Comparative Study of Ground-Based and Satellite Observations of Pc5 Geomagnetic Pulsations During Solar Cycle 23

doi:10.21203/rs.3.rs-4995901/v1

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Comparative Study of Ground-Based and Satellite Observations of Pc5 Geomagnetic Pulsations During Solar Cycle 23

https://doi.org/10.21203/rs.3.rs-4995901/v1

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Pc5 geomagnetic pulsations (PGP) are ultra-low frequency (ULF) waves within the 1–7 mHz frequency band observed both in space and on the ground. PGPs offer versatile methods for studying the interaction between the magnetosphere and ionosphere in space. This study presents a comparative analysis of Pc5 pulsations observed in space and on the ground. The dataset used is the magnetic field-aligned readings obtained from the Geostationary Operational Environmental Satellite-10 (GOES-10) and ground-based magnetometer stations from the Svalbard network located in the auroral zone during solar cycle 23. Using the Empirical Mode Decomposition (EMD) method, we transformed the magnetic field time series from GOES-10 into the mean field-aligned coordinate system. PGPs were extracted from the toroidal component using a bandpass Butterworth filter. In addition, Pc5 waves were extracted from the Bz component of the ground magnetometer stations to enable effective comparison. Before conducting the comparative analysis, both Pc5 events on the ground and in space were denoised using the heuristic Stein Unbiased Risk Estimate (SURE) approach with soft thresholding. Consequently, a good coherence between events from space and on the ground was observed, indicating the possibility of the same generation source. However, space-borne Pc5 events have a smaller average amplitude of 21 nT compared to Pc5 events observed on the ground having an average amplitude of 350 nT. We attributed this difference in amplitude to the transformative mechanisms during the wave's propagation to the ground. The average percentage of occurrence of Pc5 geomagnetic pulsations observed in space was found to be 94%, and that on the ground was 86%. The percentage difference was found to be due to the spatial distribution of these waves. The integrity of the retrieved events was demonstrated by the strong correlation between the Kp index and events extracted from the ground magnetometer stations. Our results demonstrate a good understanding of Pc5 geomagnetic pulsations to the space weather community. This will help in developing forecasting and predictive models for effective studies of these waves, mitigating the potential impacts of such events on human activities and infrastructure.

Pc5 pulsations

Ultra-low-frequency waves

Svalbard network

Wavelet analysis

Satellite observation

Solar cycle 23

Pc5 pulsations are continuous narrow-band ultra-low frequency (ULF) waves frequently observed in space and on the ground [1]. These disturbances are linked to a closed system of electric currents in the ionosphere and magnetosphere [2], ultimately impacting the Earth's magnetic field. Pc5 waves have frequencies within the bandwidth ranging from 1.67–6.67 mHz [3]. Detection of Pc5 pulsations in space has been accomplished through the use of satellite fluxgate magnetometers [4–6], while on-ground detection has been achieved with ground-based magnetometers [7, 8]. Measurements made from the ground that track variations in the geomagnetic field of the Earth throughout time play a pivotal role in advancing our comprehension of space weather and the impacts of solar wind on magnetospheric interactions. In contrast, satellite measurements offer valuable perspectives on solar-terrestrial interactions and the Earth's magnetosphere. This dual approach, combining ground-based and satellite measurements, provides a complementary and comprehensive method for studying the terrestrial magnetosphere.

Pc5 pulsations often exhibit standing shear Alfven wave characteristics in the inner magnetosphere, as shown in studies by Chen and Hasegawa (1974), Cummings et al. (1969), and Southwood (1974). These transverse waves can effectively accelerate or decelerate plasma inside the magnetosphere during wave-particle drift resonance [12, 13]. During resonance, a crucial phenomenon occurs where transverse waves and charged particles achieve a constant phase. The resonant particle's azimuthal drift speed and the wave propagation speed are synchronized, which facilitates this alignment. This harmonization maintains a continuous exchange of energy between ULF waves and charged particles, a process vital for supplying energy to relativistic particles in the Van Allen radiation belts. Consequently, this interaction contributes to the particle acceleration and dispersion within this radiation band [14–16]. The implications of such interactions extend to their substantial effect on space probes, including humans in space and satellites in low Earth orbit. This phenomenon is due to the potential increase in the energy of ionospheric plasma resulting from these resonant processes [17–19]. The heightened energy levels in the ionospheric plasma can pose challenges and considerations for the operational integrity of space missions and the well-being of astronauts.

Pc5 pulsations originate from diverse mechanisms within the magnetosphere, shaped by the intricate interplay between the solar wind and the magnetosphere [20]. Depending on the specific mechanism in operation, Pc5 pulsations can manifest internally and externally. These mechanisms encompass drift mirror instabilities induced by pressure anisotropies arising from the interaction between energetic particles and magnetic field fluctuations [21]. Additionally, low-frequency ring current plasma instability [22] and Kelvin-Helmholtz (K-H) near magnetopause flanks, caused by velocity shear between adjacent plasma regions [23], may serve as sources of energy for internally generated ULF waves. Externally, Pc5 ULF waves can be generated through phenomena such as shear instabilities at magnetopause flanks or compressive solar wind fluctuations [24]. The abrupt switch of IMF Bz from positive to negative on the nightside, especially after midnight [25], as well as flux transfer events (FTEs), solar wind buffeting, and variations in solar wind density [26], contribute to the generation of Pc5 ULF waves.

In space plasma physics, several studies have been dedicated to enhancing the understanding of the detection, prediction, and origin of ULF waves in space and on the ground. For example, Kozak et al., (2022) conducted comprehensive investigations utilizing both satellite and ground-based magnetometer measurements to examine ULF waves, which typically occur within the frequency range of 1 mHz to 5 Hz. Their findings revealed that ULF waves detected on the ground in the auroral oval region are generated by processes within the Earth's magnetosphere and ionosphere system, particularly during substorms. Balasis et al., (2015) used wavelet analysis to examine the power of ULF waves on the upper side of the ionosphere. Balasis et al., (2019) then presented the results of their wavelet and spectral analysis of ULF wave detection. Furthermore, Omondi et al., (2023) concentrated on utilizing the wavelet approach and data from ground-based magnetometers to examine ULF waves on the ground. Their conclusion highlighted that most selected stations observed similar ULF wave events, employing the wavelet coherence technique. In a different approach, Sung et al., (2006) investigated the source mechanisms of ULF waves using satellite and ground-based magnetometer measurements. Their study revealed that toroidal-mode Alfven waves traveling across magnetic field lines are linked to the source mechanisms of Pc5 waves seen on the ground. Their finding implies that a combined analysis using satellite and ground-based measurements is essential for exploring the relationship between Pc5 pulsations observed in space and on the Earth's surface.

Wavelet transforms are required to extract local features because geospace measurements, especially geomagnetic data are complex and require intricate processing and analysis. The time-frequency localization of fluctuations in the geomagnetic field can be investigated using mathematical methods. Wavelet analysis has proven to be a valuable tool in examining ULF waves. In a study by Balasis et al., (2019), the wavelet technique was applied for the automatic recognition of ULF waves. Similarly, in a previous work (Balasis et al., 2013), the same technique was utilized for the automatic detection of ULF waves in magnetic field observations within the context of the swarm mission. Recently, Pappoe et al., (2023) and Omondi et al., (2023) independently employed the wavelet technique for the automatic detection of Pc5 geomagnetic pulsations. Given the promising outcomes achieved by these researchers, our study aims to extend this approach. Herein, we employ the wavelet technique for a comparative study of Pc5 geomagnetic pulsations observed both in space and on the ground. This article provides a comparative analysis of Pc5 geomagnetic pulsations measured both in space and on the ground during solar cycle 23.

The paper is structured as follows: Section 1 introduces the phenomenon of Pc5 pulsations, while Section 2 explains the techniques employed to extract Pc5 waves from ground and satellite magnetometers and conduct wavelet-based analysis. Section 3 presents and discusses the results, and Section 4 summarizes the study findings.

2.1. Satellite Data Acquisition and Pre-processing

This study utilizes the 1-min sampled magnetic field-aligned measurements obtained from the GOES-10 satellite from 2000–2009. The satellite was positioned in geostationary orbit at longitudes 135^o and 60^o west during these years. The GOES-10 satellite data files are publicly accessible through following the link:https://www.ncei.noaa.gov/data/goes-space-environment-monitor/access/avg/. The satellite's position is given in the geocentric coordinates H_p, H_e, and H_n, respectively. In this system, H_e points towards the Earth and is perpendicular to $\:{H}_{p}$, $\:{H}_{n}$ is aligned in the eastward direction and perpendicular to both $\:{H}_{e}$ and $\:{H}_{p}$. $\:{H}_{p}$ is oriented perpendicular to the plane of the satellite's orbit [31]. The empirical mode decomposition (EMD) approach described by Pappoe et al., (2023) and Regi et al., (2016) was used to convert the satellite's geocentric coordinate system into the mean field-aligned (MFA) coordinate system. This transformation enhances the comprehensive analysis of ULF waves along and perpendicular to the field perturbations. We defined the time series of the magnetic field (B), enabling a detailed examination of its behavior according to Eq. (1) below.

$$\:B\left(t\right)={B}_{o}\left(t\right)+b\left(t\right)+n\left(t\right)$$

Where $\:{B}_{o}\left(t\right)$ is the slowly varying ambient magnetic field (i.e., perturbation of lower frequency), $\:b\left(t\right)$ is the perturbation of higher frequency and $\:n\left(t\right)$ is an incoherent noise.

To extract the slowly varying magnetic field, $\:{B}_{o}\left(t\right)$, and obtain the time series $\:{B}_{MFA}\left(t\right)$ in the MFA reference system, the EMD transformation method was employed. The EMD method, renowned for identifying nonlinear and non-stationary processes, effectively eliminated noise and higher frequency fluctuations in each time series [6]. Importantly, it enabled the determination of $\:{B}_{o}\left(t\right)$ while maintaining stability by minimizing minor variations and accommodating occasional significant deviations in the local context [6, 32]. The resulting time series was partitioned into residual term (Res) and intrinsic mode functions (IMFs), which are non-overlapping orthogonal components. Initially, the process involves computing an envelope $\:B\left(t\right)$ based on the time-series data of the magnetic field. This envelope was derived using cubic spline interpolation to identify the upper and lower boundaries of the magnetic field's time series separately. Subsequently, a component denoted by $\:{q}_{i}$ was extracted from the difference between $\:B\left(t\right)$ and the mean $\:⟨{x}_{i}⟩$ of the envelope values using Eq. (2).

$$\:{q}_{i}=B\left(t\right)-⟨{x}_{i}⟩$$

The extraction process was repeated multiple times until certain stopping conditions were satisfied [33, 34]. If these conditions were met at the $\:{n}^{th}$ iteration, the initial IMF was denoted as $\:{q}_{n}$ and labeled as $\:{B}_{1}$. After this, $\:{B}_{2}$ was obtained using a shifting technique on $\:B\left(t\right)-{B}_{1}$, and the same process was used for extracting $\:{B}_{3}$ and so forth [30]. The final mode obtained was called the residue. The empirical mode decomposition in Eq. (3) describes the time series composition of the magnetic field, which comprises the sum of all the intrinsic mode functions (IMFs) and the residue.

$$\:B\left(t\right)=Res+\sum\:_{k=1}^{{n}_{m}}{B}_{k}$$

$\:{B}_{k}$ denotes the IMFs. By simply combining the Res derived from the EMD approach and the IMFs We generate $\:{{B}_{O}}_{EMD}\left(t\right)$ (Mauro Regi et al., 2016). The satellite geocentric coordinate system was effectively converted into the MFA coordinate system by the EMD-based process, allowing the retrieval of the toroidal, poloidal, and compressional components. In this study, we employed the toroidal component to isolate Pc5 pulsations recorded by the magnetometers onboard the GOES-10 satellite. These pulsations represent ultra-low-frequency waves associated with toroidal mode Alfvén waves on the Earth's surface (Sung et al., 2006).

2.2. Ground-based Data Acquisition and Pre-processing

The ground magnetic field dataset utilized in this study is the Bz component of the Longyearbyen (LYR) station, located at coordinates (geomagnetic latitude 75.12° and longitude 113.00°, and geographic latitude 78.20°N and longitude 15.82°E), and the Hornsund (HOR) station, situated at coordinates (geomagnetic latitude 74.13° and longitude 109.59°, and geographic latitude 77.00°N and longitude 15.60°E). These stations are part of the Svalbard network of the International Monitor for Auroral Geomagnetic Effect (IMAGE) network and operate as ground-based magnetometer stations. The dataset is accessible at https://space.fmi.fi/image/www/index.php. These measurements were recorded for a period from 2000 to 2009, at one-minute intervals and reported in corrected geomagnetic (CGM) coordinates. In CGM, the X-axis denotes the horizontal magnetic field directed toward the northern magnetic pole, the Y-axis denotes the eastward horizontal component, and the Z-axis represents the downward magnetic component. The LYR and HOR stations from the Svalbard network were chosen for this study due to their strategic location in the auroral zone. Figure 1 displays the geographical location of the stations in the Svalbard network.

The selection of the Bz component is based on its critical role as a radial component, often observed at the north-south boundary of zonal ionospheric currents or within the magnetosonic component of the magnetosphere [35].

Before wavelet analysis, Pc5 pulsation data were obtained from the Bz component of terrestrial geomagnetic field measurements and the toroidal component of satellite magnetometer measurements. Pc5 pulsation data extraction was performed using a bandpass Butterworth filter to focus on the frequency range of interest (1.6 to 6.7 mHz), sampled at a rate of 16 mHz. The main objective was to eliminate high-frequency fluctuations, unwanted artificial interference, and naturally occurring sources of signals that had left their imprints on the time series of magnetic field data.

2.3. Processing of Data using Wavelet Techniques

Wavelet-based coherence analysis was applied to integrate a Pc5 pulsation dataset from two ground-based magnetometer stations in the Svalbard network and onboard GOES-10 satellite magnetometers. Wavelet-based analysis, providing a dual characterization of a signal's attributes in both time and frequency domains, is a robust procedure for extracting ULF waves [27, 29]. This analysis was motivated by the expectation that Pc5 events observed at the ground-based stations should show simultaneous occurrences in the satellite magnetometer observations.

In this study, we employed the discrete wavelet transform on two distinct datasets: ground-based geomagnetic field data sampled at 1 Hz and satellite data. The primary goal was to identify Pc5 pulsation events through this analytical approach. By doing so, we improved the precision of capturing temporal and frequency characteristics. The improvement enhances the detection of subtle waves alongside more prominent pulsations that extend beyond the baseline wave level [8]. It was observed that not all signals in the Pc5 band with lower wave power were genuine ULF pulsations, as sensor errors and background noise from the space environment could introduce irregularities. To tackle this issue, we utilized the Daubechies Wavelet Transform (DWT) to extract Pc5 signals from both satellite magnetometer observations and ground-based geomagnetic field measurements. The extraction involved separating geomagnetic pulsations in the Pc5 frequency range, $\:x\left({t}_{h}\right)$, into details (high-frequency) and approximations (low-frequency) [36–38]. The wavelet transform decomposition, described by Eq. (4), produced level-one wavelet coefficients given by

$$\:G\left(u,a\right)=\frac{1}{{\left|a\right|}^{\frac{1}{2}}}\sum\:_{h=1}^{r}x\left({t}_{h}\right){\Psi\:}\left\{\frac{{t}_{h}-u}{a}\right\}$$

where $\:u=k{2}^{-j}$ and $\:a={2}^{-j}$ are two dyadic functions defined in terms of powers of two. Here, $\:j$ is the parameter for scaling, $\:k$ is the wavelet transform and $\:x\left({t}_{h}\right)$ is the obtained Pc5 pulsation signal. The denoising process for Pc5 pulsations utilized the heuristic SURE approach [39] with soft fixed thresholding and the application of unscaled white noise to the details. To obtain the denoised Pc5 pulsations, Eq. (5) guides the threshold functions used in the nonparametric estimation of the anomalous local characteristics $\:v\left(t\right)$ of a signal occurring at random times.

$$\:v\left(t\right)=\sum\:_{u,a}{p}_{u}\left({G}_{u,a}\right){{\Psi\:}}_{u,a}\left(t\right)$$

Eq. (6) illustrates the soft thresholding employed as the shrinkage rule for the details during the signal-denoising process (Mandrikova et al., 2019).

$$\:{p}_{u}\left({G}_{u,a}\right)=\left\{\begin{array}{c}G-T\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:if\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left|G\right|>T\\\:0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:if\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left|G\right|\le\:T\\\:G+T\:\:\:\:\:\:\:\:if\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left|G\right|<\:-T\end{array}\right.$$

where $\:T$ stands for the threshold, $\:\left({G}_{u,a}\right)$ for the wavelet coefficients, and $\:{{\Psi\:}}_{u,a}\left(t\right)$ for the wavelet. The research conducted by Mandrikova et al. (2021) emphasizes the importance of meeting the Lipschitz condition to maintain threshold scaling. Following [42], we chose a threshold likely to surpass the maximum noise coefficient. The soft thresholding method, which divides the $\:\alpha\:$ value space into two distinct and non-overlapping domains, $\:{\alpha\:}_{1}$ and $\:{\alpha\:}_{2}$, was employed to preserve signal integrity. This involves retaining signals like the original and avoiding abrupt transitions caused by noise. Eq. (7) is used to calculate the average loss when applying this threshold function to a specific state $\:{l}_{c}$ (Mandrikova et al., 2021).

$$\:{R}_{c}\left(x\right)=\sum\:_{s=0}^{1}\prod\:_{cs}p\left(xϵ\raisebox{1ex}{${\alpha\:}_{s}$}\!\left/\:\!\raisebox{-1ex}{${l}_{c}$}\right.\right)$$

Where the loss function is provided by $\:{\prod\:}_{cs}=\left\{\begin{array}{c}1,\:c\ne\:s\\\:0,\:c=s\end{array}\right.$ and if the state $\:{l}_{c}$ exists, where $\:c$ and $\:s$ are the state indices, then the average risk is represented by Eq. (8) and the conditional probability of falling within the domain $\:{\alpha\:}_{s}$ is represented by the formula $\:p\left(xϵ\raisebox{1ex}{${\alpha\:}_{s}$}\!\left/\:\!\raisebox{-1ex}{${l}_{c}$}\right.\right)$.

$$\:R=\sum\:_{c=0}^{1}{P}_{c}{R}_{c}$$

Where $\:{P}_{c}$ stands for the a priori likelihood that the state $\:{l}_{c}$ exists (Mandrikova et al., 2021). Pc5 category ULF waves, observed at the Svalbard network and derived from GOES-10 satellite magnetometer data, were characterized using specific thresholds of 20nT and 0.5nT, respectively. These thresholds were applied for background noise filtering and excluding non-ULF signals. This process aimed to reconstruct signals compatible with the initial Pc5 events, enabling a more accurate analysis of Pc5 wave properties and behavior. The flowchart in Fig. 2 illustrates the stages involved in wavelet denoising, depicting the process of extracting denoised Pc5 events from the Bz component of terrestrial geomagnetic field measurements and the toroidal component of satellite magnetometer measurements.

The study compared Pc5 geomagnetic pulsations observed in space and on the ground. A two-fold verification process was employed to ensure the reliability of ground-based observations for comparison with satellite data. Initially, the simultaneous recording of Pc5 ULF waves at both magnetometer stations was deemed essential. This condition was met by employing a discrete wavelet transform to detect auroral Pc5 pulsations. Subsequently, a wavelet-based coherence analysis was conducted on the denoised Pc5 pulsation dataset obtained from the LYR and HOR stations of the Svalbard network located in the polar region. The LYR and HOR stations were chosen for this analysis due to their proximity along nearly the same geomagnetic longitude. Additionally, these stations concurrently recorded identical Pc5 event signals within a frequency range of 1 mHz to 6.7 mHz. The simultaneous recording served as a crucial indicator of genuine Pc5 events, effectively distinguishing them from background noise signals and non-ULF (ultra-low frequency) signals [8].

The denoised Pc5 pulsation signal was obtained using Daubechies wavelet analysis applied to the Pc5 pulsation dataset collected from two ground-based magnetometer stations in the Svalbard network and onboard GOES-10 satellite magnetometers. This method successfully removed high-frequency residuals, categorized as non-events, from the original signal. The main objective of this procedure was to eliminate artificial noise from the original signal, ensuring that only clear signals, recognized as denoised signals, were retained. The wavelet-based analysis proved its suitability for this application by adeptly detecting, identifying, and classifying signals with time-varying frequency levels [27, 29].

Figure 3 illustrates the simultaneous occurrence of Pc5 pulsations on October 30th, 2003, a day of geomagnetic disturbance, characterized by a Kp index of 9 and Ap = 191, which were identified at two ground stations. The top panel displays the Pc5 pulsation recording at the LYR station, and the bottom panel illustrates the Pc5 recording at the HOR station. After examining their plots, it was discovered that both stations simultaneously recorded the same pulsation signals. In both stations, the pulsation intensity showed a high peak with a mean amplitude of ~ 100nT at 02:45 UT and consistently remained very low with small amplitude fluctuations from 06:00 UT to 16:30 UT during the daylight hours. Subsequently, the intensity sharply spiked again around 17:15 UT and persisted before midnight. These fluctuations highlight the magnitude of the storm experienced by our terrestrial system on days of strong geomagnetic activity. The mid-magnitude pulsations that occur after powerful occurrences provide insights into the consequences of substorms. They also shed light on the internal magnetospheric processes that give rise to them [43].

The study employed wavelet-based coherence to assess signal coherence between two ground-based magnetometer stations. Signal coherence was also investigated between Pc5 pulsations measured on the ground and those observed from space. The wavelet-based coherence measures the time-varying correlation of two signals across different frequencies, allowing a comprehensive understanding of signal relationships. The color bar on a specific wavelet coherence graphic represents the degree of agreement between the two signals. A right-pointing arrow indicates strong phase coherence between them. The coherence of Pc5 pulsation signals in ground-based magnetometer measurements at both stations was examined to confirm the presence of the same signal within complex, undetected sections. In Fig. 4, the wavelet coherence analysis revealed significant correlations among time-varying events. LYR and HOR stations in the Svalbard network exhibited a shared frequency range of 1 mHz to 6.7 mHz, encompassing Pc5 pulsations. The colors in the display correspond to the coherence values of Pc5 pulsation signals between stations. The arrows on the display represent the phase relationship between the signals, with right arrows indicating in-phase and left arrows indicating anti-phase. Additionally, the dashed white curve represents the cone of influence (COI). This outcome served to validate the integrity of the recorded events. Notably, the wavelet analysis of Pc5 ULF waves at LYR demonstrated high coherence with the HOR station, further confirming the strong data integrity and reliability between the two stations.

In Fig. 4., like subsequent wavelet-based coherence Figs. 7, 8, 9, and 10, the relative angular phase relationships between the examined signals are displayed as arrows. Left-pointing arrows indicate anti-phase relationships, while right-pointing arrows indicate in-phase interactions. A lead of π/2 or one quarter (downward a lag) is represented by vertically upward arrows between the examined signals. The dashed line represents the COI.

The corresponding magnetic field pulsations in space are not directly detectable by magnetometers on the ground because ULF waves are large-scale, both geographically and temporally. Therefore, spacecraft measurements are required to probe the relationship between fluctuations in the terrestrial magnetic field and space magnetic field oscillations. The complementary nature of satellite and ground magnetic field monitoring yields a wealth of knowledge regarding the features and composition of the terrestrial magnetosphere. The Pc5 ULF waves recorded simultaneously at the LYR and HOR ground-based magnetometer stations were correlated with those detected by the onboard GOES-10 satellite magnetometers. The GOES-10 satellite was selected for its distinctive and valuable capabilities, which encompass global coverage, high resolution, broadband measurements, low noise, and a lengthy data record. These attributes render it an indispensable tool for understanding the characteristics and impacts of Pc5 ULF waves. Pc5 waves, with a frequency range of 1.6–6.7 mHz, pose a challenge for accurate detection by fast-moving Low Earth Orbit (LEO) satellites traversing field lines in a LEO orbit. This difficulty arises because the period of Pc5 waves exceeds the spacecraft transition time through the wave region [44]. Unlike LEO satellites, the geostationary GOES-10 is not affected by the Doppler effect, making it an invaluable tool for comprehending Pc5 ULF wave properties and impacts [45].

To analyze Pc5 geomagnetic pulsation observations effectively, both in space and on the ground, observational data were temporally and spatially synchronized to ensure the accuracy and reliability of the results. About 86% of Pc5 events were retrieved from both ground magnetometer stations with a corresponding 94% from space throughout the years. The percentage difference between both events may be due to the spatial distribution of the waves. Thus, not all waves from space may reach the auroral magnetometer stations. It is worth stating that, Pc5 events observed on the ground are not incident on the Earth from outer space but are generated as a result of cavity field lines resonances that drive currents in the ionosphere, and the resulting energy is radiated as geomagnetic pulsations in the form of electromagnetic waves [46]. Magnetic field measurements from the onboard magnetometers of the GOES-10 satellite and the two ground-based magnetometer stations within the Svalbard network were analyzed on both a storm and a quiet day to visualize event patterns. The occurrence of Pc5 pulsations on a storm day on October 30th, 2003, with Kp = 9 and Ap = 191 is depicted in Fig. 5, with the top, middle, and bottom panels illustrating simultaneous observations at the LYR station, HOR station, and geostationary satellite GOES-10, respectively. Throughout the day, during the storm, there were consistently low occurrences of Pc5 pulsations observed both in space and on the ground, in contrast to the night. Pc5 pulsations with high amplitudes were recorded around 22:00 UT at night. These observed Pc5 pulsations on the Earth's surface, within the auroral region, result from wave processes such as nightside reconnection and drift-bounce instability occurring in the Earth's magnetotail during substorms. [2].

On a quiet day, March 20th, 2005, with Kp = 2 and Ap = 4, Pc5 pulsations were predominantly observed during daylight hours at 14:50 UT both on the ground and in space. Monochromatic Pc5 waves observed during the day are a manifestation of the K-H instability at the magnetopause, confined by the plasma flow in the magnetosheath. These waves are induced by the K-H instability at the magnetopause flanks, triggered by the abrupt interaction of the solar wind. This interaction leads to wave excitation through field line resonance, enabling the transfer of energy to the inner magnetosphere [23, 43, 47]. However, Pc5 waves produced on quiet days are largely caused by internal magnetospheric processes, as seen by their low amplitude values [48]. The bottom panel in Fig. 6 illustrates Pc5 pulsations observed by onboard GOES-10 satellite magnetometers. These pulsations demonstrate low amplitude values, which may be attributed to the consistent flow of solar wind toward Earth, characterized by minimal or no instabilities [49].

When we compared Fig. 5 And Fig. 6, it became evident that Pc5 waves persist even on quiet days. Although their intensity may diminish, it is notable that some of these waves are generated by other Earth system processes.

The concurrent incidence of Pc5 pulsations both in space and on the ground was observed, as illustrated in Fig. 5 and Fig. 6. Analysis of plots from both the two ground-based magnetometer stations and the onboard GOES-10 satellite magnetometers revealed identical pulsation signals occurring simultaneously. Furthermore, the wavelet-based coherence analysis of Pc5 pulsation signals observed both in space and on the ground exhibited remarkably high coherence within the frequency range of 1 mHz to 6.7 mHz on both a storm day 30th October 2003 with Kp = 9 and Ap = 191 and a quiet day 20th March 2005 with Kp = 2 and Ap = 4. Figure 7 and Fig. 8 illustrate the coherence of Pc5 events recorded both in space and on the ground during a storm, while Fig. 9 and Fig. 10 depict the coherence of Pc5 events recorded both in space and on the ground on a quiet day. The significance of potential Pc5 pulsation signals is represented by a color gradient transitioning from blue to yellow and arrows indicate the phase relationship. The curved white dashed line is referred to as the COI. This analysis was conducted to validate the occurrence of Pc5 signals both in space and on the ground, confirming that the observed Pc5 ULF waves originate from a common source.

In both geomagnetically disturbed and quiet conditions, Pc5 pulsations with higher amplitudes were recorded on the ground compared to those recorded in space. High-amplitude fluctuations were observed on a geomagnetically disturbed day, whereas low-amplitude fluctuations were noted on a quiet day. The average amplitude of the Pc5 pulsations recorded on the ground by the two magnetometer stations between 2000 and 2009 was 350 nT, whereas in space, it averaged 21 nT. This difference arises from processes occurring within the magnetosphere that transform and amplify the wave energy of the ULF waves entering the magnetosphere from the solar wind as they travel toward Earth [46]. These transformative mechanisms include phenomena like the partial absorption or reflection of waves by heavy ions in the magnetosphere or lower ionosphere, ionospheric ducting of waves originating from a remote source region, and fluctuations in the spatial extent of the wave source region [45]. Figure 11 displays the amplitudes of Pc5 events detected both in space and on the ground.

On the other hand, the onboard magnetometers of the GOES 10 satellite detected a higher percentage of space events compared to those recorded on the ground by the two ground-based magnetometer stations, as illustrated in Fig. 12. The higher percentage of Pc5 events observed in space, as compared to the ground, can be attributed to differences in observation altitudes and instrumentation. The onboard magnetometers on the GOES 10 satellite demonstrate higher sensitivity and resolution compared to the magnetometers used at the two ground-based magnetometer stations in the polar region. This enhanced capability allows the satellite to detect smaller changes in the magnetic field, including Pc5 events, which might be missed by ground-based instruments [28, 50, 51]. Furthermore, the high percentage of Pc5 events observed in space suggests that the GOES 10 satellite is in an optimal position to detect these events. This is attributed to its geostationary orbit, enabling continuous monitoring of the same region of the Earth’s surface.

The results displayed in Fig. 11 highlight that the peak amplitude of Pc5 events, observed both in space and on the ground, reached its maximum in 2003 and its minimum in 2009. Furthermore, as depicted in Fig. 12, the highest occurrence percentage of Pc5 events in both space and on the ground was recorded in 2003, with the lowest observed in 2009. The variations in both amplitude and occurrence percentage of Pc5 events between 2000 and 2009 can be attributed to varying levels of geomagnetic activity during these years. Specifically, heightened geomagnetic activity characterized 2003, whereas 2009 saw a period of lower geomagnetic activity. These results emphasize a strong correlation between the Pc5 pulsations observed in space and those recorded on the ground.

The Kp index is an essential parameter in forecasting and the most extensively used parameter for the description of geomagnetic activity. The Kp index has been proven to have a good correlation with ULF waves both in space and on the ground (e.g. Omondi et al., 2023; Pappoe et al., 2023). We validated our extracted events on the ground with the Kp index, and the result is shown in Fig. 13. Figure 13 shows a line plot for the Kp index and a bar plot for the total number of Pc5 events that occur each year. Every yearly Pc5 event, with a maximum response in 2003 and a minimum in 2009, correlates well with the Kp index profile. Several studies reported that the highest ULF power was recorded in 2003 for the solar cycle 23, and 2009 was the quietest year for geomagnetic activity [43]. There was a clear consistency between Pc5 waves observed in space and Kp indices as depicted in Pappoe et al., (2023)findings as shown in Fig. 9.

In this study, we employed wavelet-based analysis to compare Pc5 waves observed in both space and on the ground. We retrieved Pc5 waves observed at geostationary orbit from GOES-10 and two auroral ground-based magnetometers from the Svalbard network from 2000 through 2009 comprising solar cycle 23. To distinguish between field perturbations aligned with and transverse to the magnetic field, time series values of the magnetic field obtained from GOES-10 were converted into the mean field-aligned coordinate system using the EMD method. Specifically, we extracted Pc5 geomagnetic pulsations from the Bz component of terrestrial geomagnetic field measurements and the toroidal component of satellite magnetometer measurements. The SURE method with soft thresholding was employed to denoise the extracted Pc5 events from both space and on the ground for effective comparative analysis. We observed a good coherence between Pc5 events in both space and ground indicating that these waves may have been generated from the same source. However, Pc5 geomagnetic pulsations in space were observed to have smaller amplitudes of 21 nT compared to Pc5 pulsations observed on the ground which have an amplitude of 350 nT. The possible reason for this was attributed to transformative mechanisms including partial absorption or reflection of waves by heavy ions in the magnetosphere or lower ionosphere, ionospheric ducting of waves originating from a remote source region, and fluctuations in the spatial extent of the wave source region. The ability of wavelet-based analysis to study signal characteristics in both the time and frequency domains was demonstrated through its successful identification of Pc5 ULF wave events. This method also proved effective as a selection criterion for validating signals originating from the same source and recorded at two different ground-based stations, as well as in space and on the ground. Hence, Concurrent recording of Pc5 event signals is essential for detecting genuine Pc5 events and distinguishing them from background noise signals and non-ULF signals. This technique plays a vital role in advancing our knowledge of ultra-low-frequency phenomena by ensuring accurate data collection, validating results, improving our understanding of Pc5 events, and fostering collaboration among researchers. The geomagnetic field measurements obtained from the LYR and HOR ground-based magnetometer stations were found to be consistent with those recorded by the onboard magnetometers of the GOES-10 satellite. This alignment illustrates a strong coherence in the measurement of ULF waves, both in space and on the ground, as revealed by wavelet coherency detection through wavelet transform analysis. Consequently, the wavelet coherence transform emerges as a valuable tool for investigating Pc5 pulsations, demonstrating its effectiveness in studying these phenomena both in space and on the ground. Pc5 events extracted from the auroral ground magnetometer stations showed a high correlation with the Kp index, validating the integrity of the extracted Pc5 events.

Finally, we observed that the percentage of events retrieved from the ground was 86%, and that in space was 94%. The difference between both events during the years was due to the spatial distribution of Pc5 events. The observational results obtained from our study are essential for both theoretical and numerical modeling. These findings play a crucial role in coordinated GOES 10-ground observations of Pc5 waves. They enable us to analyze and assess the alignment between ground-based magnetometer observations of ULF waves and measurements obtained by space-borne magnetometer satellites. By comparing ground-based observations with satellite data, scientists can gauge the accuracy of ground-based magnetometers in representing magnetospheric wave activity. This comparison helps identify any discrepancies between the two datasets, contributing to the refinement of theoretical models and numerical simulations that describe the behavior of these waves.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data Accessibility Statement

The magnetic field observations used in this study were obtained from the Svalbard network within the International Monitor for Auroral Geomagnetic Effects (IMAGE), accessible via this link (https://space.fmi.fi/image/www/index.php). The magnetic field-aligned measurements were retrieved from the GOES-10 satellite through the National Oceanic and Atmospheric Administration (NOAA) at this link (https://www.ncei.noaa.gov/data/goes-space-environment-monitor/access/avg/). Additionally, Kp data was acquired from the NASA data center via Omni Web at this link (https://omniweb.gsfc.nasa.gov/form/dx1.html).

Author Contribution

Sebwato Nasurudiin was responsible for collecting and processing data from ground-based magnetometer stations, particularly those from the Svalbard network, Akimasa Yoshikawa provided the theoretical foundation for understanding the interaction between the magnetosphere and ionosphere during Pc5 geomagnetic pulsations, Ahmed Elsaid led the processing of magnetic field data from the Geostationary Operational Environmental Satellite-10 (GOES-10). He was instrumental in transforming the satellite data into the mean field-aligned coordinate system using the Empirical Mode Decomposition (EMD) and Ayman Mahrous conducted the comparative analysis between the ground-based and satellite observations of Pc5 pulsations. He applied statistical methods to evaluate the coherence between the two datasets, explored the amplitude differences, and correlated the results with solar activity indices such as the Kp index, thereby contributing to the overall understanding of the spatial and temporal distribution of Pc5 waves.

Acknowledgement

We thank NOAA for providing access to GOES-10 satellite data for the public, and the Norwegian Polar Institute, responsible for maintaining the magnetometers at the Longyearbyen (LYR) and Hornsund (HOR) stations of the Svalbard network within the International Monitor for Auroral Geomagnetic Effect (IMAGE) network. Additionally, we appreciate P. Flandrin, G. Rolling, and P. Gonçalves for making their EMD code publicly available. We also express our gratitude to Mauro Regi, Alfredo Del Corpo, and Marcello De Lauretis for sharing their EMD codes with us. The first author expresses sincere gratitude to Mr. Stephen Owino Omondi and Mr. Justice Allotey Pappoe for their unwavering commitment and guidance during the writing of this essay. Finally, I extend heartfelt thanks to the TICAD 7 scholarship for providing the necessary funding that enabled my pursuit of a master's degree in space environment at the Egypt-Japan University of Science and Technology (E-JUST) in Egypt.

Data Availability

Data Accessibility StatementThe magnetic field observations used in this study were obtained from the Svalbard network within the International Monitor for Auroral Geomagnetic Effects (IMAGE), accessible via this link (https://space.fmi.fi/image/www/index.php). The magnetic field-aligned measurements were retrieved from the GOES-10 satellite through the National Oceanic and Atmospheric Administration (NOAA) at this link (https://www.ncei.noaa.gov/data/goes-space-environment-monitor/access/avg/). Additionally, Kp data was acquired from the NASA data center via OmniWeb at this link (https://omniweb.gsfc.nasa.gov/form/dx1.html).

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Comparative Study of Ground-Based and Satellite Observations of Pc5 Geomagnetic Pulsations During Solar Cycle 23

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Abstract

Figures

1. Introduction

2. Methodology

2.1. Satellite Data Acquisition and Pre-processing

2.2. Ground-based Data Acquisition and Pre-processing

2.3. Processing of Data using Wavelet Techniques

3. Results and Discussion

4. Summary and Conclusion

Declarations

Declaration of competing interest

Data Accessibility Statement

Author Contribution

Acknowledgement

Data Availability

References

Additional Declarations

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