1 Introduction

Geomagnetic storms are commonly the largest source of geomagnetic disturbances. These events constitute a major natural hazard due to their potential to harm technological and electrical systems, which our society is increasingly dependent on. The intensity of geomagnetic storms is often measured using various geomagnetic indices.

The geomagnetic Kp index (Matzka et al. 2021, and references therein) was first introduced by Bartels (1938) to monitor geomagnetic disturbances on a planetary scale. It is derived from observatory-specific three-hourly K indices, which are defined as a quasi-logarithmic measure, ranging in steps of 1 from 0 to 9, of the range of geomagnetic disturbance at a geomagnetic observatory in a three-hourly UT interval (00–03, 03–06,..., 21–24).

After the International Geophysical Year, new indices were designed as a result of a better understanding of magnetospheric physics and of improvement in the observatory network (Menvielle et al. 2010, and references therein): the Dst, as a proxy of the ring current behavior, AE, to quantify the maximum of the auroral electrojet intensity, and am indices, for planetary activity like Kp, but containing information on the universal time (UT) dependent variation of geomagnetic disturbance.

Besides these indices are unique tools for selecting storm events, some limitations were discovered. For example, the 3 h granularity of planetary indices (K-derived) result in limited usefulness in solar wind–magnetosphere event analysis. Also, the Dst, which is a weighted average of the deviation from the quiet level of the H component measured at four low-latitude magnetometer observatories spread in longitude, was aimed to measure the axially symmetric ring current source. However, the low-latitude geomagnetic field was discovered to develop very differently at different local times, as several other current systems contribute to the magnetic variations at low and mid latitude. In addition, the low (1 h) resolution of Dst was limited, for example, to analyze the solar structure responsible for the Dst decrease in the main phase of a storm. Then, to describe the asymmetric and symmetric disturbance fields in mid-latitudes with high-time (1 min) resolution, longitudinally asymmetric (ASY) and symmetric (SYM) disturbance indices were introduced for both H and D magnetic field components (Iyemori 1990). The symmetric disturbance field in H, SYM-H, is essentially the same as the hourly Dst index, although 1 min values from different sets of stations (Wanliss and Showalter 2006). SYM and ASY indices are nowadays routinely produced by the World Data Center for Geomagnetism, Kyoto, Japan, and extensively used for scientific purposes.

Geomagnetic storms are extraordinary disturbances. However, not all storms have the same intensity, leading to different consequences. Since the intensity of storms is measured using the disturbance caused in the geomagnetic indices, they are often classified into different classes depending on the maximum disturbance caused in the indices. Consequently, thresholds are used to determine the different classes of storms, based on their intensity and probability of occurrence.

An accurate classification of the intensity of geomagnetic storms serves two main purposes. First, from an academic perspective, understanding the underlying mechanisms that generate the storms. Several studies analyze geomagnetic storms focusing on those of similar intensity (Kamide et al. 1998; Brueckner et al. 1998; Richardson and Cane 2012; Uwamahoro and Habarulema 2015). Second, there is a natural concern for mankind (Gonzalez et al. 1994) due to the varying intensity of geomagnetic storms and their potential consequences. These consequences range from damaging satellites (SpaceX 2022) and increasing their orbital drag (Doornbos and Klinkrad 2006; Oliveira et al. 2020) to disrupting GNSS signals (Ma and Maruyama 2006; Astafyeva et al. 2014) and even damaging the power grid infrastructure (Kappenman 2010).

Despite the great importance of having an accurate classification of geomagnetic storms based on their intensity, there is no consensus among authors. Nevertheless, the most used index to determine the intensity of geomagnetic storms, at least in scientific literature, is the Dst index. Initially, Gonzalez et al. (1994) classified the geomagnetic storms depending on the minimum value reached by the Dst values from 1976 to 1986 (solar cycle 21) . They set the thresholds shown in Table 1 to classify the geomagnetic storms into weak, moderate and intense groups, using the distribution of the observed hourly values as a guideline. Weak storms are those when the minimum value reached by the Dst is between \(-\)30 and \(-\)50 nT, corresponding to 25% of the hourly distribution of the observed values; moderate storms encompass those with a minimum Dst value between \(-\)50 and \(-\)100 nT, corresponding to 8% of the values; finally, storms when the index falls below \(-\)100 nT are considered intense, corresponding to 1% of the observed values. This classification was also used by other authors, such as Kamide et al. (1998), to analyze storms of similar intensity.

Table 1 Geomagnetic storms classification by Gonzalez et al. (1994)
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Later, Gonzalez et al. (2002) and Echer et al. (2008) proposed a new category of superintense storms for those storms in which the Dst index reached values lower than \(-\)250 nT. This classification is the most widely used in the literature (e.g., Astafyeva et al. 2014). Nevertheless, authors like Rawat et al. (2010) and Li et al. (2011) considered the superintense storms those where the index reached values lower than \(-\)300 nT. A different classification was proposed by Loewe and Prölss (1997). They considered storms whenever a depression in the Dst index exceeds \(-\)30 nT. Then, they qualified the storms into four classes with different thresholds. They considered storms in which the Dst peak is between \(-\)30 and \(-\)50 nT as weak storms, corresponding to 44% of the identified storms then, between \(-\)50 and \(-\)100 nT to be moderate storms corresponding to 32% of their identified storms, between \(-\)100 nT and \(-\)200 nT are considered strong, corresponding to 19% of the detected storms, from \(-\)200 nT until \(-\)350 nT are considered severe storms, corresponding to 4% of the detected storms. Finally, storms more intense than \(-\)350 nT are considered exceptional, corresponding to the 1% most intense storms. However, they performed the percentile calculations to determine each class over the detected storms, as opposed to considering the whole time series as other authors. This classification has been used by other authors, such as Uwamahoro and Habarulema (2015), to model the total electron content during storms. In Loewe’s work, they also performed a superposed epoch analysis on the different classes, using the Dst peak as the common epoch time.

Nonetheless, the Dst is not the only index that has been used to classify geomagnetic storms. For instance, Gosling et al. (1991) used the Kp index to classify the storms into four groups: major, large, medium and small. For example, this classification has been used by Richardson and Cane (2012) but the applications are limited due to the 3-hour time resolution of the Kp index as some space weather impacts are driven by short-time (\(\sim \)1.5–2 h) disturbances (Saiz et al. 2023).

Fig. 1
figure 1

Geomagnetic storm of November 2003. The SYM-H index deviates from the Dst index on very high intensities, below \(-\)300 nT

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One of the indices that is being increasingly used by the community is the SYM-H index. Wanliss and Showalter (2006) proved that the SYM-H index is comparable to the Dst index until \(-\)300 nT. For quiet times and for small storms, the deviations are typically no more than 10 nT between both indices. Moderate storms feature deviations typically only slightly more than 10 nT, while intense storms have deviations that are usually less than 20 nT. Nevertheless, in those storms where the SYM-H index reaches values below -300, the indices are no longer comparable. For example, in the geomagnetic storm of November 2003, depicted in Fig. 1, the peak value of the Dst index is \(-\)422 nT, while the SYM-H peak is \(-\)488 nT, 1.15 times lower.

Therefore, the previous classification based on the Dst index cannot be used as a direct proxy for the SYM-H index. Additionally, the thresholds set by Gonzalez et al. (1994) only used the Dst data from 1976 to 1986; for half of the temporal frame used to determine the thresholds the SYM-H is not even available, since it has been calculated from 1981 onward. Since then, we have had more than 40 years’ worth of SYM-H measurements with new storms that are more intense than any of the storms which happened during that period. Taking that into account, the distribution of the index calculated by Gonzalez et al. (1994) has changed considerably when considering all the available data for the SYM-H index. In this regard, Hutchinson et al. (2011) separated the storms into three categories based on the minimum value reached by the SYM-H: weak (\(-\)150 < SYM-H < \(-\)80) nT, moderate (\(-\)300 < SYM-H < \(-\)150) nT and intense (SYM-H < \(-\)300) nT. However, the threshold values were selected without offering explicit reasoning.

Currently, there are several applications and users that can take advantage of a proper storm classification. One of those is the forecasting of the geomagnetic indices. This is an ongoing problem that is constantly gaining more importance: by forecasting the indices it could be possible to predict a geomagnetic storm, and, therefore, to take the appropriate preventive containment measures. Particularly, most forecasting systems are focused on geomagnetic storms, when the consequences are more severe. Several techniques have been used to forecast the various geomagnetic indices, ranging from mathematical models to machine learning based solutions. Zhelavskaya et al. (2019), Shprits et al. (2019) and Wintoft et al. (2017) forecast the Kp index. O’Brien and McPherron (2000), Gruet et al. (2018) and Lazzús et al. (2019) forecast the Dst index. More recently, attention has shifted to forecast the SYM-H and ASY-H indices (Cai et al. 2009; Bhaskar and Vichare 2019; Siciliano et al. 2020; Collado-Villaverde et al. 2021; Iong et al. 2022) due to their high temporal resolution compared to the previous indices.

The works that forecast the SYM-H and ASY-H indices focus only on the prediction of the index during intense geomagnetic storms. However, it is not clearly defined which storms are considered intense and, therefore, used to train and evaluate the forecasting models. For instance, Cai et al. (2009) considered the storms in which SYM-H peak (the minimum value reached by the SYM-H) was less than \(-\)60 nT, while Bhaskar and Vichare (2019) considered the storms in which the SYM-H peak was less than \(-\)85 nT. By its side, Siciliano et al. (2020) considered the storms with a SYM-H peak of less than \(-\)100 nT. Moreover, for other indices, such as the ASY-H, currently there is no classification of the geomagnetic storm.

Trying to provide a comprehensive and objective storm classification based on the SYM-H and ASY-H indices, we propose a classification method based on the cumulative distribution function of the indices. We apply the industry-wide percentiles used in risk assessment to the distribution to separate the different classes of geomagnetic storms according to the peak values of the indices. Using the calculated percentiles, the storms can be classified according to their intensity and asymmetry, based on the probability of occurrence. Then, we set the boundaries of the storms using a superposed epoch analysis. This approach allows us to arrange an ‘intensity-classified storms set’ useful for later studies.

The remainder of the paper is structured as follows. The next section describes the process followed to determine the different classes of geomagnetic storms based on the peak value reached by the index. Section 3 describes how we determine the boundaries of the storm, that is the time when the storm starts and ends. Section 4 summarizes the procedure to select and classify geomagnetic storms and presents the identified storms for each index. We outline some conclusions in Sect. 5 with a summary of the key points and applications of the findings.

2 Classifying geomagnetic storms

The procedure to classify the geomagnetic storms based on their intensity and asymmetry according to the SYM-H and ASY-H indices is the same for both indices: the only difference between the SYM-H and the ASY-H indices is that for the SYM-H intense values are represented with increasingly negative values, whereas they are represented with positive values for the ASY-H.

If we consider the geomagnetic storms as infrequent events that pose a risk, the severity of the risk can be quantified using the peak value reached by the evaluated geomagnetic index (maximum in the case of the ASY-H index or minimum in the case of the SYM-H). Additionally, the time interval of similar events can be estimated as the inverse of the probability, which is indicated by the cumulative distribution function (CDF). For this purpose, the time series data of indices have to be made of random variables, that is, their values have to be independent. Notwithstanding, both the 1-minute and 5-minute aggregated series of the indices are not random variables as the observations are highly correlated with the previous value, having an autocorrelation greater than 0.95. Additionally, the great amount of quiet time skews the distribution function of the original time series toward values corresponding to nominal behavior.

To make the time series useful for a probability analysis, we have resampled the series of SYM-H and ASY-H indices so subsequent data points do not have a causal relationship, which is indicated by a low autocorrelation value. For this purpose, we have aggregated the data in 27 days intervals. The choice of 27 days is motivated to avoid the persistence in the indices caused by the disturbances associated with fast streams from coronal holes lasting several solar rotations. Then, we have chosen the peak value of the index of each aggregation period to identify the maximum disturbance in each period. The objective is to make the resampled series have a low autocorrelation value, making the time series statistically independent.

The approach of resampling the time series using the peak value brings forth a reduction in the number of data points, effectively eliminating periods of relative calm and thus magnifying the significance of active periods. We have also tested using other periods to perform the resample of the time series. Periods shorter than 27 days have considerable autocorrelation values. Moreover, opting for shorter intervals yields a surplus of data points corresponding to quieter times, resulting in smaller values within the CDF. Nevertheless, the autocorrelation of the values due to the rotation of the Sun invalidates the CDF calculations. Conversely, the longer the aggregation interval, the greater prominence intense storms acquire. However, longer periods have an asymptotic behavior.

We have also tested the option of performing the statistical calculations using the bootstrap method to eliminate the autocorrelation. However, the great imbalance of inactive time compared to the active time is still present, making the average values of the percentiles in the CDF almost similar to the original time series.

To have statistical reasoning behind the selection of the thresholds to classify the storms, we decided to use the percentiles of the distribution of the intensity of the indices’ time series, following Cid et al. (2020). We have chosen the 60th percentile as the cutoff to determine when the disturbance is strong enough to be considered a geomagnetic storm. Values less intense than the 60th percentile can be considered inactive or quiet time. Once the starting point of the 60th percentile has been set, we have chosen to differentiate the remaining CDF into four different classes, starting with the geomagnetic storms of low intensity for those storms in which the peak value for the index is more intense than the 60th percentile.

Then, we chose the 80th percentile as the upper boundary for the low intensity storms and the start for the moderate storms. That particular percentile is in line with the IFRS 17 (Jiang 2020), in which industry-wide consensus for risk assessment is between the 70th to the 80th percentiles. Additionally, storms with an intensity between these thresholds already can harm technological systems in space such as satellites or disrupt GNSS signals.

After that, we considered the 95th percentile as the upper boundary for moderate storms. Storms in which the index reaches a peak value more intense than the 95th percentile will be considered as intense. Finally, we have chosen to further classify the remaining distribution in two classes: the intense and superintense storms, using the 99th percentile as the boundary. The reasoning behind that is because above the 95th percentile the data points are very different: for both indices the range of values over the 99th percentile is greater than all the values under it, making the extra class necessary to keep the groups as consistent as possible.

Note that in the following sections the values for the selected percentiles are rounded to the nearest ten.

2.1 Analysis of the SYM-H index

To perform the classification, we consider the historical records of the SYM-H index from 1981 to 2022. To resample the SYM-H, we have chosen the minimum value in each time period of 27 days; the resulting series is depicted in Fig. 2. Then, to test the independence of the time series we calculate the autocorrelation value for the nine subsequent time steps, as shown in Fig. 3. After performing the resample, we obtain that the autocorrelation value is lower than 0.3 for any time lag.

Fig. 2
figure 2

Time series of the resampled SYM-H index

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Fig. 3
figure 3

Heatmap of the autocorrelation for the resampled series of the SYM-H index

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Once we have a resampled series that is statistically independent, we can perform the CDF to estimate the thresholds for each of the identified classes. Figure 4 depicts the CDF of the SYM-H index, being the vertical dashed lines the selected percentiles for the different storm categories as stated below:

  • The green area represents the inactive distribution, it extends until the 60th percentile, corresponding to \(-\)90 nT.

  • The yellow area represents the distribution for the low intensity storms, extending from the 60th percentile to the 80th, corresponding to \(-\)130 nT.

  • The orange area represents the distribution for the moderate storms, starting on the 80th percentile and extending until the 95th, corresponding to \(-\)230 nT.

  • The red area represents the distribution of the intense storms, encompassing from the 95th percentile to the 99th, corresponding to \(-\)390 nT.

Fig. 4
figure 4

CDF of the minimum SYM-H (nT) every 27 days

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The starting point of the 60th percentile on the resampled time series corresponds to \(-\)90 nT. This threshold is a bit higher than the classification made by Hutchinson et al. (2011), which considered \(-\)80 nT to be the lower bound for weak storms. It is also higher than the threshold for low storms considered in the earlier forecasting works (Cai et al. 2009; Bhaskar and Vichare 2019) where they used \(-\)60 nT and \(-\)85 nT as the threshold for low intensity storms. However, it is a bit lower than the threshold used in the later forecasting works (Siciliano et al. 2020). Compared to the Dst index, our proposed threshold is higher than the established classifications for the Dst. Nevertheless, this is related to the fact that Dst values are generally lower than SYM-H due to the hourly average nature of the index. We decided to set the upper bound for this classification at the 80th percentile, corresponding to \(-\)130 nT.

Then, we consider the storms with a SYM-H peak lower than \(-\)130 nT to be of moderate intensity; it extends until the 95 percentile, corresponding to \(-\)230 nT. Those values are in line with what have been considered moderate storms in the literature: a bit lower than the threshold considered by Hutchinson et al. (2011) of \(-\)150 nT for the SYM-H for the moderate storms, but also higher than the threshold commonly used for moderate storms in the Dst index. Storms in this range are considered moderate since they can harm satellites and disturb GNSS signals (Ma and Maruyama 2006; SpaceX 2022), but they are supposed to be not intense enough to cause black-outs and damage the electrical infrastructure.

After that, the intense storms range from a SYM-H peak of \(-\)230 nT, corresponding to the 95th percentile, to \(-\)390 nT, corresponding to the 99th percentile. Finally, we have chosen to create a fourth class for the remaining distribution to differentiate storms in which the SYM-H peak surpasses the 99th percentile. This distinction is needed because the data points in the resampled time series outside the 95th percentile are very different. As there are 29 samples with values lower than \(-\)230 nT, if they were grouped into the same class, the standard deviation would be 100 nT with a mean of \(-\)335 nT, which make the distribution of the group too sparse. Instead, we propose a superintense class for the storms with a SYM-H peak more intense than the 99th percentile, which corresponds to \(-\)390 nT.

This split separates the 29 data points into 22 intense and 7 superintense storms. The resulting intense group is much more consistent, having a mean of the SYM-H of \(-\)290 nT and a standard deviation of 43 nT. Despite that, the superintense group has one outlier caused by the storm of 1989 with a SYM-H peak of \(-\)714 nT, which in conjunction with the small amount of data greatly pollutes the mean and standard deviation of the group. In case of removing that data point, the remaining six superintense storms would have a mean of \(-\)430 nT and a standard deviation of 31 nT. However, keeping it in the sample, the resulting group has a mean of \(-\)470 nT and a standard deviation of 113 nT, evidencing the relevance of rare events in the analysis. Table 2 summarizes the classification for the SYM-H index.

Table 2 Geomagnetic storms classification using the SYM-H
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2.2 Analysis of the ASY-H index

Similar to the SYM-H index, for performing the resample and CDF computation, we consider the ASY-H records from 1981 to 2022. The resampled time series is depicted in Fig. 5. The main difference between the indices’ values of the SYM-H and ASY-H is that the disturbances are measured with positive values in the ASY-H. Thus, we select the maximum value of each 27 days group instead of the minimum. Considering that the index measures asymmetric disturbances, its behavior is more chaotic. This is reflected by a low autocorrelation value in the resampled time series. For this index, the autocorrelation is lower than 0.2 in the subsequent nine time steps as shown in Fig. 6, which is significantly lower than the autocorrelation for the SYM-H.

Fig. 5
figure 5

Time series of the resampled ASY-H index

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Fig. 6
figure 6

Heatmap of the autocorrelation for the resampled series of the ASY-H index

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After confirming the independence of the time series, we have calculated the CDF, presented in Fig. 7. The vertical dashed lines depict the percentiles that define the thresholds between classes. Since there is no previous classification of geomagnetic storms based on the ASY-H index, we cannot compare the proposed thresholds to other authors. If we compare the shape of CDF between the ASY-H and the SYM-H, they are fairly similar, with the main difference being that the ASY-H has, generally, higher absolute values. For instance, in the resampled time series, the average ratio between SYM/ASY is around 1.4, being the greatest in the most intense times. These values are in line with Echer et al. (2008) findings, indicating a higher degree of asymmetry for the superintense storms. Considering that, despite not having other works to compare the thresholds for the different classes of geomagnetic storms for the ASY-H, we will use the same percentiles as the selected for the SYM-H as guidelines.

Fig. 7
figure 7

Complementary CDF of the maximum ASY-H (nT) every 27 days

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We consider the 60th percentile as the threshold for differentiating between inactive time and the start of low asymmetric disturbance. Then, storms are considered as of low asymmetry when the ASY-H peak is between the 60th and 80th percentile, corresponding to 130 nT and 170 nT. This group is the largest. In this case, the average ratio between the SYM/ASY is 1.35. A lot of similar data points are condensed in this group, as the standard deviation of low asymmetric data points is less than 11 nT, lower than the standard deviation for the same class in the SYM-H index.

Next, moderate asymmetric storms range from those with a ASY-H peak of 170 nT to 290 nT, which corresponds to the 80th and 95th percentiles, respectively. In this case, the disparity in the data points increases, having a standard deviation of 35 nT, which is higher than the standard deviation for the SYM-H in the same group (29 nT). This suggests that the asymmetrical component of the storms is accentuated by the intensity of the disturbances.

Finally, we have differentiated between intense and superintense asymmetric storms for the remaining distribution. We use the 99th percentile as the threshold value for separating both classes. There are 29 data points in which the peak value is above the 95th percentile. If no distinction is made, the standard deviation of the ASY-H peaks for those data points is almost 140 nT. Considering that the starting threshold value for that category is 290 nT, 140 nT is a relevant disparity in the remaining data points. Thus, we separate the storms creating the category of superintense with the 99th percentile, corresponding to 540 nT as the thresholds between both groups. The 29 previous data points are separated into 23 intense ones, with a standard deviation around 65 nT, and six superintense storms with a standard deviation of 90 nT. In this case, since there is no extreme outliers like in the SYM-H case, even the superintense group has similar ASY-H peak values. This makes this group have a smaller standard deviation than the superintense group of the SYM-H index, but the mean is considerably higher, as the ratio between the indices is around 1.5 for this class. Table 3 summarizes the classification for the ASY-H index.

Table 3 Geomagnetic storms classification using the ASY-H
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2.3 Analysis of the Dst index

We have performed the same analysis for the Dst index, resampling the data using the same time interval (27 days) as in the cases of SYM-H and ASY-H. The covered time range includes data from 1981 to 2002, i.e., the same time range as for the SYM-H and ASY-H analysis. The results are very similar compared to those obtained with the SYM-H, albeit the autocorrelation values are slightly higher.

Figure 8 depicts the CDF of the Dst index. Meanwhile, the general shape of the CDF is similar to the SYM-H, the values corresponding to the selected percentiles are 10 to 30 nT higher, except the value for the superintense percentile which is 60 nT higher, as shown in Table 4. The obtained thresholds for the different storm classes are in line with previous works.

Fig. 8
figure 8

CDF of the minimum Dst (nT) every 27 days

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Table 4 Geomagnetic storms classification using the Dst
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3 Setting the boundaries of a storm

To properly characterize the storms, aside from classifying them based on the disturbance caused on a geomagnetic index, we also need to timely determine the different parts of a geomagnetic storm. Different authors have defined the different parts of the storm using different approaches. For instance, Murphy et al. (2018) defined each storm using three distinct times: the storm start, the epoch (defined as the time of minimum Dst during the storm) and the storm end. The storm’s beginning is marked by increased solar wind activity, while its conclusion is determined by the recovery of the Dst after the solar wind activity diminishes. These phases correspond to the main phase and recovery phase of the storm but may vary in duration for each event. To conduct a superposed epoch analysis, Murphy et al. (2018) normalized that the initial phase of each storm is normalized to 30 h, and the subsequent phase is normalized to 120 h. On the contrary, Echer et al. (2008) stated that the storm’s main phase had a duration from 3 to 33 h, averaging around 11 h. Aguado et al. (2010) analyzed the recovery duration of geomagnetic storms up to 48 h after the Dst peak. Hutchinson et al. (2011) considered that the recovery phase lasted until the index reached a ‘quiet’ condition of \(-\)15 nT. Mannucci et al. (2008) performed a superposed epoch analysis of the four most intense geomagnetic storms of 2003 and 2004, extending the recovery phase up to 25 h after the start of the storm.

Wharton et al. (2020) used four key dates to characterize the geomagnetic storms: the initial, main and recovery phases of geomagnetic storms. The algorithm utilized the SYM-H index and a threshold of \(-\)80 nT to detect the storm minima. The end of the main phase was defined by the SYM-H minimum, while the beginning of the main phase was determined by the time when the SYM-H reaches \(-\)15 nT. Before that, the initial phase ranges from the last time the SYM-H index had values greater than \(-\)15 nT. Finally, the recovery phase ranges from the SYM-H minimum until the index has recovered to values higher than \(-\)15 nT. However, there are cases in which relying on a specific value to set the bounds of the storm yields either too short or too long initial times. For example, in the storm of April, 1994, depicted in Fig. 13, the first value over \(-\)15 nT before the SYM-H peak happened 15 days before.

Like the classification of storms based on their intensity, the duration of the storms is also a discussed topic and the duration varies among authors. In general, it is considered that the storm begins when the index starts taking values outside of the nominal values before the index peak, and is finished once the index has recovered to the nominal values. Some authors even separate the time between the nominal phase and the index peak in two different phases.

However, our focus is not on the morphology of the storm but the identification and selection of the time interval covering the whole storm. In this regard, we have chosen to perform a superposed epoch analysis for the different identified classes of geomagnetic storms. This analysis can help to identify patterns in the temporal evolution of the storms. It has also been used in previous works to determine recovery approximation functions, such as Aguado et al. (2010) and Hutchinson et al. (2011), or to study storms of similar intensity (Mannucci et al. 2008).

Since we are not trying to define the morphology of the storm, we have not divided the storm into the initial, main and recovery phases similar to other authors. We have set the duration of the storm based on how the time series for the indices behaves surrounding the peak in the superposed epoch plot for each of the different classes.

The analysis consists of aligning the storms of the same class at a particular time, and then, all the storms are averaged and plotted to study the evolution of similar storms. We have chosen to align the storm on the indices peaks, that is, the minimum SYM-H and the maximum ASY-H. Then, we select the 120 h surrounding the peak, average all the storms of every class and plot the ‘average storms’ together.

Fig. 9
figure 9

SYM-H superposed epoch plot. The bounds of the storm are represented by the vertical lines. The dotted line depicts the start of the storm, two days before the index peak and the dashed line depicts the end of the storm, four days after the peak

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Fig. 10
figure 10

ASY-H superposed epoch plot. The bounds of the storm are represented by the vertical lines. The dotted line depicts the start of the storm, two days before the index peak and the dashed line depicts the end of the storm, four days after the peak

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To determine the bounds of the storm, we use the pruned exact linear time (PELT) (Killick et al. 2012) algorithm to identify change points in the superposed epoch plot, which indicates where significant shifts in data behavior occur. The PELT algorithm is widely used in environmental monitoring, allowing to detect locations where data significantly changes, pinpointing when a time series departs from its usual patterns.

Figure 9 depicts the superposed epoch plot for the SYM-H index, while Fig. 10 presents the superposed epoch plot for the ASY-H index along with the detected change points for the different classes. In both cases, we can note that the scarce amount of superintense storms makes the superposed epoch plot a bit unstable for that category.

Regarding the SYM-H index, we have considered two days before the peak as the start of the storm. For all the classes, the disturbances start around one day and a half before the peak, being two days as the safe threshold to consider. All the change points detected with PELT are condensed during that time. Particularly, in the intense and superintense classes, the disturbances are greater before the peak and start earlier. While considering only one day would be enough for the low and moderate intense classes, it is not enough for the other two, making the two days before the peak the appropriate bound.

For all the classes, the index starts to rapidly recover after the peak to its nominal values. It takes around three to four days to reach nominal values of around \(-\)20 nT, being four days as the safe threshold to determine the recovery period. Therefore, we have chosen to set the end of the recovery phase to four days after the peak of the index. In the superposed epoch plot, all the average storms converge to similar values after such time following the peak.

The ASY-H index presents a much higher variation one day around the peak but is more stable outside that range. In the same way as the SYM-H index, one day before the peak is not enough time to properly capture all the disturbances, as in some storms the disturbances start earlier, being two days again the appropriate bound for the start of the storm. In this case, the recovery is much faster; the disturbances after the second day are minor for all the classes but it has not completely recuperated until the fourth day after the peak when it finally stabilizes at around 20 nT.

Considering the superposed epoch analysis for both indices, we have set two days before the index peak as the starting bound and four days after as the end bound for the storms.

4 Identification of geomagnetic storms

Once the threshold has been determined for what intensity is considered a storm of a given class and how long before and after the peak it extends, storms can be identified and classified in the time series for each index following the next procedure, which is depicted in Fig. 11:

  1. 1.

    Identify a time period in which the index falls below the ‘low’ threshold category.

  2. 2.

    Extend the selection two days before the first value in which the index falls below the ‘low’ threshold category, rounding to the start of the day.

  3. 3.

    Extend the selection four days after the last value in which the index falls below the ‘low’ threshold category. If in that section a new date in which the index is below the ‘low’ threshold category is found, there is another storm before the current one has completely recovered, so we select four days after the new last ‘low’ value, rounding to the end of the day.

Fig. 11
figure 11

Flowchart for the identification of geomagnetic storms

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Once all the storms have been identified, they can be categorized into their respective category based on the peak value of the SYM-H or ASY-H index value.Footnote 1 Summarizing, for the SYM-H index we have identified 166 storms of low intensity, 90 of moderate intensity, 23 intense storms and 7 superintense ones. For the ASY-H index, we have identified 164 storms of low asymmetry, 91 of moderate asymmetry, 23 intense asymmetric storms and 6 superintense asymmetric storms. The number of storms of each type for each index by year is depicted in Table 5, along with the corresponding solar cycle.

Figures 12 and 13 depict two storms identified using the previous procedure for the SYM-H index. In the first storm, the recovery period is considerably large because the index falls below the low intensity threshold multiple times after the first index peak, to finally stabilize four days after the last one. The second storm is a regular storm in which there are no previous or subsequent peaks in the SYM-H so the initial and recovery period are not extended. For this particular storm, other approaches to set the storm phases, such as Wharton et al. (2020), which rely on the index crossing the threshold of \(-\)15 nT (marked with the dotted horizontal line in the plot) would mark a very long initial phase, since the last time the SYM-H was above \(-\)15 nT was around 15 days earlier.

Figures 14 and 15 show two example storms for the ASY-H index. In the first one, the recovery period is considerably long, due to the multiple disturbances that caused a complex geomagnetic storm, while in the second figure there are no multiple peaks, leading to the minimal initial and recovery times.

Fig. 12
figure 12

Example of an identified storm for the SYM-H index, the green shaded area corresponds to the initial phase and the blue shaded area to the recovery phase. The horizontal dashed lines are the thresholds for the different classes

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Fig. 13
figure 13

Example of an identified storm for the SYM-H index, the green shaded area corresponds to the initial phase and the blue shaded area to the recovery phase. The horizontal dashed lines are the thresholds for the different classes. The horizontal dotted line is the \(-\)15 nT mark that has been used by other authors as a threshold to mark the initial phase

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Fig. 14
figure 14

Example of an identified storm for the ASY-H index, the green shaded area corresponds to the initial phase and the blue shaded area to the recovery phase. The horizontal dashed lines are the thresholds for the different classes

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Fig. 15
figure 15

Example of an identified storm for the ASY-H index, the green shaded area corresponds to the initial phase and the blue shaded area to the recovery phase. The horizontal dashed lines are the thresholds for the different classes

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Table 5 Number of geomagnetic storms for the SYM-H and ASY-H index per year.
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5 Conclusions

Intense geomagnetic disturbances are a hazard for a technology dependent society, creating a need to quantify this risk for different impact scenarios. Geomagnetic disturbances have been quantified by scientific community by different indices, but the use of these indices by the operational community is not straightforward. Additionally, time resolution and local time dependence is also outstanding.

Kp or Dst indices have demonstrated a low operational performance, for example, as a proxy for the impact of geomagnetic disturbances in power networks and 1 min local indices have been recently developed for operational purposes (Cid et al. 2020). The lack of wide-spread local ground magnetic field measurements to obtain local indices everywhere makes SYM-H and ASY-H a good selection of geomagnetic indices for those places at low and mid latitude, where world population concentrates, but local indices are not available. In these cases, the SYM-H appears as an accurate proxy for the local disturbance with an uncertainty equal to the ASY-H index.

The selection of the best index is not the unique task regarding the geomagnetic storm hazards. Once the proper index is chosen, a quantification of the severity of the disturbance to provide an estimation of the vulnerability is the next step, but existing threshold values establishing low, moderate, intense or superintense activity were fixed without offering explicit reasoning.

The aim of this study of using a probability approach to fix the threshold values for vulnerability requires independent time series of data. However, SYM-H and ASY-H are not random variables as the observations are highly correlated with the previous value. To tackle this issue, we have resampled the series of both indices in 27 days intervals. The selection of this time interval is based on physical reasons (the solar rotation period) and also in the asymptotic behavior of the thresholds with the time of the interval. The time of 27 days is fixed considering that we have reached the asymptotic behavior while keeping a significant number of data contributing to every percentile.

The results provide a classification of geomagnetic storms using the peak value reached by a geomagnetic index into four classes. Having as starting point the existing classification for the Dst index, we provide a statistically-backed classification of the geomagnetic storms based on the intensity of the disturbance according to the SYM-H and ASY-H indices, using the industry-wide percentiles for risk assessment as guidelines.

The identification and classification of geomagnetic storms eases the development of downstream applications. One example is the development of forecasting models that need to separate the available storms into training and testing sets. Having a complete selection of geomagnetic storms classified by their intensity simplifies the selection of the storms to train and validate forecasting models. Moreover, previous forecasting works for the ASY-H index used the intense storms identified using the SYM-H index as a basis instead of the ASY-H index itself.

Aside from the forecasting applications, the classification can also be used to compare different storms of the same class, studying their evolution. Moreover, the proposed procedure can be applied to other geomagnetic indices assuming there is sufficient data available to resample the time series into independent variables.