subsets on 1 March, with five-cloud subsets on other days (subsets sets ∊ P′) (in red).

Figure 12. Count of common stations inside the five-cloud subsets intersection in each group (

P^{'}

Figure 12. Count of common stations inside the five-cloud subsets intersection in each group (

P^{'}

Figure 13. Center coordinate variations for 36 peak clouds in March 2015 (on the left side

P

, see Supplementary Files, Figure S5) and 149 clouds during the geomagnetic storm on 17 March (on the right side

B

, see Supplementary Files, Figure S6), where the last peak batch of 17 March is not included.

Figure 13. Center coordinate variations for 36 peak clouds in March 2015 (on the left side

P

, see Supplementary Files, Figure S5) and 149 clouds during the geomagnetic storm on 17 March (on the right side

B

, see Supplementary Files, Figure S6), where the last peak batch of 17 March is not included.

Figure 14. Latvian CORS stations and their respective loss-of-lock start times and durations in minutes (B).

Figure 15. All faulty events and a count of faulty solutions on 16–18 March 2015, in the set of RIMS station solutions GVLA and GVLB, LAPA and LAPB, and WRSA and WRSB.

Figure 16. RIMS stations and their respective loss-of-lock start times and durations in minutes.

Figure 17. Typical plot of 90 s sequential discrepancies of RIMS station, GVLB N (blue), E (orange), Up (red). No. of sequential 90 s events on the x-axes. Event No. 64 in Tables S13 and S14, correspondingly. No. of sequential recurrence of loss of lock on x-axes.

Table 1. A sample of cardinality of subsets and intersection resulting in subset

c_{k}

(copied from Table S9).

Table 1. A sample of cardinality of subsets and intersection resulting in subset

c_{k}

(copied from Table S9).

Intersection of Clouds on 1 March and 17 March
CLOUD CARDINALITY ON MARCH 1	18 24 28 28 25
CLOUD CARDINALITY ON MARCH 17	26 26 30 21 17
INTERSECTION CARDINALITY	18 23 28 19 13	82.1% OF MARCH 1 STATIONS

Table 2. Time of the max peak on March 17 (Time S) compared to the peaks of the nearest ‘calm’ days (Time C).

Date	Peak No.	Time S	Time C
16 March	15th peak		22:19:29
17 March	22nd peak	22:16:29
18 March	23rd peak		22:10:29

Table 3. Parameters of the peak cloud (

P

) and five-cloud (

P^{'}

) center coordinates.

Table 3. Parameters of the peak cloud (

P

) and five-cloud (

P^{'}

) center coordinates.

	Peak-Cloud Sets		5-Cloud Sets 1–16 March		5-Cloud Sets 17 March		5-Cloud Sets 18–31 March
	Longitude	Latitude	Longitude	Latitude	Longitude	Latitude	Longitude	Latitude
Mean	24.85°	56.93°	24.94°	56.93°	24.55°	56.91°	25.15°	56.95°
STD	0.29°	0.03°	0.39°	0.06°	0.23°	0.05°	0.57°	0.08°
MAX	25.32°	57.03°	26.10°	57.16°	25.09°	57.02°	26.42°	57.19°
MIN	24.38°	56.85°	24.17°	56.75°	24.13°	56.77°	24.15°	56.80°
MAX-MIN	0.94°	0.18°	1.93°	0.41°	0.96°	0.25°	2.27°	0.39°

Table 4. Total count of faulty solutions in selected RIMS stations.

	Station No.	GVLA	GVLB	APA	LAPB	WRSA	WRSB
3269	TOTAL FAULTS IN MARCH 2015	646	930	567	408	453	265

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Balodis, J.; Normand, M.; Zarins, A. The Movement of GPS Positioning Discrepancy Clouds at a Mid-Latitude Region in March 2015. Remote Sens. 2023, 15, 2032. https://doi.org/10.3390/rs15082032

AMA Style

Balodis J, Normand M, Zarins A. The Movement of GPS Positioning Discrepancy Clouds at a Mid-Latitude Region in March 2015. Remote Sensing. 2023; 15(8):2032. https://doi.org/10.3390/rs15082032

Chicago/Turabian Style

Balodis, Janis, Madara Normand, and Ansis Zarins. 2023. "The Movement of GPS Positioning Discrepancy Clouds at a Mid-Latitude Region in March 2015" Remote Sensing 15, no. 8: 2032. https://doi.org/10.3390/rs15082032

APA Style

Balodis, J., Normand, M., & Zarins, A. (2023). The Movement of GPS Positioning Discrepancy Clouds at a Mid-Latitude Region in March 2015. Remote Sensing, 15(8), 2032. https://doi.org/10.3390/rs15082032

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