The local K index and the consequent global Kp index are well-established 3 h range indices used to characterize geomagnetic
activity. The K index is one of the parameters that INTERMAGNET observatories
can provide, and it has been widely used for several decades, although many other
activity indices have been proposed in the meanwhile. The method for
determining the K values has to be the same for all observatories.
The INTERMAGNET consortium recommends the use of one of the four methods endorsed
by the International Service of Geomagnetic Indices (ISGI) in close
cooperation and agreement with the ad hoc working group of the International
Association of Geomagnetism and Aeronomy (IAGA). INTERMAGNET provides the
software code KASM, designed for an automatic calculation of the K index
according to the adaptive smoothed method. K values should be independent of
the local dynamic response, and therefore for their determination each
observatory has its own specific scale regulated by the L9 lower limit,
which represents the main input parameter for KASM. The determination of an
appropriate L9 value for any geomagnetic observatory is then fundamental. In
this work we statistically analyze the K values estimated by means of KASM
code for the Italian geomagnetic observatories of Duronia (corrected
geomagnetic latitude

In their pioneering work, Bartels et al. (1939) introduced the 3 h range K index with the purpose of quantifying the solar wind (or particle) effects on the geomagnetic field. The K index is represented with an integer in the range 0–9 (“K” is from the German word Kennziffer, meaning “characteristic digit”), with 0 and 1 being an indication of quiet conditions and 5 or more referring to an increased level of magnetic activity, generally related to a geomagnetic storm. It is derived for a specific observatory from the maximum fluctuations of horizontal components observed on a magnetogram during a 3 h interval, evaluated as the difference between the maximum positive and negative deviations with respect to a reference curve, which essentially reflects the local diurnal variation at the observatory. These maximum deviations may occur at any time during the 3 h period. The proposed K index was originally calculated for the Niemegk observatory.

As a natural consequence of the K index, the planetary geomagnetic activity index Kp was proposed by Bartels (1949). It is derived from the standardized K index (Ks) of 13 magnetic observatories at midlatitude, and it is representative of the large spatial scale of the solar wind–magnetosphere coupling energy. Therefore, the K index is the fundamental parameter for Kp estimation; Kp, as any other index, has limitations and drawbacks. However, it is precious since it is a historical parameter and long data series are available. It is widely used, for example, in space weather applications to identify the quietest days (Johnston, 1943), which are used in International Geomagnetic Reference Field (IGRF) modeling and to verify solar-wind-driven modulation in the atmospheric parameters during disturbed conditions (Regi et al., 2017).

The main difficulty in K-index evaluation is to assign a proper
quasi-logarithmic scale to the geomagnetic fluctuations amplitude (A) that satisfy the
principle of the assimilation of frequency distributions (AFDs): the
frequency distributions (or occurrences) of K-index values at different
sites are, in principle, the same (Bartels et al., 1939). In other words,

For Kp determination (Bartels et al., 1939), from higher to lower latitude,
at Sitka (AACGM latitude

The original determination of K indices (Bartels et al., 1939) required hand-scaling analogic magnetograms. For many years, the K index was in fact manually scaled by visual determination and removal of the regular daily variation; the remaining largest amplitude of geomagnetic disturbances in the two horizontal components during each 3 h UT interval was used to determine the K-index values from a conversion table between classes of ranges (in units of nanotesla – nT) and K indices.

The question of the derivation of geomagnetic indices from digital data arose at the end of the 1970s. Different algorithms enabling the computer derivation of K indices were then developed and carefully assessed in the framework of an international comparison organized by the International Association of Geomagnetism and Aeronomy (IAGA) Working Group “Geomagnetic indices” (Coles and Menvielle, 1991; Menvielle, 1991; Menvielle et al., 1995).

This implies the production of computer plots of digital data with scale
values similar to those of photographic magnetograms (Menvielle et al.,
1995). The International Association of Geomagnetism and Aeronomy (IAGA;

Different methods were proposed and carefully compared and assessed in
international meetings organized by the IAGA Working Group
“Geomagnetic indices” during the Vienna IUGG General Assembly in 1991, and
four methods were acknowledged: FMI (provided by the Finnish Meteorological
Institute, Finland), LRNS (Hermanus Magnetic Observatory, CISR, South
Africa), KASM (Institute of Geophysics, Polish Academy of Science), and USGS
(USGS, USA), whose Fortran 77 codes are available at the International
Service of Geomagnetic Indices (ISGI;

We used one of the four methods endorsed by the IAGA, through the ISGI, for the calculation of local geomagnetic activity indices K and, in particular, the KASM method that is based on the adaptive smoothed method (Nowozyński et al., 1991). For the calculation of the K index, IAGA-formatted files are used by KASM code. It requires three daily files, the one under analysis and the files of the previous and following days on which the code estimates the regular daily variation. The code also needs as input parameters the L9 value and the yearly average of the H component relative to the year of interest.

We want to point out that there is no unique L9 at a given geomagnetic latitude since each site might be affected by different local features such as crustal anomalies (Chiappini et al., 2000) and/or coast effects (Parkinson, 1962; Regi et al., 2018). Moreover, there is the inevitable magnetic local time (MLT) dependence of magnetic disturbances, which can be smoothed out through a statistical approach, considering long-time observations. For the inclusion of a new geomagnetic observatory into the INTERMAGNET network, an L9 value can be initially assigned according to the ISGI indication, but it can be refined by comparing long-term geomagnetic field variations at the new observatory and at historical ones for which K indices are estimated by using well-defined L9 levels.

We used the geomagnetic data from two Italian geomagnetic observatories at Duronia (DUR) and Lampedusa (LMP) and evaluated the K index with the purpose of estimating the best L9 value for each observatory.

DUR observatory is operating in central Italy in the area of the village of
Duronia (41

LMP is the southernmost observatory in European territory (35

Up to now, the K index was evaluated only for DUR observatory, using L9

In this work we evaluated L9 through a correlation analysis performed between the K index at DUR and that provided by historical observatories. In order to take into account the magnetic local time dependency of the reference K index, European observatories were selected. As possible reference observatories we chose Wingst (WNG) and Niemegk (NGK), since they are among the 13 observatories that contribute to the Kp estimation and their local magnetic time is quite close to that of our Italian observatories.

Our investigations suggest that NGK is the best reference observatory for the Italian geomagnetic observatory of DUR, probably due to the closest magnetic local times: indeed, the amplitude of magnetic disturbances has a dependence on (magnetic) local time, which affects the K-index values (Chambodut et al., 2013). By comparing DUR with NGK we estimated a reliable DUR L9 level of 320 nT. Finally, by also comparing LMP with NGK, a reliable LMP L9 level of 310 nT is estimated.

Geomagnetic field variations at the Italian geomagnetic observatories of DUR and
LMP are measured by using three-axis fluxgate magnetometers along the
northward (

In this work we used minute data computed from second data using an INTERMAGNET 1 s to 1 min filter, available in the time interval 1 January 2017–31 December 2018, a temporal window that falls in the lower part of the sunspot number curve for the cycle 24 (Upton and Hathaway, 2018).

These data are used for estimating K indices with the KASM algorithm that
is recommended by INTERMAGNET. In this work, the definitive L9 level at DUR
is empirically estimated through the following procedure:

we selected a reference observatory;

K-index time series at DUR are computed by using KASM for different L9 values (K

each K

the definitive L9 level at DUR is estimated in correspondence to the maximum correlation coefficient.

As a possible reference we selected the historical observatories of NGK and WNG since they are among the 13 observatories used for Kp evaluation, and they are both in Europe at an MLT close to that of DUR and LMP (see Table 1 and Fig. 1). DUR is at the moment the principal Italian observatory and a member of the INTERMAGNET network. We then used it in this work as a reference observatory for any Italian site. By following our procedure at point (c), independently using NGK and WNG, we found that a higher correlation is reached with NGK. The same procedure from (a) to (d) is applied to the lower-latitude Italian observatory of LMP.

Geomagnetic observatories used in this study, geographic coordinates, altitude-adjusted corrected geomagnetic (AACGM) coordinates estimated by using the Shepherd (2014) algorithm at 100 km above the observatory, and magnetic local time at 00:00 UT.

European geomagnetic observatories used in this work.

We note that the K indices at NGK and WNG are both generated by using the FMI algorithm. Then, we find it useful to verify that FMI and KASM are consistent methods by comparing the K values estimated with both methods at NGK.

Finally, we compared L9 values estimated at Italian geomagnetic observatories by means of our method with those estimated using a historical method proposed by Mayaud (1980).

We maintain that it is important to know how K indices are distributed at the consolidated reference observatories of NGK and WNG and how they are in relation to each other.

Figure 2 shows the K index at NGK (panel a) and WNG (panel b) and the
difference

We investigated the frequency distribution

Frequency distributions of the K index at NGK (red dashed line)
superimposed on distributions of both K

Figure 4 shows the result of the correlation analysis between K indices at
the Italian observatories of DUR (panel a) and LMP (panel b) and those at NGK
(red thin line) and WNG (black thin line) as functions of the L9 level used by
KASM for the time interval 2017–2018. In this figure L9 levels are in the
range 200–450 nT, with a step size of 10 nT. The tick lines, which show the
smoothed curves computed by using a five-point triangular window, will be
used hereafter as actual experimental results for our investigations. It can
be seen that the correlation

Correlation analyses between the K index at NGK and that computed at
DUR

As expected, both the L9 limit and

From these results we can assert that for the comparison with
Italian observatories NGK is slightly better than WNG, and it will be used
hereafter as the reference observatory for DUR and LMP. We can also assume
that the best estimation of the L9 value at DUR and LMP is 320 and 310 nT, respectively, so the K indices computed by using KASM at DUR with
L9

Figure 5 shows the frequency distribution of the difference between these
K-index time series and that computed at NGK. The occurrences for both DUR
and LMP are distributed around zero and in the range [

Since our validation procedure aims to estimate comparable K indices at
Italian observatories, we found it useful to compute

Frequency distribution of

It should be noted that our comparative investigation is based on K indices
at the reference observatories of NGK and WNG, which are computed by using the FMI
algorithm with L9

In order to answer to this question, we performed a correlation analysis
between the K indices obtained using FMI (K

The FMI and KASM consistency test.

Figure 7a shows the correlation analyses between the K indices at NGK (from the FMI
algorithm) and that computed by KASM using L9 in the range 350–600 nT,
with a step size of 10 nT. It can be seen that the

As explained in the Introduction, geomagnetic indices are historically
assigned through the visual inspection of magnetograms. The main difficulty
for K-index evaluation is to assign a proper value for the L9 limit from
which to determine the quasi-logarithmic scale for the geomagnetic
fluctuations in order to satisfy the AFD principle (Bartels et al., 1939).
Mayaud (1968, 1980) proposed a method for calculating the geomagnetic
activity level L at a given site by comparing the amplitude of geomagnetic
fluctuations at the reference observatory (

We searched for a simple relationship that relates L9 (or L) to the geomagnetic latitude of the observatory.

As shown by Mayaud (1980), L9 increases with decreasing

The linear relation between the L9 limit and

Therefore, by using x

Equation (1) is therefore useful for estimating a reasonable L9 limit at a
different site. In order to evaluate L9 at DUR, LMP, and, for comparison,
NGK, the corresponding

The linear relation between

In this regard, we empirically estimated

L9 estimated by different procedures;

All these results are reported in Table 2, which also shows for comparison the
L9(

It can be seen that all L9

we computed the AACGM latitudes

we performed a linear fit of

finally we performed a linear fit of L9(

With respect to the L9(

Four different automated methods for the calculation of local geomagnetic
activity indices K were endorsed by the IAGA, through the ISGI and distributed from the ISGI (

An input parameter required by KASM code, as well as FMI code, is the L9 value, the so-called “K

We found L9 values for DUR and LMP through a correlation analysis using as a reference the corresponding data from the two European observatories of Wingst (WNG) and Niemegk (NGK), both located in Germany. The choice of these two observatories was prompted by the fact that they are among the 13 observatories that provide their K indices for the determination of the planetary Kp index, and their magnetic local time is very close to that of the Italian observatories.

We note that NGK is the best reference observatory for the Italian geomagnetic observatory of DUR, possibly due to the closest magnetic local time; indeed, the amplitude of magnetic disturbances has a dependence on (magnetic) local time, which inevitably affects different K-index values (Chambodut et al., 2013).

Based on a dataset related to 2 years (2017 and 2018), this analysis allowed us to establish that for DUR and LMP the L9 values are 320 and 310 nT, respectively. These values are in good agreement with the ones directly obtained from Mayaud's method, which leads to approximately 355 and 315 nT for DUR and LMP, respectively (personal communication with ISGI members, 2019). The method can be generalized and applied to every observatory in the world to verify if the choice to scale local fluctuations of the Earth's magnetic field is properly calibrated by a suitably selected L9 value, regardless of whether it is manually or automatically computed. Our analysis also highlighted the possibility of establishing a linear relationship between a pair of analyzed observatory datasets, which can be useful for predicting or deriving the index of one when the other is known.

Another interesting result that we found is related to the consistency of the KASM code and the FMI code; the latter is in use at the two German observatories for the K-index computation and subsequent release. Although FMI code is based on a different procedure, we verified that the results obtained are consistent with those obtained by KASM code and stable in the 2-year time interval, although with a slightly different value of the input L9 parameter. This confirms that the choice of a certain algorithm in place of another does not invalidate the results.

Before the introduction of automatic procedures, based on the definition
introduced by Bartels et al. (1939) for the K-index concept, in the 1980s Mayaud (1980) used an empirical relation to calculate the
level of local magnetic activity L (equivalent to the L9 values) for a
generic point of observation with respect to a referenced observatory.
Through a linearization process, we used this relation, which includes some
approximations and the necessity of determining the minimum angular
separation between the observational point and the auroral region, i.e., a
method for determining the geomagnetic latitude, to obtain an independent
estimate of the L9 values for our observatories that is consistent, within
the 95 % interval of confidence, with that obtained by our previous
analysis. Moreover, Mayaud (1980) notes that the limitation of the method he
proposes is that it is conceived for sub-auroral and midlatitudes; indeed,
he suggests that for lower latitudes a constant L9

Data from the geomagnetic observatories (DUR, NGK, and WNG) that are members of the INTERMAGNET consortium can be downloaded at the following URL:

DDM, SL, and MR planned the study. MR performed the data analysis and wrote the codes. PB studied the KASM code functionality and, together with MR, tested and validated its results. DDM, LC, and SL improved the quality of the paper. All authors read and approved the final paper.

The authors declare that they have no conflict of interest.

The results presented in this paper rely on data collected at magnetic
observatories. We thank the national institutes that support them and
INTERMAGNET for promoting high standards of magnetic observatory practice
(

Paolo Bagiacchi was partially supported by Programma Nazionale di Ricerche in Antartide (PNRA).

This paper was edited by Valery Korepanov and reviewed by three anonymous referees.