Geomagnetic Activity Index Hpo

The geomagnetic activity index Kp is widely used but is restricted by low time resolution (3‐hourly) and an upper limit. To address this, new geomagnetic activity indices, Hpo, are introduced. Similar to Kp, Hpo expresses the level of planetary geomagnetic activity in units of thirds (0o, 0+, 1−, 1o, 1+, 2−, …) based on the magnitude of geomagnetic disturbances observed at subauroral observatories. Hpo has a higher time resolution than Kp. 30‐min (Hp30) and 60‐min (Hp60) indices are produced. The frequency distribution of Hpo is designed to be similar to that of Kp so that Hpo may be used as a higher time‐resolution alternative to Kp. Unlike Kp, which is capped at 9o, Hpo is an open‐ended index and thus can characterize severe geomagnetic storms more accurately. Hp30, Hp60 and corresponding linearly scaled ap30 and ap60 are available, in near real time, at the GFZ website (https://www.gfz-potsdam.de/en/hpo-index).

The Kp index has a wide range of applications in space physics studies. For example, Kp can be used to select undisturbed data from the measurements obtained from the magnetosphere, ionosphere or thermosphere to determine their climatological base states (e.g., Drob et al., 2015;Fejer et al., 2008). Kp is also often used for modeling the geospace response to solar wind variations. Just to give a few examples, Kp is used to drive the 3-D Versatile Electron Radiation Belt model , the Whole Atmosphere Community Climate Model with thermosphere and ionosphere extension (WACCM-X; Liu et al., 2018) and the Naval Research Laboratory Mass Spectrometer Incoherent Scatter radar empirical atmospheric model (Emmert et al., 2021), among many other models of the magnetosphere, ionosphere and thermosphere. Thomsen (2004) argued that what makes Kp so useful is its sensitivity to the latitudinal distance from the Kp stations to the equatorial edge of auroral currents, which is tightly linked to the strength of magnetospheric convection.
Kp has two important limitations. One is the temporal resolution. Kp cannot resolve temporal features within 3 hr. For example, the onset of geomagnetic disturbance determined by Kp could be off from the actual onset by up to 3 hr. This could be an issue when Kp is used to drive a geospace model, because the state of the magnetosphere, ionosphere and thermosphere can change significantly within the 3-hr interval. As a compromise, some models use interpolated Kp values as input data, for example, thermospheric density models (Vallado & Finkleman, 2014), WACCM-X (Liu et al., 2018). The other limitation of Kp is its upper limit at 9o. Kp is not able to quantify geomagnetic activity after it reaches 9o. Extreme geomagnetic storms involving Kp = 9o are not necessarily equally strong in terms of geomagnetic disturbance. Extrapolated values of Kp above 9o are sometimes used for a better representation of geomagnetic activity during severe geomagnetic storms (e.g., Shprits et al., 2011).
The objective of this paper is to introduce a new group of Kp-like geomagnetic indices. The indices are collectively called Hpo, where "H" stands for half-hourly or hourly, "p" for planetary, and "o" for open-ended. Hpo has been conceived and developed under the EU Horizon 2020 project, Space Weather Atmosphere Model and Indices (SWAMI; Jackson et al., 2020). Hpo is designed to represent planetary geomagnetic activity in a similar manner as Kp but with higher time resolution and without an upper limit, to overcome the limitations of Kp described above. The derivation of 30-min (Hp30) and 60-min (Hp60) indices is outlined in Section 2, and their basic properties are described in Section 3.

Derivation of Hpo
Hpo indices are derived using 1-min magnetic data from the same 13 subauroral observatories as Kp (see Section 2.2 of . Time series of Hpo starts from the year 1995, because 1-min digital data are not available from all the observatories before 1995. The procedure for deriving Hpo is similar to that for nowcast Kp described in , involving the steps described below.

Evaluation and Removal of Quiet Curve
Records of the geomagnetic field from a ground station contain regular quiet daily variation and geomagnetic disturbance (Chapman & Bartels, 1940). The estimation of the quiet curve for Hpo is based on the Finnish Meteorological Institute method (Sucksdorff et al., 1991), which uses 1-min data from the previous day, present day, and subsequent day. The quiet curve is obtained for the northward X and eastward Y components of the geomagnetic field, and subtracted from the corresponding data, which leaves geomagnetic disturbance.

Evaluation of the Magnitude of Geomagnetic Disturbance
The magnitude of geomagnetic disturbance is evaluated for every 30-min interval for Hp30 and 60-min interval for Hp60. For a given time interval, the range of geomagnetic disturbance (i.e., maximum minus minimum value) is compared with the maximum absolute value of geomagnetic disturbance, and the larger value of the two is adopted as the magnitude of geomagnetic disturbance. This contrasts with the derivation procedure for Kp, which always uses the range of geomagnetic disturbance. We found that this modification of the procedure improves the compatibility between Hpo and Kp. The magnitude of geomagnetic disturbance is obtained for the X and Y components, and the larger value is used in the next step.

Evaluation of H30 and H60 Indices
H30 and H60 indices are analogous to K indices for Kp, and are collectively called H herein. For the evaluation of K, an observatory-specific table is used for converting the magnitude of geomagnetic disturbance (in nT) to an integer K value (0-9). An example of the conversion table for the Niemegk observatory can be found in Table 1. New tables have been created for each observatory that convert the magnitude of geomagnetic disturbance to an H value (0-9). This was done, for each observatory, by generating a conversion table for H in such a manner that the frequency distribution of H is as similar as possible to the frequency distribution of K. The construction of the conversion tables for H is based on the geomagnetic data during 1995-2017, which were all the available data when the construction of Hpo was initiated. The conversion table for H30 and H60 for Niemegk is presented in Table 1. Furthermore, extended conversion tables are produced in order to allow H to go beyond 9. In the extended conversion tables, the maximum value of H is unlimited. The lower limit for H = 10 is given by the lower limit of H = 9 multiplied by a factor of 1.35. The lower limit of H = 11 is given by the lower limit of H = 10 multiplied by a factor of 1.30, and the lower limit of H = 12 is given by the lower limit of H = 11 multiplied by a factor of 1.20. For values of H greater than 12, the multiplication factor will be always 1.20, so that H can be defined no matter how large the magnitude of geomagnetic disturbance is. These multiplication factors were determined on a trial-and-error basis so that the behavior of the final Hpo index above 9o will be compatible with those of other open-ended indices (see Section 3).

Evaluation of Hp30 and Hp60 Indices
H indices are converted to standardized Hs indices using the same method for converting K to Ks. The conversion tables can be found in the Supporting Information of . The conversion of H to Hs minimizes the influence of seasonal and UT biases. Finally, the average of the 13 Hs indices is converted into Hpo values in units of thirds (0, 1/3, 2/3, 1, 4/3, 5/3, 2, …) in analog fashion as with the nowcast Kp (see Section 3.3 of  and expressed as (0o, 0+, 1−, 1o, 1+, 2−, …) following the convention for Kp. The Hpo value is derived using the H indices evaluated with the conversion tables capped at 9 (like the one shown in Table 1). If this initial Hpo value is 9o, all the H indices are re-evaluated using the extended conversion tables, in which H can go beyond 9, to re-calculate Hpo. This ensures that Hpo and Kp behave similarly up to 9− (and differently only at 9o and above).
Like Kp, Hpo indices are a quasi-logarithmic, rather than linear, measure of geomagnetic activity, and thus are not suitable for basic arithmetic operations such as addition and multiplication. To avoid this issue, linearly scaled ap30 and ap60 indices (collectively called apo) are produced for Hp30 and Hp60, respectively, by using the table that is used for producing ap from Kp  but extending its higher end in a similar manner as the extension of H tables above 9. The relationship between Hpo and apo is illustrated in Figure 1a. Like ap, values of apo correspond to half the magnitude of geomagnetic disturbance at Niemegk.
Hp30 and Hp60, along with their corresponding ap30 and ap60, are archived since 1995 and available, in near real time, from the GFZ website (https://www.gfz-potsdam.de/en/hpo-index) with DOI (https://doi.org/10.5880/ Hpo.0002) under the CC BY 4.0 license (Matzka et al., 2022, for data publication).  The linearly scaled ap30 and ap60 indices are suitable for assessing average geomagnetic activity over a certain period. Monthly mean values of ap30 and ap60 are plotted in Figure 1k. They are in good agreement with monthly mean ap, showing 11-year solar-cycle variation. The sunspot number is also displayed in Figure 1k for comparison. Geomagnetic activity is known to be highest during the declining phase of solar cycle due to the effects of recurrent high speed solar wind streams (Lockwood et al., 1999).
In Figure 2, Hp30 (top), Hp60 (middle), and Kp (bottom) are compared with other geospace indices. The left panels show comparisons with Newell's coupling function (Newell et al., 2007), which is a measure of the energy input from the solar wind into the magnetosphere. The coupling function was derived using OMNI 5-min solar wind data (King & Papitashvili, 2005). Panels in the middle and right columns show comparisons with AE and PC indices, respectively. The AE index is a measure of auroral electrojet activity based on geomagnetic field measurements in the auroral region. The PC index represents geomagnetic activity in the polar region (Troshichev et al., 1988). Following Stauning (2007), the average of the PC indices from the northern (PCN) and southern (PCS) hemispheres were calculated using non-negative values. For comparisons with Hpo and Kp indices, 5-min solar wind data and 1-min AE and PC indices were averaged over every 30-min intervals. Hp60 and Kp are assumed to remain the same within their temporal windows. The solar wind data were shifted by 20 min to account for the delay due to energy transfer from the bow shock to the ionosphere (Manoj et al., 2008).
The solar-wind coupling function, AE and PC indices averaged at each value of Hpo and Kp from 0o to 9− are indicated in Figure 2 by black dots, with error bars representing the standard deviation. Curves in green show the best-fitting third-degree polynomial function for Hpo and Kp below 9o. The fitted curves for Hp30, Hp60, and Kp are similar to each other. The results suggest that for Hpo <9o, the dependence of Hp30 and Hp60 on the solarwind coupling function, AE and PC indices is consistent with that of Kp. For Hpo ≥9o, the number of data points is rather small, and thus the average solar-wind coupling function, AE and PC indices were not calculated for each Hpo value. Instead, a single average value was derived using all the data corresponding to Hpo ≥9o (gray dots), which is indicated by the yellow dot in each panel of Figures 2a-2f. It is seen that the average value falls near the polynomial curve derived from the data for Hpo <9o. The results suggest that Hp30 and Hp60 can represent geomagnetic activity for Hpo ≥9o in the manner expected from their behavior for Hpo <9o.
The behavior of Hpo at its high end is further illustrated in Figure  Thus, according to Hpo, the October 2003 event is the strongest among the five. Hpo ≥9o is seen mainly during the storm main phase, when the Dst index rapidly decreases. The right panels compare the 3-hourly mean of Hp30 (calculated from ap30) and Kp. The correlation is rather good; the correlation coefficient r is greater than 0.98 in all cases. Similarly good correlation is found for the comparison between 3-hourly mean of Hp60 and Kp (not shown here). These results suggest that Hpo can represent geomagnetic activity in a similar way as Kp even during the strongest geomagnetic storms.
10.1029/2022GL098860 6 of 9 To provide some insight into variations of Hp30 and Hp60 within 3 hr, Figure 4 depicts the response of ap30, ap60, and ap to isolated substorms. The substorm onset list based on the technique described by Newell and Gjerloev (2011a) was obtained from the SuperMAG website (https://supermag.jhuapl.edu/). We selected isolated substorm events where there is no other substorm onset in the preceding 6 hr and following 12 hr. A total of 1947 isolated substorm events have been identified during 1995-2018. Figure 4a shows the variation of the AE index averaged over those substorm events. The average AE index peaks approximately 1 hr after the onset, and decays gradually to go back to the pre-onset level in 3-4 hr. The average ap30 and ap60 indices (Figures 4b and 4c) show the increase and decrease of geomagnetic activity that occur within 3 hr around the substorm onset. ap (Figure 4d) is not able to fully resolve such a short-term variation due to its low time resolution. The results suggest that variation of Hpo within 3 hr can contain physically meaningful information, which is not resolved by Kp.

Summary and Outlook
We have described a group of new open-ended geomagnetic activity indices Hpo. Hourly (Hp60) and half-hourly (Hp30) indices, along with their linearly scaled counterparts (ap30 and ap60), are available in near real time from the GFZ website (https://www.gfz-potsdam.de/en/hpo-index) with DOI (Matzka et al., 2022). Important properties of Hpo that are revealed by our initial analysis can be summarized as follows: 1. The frequency distributions of the occurrence of Hp30 and Hp60 values are consistent with that of Kp at different phases of the solar cycle (Figures 1a-1i). 2. Month-to-month variations of Hp30 and Hp60 are consistent with that of Kp (Figure 1k). 3. The relationships between Hpo indices and Newell's solar wind coupling function, AE and PC indices are similar to those between Kp and these three quantities. 4. Hp30 and Hp60 can capture temporal variation of Kp during strong geomagnetic storm events (Figure 3). 5. Hp30 and Hp60 can reproduce short-term variation of geomagnetic activity within 3 hr associated with substorms ( Figure 4).
These results demonstrate that Hpo can be used as a higher time-resolution alternative to Kp. Indeed, there are already a few studies that utilized Hpo for its advantage over Kp. Yamazaki et al. (2021) used Hp30 to select quiet-time measurements of the geomagnetic field from Swarm satellites. The orbital period of a Swarm satellite is approximately 90 min, thus using Hp30, geomagnetic activity can be evaluated for every one third of the orbit, while there is only one Kp value for every two orbits. The high-cadence output of Hpo enables a more accurate selection of quiettime data than the three-hourly Kp index. Bruinsma and Boniface (2021) used Hp60 to drive a recent version of the Drag Temperature Model, DTM-2020, which is a semi-empirical model of the Earth's thermosphere, developed for orbit determination and prediction of spacecraft and debris. They showed that the use of Hpo leads to the improvement of the model compared with the predecessor model DTM-2013 (Bruinsma, 2015) that is driven by Kp. Similarly, Hpo may be used for improving other geospace models driven by Kp. Recalibration and validation are recommended when Hpo is used as an input for existing models that are parameterized with Kp.

Data Availability Statement
Hpo and apo indices (Hp30, Hp60, ap30, and ap60) are available from the GFZ website (https://www.gfz-potsdam.de/en/hpo-index); see Matzka et al. (2022) for data publication. Kp and ap indices are also available from the GFZ website (https://www.gfz-potsdam.de/en/kp-index/); and see  for data publication. The sunspot number data are provide by the World Data Center SILSO, Royal Observatory of Belgium, Brussels, and can be downloaded from their website (https://wwwbis.sidc.be/silso/datafiles). The 5-min solar wind data are available from the OMNIWeb (https://omniweb.gsfc.nasa.gov/form/omni_min.html); see also Papitashvili and King (2022). AE and Dst indices are provided by the World Data Center (WDC) for Geomagnetism, Kyoto, and are available at http://wdc.kugi.kyoto-u.ac.jp/dstae/index.html. PCN and PCS indices are provided by the Arctic and Antarctic Research Institute and Technical University of Denmark/DTU Space, and can be obtained from the PC index website (https://pcindex.org/archive). The substorm list is available from the SuperMAG website (https://supermag.jhuapl.edu/substorms/).  Newell and Gjerloev (2011a). Error bars represent the standard error of the mean. Zero in the horizontal axis corresponds to the substorm onset.