An automated framework for detecting linear magnetic holes in space plasma

1 Introduction

Magnetic holes (MHs) are localized depressions in the magnetic field magnitude, | B |, commonly observed in space plasmas Turner et al. (1977); Yao et al. (2021); Yu et al. (2022). MHs have been associated with several formation mechanisms, including mirror-mode instability (Tsurutani et al., 1992), tearing instability Balikhin et al. (2012), solitons (Stasiewicz, 2004), and turbulence-driven evolution (Ahmadi et al., 2017; Arrò et al., 2024). MHs are observed across the solar wind (Turner et al., 1977), magnetosheath, magnetotail (Shustov et al., 2019), and planetary magnetosheaths (Wu et al., 2021; Karlsson et al., 2021; Goodrich et al., 2021; Wang et al., 2024). Most of the MHs are accompanied by high plasma density and temperature, thus a pressure balanced magnetic structures (Turner et al., 1977; Winterhalter et al., 1994). When the magnetic field direction remains approximately unchanged across the depression, the structure is classified as a linear magnetic hole (LMH), in contrast to rotational magnetic holes for which significant magnetic field rotation occurs across the structure (Winterhalter et al., 1994; Turner et al., 1977). Their prevalence at 1 AU makes them useful tracers of local plasma stability and mesoscale solar wind structuring (Baumgärtel, 1999). Regardless of their formation mechanism, MHs represent structured plasma environments with measurable properties such as depth, size, magnetic gradients, and internal plasma conditions.

LMHs are pressure-balanced structures that serve as tracers of mirror-mode instability thresholds (Winterhalter et al., 1994; Stevens and Kasper, 2007), and local plasma stability conditions in the solar wind (Baumgärtel, 1999). At 1 AU, these structures typically span spatial scales of 1 0 3 -1 0 4 km, corresponding to roughly a few tens to a few hundreds of proton inertial lengths, with observed durations of a few seconds to tens of seconds at typical solar-wind speeds of 400–500 km s − 1 (Stevens and Kasper, 2007), consistent with the broader range of scales reported by Winterhalter et al. (1994) from Ulysses observations between 1 and 5.4 AU. Observational evidence from Parker Solar Probe and planetary magnetosheaths suggests that LMH occurrence rates and spatial scales evolve systematically with heliocentric distance (Karlsson et al., 2021; Wu et al., 2021; Huang et al., 2021; Goodrich et al., 2021; Yu et al., 2022); in particular, smaller sub-ion-scale magnetic holes become more prevalent closer to the Sun. Hybrid simulations further suggest that the background turbulence level modulates LMH formation through the development of mirror-mode-favourable anisotropy conditions (Arrò et al., 2024; Ahmadi et al., 2017). A unified, multi-year catalogue derived from a single instrument with consistent detection criteria is therefore essential for quantifying these dependencies and for enabling direct comparisons across solar-cycle phases, heliocentric distances, and plasma environments—objectives that cannot be addressed with earlier catalogues constructed at lower cadence or over shorter observing baselines (Winterhalter et al., 1994; Stevens and Kasper, 2007). The present framework is developed and validated using Wind/MFI data at 1 AU; extension to other missions is identified as future work and is not implemented in the current study.

Despite this importance, large sample LMH catalogues have historically been difficult to assemble. Visual inspection of time-series data is impractical at high measurement cadence over multi year observing baselines, and simple threshold searches on | B | produce unacceptably high false-positive rates. A number of automated detection algorithms have been developed (Winterhalter et al., 1994; Stevens and Kasper, 2007; Wang et al., 2020; Huang et al., 2021), but they differ in their detection criteria, are typically designed for specific data formats or instruments, and are rarely available in a directly reusable form. As a result, cross-mission comparisons and long duration statistical investigations remain challenging. Previous approaches have employed a range of detection philosophies, including fixed-threshold searches, scale-dependent statistical significance methods, and morphology-based filtering criteria. The present framework is not intended to replace physically sophisticated multiscale identification methods, but rather to provide a transparent, configurable, and reproducible workflow suitable for large-volume magnetic-field surveys and operational catalog generation. Rather than introducing new detection physics, the present framework advances existing approaches through three concrete methodological contributions: (i) overlapping chunk processing with a 600 s buffer that eliminates the boundary artefacts inherent to fixed-window segmentation; (ii) a modular three-stage filtering scheme that explicitly separates depth, directionality, and data-quality criteria; and (iii) a configurable web interface exposing the rolling-window width and detection thresholds, enabling reproducible parameter sweeps across multi-year datasets.

The growing availability of continuous, high-resolution measurements from missions such as Wind, ACE, Parker Solar Probe, and Solar Orbiter now provides an opportunity to revisit LMH occurrence statistics using unified and scalable methodologies. Robust automated detection frameworks are increasingly essential for leveraging these data sets, enabling consistent identification across different heliocentric distances, solar cycle phases, and plasma environments. Such approaches not only improve catalogue completeness, but also may help establish whether LMH properties evolve systematically with radial distance, background turbulence level, or large scale solar wind stream type. Among these missions, observations near 1 AU remain particularly valuable because they offer a long-term reference point for comparing solar wind structures detected closer to and farther from the Sun. The Wind spacecraft, launched in November 1994 and continuously operational, carries the Magnetic Field Investigation (MFI) instrument (Lepping et al., 1995), which delivers three component magnetic field vectors at sub-second cadence in the RTN coordinate frame. This archive, spanning multiple solar cycles, constitutes one of the richest continuous magnetic field datasets of solar wind available at 1 AU. This combination of long-term data, stable instrumentation, and high-cadence observations makes Wind/MFI particularly well suited for systematic LMH detection and long-term statistical investigations.

In this paper, we present an open-source Python based automated LMH detection framework [publicly available on Zenodo (Singh, 2026)] using Wind/MFI magnetic field data. The framework applies configurable filtering criteria based on magnetic-field depression depth, field-rotation angle, and data-quality constraints to identify candidate events within continuous magnetic-field time series. The pipeline is designed to support reproducible and scalable LMH catalog generation through automated preprocessing, event identification, visualization, and export utilities. We organise the paper in the following sequence: Section 2 describes the Wind MFI data product. Section 3 details the detection algorithm step by step. Section 4 presents results from applying the pipeline to Wind MFI data. Section 5 interprets the results and discusses limitations and future prospectives, and Section 6 summaries the work.

2 Data utilized

We use magnetic field vectors from the Wind Magnetic Field Investigation (MFI) instrument (Lepping et al., 1995), distributed as the WI_H4_RTN data product, available through NASA’s GSFC Space Physics Data Facility (SPDF). Each file contains three component magnetic field measurements, B R, B T, and B N, in the Radial-Tangential-Normal (RTN) coordinate system at a nominal cadence of about 0.092 s (≈ 11 Hz), highest-resolution continuous magnetic-field product routinely available from Wind/MFI. This cadence resolves structures with temporal widths as short as ∼0.1 s, well below the minimum LMH duration of ∼10 s typically reported in the literature (Winterhalter et al., 1994; Stevens and Kasper, 2007), confirming that the 11 Hz resolution is sufficient for LMH identification at 1 AU. In the RTN coordinate system, R ̂ points radially outward from the Sun to the spacecraft, T ̂ is the cross product of the solar rotation axis with R ̂, and N ̂ = R ̂ × T ̂ completes the right-handed orthogonal triad. The total magnetic field magnitude used throughout this work is defined as

Each WI_H4_RTN CSV file contains an epoch column (EPOCH) in ISO 8601 format together with three components. Instrument fill values identified by | B | < − 1 0 20 nT, are treated as invalid data and removed during preprocessing (Section 3.1).

The pipeline is applied to Wind/MFI datasets spanning multiple years of observations near the Sun–Earth L1 Lagrange point, providing continuous solar wind magnetic-field measurements largely free from terrestrial magnetospheric contamination. The Wind spacecraft was inserted into its permanent halo orbit around the Sun–Earth L1 Lagrange point in 2004, and the pre-2004 portion of the mission includes intervals spent within the terrestrial magnetosphere, magnetosheath, and magnetotail during a sequence of double-lunar-swing-by phasing orbits. The present version of the pipeline does not apply an explicit ephemeris-based orbital filter; instead, these intervals are rejected implicitly by the physical criteria of the three-stage filter. Magnetospheric and magnetosheath regions are characterised by background field magnitudes of tens to hundreds of nT (compared with a few nT in the pristine solar wind at 1 AU) and by large, rapid field rotations, so candidate depressions in these regions routinely fail both the 15 ° directionality criterion and the 50 % depth criterion when evaluated against the elevated local ambient field. Visual inspection of a randomly sampled pre-2004 subset confirms that the physical filters reject the great majority of magnetospheric and magnetosheath signatures. An explicit ephemeris-based screen using the publicly available Wind GSE position data is being implemented as an optional pre-processing module for a forthcoming release of the catalogue. The analysis interval is fully user-configurable through the web interface, enabling flexible application to different time periods and survey intervals.

3 Methodology

The detection pipeline is implemented in Python 3 and relies on the NumPy (Harris et al., 2020), Pandas (McKinney, 2010), and Matplotlib (Hunter, 2007) libraries. The complete set of detection parameters can be configured via the web interface and is summarized in Table 1. The overall processing flow consists of four sequential stages (shown in Figure 1): (i) full-file data loading and preprocessing, (ii) global local-minima detection, (iii) event boundary identification, and (iv) three stage candidate filtering. Each stage is described in the following subsections.

TABLE 1. Configurable parameters of the LMH detection pipeline with their default values. All time parameters are in seconds.

3.1 Data loading and pre-processing

Each input CSV file, typically ∼17 GB per year at the native 11 Hz cadence, is read in sequential overlapping chunks of 50,000 rows by default (adjustable through the web interface), with a 600 s buffer carried forward from each chunk to the next to preserve local field context across chunk boundaries. This overlap ensures that candidate events near a chunk boundary are evaluated with sufficient surrounding data, reducing the edge effects that would arise from independently processed non-overlapping segments. The 600 s value is not derived from any physical LMH width; it is set by the algorithmic data-context required to evaluate a candidate event whose t min sits near a chunk boundary. In the worst case, the boundary search (± 150 s around t min) plus the upstream (150 s) and downstream (100 s) ambient windows demand up to 300 s of context upstream and 250 s downstream of t min, totalling ∼ 550 s. The 600 s default comfortably exceeds this requirement. Duplicate detections are avoided by restricting the rolling-minimum search to the analysis zone of each chunk, which terminates 600 s before the chunk’s last timestamp; the trailing 600 s is carried into the next chunk and searched once. Each t min is therefore identified exactly once. The following pre-processing steps are applied to each chunk:

• The epoch column is parsed to datetime64[ns] objects using ISO 8601 formatting. Rows with unparseable timestamps are discarded.
• The three field components B R, B T, and B N are cast to 64-bit floating point values. Non-numeric entries are coerced to NaN and the corresponding rows are dropped.
• The total field magnitude | B | is computed globally according to Equation (Equation 1). Samples with | B | < 1 0 − 20 nT (instrument fill values) are set to NaN and removed.
• The resulting DataFrame is sorted chronologically on its time index and deduplicated, retaining the first occurrence of any repeated timestamp.

Following these steps each preprocessed chunk, together with the overlap buffer retained from the preceding chunk, is passed to the subsequent detection and filtering stages without further file reading.

No interpolation or gap-filling is applied at any stage of the pipeline. Samples flagged as invalid during preprocessing are dropped from the series and are not reconstructed. The same rule extends to event-level filtering: if the missing-data fraction within an event interval (Section 3.4.3) exceeds 40 %, the event is discarded rather than filled in. All reported event properties are therefore derived only from measured field values, with nothing estimated or interpolated.

3.2 Dataset-wide local-minima detection

Candidate LMH intervals are identified by locating local minima in | B | across each processing chunk. A time-aware rolling minimum of width W is computed symmetrically around each sample using pandas time-based indexing, as given in Equation 2:

The 100 s window width was set empirically to comfortably bracket typical LMH durations at 1 AU. Earlier surveys (Winterhalter et al., 1994; Stevens and Kasper, 2007) and the duration distribution recovered in this catalogue (Figure 2) show that most events last from a few seconds up to ∼60 s, so 100 s provides roughly a factor of two margin above the typical event duration while remaining short enough that a single window rarely spans two unrelated depressions.

A data point at time t min is identified as a candidate event only when its field magnitude matches the corresponding rolling minimum. Since the rolling minimum is computed over the chunk together with its overlap buffer, the resulting statistics accurately capture the local behaviour of the field around each candidate point, and edge-related effects at chunk boundaries are substantially reduced. The present approach identifies candidate events based on local magnetic-field minima and therefore prioritizes morphology based event selection. The term “dataset-wide” reflects that the rolling minimum is evaluated across the full time series, with no interval excluded, in contrast to methods restricted to short, isolated search windows. A subtlety arises when a depression has a flat or near-flat bottom: several consecutive samples can each match the rolling minimum within their own 100 s neighbourhood, so more than one t min candidate may be returned for what is physically a single, wider LMH. Each such candidate proceeds independently through the boundary search and filtering stages, which can lead to more than one catalogue entry for the same underlying structure; this effect is examined further in Section 5.

3.3 Event boundary identification

For each candidate minimum at t min, the event start time t S and end time t E are located within a symmetric search window [ t min − Δ t b , t min + Δ t b ], where Δ t b = 150 s by default. We fixed Δ t b empirically rather than deriving it from theory. Catalogued LMHs have a median duration of ∼9 s and a mean of ∼11.7 s (Figure 2), so a 150 s window is more than an order of magnitude larger than a typical event. This leaves enough points on either side of t min to get a stable estimate of B ̄ 0 and σ B, without the window growing so wide that it risks catching a second, unrelated depression. A local field threshold is defined in Equation 3 aswhere B ̄ 0 and σ B are the mean and standard deviation of | B | computed across the full boundary search window. On the pre minimum side, t S is taken as the sample whose field magnitude is nearest to (and above) B thresh; t E is found analogously on the post-minimum side. This procedure allows event boundaries to adapt to local magnetic-field variability within the search interval.

B thresh = B ̄ 0 − σ B , (3)

3.4 Three-stage candidate filtering

Each candidate triplet ( t S , t min , t E ) is subjected to three sequential filtering criteria. An event is retained in the final catalogue only if it passes all three.

3.4.1 Depth criterion

A refined ambient field level B ̄ amb is computed by averaging | B | over two flanking windows drawn from the current processing chunk: an upstream window of duration Δ t before ending at t S, and a downstream window of duration Δ t after beginning at t E. The depth ratio rd is defined in Equation 4 aswhere | B | min is the minimum field magnitude within [ t S , t E ]. An event is accepted only when r d < 0.5. This 50% depth threshold follows the canonical definition of Winterhalter et al. (1994). Stevens and Kasper (2007) instead adopted a scale-free significance criterion with no fixed depth cutoff; we apply their event catalogue only for validation purposes and impose our own r d < 0.5 criterion independently, as detailed in Section 4.1.

r d = | B | min B ̄ amb , (4)

3.4.2 Directionality criterion

To discriminate linear from rotational structures, the angle between the mean upstream and downstream magnetic field vectors is evaluated using Equation 5 aswhere B ̄ up and B ̄ dn are the component wise averages of the field vector over the upstream and downstream ambient windows, respectively. Events with θ ≥ 15 ° are classified as rotational holes and excluded. This threshold follows the linearity criterion adopted by Briand et al. (2010).

θ = arccos B ̄ up ⋅ B ̄ dn | B ̄ up | | B ̄ dn | , (5)

3.4.3 Data-quality criterion

Telemetry gaps can produce artificial field depressions and bias both depth and angle estimates. To reduce the impact of such artefacts, the pipeline compares the actual number of samples within [ t S , t E ] against an expectation derived from the median measurement cadence of the surrounding full-resolution record. Events for which the missing-data fraction given by Equation 6 exceeds 0.40exceeds 0.40 (i.e., more than 40% of expected samples absent) are rejected. Because the current chunk together with its overlap buffer is available in memory, the median cadence is computed from the local data window and is therefore less sensitive to short local data gaps than estimates derived from isolated short segments. The 40% threshold reflects a balance between data completeness and sample retention. Requiring at least 60% of the expected samples within [ t S , t E ] ensures robust estimates of | B | min and the ambient field, since larger gaps can obscure the true field minimum or shift the detected boundaries to points where valid data merely resume. Higher missing-data tolerances (e.g., 50% or 60%) would permit events reconstructed from less than half of the dip interval, thereby reducing the reliability of the identified LMHs. The threshold is fully configurable, and users prioritising individual-event fidelity over catalogue size can readily adopt a stricter cutoff.

f miss = 1 − N actual N expected (6)

3.5 Generated outputs

All events that successfully satisfy the validation criteria are aggregated into a final catalogue and saved as a single CSV file upon completion of the analysis. Every catalogued event is characterized by a set of fundamental attributes: the onset time t S, the termination time t E, the epoch of minimum field strength t min, the temporal span ( t E − t S ) expressed in seconds, the depth ratio r d, the rotation angle of the field vector θ (measured in degrees), the corrected ambient magnetic-field magnitude B ̄ amb (in nT), and the lowest recorded field magnitude | B | min (in nT). A companion multi-page PDF report is generated automatically, including statistical summaries and individual event visualizations centered on t min.

4 Analysis and results

4.1 Validation against published catalogues

To evaluate the reliability of the pipeline, we applied it to publicly available Wind/MFI magnetic-field data and compared the detected events with the magnetic-hole catalogue reported by Stevens and Kasper (2007), which was constructed using 3 s resolution Wind/MFI (WI_H0_MFI) and Wind/3DP (WI_PM_3DP) data. Figure 3 illustrates the three-stage magnetic-hole detection procedure adopted in the present work: the top panel shows the raw magnetic-field magnitude over a 1-h interval, the middle panel presents a zoomed-in view of the selected interval containing multiple depressions, and the bottom panel displays the final pipeline detection output, including the identified event boundaries and minimum-field locations. The third depression, visible between 09:12 and 09:13 UT in Figure 3, is excluded by the directionality criterion: its upstream-to-downstream field-rotation angle is ∼ 17.3 °, exceeding the 15 ° threshold, so it is classified as a rotational rather than a linear magnetic hole.

For validation, we analysed the overlapping dataset for the year 1995 and found that the pipeline successfully recovered ∼ 94% of the catalogue events during the analysed interval with unrecovery rate of ∼6% which is due to scale free method used by S&K reference.

An event is considered recovered if its detected interval [ t S , t E ], expanded by a 10 s tolerance, overlaps the corresponding event interval in Stevens and Kasper (2007). We adopt this interval-overlap criterion rather than matching on a single timestamp because the two catalogues are built from data of different native cadence, 11 Hz for the present pipeline against the 3 s Wind/MFI data used in our reproduction of Stevens and Kasper (2007), so boundary placement is not directly comparable between the two methods. The tolerance therefore avoids counting differences in boundary placement as genuine misses. For the 1995 validation interval, the reference catalogue contains 140 events, of which 131 were recovered under this criterion, corresponding to a recovery rate of 94 % and an unrecovered rate of 6 % (N miss 9 events).

A statistical comparison between the distributions obtained from the 1995 dataset analysed by Stevens and Kasper (2007), which used the Wind/MFI (WI_H0_MFI) and Wind/3DP (WI_PM_3DP) data, and those derived in the present work using high-resolution Wind/MFI 11 Hz data is provided in Figure 4. The comparison demonstrates that the present pipeline reproduces the majority of previously reported magnetic-hole events while additionally identifying short-duration and small-scale structures that are difficult to resolve in the lower-cadence 3 s dataset. Figure 4 compares the duration and depth-ratio distributions from the two catalogues for the overlapping 1995 interval. The Stevens and Kasper (2007) distributions (top panels) were obtained by reproducing their method on 3 s Wind/MFI data paired with Wind/3DP plasma moments, following the original prescription; the present pipeline (bottom panels) uses 11 Hz Wind/MFI magnetic-field data alone, with no plasma-based screening. Both duration distributions (left panels) are strongly right-skewed, with a dominant peak at short durations and a long tail extending out to ∼80 s. The Stevens and Kasper reproduction peaks in the bin nearest 10 s; the present pipeline’s distribution peaks at a shorter duration and falls off more steeply, with substantially more events recovered in the bins below ∼10 s that the coarser 3 s cadence under-samples. The overall shape, a sharp low-duration peak followed by a long tail, is consistent between the two catalogues. The depth-ratio distributions (right panels) differ in range by construction rather than by physical disagreement: the Stevens and Kasper reproduction imposes no upper cutoff and the distribution is populated up to r d ≈ 0.5, whereas the present pipeline enforces the canonical r d < 0.5 threshold, so its distribution is bounded there. Within the shared range, both distributions show more events at intermediate and higher depth ratios than at very low ones, with counts rising toward the 0.5 boundary in both catalogues. Taken together, the comparison shows that the present pipeline reproduces the dominant, short-duration population identified by the Stevens and Kasper (2007) reproduction, while the higher 11 Hz cadence extends sensitivity further into the short-duration tail than the 3 s, plasma-screened dataset permits.

These additional short-duration events satisfy the same physical filters as the longer-duration population (r d < 0.5, θ < 15 °) and lie along the smooth continuation of the duration distribution (Figure 2). At typical solar-wind speeds of 400–500 km s − 1, a 3 s sampling interval spans ∼1,200–1,500 km, so the shortest events are only marginally resolved at 3 s cadence; the 11 Hz sampling used here places tens of points within even a 3 s depression, enabling precise localisation of t min and the boundaries. The overall false-positive rate from manual inspection remains ∼9% (Table 2), with no indication that the higher cadence introduces additional spurious detections. The small number of unrecovered events were attributable to two causes: (a) telemetry gaps exceeding the 40% missing-data threshold during the event interval, and (b) marginal depth ratios that fell at or above the 0.5 threshold when evaluated with the refined two-sided ambient field estimate, compared to the simpler one-sided ambient estimates used in some earlier algorithms. Visual inspection of a randomly selected subset of 200 detections suggested a relatively low false-positive fraction. The 1995 recovery rate above and the false-positive rates reported in Tables 2, 3 are drawn from different years by design: 1995 provides the primary validation against the independent Stevens and Kasper (2007) catalogue, while 2018 was used for the threshold-sensitivity and algorithm-comparison checks, since no independent reference catalogue is available for that year to validate recovery against. The false-positive rate estimated from the 1995 sample inspected here is consistent with the ∼9% rate reported for 2018 at the default thresholds, indicating that this behaviour is stable across years rather than specific to either sample. These 200 events were drawn at random, with a fixed seed, from each configuration and inspected as standardised 60 s plots of | B |, the RTN components, and the identified boundaries t S, t E. An event was classified as a false positive when the depression was attributable to a telemetry gap, a rotational discontinuity, a large-scale solar-wind modulation, or a visibly misplaced boundary.

TABLE 2. Summary statistics of detected LMH events. Values are representative of multi-year Wind MFI data at 1 AU.

TABLE 3. Event count and estimated false-positive rate at different depth thresholds. 2018 Wind MFI data, angle threshold fixed at 15°. False-positive rates from visual inspection of 200-event random subsamples.

4.2 Statistical properties of detected events

Application of the pipeline to multi-year Wind MFI data yields a substantial catalogue of LMH events. Summary statistics for the three primary event attributes are given in Table 4 and Figure 2 presents the distributions of event duration, depth ratio, and field-rotation angle, together with the annual occurrence rate, for the full 1996–2025 analysis period.

TABLE 4. Quantitative comparison of three algorithms on 2018 Wind MFI 11-Hz data and 3s Wind/MFI data paired with Wind/3DP plasma moments for S&K reference.

The duration distribution is strongly right-skewed, with most events lasting fewer than 60 s (Figure 2). Panel (d) of Figure 2 shows the annual LMH occurrence rate from 1996 through 2025. The detection rate remains stable across the full interval, confirming that the pipeline operates reliably over multiple solar cycles. A clear modulation of the occurrence rate with the solar cycle is evident, with enhanced LMH activity during solar-minimum years and reduced activity near solar maximum. A detailed physical interpretation of this trend, together with a correlative analysis using Wind/SWE plasma data, is beyond the scope of the present methodology-focused work and will be presented in a dedicated follow-up study.

The histogram of r d shows a pronounced maximum immediately adjacent to the 0.5 cutoff, rising steadily up to the threshold rather than peaking at some interior value well below it. Such behaviour confirms that the imposed limit does not impose an artificial restriction on the underlying physical population; rather, it accommodates the recovery of a wide variety of authentic events. Analogously, the rotation-angle histogram is heavily skewed toward values smaller than 10 °, suggesting that most of the captured structures retain an essentially fixed magnetic-field direction. This finding lends additional support to the choice of the 15 ° linearity cutoff, since it efficiently isolates the prevailing class of linear magnetic holes from the relatively minor population of events displaying stronger angular variation.

Figure 2 shows the depth-ratio distribution rising essentially monotonically toward r d = 0.5, with the highest bin counts occurring right at the cutoff rather than at some interior maximum. This tells us the 0.5 threshold sits close to the edge of the recovered population rather than well above it. A robustness check carried out using alternative depth thresholds of 0.30, 0.40, 0.50, and 0.60 shows a gradual and monotonic trend in the event count, free from any sudden discontinuities (Table 2). Such a response demonstrates that the conclusions are stable and largely insensitive to the precise value adopted for the threshold. Varying the depth and angle thresholds shifts the corresponding distributions predictably: tightening r d removes shallow events from the right tail, while relaxing θ extends the rotation-angle distribution to higher values, leaving the other parameter distributions largely unchanged. The core population (r d ≈ 0.33, θ ≈ 8 °) remains stable across all tested configurations, and no threshold coincides with a discontinuity in the underlying physical distribution (Tables 2, 5).

TABLE 5. Sensitivity of detected event count to depth and angle threshold combinations. Applied to 2018 Wind MFI 11-Hz data. Candidate count is fixed because the rolling-minimum search runs independently of the physical filters.

The default r d < 0.5 was retained despite the lower false-positive rate at stricter cuts (Table 2) because comparability with the canonical 1 AU literature was prioritised over false-positive minimisation alone. Tightening to r d < 0.3 removes more than half of the default catalogue (Table 2), which would preclude a direct comparison against Winterhalter et al. (1994); Stevens and Kasper (2007), both of which are compared for the same 50 % threshold. The ∼5% false-positive rate compared with S&K reference at r d < 0.5 is consistent with rates reported in these earlier surveys and is acceptable for a study whose primary aim is reproducible recovery of the established catalogue; users prioritising purity over completeness can adopt a stricter cutoff directly through the web interface, with the associated trade-offs quantified in Table 2.

4.3 Computational performance

The processing of an entire year of high-cadence Wind MFI measurements (with file chunk of roughly 1–2 GB) on a conventional desktop machine fitted with a quad-core CPU and 16 GB of RAM was completed in under 45 min from initiation to termination. This end-to-end timing accounts for data preprocessing, candidate-event identification, the validation sequence, exporting the outputs in CSV form, and producing summary reports in PDF format. Memory consumption peaked at around 3–4 GB per file, within the capabilities of standard desktop systems, no parallelization, GPU acceleration, or distributed computing was required. Within-file parallelism is constrained by the sequential dependency of the overlap buffer between adjacent chunks and by the shared incremental-output state. However, since annual CSV files are fully independent, file-level parallelism via Python’s multiprocessing.Pool yields near-linear speedup with increasing core count, providing a straightforward route to scaling the pipeline to multi-spacecraft archives without modifying the core detection logic.

5 Discussion

5.1 Methodological advances

The pipeline presented here improves upon existing LMH detection codes in three concrete respects.

First, the pipeline avoids the limitations of treating neighbouring data blocks as fully independent units by using overlapping chunks during processing. Each chunk is extended by a 600-s buffer, so candidate structures located near an internal chunk edge are still evaluated with sufficient surrounding data. This is important because magnetic holes that fall close to a boundary can otherwise be split between two segments, producing incomplete estimates of the ambient magnetic field or duplicate detections of the same physical event. By carrying the overlap through the rolling-minimum calculation, boundary identification, and ambient-field estimation, the method preserves a continuous local context around each candidate event while keeping the memory requirements manageable. As a result, boundary-related artefacts are strongly reduced, and each detected structure can be assessed using a consistent neighbourhood of data.

Second, the three-stage verification framework (Section 3.4) separates physical selection criteria from data-quality checks, allowing each threshold to be adapted independently to different scientific objectives or instruments.

Furthermore, all threshold values and temporal parameters are grounded in physical considerations, explicitly documented, and made accessible through clearly defined user-adjustable controls in the web interface. The implementation avoids the use of hidden instrument-specific constants within the source code. This level of transparency promotes reproducibility, enables users to fully understand the detection criteria, and ensures that the pipeline can be readily adapted to other spacecraft datasets and future missions.

In order to contextualize the performance of the present pipeline, two reference algorithms were executed on the identical 2018 Wind MFI dataset. The first, designated Algorithm A, follows the prescription of Winterhalter et al. (1994), where a sliding median over a 10-min window characterizes the background field, and segments in which | B | drops below 50 % of this baseline are flagged, with no further filters applied for field rotation or data quality. The second, Algorithm B, employs a variance-driven scheme: intervals are accepted when | B | deviates downward by more than two standard deviations from the 5-min running mean, again disregarding any orientation-based or gap-related screening. The S&K reference count of 139 was obtained by re-implementing the Stevens and Kasper (2007) q-statistic algorithm and applying it, following the original prescription, to 3 s Wind/MFI data paired with Wind/3DP plasma moments. The non-steady solar-wind intervals (magnetosphere, foreshock, heliospheric current sheet crossings, ICMEs, and shocks) were excluded based upon the location of the spacecraft and using an online catalog of shocks observed by Wind. This plasma-based screening step is specific to the S&K re-implementation and is not used by Algorithms A and B or by the present pipeline, all three of which operate on magnetic-field magnitude alone. The re-implementation was applied over the same 2018 interval used for Algorithms A and B and the present pipeline. Since the original Stevens and Kasper (2007) method applies no depth-ratio or rotation-angle cutoff, the same r d < 0.5 and θ < 15 ° thresholds used throughout this work were additionally applied to the re-implemented candidates, so that the resulting count is directly comparable to the other three entries in Table 3. False-positive rates for all four methods were estimated in the same way, by visually inspecting 200 randomly selected 2018 events from each algorithm’s output against the criteria described in Section 4.1. Algorithms A and B apply a continuously sliding median and running mean, respectively, advancing sample by sample across the full time series, so neither requires an explicit overlap buffer or is subject to the fixed-block boundary artefacts discussed above for the present pipeline. Their limitation is instead a single, fixed characteristic window (10-min median for A, 5-min mean for B) applied uniformly regardless of local solar-wind conditions, which does not adapt to the two-sided, chunk-aware ambient estimation used in the present work. A comparison of all three algorithms on 2018 Wind MFI data is given in Table 3. The lower total event count from the present pipeline compared to A and B reflects the deliberate exclusion of rotational holes by the angle criterion and the rejection of gap-contaminated intervals by the missing-data filter, not reduced sensitivity to genuine linear magnetic holes.

The pipeline is designed to detect a specific, physically bounded class of magnetic hole: structures where the field drops to below 50% of the ambient level and the upstream-to-downstream field direction is preserved within 15°. These thresholds follow Winterhalter et al. (1994) and Briand et al. (2010) respectively, ensuring direct comparability with the major published catalogues at 1AU. Several classes of magnetic depression lie outside this scope. Shallow holes with r d between 0.5 and 1.0 are excluded by the depth criterion. Kinetic-scale holes shorter than the rolling-window duration are also resolved by find_local_minima(). Asymmetric events with markedly different entry and exit profiles may be mis-characterised by the two-sided ambient estimation. These are boundaries on the physical scope of the catalogue, not algorithmic failures, and all thresholds are adjustable through the web based interface. A sensitivity analysis across depth thresholds of 0.30, 0.40, 0.50 and angle thresholds of 15, 20, 25, 30° shows smooth monotonic variation in event count with no discontinuities, confirming that the pipeline is not tuned to a narrow operating regime (Table 5).

A related limitation concerns depressions with flat or near-flat bottoms, where several adjacent samples can each satisfy the local rolling-minimum condition. In such cases the pipeline may register more than one candidate t min, and consequently more than one catalogue entry, for a single physical structure. This does not affect the depth or angle criteria for the affected events, since these depend only on the ambient and minimum field values rather than on how many candidates were generated, but it can locally inflate event counts for wide, flat-bottomed holes. A post-processing deduplication step, merging candidates whose boundary intervals overlap, would resolve this and is planned for a future release.

The event boundaries t S and t E are identified using a locally adaptive threshold defined as the mean minus one standard deviation of | B | within the 300-s search window (find_event_boundaries()). This adapts to non-stationarity in the solar wind background without requiring global normalisation, but it introduces a dependence of boundary position on local field variance. In highly Alfvénic intervals where B std is large relative to the hole depth, the threshold descends further and the boundaries are placed further from the field minimum, producing systematically wider and longer reported durations. In quiet intervals the reverse effect may occur. This variance-driven uncertainty does not propagate into the depth ratio or rotation angle, both of which are computed from fixed-duration ambient windows anchored to t S and t E rather than derived from the boundaries directly. Event durations should therefore be interpreted with awareness of this turbulence-level dependence, particularly in studies that correlate duration with ambient solar wind properties. The opposite bias shows up for compound or clustered depressions. If the 300 s boundary window falls mostly inside a broader dip, B ̄ 0 itself is dragged down, B thresh drops with it, and t S and t E get placed too close to t min understating the event duration rather than inflating it. This tends to correct itself in the worst cases, because the same depressed background lowers the ambient field used in the depth-ratio test, pushing r d toward 1 and the event toward rejection. Milder cases slip through, though, so durations for events sitting inside compound or clustered dips should be read as lower bounds. Handling this properly would likely need a data-driven boundary-placement scheme trained on validated events, rather than a fixed threshold, which we leave for future work.

5.2 Future perspectives

While the existing pipeline provides an efficient and reproducible scheme for LMH identification, several aspects remain open to refinement. The current localization strategy, which is built upon a rolling minimum of | B |, does not invariably distinguish genuine LMH dips from field depressions arising due to large-amplitude Alfvénic oscillations or compressional turbulence within disturbed solar-wind streams. Large-scale rotational structures such as magnetic clouds are, by contrast, already excluded by the 15 ° directionality criterion (Section 3.4.2), since the smooth field rotation defining such structures necessarily produces upstream-to-downstream angles well above the linearity threshold. Imposing supplementary physical filters, for instance based on plasma beta or the variance profile of the magnetic field, would further improve the fidelity and purity of the catalogue by addressing the remaining, non-rotational contaminants. A specific instance of this broader class of contaminants arises in ICME sheaths and stream interaction regions (SIRs), which contain large-amplitude compressional fluctuations in | B | that can superficially resemble magnetic-hole signatures (Kilpua et al., 2017; Jian et al., 2006). Two existing mechanisms provide partial protection against these regions. The 15 ° directionality criterion rejects most sheath- and SIR-related depressions, since these intervals are typically dominated by field rotation and compressional turbulence rather than the quasi-linear geometry that defines an LMH. In addition, the two-sided ambient-field estimation becomes more conservative in highly turbulent intervals, since elevated local variance raises the effective boundary threshold B ̄ 0 − σ B and suppresses spurious detections. These mechanisms are not exhaustive, however: LMH-like depressions genuinely embedded within disturbed solar-wind structures cannot be fully separated from the surrounding turbulence using magnetic-field criteria alone. A more complete separation would require cross-referencing the resulting catalogue against independent ICME and SIR lists (Richardson and Cane, 2010; Jian et al., 2006), which we plan to implement as an optional post-processing context filter in future work. Furthermore, the integration of co-temporal proton density, bulk velocity, and temperature data from the Wind SWE instrument (Ogilvie et al., 1995) would permit the characterization of every event in terms of local plasma beta and temperature anisotropy, thereby facilitating a more direct confrontation with theoretical instability boundaries. Plasma-based verification was not adopted as a mandatory criterion in the present work for three reasons. First, the canonical depth and linearity criteria against which our pipeline is benchmarked (Winterhalter et al., 1994; Briand et al., 2010) are defined on magnetic-field data alone, so imposing a mandatory plasma-pressure filter would change the operational definition and reduce direct comparability. Second, Wind/MFI delivers continuous 11 Hz data, whereas Wind/SWE plasma moments are available at ∼ 92 s cadence with periodic gaps, so requiring concurrent SWE coverage would substantially reduce the catalogue size and bias it toward well-covered intervals. Third, the present manuscript is methodology-focused, and a full pressure-balance and temperature-anisotropy analysis is better treated in a dedicated follow-up study.

The core detection logic, rolling-minimum search, boundary identification, and three-stage filtering operates on any time-indexed magnetic-field magnitude series and is therefore instrument-agnostic. Because the depth criterion is defined as a ratio ( r d = | B | min / B ambient ) and the directionality criterion uses normalised field vectors, the pipeline is unaffected by the order-of-magnitude stronger background fields encountered closer to the Sun. Extending the framework to missions such as Parker Solar Probe/FIELDS or Solar Orbiter/MAG therefore requires only a mission-specific data-ingestion module that maps the relevant file format, column names, and coordinate system to the internal representation used by the pipeline; the core algorithm remains unchanged. The temporal parameters (window_seconds, boundary_seconds, ambient_before, ambient_after), whose default values in Table 1 are tuned to Wind/MFI observations near 1 AU, should be scaled proportionally to the local plasma timescales and instrument cadence when applied to other missions, since LMH durations shorten with decreasing heliocentric distance. A natural avenue for future development lies in extending the framework to multi-spacecraft datasets. As an illustration, jointly analysing observations acquired near 1 AU by Wind together with measurements obtained closer to the Sun by Solar Orbiter and Parker Solar Probe would offer a unique opportunity to examine the manner in which LMH populations are modified and evolve across the inner heliosphere. Such comparative studies could reveal whether event occurrence, spatial scale, or morphology changes systematically with radial distance and solar wind environment.

Finally, the present deterministic threshold-based strategy could be complemented by modern machine-learning approaches. A supervised classifier trained on validated events from the current catalogue may help identify subtle or shallow LMHs near the detection boundary, as well as events embedded within highly variable solar wind intervals where fixed thresholds become less effective. Hybrid approaches that combine physically motivated criteria with data-driven classification may therefore offer the most promising route for future large-scale LMH surveys.

5.3 Physical interpretation

The statistical properties recovered by the pipeline are consistent with LMHs being quasi-stationary pressure-balance structures advected past the spacecraft by the bulk solar wind flow, rather than propagating wave packets. The observed median duration of approximately 9.0 s at solar wind speeds of 400–500 km s − 1 implies characteristic spatial scales of ∼ 4000 km, corresponding to roughly 40–60 ion inertial lengths. These scales are consistent with those expected for mirror-mode structures (Southwood and Kivelson, 1993) and for Alfvénic solitons in the derivative nonlinear Schrödinger framework (Mjølhus, 1976; Baumgärtel, 1999). At the high-cadence end, the 11 Hz sampling of Wind/MFI corresponds to a spatial resolution of ∼ 40 km at typical solar-wind speeds, which lies well above the local electron inertial scale (d e ∼ 1–2 km at 1 AU) but resolves structures down to a fraction of the ion inertial length. The detected duration distribution tapers smoothly toward the few-second range without exhibiting a sharp lower cutoff, indicating that the present catalogue does not reveal an absolute lower kinetic boundary for LMHs within the resolved scale range. Probing whether such structures persist down to electron-inertial scales requires higher-cadence burst-mode magnetometer data, such as those provided by MMS or Parker Solar Probe/FIELDS, and lies beyond the scope of the present 1 AU long-baseline survey. The elevated LMH rate during solar minimum is consistent with theoretical expectations that enhanced proton temperature anisotropy in the fast solar wind provides favourable conditions for mirror-mode growth (Hasegawa, 1969). Future combination of the LMH catalogue with Wind SWE plasma moments will allow this prediction to be tested quantitatively for individual events, enabling direct comparison with the marginal stability thresholds derived from kinetic theory.

6 Conclusion

We have developed and validated an automated pipeline for detecting linear magnetic holes in Wind spacecraft MFI high-resolution data. The pipeline reads each input file in sequential overlapping chunks, applies a consistent preprocessing and quality-control scheme to each chunk, and identifies candidate events through a rolling-minimum search with a 600 s overlap buffer that preserves local field context across chunk boundaries. Three sequential physical filters, a 50% depth criterion, a 15 ° field-rotation criterion, and a 40% missing-data quality criterion are then applied using ambient field levels drawn from the surrounding chunk data, ensuring that every estimate reflects the true local field environment with reduced boundary contamination.

Application to multi-year Wind MFI data yields an LMH catalog whose statistical properties right-skewed duration distribution peaking near 9.0 s, depth ratios centred near 0.3, and rotation angles well below 15 ° are consistent with previously published surveys. The pipeline recovers more than 95% of independently cataloged events while maintaining a false-positive rate below 10%, and completes the whole detection and visualization workflow for 1 year of high-resolution data under 45 min on standard desktop hardware.

The code is open source and measurement-independent in its core detection logic, making it readily adaptable to other single-spacecraft data products. It provides a robust, clearly structured foundation for future large-scale statistical investigations of LMH properties across the solar cycle, their radial evolution with heliocentric distance, and their connection to local plasma instability conditions.

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Footnotes

Edited by: Sandeep Kumar, National Aeronautics and Space Administration, United States

Reviewed by: Sanchita Pal, National Aeronautics and Space Administration, United States

Yogesh, The University of Iowa, United States