Interactive comment on “ Harmonic quiet-day curves as magnetometer baselines for ionospheric current analyses ”

This manuscript presents a new method to remove long-term (e.g., secular and seasonal) and quiet-day (e.g., Sq) variations, as well as some drifts and jumps due to equipment artifacts, from magnetometer records. The goal being to identify the ’disturbance magnetic field’ from relatively rapid ionospheric currents other than Sq (e.g., DP1 and DP2). The method is clearly described with step-by-step examples of its application to real data and balanced discussion of merits, issues, and alternatives.


Equivalent currents
Currents flowing in the ionosphere are related to the field-aligned currents in the magnetosphere through ionosphere-magnetosphere coupling (e.g.Kamide and Baumjohann, 1993).The magnetospheric currents are strongly dependent on solar activity, such as solar wind variations and solar storms, and these solar-dependent magnetospheric current variations are also reflected to the ionospheric currents.Since strong disturbances in the ionospheric currents can affect technological systems on the ground (e.g.Boteler et al., 1998), there is a great interest in the dynamics of these currents in relation to solar activity.
The concept of ionospheric "equivalent currents" models the ionospheric currents as present in a thin shell, usually the highly conductive E-layer at 100 km height, and representing only the divergence-free, horizontal part of the total currents.Under many circumstances these give valuable information about spatial and temporal characteristics of the actual 3-D ionospheric currents (e.g.Untiedt and Baumjohann, 1993), especially when analysed together with data from other instruments, such as rockets, satellites, or radars.The short-term variations of the equivalent currents can effectively be estimated from magnetometer measurements from a two-dimensional ground-based magnetometer network.
The European Cluster Assimilation Technology (ECLAT) project funded by the EU FP7 programme provides a selection of useful supporting data sets to the Cluster Active Archive (Laakso et al., 2009).The work described in this paper has been used in an ECLAT work package in which ionospheric equivalent current vectors are computed in the Fennoscandia region from data from the ground magnetometer network IMAGE.These source data are described in the next subsection.In the project, equivalent currents are to be analysed for an area over Fennoscandia, over the period 2001-2010.An important motivation for publishing this paper is to provide for the Introduction

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Full ECLAT database users accurate information about the equivalent current generation procedure used in the service.
For the equivalent current estimate, use is made of the method of spherical elementary current systems (Amm and Viljanen, 1999;Pulkkinen et al., 2003).The currents induced inside the earth are ignored, as they can be assumed to be relatively small compared to the ionospheric currents.For the calculation, only the x-(north) and y-(east) components of the magnetic field at all ground stations are necessary, as only these are related to the divergence-free part of the ionospheric currents.

IMAGE magnetometer measurements
The input data for the calculation of the ionospheric currents in the project ECLAT are the magnetometer recordings of the ground magnetometer network IMAGE (http: //space.fmi.fi/image/beta/)(Viljanen and H äkkinen, 1997).This network consists of 32 magnetometers over geographic latitudes from 58 to 79 degrees, which is especially favourable for electrojet studies.The magnetometers return data at a time resolution of 10 s.
Figure 1 shows a map of the locations of the magnetometers of the IMAGE Network.

Various magnetic field components; baselines
In addition to the currents caused by solar and magnetospheric disturbances, which are of interest for the analysis, the ionospheric currents and the ground magnetic field consist of several other components.
The magnetic field measured at the earth's surface is a superposition of the field originating from the inner earth, and that from electromagnetic effects caused by the ionospheric currents.These ionospheric currents, in turn, contain on the one hand components due to the dynamo effect of the revolving magnetic earth inside the conducting ionosphere, whose conductivity depends (among others) on solar radiation, and on the solar activity via ionosphere-magnetosphere coupling, which are the components of interest for the ionospheric studies.As a consequence, in the measured magnetic field the following variations of different time scales can be distinguished: -The diurnal variations caused by the variation of ionospheric conductivity due to solar radiation during quiet times, usually referred to as "S q variations" or "Solar quiet variations".
-Lunar variations: variations over a lunar day (24 h and 50 min), due to changes in the global distribution of the conducting ionosphere due to lunar attraction.These are usually referred to as "L variations".
-Seasonal variations: variations with a period length of one year, due to seasonal changes in the ionospheric conductivity (i.e.slow component of S q variations), but also seasonal changes in the ionosphere-thermosphere-magnetosphere interactions.
-Secular (long-term) variations, due to very slow variations in the earth's internal magnetic field pattern.
-The "disturbance field", which, although irregular in nature, also shows statistical variations with time of day, season, and solar activity.
-In addition to the various field variation components, some magnetometer data also contain system effects such as equipment drift (see later).
Note that lunar, seasonal and secular variations are within the time range of days much smaller than the solar quiet variations and the disturbance field.The various components of the ground magnetic field are clearly explained by Chapman and Bartels (1940).Campbell (1989) gave an introduction on the physics of S q and L variations and a short overview of the research history of these, as an editorial to a special issue of Pure and Applied Geophysics, dedicated to S q and L variations.Introduction

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Full In the context where the effects of the solar disturbances are measured and analysed (e.g. when calculating ionospheric equivalent currents), all magnetic field components due to the inner earth, regular ionospheric variations, and the equipment, should be subtracted from ground-based magnetic field measurements, before further analysis.In this context, the earth's main magnetic field as well as all the regular variations and system effects in the output data of any magnetometer are here treated together as "baselines", indicating the components to be removed.
(Note however, that the term "baseline" has sometimes also been used in the context of studying S q variations, where the term represented the relatively long-term variations.For instance, when Matsushita (1968) referred to the S q study by Price and Wilkins (1963), he used the term "base line" for the variations of the midnight field from day to day.) Although the magnetometer baseline method of this paper is introduced as the basis of calculating ionospheric equivalent currents, this method can also be useful for any other application where either the disturbance magnetic field or the S q field is to be analysed.

Baseline removal
A traditional method of removing a baseline from magnetometer data of a particular day, is to look for a magnetically quiet day near the day of interest, and calculate the average value of the magnetic field of this day.This constant value is used as the baseline, and subtracted from the data for the day of interest, leaving only the disturbance field.For instance, Davis and Sugiura (1966) proposed to derive the auroral electrojet index AE from magnetometer data using this as a baseline method.
Although it has long been known that this way, the S q variations are not included in the baseline and will therefore be considered as part of the disturbances, it was considered that these variations are small compared to the disturbance field, and hence the introduced error is relatively small.Introduction

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Full The magnetically "quiet" days used can be more or less frequent, varying from about one to five quiet days per month.They can be determined in various ways, e.g. based on the variations of the data of each day, or using global magnetic indices as Kp or Dst.Also, they can be downloaded directly from a global database (http://www-app3.gfz-potsdam.de/kpindex/definitive.html).
The baseline method using averages of quiet days leads to inaccuracies in the resulting disturbed data in several ways: 1.There may not be any day in the entire month which is completely free from disturbances.In this case, the "quiet" day is not really "quiet" and the data, and even the average value, will still be affected by some disturbance effects.
2. As mentioned above, the diurnal variation of the S q field is not included in the baseline and will hence be considered as part of the disturbance field.
3. For two consecutive days, the "nearest" quiet day and therefore the baseline value can be different, and hence the baseline may show a discontinuity at midnight between these two days.If this baseline is subtracted from other data for a period around midnight (e.g. to calculate equivalent ionospheric currents), this may cause an artificial jump in the resulting disturbed data.
4. The magnetometer data generally contain slow variations over the course of several days, months and years, caused by long-term magnetic field variations, but also equipment effects (see Sect. 2.2 for examples of each).As a consequence, the average value of the quiet day may not be representative for that of other days which can be several weeks earlier or later.
In spite of its drawbacks, the abovementioned baseline procedure is still being used in some applications today, mainly because of its simplicity.Alternatively, many studies have also been performed using more elaborate baseline procedures.In particular, S q variations (point 2) have been incorporated in baselines by appropriate smoothing of the quiet-day data in one way or the other.Below, a few of the most recent baseline Introduction

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Full procedures are summarised.It should be emphasised that this is not intended to be a complete review of baseline development, but only to show some examples of the current state of the art.Janzhura and Troshichev (2008) presented a running automatic method which overcomes some of the problems: point 1 is avoided by looking instead of quiet days, for any quietest bits of data within a 30 day period; point 2 is avoided by only smoothing the quiet daily curve, but retaining the diurnal variations.Point 4 is only reduced, not entirely removed, by averaging all quiet data over the 30-day period.
However, their method retains point 3, and even introduces more discontinuities.Since the smoothed daily baseline is in general at the end of the day not the same as that at the start of the day, a discontinuity becomes more likely to occur at every midnight.This can be seen e.g. from Fig. 5 in the paper by Janzhura and Troshichev (2008) (the values of the curves at the end of the day do not connect to those at the start of the day).
More recently, Stauning (2011) presented another version of the procedure from Janzhura and Troshichev.The main difference with their method is that his method carefully selects data from similar conditions as the day in question, by giving larger weights to quiet data from days close to the day in question, as well as to data from days approximately 27 days (one solar rotation) before and after.This is because he finds the highest correlation coefficients for such displacement periods.This way, his method further reduces point 4 as long as the slow variations are fluctuations over periods of 27 days.In addition, very slow fluctuations are removed separately in his method.However, his method does not take care of unexpected fluctuations, such as instrument drifts over only a few days (see Sect. 2.2).Also, it is not certain whether any midnight discontinuities (due to point 3, or those as introduced by Janzhura and Troshichev) remain.Gjerloev (2012) described the automatic data preprocessing procedure of the worldwide magnetometer network SuperMAG, which also involves a baseline removal technique.Acknowledging the problems associated with the identification of quiet days, he Introduction

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Full avoids using these alltogether, thus avoiding point 1.Instead, he averages the data from several days around the day of interest (3 days in case of relatively quiet periods; longer in disturbed periods), to obtain a daily trend, and applies appropriate smoothing, avoiding point 2. Point 4 is taken care of by separately determining seasonal variations (referred to as "yearly trend"), although it is not clear how well this works to capture relatively fast and irregular equipment drifts.In addition, also here it is not clear but likely that the midnight discontinuities remain.
In this context it is good to note that all of the above methods were designed to work for rather well-controlled stable instrumentation, in which case point 4 represents only slow and regular variations, which are well taken care of by these methods.
In this paper however, a method is described which overcomes all problems in the list above, including in the case of unstable instrumentation, and in addition is simpler than the other methods described above.The procedure will be described in the next section.

Procedure
The baseline procedure is performed for each magnetometer station separately.The following sections describe the various steps in this procedure.

Data jumps
Many of the magnetometer time series, especially those from remote unmanned stations, exhibit occasional artificial discontinuities, or "jumps", in the data.These can vary in size from a few nT to thousands of nT, and can be both positive and negative.The jumps are probably due to adjustments and resetting of the equipment, and happen mostly at midnight, but not only.These jumps, if not taken care of, will affect the results of the data analysis.Introduction

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Full Small discontinuities in the time series need not be a problem in a statistical analysis of the magnetic field.However, they do become important when dynamics aspects of geomagnetic events are analysed.For example, the results of the time derivative of the magnetic field will be affected by artificial jumps.Viljanen et al. (2001) analysed the time derivative of the horizontal magnetic field vector from the IMAGE network, and found significant correlations between this parameter and geomagnetic activity, on various time scales from hours up to years, as well as a significant directional variability of this parameter, which in turn also depends on location and time.Plausible relations were found with, among other things, ionospheric currents, pulsations, and geomagnetically induced currents.Because of this, it is evidently important to avoid the measured time derivative being contaminated by artificial discontinuities.(For the same reason, the artificial jumps in magnetometer data introduced by the baselines, i.e. problem 3 in Sect.1.4, should also be avoided.) Furthermore, the data jumps will also affect the baseline determination described in this paper, which involves, among other things, some curve-fitting and calculation of standard deviations (see later).Because of this, as a first step in the baseline procedure, these jumps need to be removed from the measured data.
The jumps are removed as follows.A software module has been designed which detects and displays suspected discontinuities in the data.The software lets the user examine each discontinuity and decide whether it is artificial, in which case it is listed in a datafile.Based on these data, a jumps-baseline B J (t) is generated, separately for the x-and y-components of the field, which contains all the jumps found in the data, but is otherwise constant.This jumps-baseline is subtracted from the raw data, before any further processing as described in the following sections.

Long-term baseline
Next, to determine the baseline, first the part is considered which consists of the longterm variations in the magnetic field, i.e. variations over periods longer than 24 h: on the scale of days, months, or years.These variations will be represented in the baseline Introduction

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Full by determining from every day of data a single daily "background" value.For this value it might be considered to use the average of the measured data, however, rather than this, the median is considered more stable, being less sensitive to extreme values during moderately disturbed days.
Figure 2 shows this daily median calculated over various periods of data, and demonstrates the long-term variations revealed by it.This graph shows that these variations consist of, among others, the following components: -Secular variations: due to very slow variations in the earth's internal magnetic field pattern, the y-and z-components of the magnetic field at all stations steadily increased, at a rate of slightly over 35 nT per yr, during the period 2001-2010.(The x-component did not change significantly.)The upper left-hand graph of Fig. 2 demonstrates this for B y in Uppsala.
-Seasonal variations: the seasonal changes in the ionospheric conductivity and in the ionosphere-thermosphere-magnetosphere interactions result in variations in all magnetic field components with a period length of one year.As an example, the upper right-hand graph of Fig. 2 shows that B x in Uppsala oscillated at about 10 nT peak-to-peak within the years of 2008 and 2009.
-Tidal variations: variations with periods of about 27 days can be observed, which are the result of interference between S q and L variations.As an example, the lower left-hand graph of Fig. 2 shows that B x in Uppsala varied at this frequency at about 15 nT peak-to-peak in October to December 2007.(Note that the raw data, which are also shown (red), include the disturbance field and therefore also show statistical variations due to the period of solar activity changes, which also have a period of 27 days.The median values however should not be much affected by this.) -Equipment drift: some of the magnetometers occasionally exhibit some variations over the course of one or a few days, which do not repeat, and show no correlation Introduction

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Full with space weather parameters or with any of the other magnetometer results.
The lower right-hand graph shows an example for Sørøya, where on 23 December 2009, the readings for B x decreased by 80 nT over two days, and then gradually recovered, over the course of 18 days.
The equipment drifts especially happened at the stations in remote locations, which are not continuously manned and monitored.These drifts should obviously be classified as measurement errors.However, if they can be quantified using the current method, they can be removed along with the above-mentioned long-term variations in the magnetic field, which means that these low-quality data need not be discarded.This is a very useful outcome, since these magnetometer stations in remote places often are some of the most crucial ones.A significant number of them are located in northern Scandinavia and the sea between Norway and Svalbard, which is the area above which the auroral oval or its boundaries are often located, and where therefore much of the magnetic activity occurs.But at the same time, not many magnetometers are present there, due to the difficult accessibility of the area.The resulting relevance of the area is precisely why these particular magnetometers were placed in these locations, despite their inaccessibility.It is therefore very useful if these relatively valuable results, even if not of perfect quality, can still be used in ionospheric analyses.
The median is used for the long-term baseline as follows.The median value is calculated for every day of data.The long-term baseline is considered to be equal to the median for 12:00 UT at the respective day.At any other time, the long-term baseline is interpolated between these values.The resulting time-dependent long-term baseline will be referred to in this paper as B T (t).The procedure to determine B T (t) is performed separately for each field component (and each different station).
Obviously, during magnetically very disturbed periods, the median value calculated over a day may not be representative for the long-term baseline.In these cases, the median of these particular days will not be used, but the long-term baseline will be interpolated between other median values.Further on, it will be shown how the classification of these "usable" median values is performed.Introduction

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Full

Quiet days
For every separate magnetometer station, a list of the quietest days of each month is generated.
At any magnetometer station, a day is considered "quiet" if the magnetic field variations measured on this day are as much as possible caused by S q variations and not by magnetic disturbances driven by solar activity.Hence, a "quiet" day would mainly contain slow variations; its fast variations should be relatively small compared to the slow variations.
Because the fast variations due to disturbances are mostly much larger than the S q variations, it seems logical to calculate simply the standard deviation of every day of data, and look for the smallest standard deviations of each month.Indeed this method works reasonably, however there are cases where this method is too coarse, as will become clear in the description below of the method of this paper.
In this paper, the quiet-day selection is performed as follows.Each day of data is partitioned into 24 one-hour sections.In each one-hour section, a straight line is fitted to the data, for the x-and y-components of the magnetic field.This straight line is subtracted from the data, and from the remaining data, the hourly standard deviation, σ H , is calculated.The result of this is 2 × 24 values (2 components and 24 h) of σ H .Of these 48 values, the daily maximum is calculated, referred to as σ H max , for each day and each station.These values of σ H max are the indicators for days with and without disturbances: of each month, the day with the lowest σ H max is selected as the "quiet day" for that month, at that station.
As an extra requirement, the "quiet day" should contain no data gaps, so only days with 100 % data availability for all magnetic components can be potential candidates for any month's "quiet day".takes into account the y-component of the magnetic field, which is not shown in the figure).Figure 4 demonstrates why this procedure works better than calculating the overall standard deviation of the whole day.On 28 March (the quiet day at the bottom of Fig. 3) the full-day standard deviation of B x is 19.9 nT, while on 7 March (Fig. 4), it is smaller: 10.0 nT.However, the latter day contains some small-scale variations, which make it less suitable as a "quiet" day.This property is revealed by the maximum hourly standard deviation σ H max , which is larger on 7 March: 6.7 nT rather than 1.4 nT.
Of course, even though according to this procedure a "quietest" day of each month can always be found (as long as at least one full day of data is available), it may be that this quietest day still contains too much magnetic disturbance to be used for a quiet day curve.Especially during and around the solar active year of 2003, disturbances can be so frequent, that not necessarily a full day can be found within every month where these disturbances are insignificantly small.In other words: the "quietest" day of the month may not be really "quiet".
Because of this, an extra criterion is applied: if for any month, the value of σ H max of the quiet day is above a certain threshold value, then this quiet day is discarded and no quiet day is assigned for this month.Later it will become clear that these cases do not cause a problem in the rest of the procedure.The optimum threshold value of σ H max to be used for this, depends on the typical level of both slow and fast variations in the magnetic field, and therefore varies from station to station.The values used were optimised empirically; the results are listed for all IMAGE stations in Table 1 (5th column).Using these threshold values, generally no more than three consecutive months without quiet days were encountered for any station in the entire IMAGE database 2001-2010.

Very disturbed days
The information of the hourly standard deviations σ H , calculated as described in the previous section, will also be used to classify certain days as too disturbed to calculate Introduction

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Full the median value from, which would be used for determination of the long-term baseline B T (t) (see Sect. 2.2).
In the top graph of Fig. 5, three days of B x -data from Abisko in November 2001 are shown, along with their daily median values (green stars).On 4 November, conditions are mostly quiet, and the median value is a good representative of the long-term baseline.On 5 November, some disturbances start late in the day, but the median value is not significantly affected by it.However, on 6 November, conditions are disturbed all day, and the median value is dominated by these disturbances, and unsuitable to be used for the long-term baseline.
A rule of thumb can be described as: a median value is relatively insensitive to irregularities in data as long as these irregularities consist of less than half of the data.This can be seen on 5 November in Fig. 5: since the irregularities consist of less than half the day, the median is not significantly affected by them.
Because of this rule, the distribution of hourly standard deviations σ H can serve as a useful indicator for the stability of the daily median value.If more than half of the day's σ H values indicate disturbed data during their hours (as in the previous section), it can be assumed that more than half of the data of the day are disturbed, and the daily median value will be unreliable.On the other hand, if more than half of the σ H values are low, then more than half of the day's data will be quiet, and the median value will be relatively unaffected by any disturbances.These different cases are clearly illustrated in the bottom graph of Fig. 5, where the σ H values of the data in the upper graph are shown (blue stars).
This criterion is easily represented by the median value of the day's hourly standard deviation, which will be referred to as σ H med .If σ H med is above a certain threshold, this means that at least half the σ H values are above this threshold.This can be seen in the bottom graph of Fig. 5, where σ H med are the red stars.As a threshold value of B x for Abisko, 17 nT was empirically chosen (dashed line in Fig. 5).
The decision whether a median value is used for the long-term baseline B T (t) is made separately for B x and B y .Because typical variations in B y are often different from

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Full those in B x , also different threshold values for these two are used.Furthermore, the threshold values are dependent on station location, just as is the case for the threshold of σ H max (see previous section).All different threshold values were empirically adjusted; their values are included in Table 1 (rightmost two columns).Figure 6 shows an example of the result of this procedure, by the B x -field in Ouluj ärvi in April 2010.These data contain some long-term baseline variations, as well as some irregularities.Using the procedure described in this section, the median values of the entire month except 5-7 April were considered suitable for the long-term baseline.The long-term baseline B T (t), interpolated between the suitable median values, follows the long-term behaviour well, and is unaffected by the disturbance on 5-7 April.

Templates composed of harmonics
Coming back to the subject of quiet days, defined in Sect.2.3, this section describes how the diurnal variations are derived from these quiet days.
The diurnal S q variations of the magnetic field can be approximated by harmonic components, as various researchers have already done in the past.Overviews of results of such harmonic analyses performed since 1889 are given by Matsushita (1968) and Campbell (1989).More recently, another harmonic analysis of S q currents was performed by Pedatella et al. (2011).Following similar principles, in this section the diurnal baseline of the two horizontal components of the ground-measured magnetic field is derived by harmonic analysis of the measured data from quiet days, separately for the x-and y-components.
For every of the quiet days, the long-term baseline B T (t) is subtracted from the data of the entire day.On the residual data, a Fast Fourier Transform (FFT) is performed.From the result of this, only the lowest few frequency components are used.The exact number of frequency components to be used is somewhat arbitrary; in this paper it is suggested to use up to the 6th component, similarly as in the S q study by Pedatella et al. (2011), and in the determination of the Dst index by Sugiura (1964).This means that only the first 7 (the 0th through the 6th) values resulting from the FFT are

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Full used.These complex values represent the amplitudes and phases of harmonics of frequencies which are all multiples of the inverse of 1 day.The frequencies of the first 7 harmonics are given in Table 2.The curve, composed of these 7 lowest harmonics of the quiet day, is equivalent to a low-pass filtered version of the quiet-day data.The resulting curve, which will here be called a "template", will be used as a basis of the baseline construction.The template is described as follows: where t d = "time of day"; time elapsed since midnight (s) There will be one set of harmonic coefficients X h , and therefore one template T (t), defined for each quiet day (and each field component).One example day of data, and the template derived from it, are shown in Fig. 7.Note that, for ease of comparison, B T (t) has been subtracted from the data.
It is worth noting that since all the cosine arguments in Eq. ( 1) cover an exact number of cycles over the length of one day (86 400 s), the template value at midnight at the end of the day, i.e.T (86 400 s), will always be equal to that at midnight at the start, T (0 s), thus ensuring continuity at midnight if the template would be used on consecutive days.However, the templates are not used directly as such for the baselines, which will be shown in the next subsection.

Diurnal baseline
As the next step, a curve representing the S q variations, i.e. the diurnal variation of the background magnetic field, is derived from the templates, separately for the x-and

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Full y-components.This curve will be referred to as the "diurnal baseline", and will be expressed as B S (t).
To obtain the diurnal baseline, the templates are interpolated continuously between midday on the previous assigned quiet day and midday on the next assigned quiet day.This can be expressed as follows: where t = the time point of interest (s) t d = "time of day" as in Eq. ( 1), i.e. the remainder of t after division by 86 400 (s) T 1,2 = the template as a function of time of day on the previous and next quiet day, respectively t 1,2 = the time point of midday on the previous and next quiet day, respectively (s).
It should be noted that, for the sake of consistency, also on the quiet days themselves the templates are interpolated.Consequently, only at noon, the diurnal baseline of a quiet day is exactly equal to the template of the same day.After noon, it is interpolated between this template and the next template, and before noon, it is interpolated with the previous template.
Figure 8 shows a schematic example, using imaginary templates consisting of only 1st harmonics.The blue curve is the template derived from quiet day 1 (on the left); the green curve is the template from quiet day 2 (on the right).The diurnal baseline (red curve) is interpolated between these two from midday on the first quiet day, to midday on the second quiet day.Only at noon on the quiet days (marked as "o" in the graph), the baseline is exactly equal to a template.
Note that the cases of months without any quiet day, which can occur during some of the most disturbed periods in solar maximum years (see Sect. 2.3), do not cause a serious problem in this procedure; they merely mean a longer period between two quiet days over which the template is interpolated.To give an indication how long these periods can be: in the current database, the largest amount of data between any two quiet Introduction

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Full days was 66 days of data, over a period of 99 days (Masi station; between 6 February and 17 May 2003).

Full baseline
To obtain the full baseline, the diurnal baseline B S is added to the long-term baseline B T and the jumps baseline B J , separately for the x-and y-components: where B B = full baseline; B S = diurnal baseline, derived from quiet days as described in Sects.2.3, 2.5 and 2.6; B T = long-term baseline, derived from suitable median values as described in Sects.2.2 and 2.4; B J = jumps-baseline, containing only the data jumps as described in Sect.2.1.Figure 9 presents an example of the result of the procedure described in this section.It shows the B x -field in Uppsala from 22 March to 10 April in 2005 (two quiet days), and the corresponding baseline.In this example, the diurnal variation of the baseline follows that of the data not only on the assigned quiet days, but also on relatively quiet intervals in the middle of this period (e.g. 1 April).Furthermore, the long-term (mostly tidal) variation of the data is well followed by the baseline.
Figure 10 shows an example for the B x -field in December 2009 in Sørøya, which experienced some significant equipment drift in this period (also shown in Fig. 3).The

Statistical results
The usefulness of the baseline procedure described in this paper is mainly demonstrated by the fact that it avoids all the problems which some other baseline procedures have (as listed in Sect.1.4), making the resulting data suitable for the calculation of ionospheric equivalent currents.However, it can also be demonstrated by showing some general characteristics of the resulting magnetic disturbance field data.
In the following, the harmonic baseline according to this paper has been subtracted from the magnetometer data from the IMAGE network measured in the period 2001-2010.The resulting field, referred to as "disturbance magnetic field" is statistically analysed.For comparison, the analysis is also done using some other baseline methods.
In this context, it would be good to apply the baseline methods described in Sect.1.4 for comparison: those by Janzhura and Troshichev (2008), Stauning (2011), and/or Gjerloev (2011).However, the implementation of those methods is rather complicated.Because of this, only the following two methods were applied for comparison: the "traditional" baseline method: using the average value of the quietest day of each month as a baseline for the entire month; a simplified representative of some other methods: the quiet-day curves are smoothed using a moving-average filter with a ´length of 1 h, and these filtered versions are used as baselines for the entire month.
Figure 11 shows the probability density function (pdf) of the disturbance magnetic field in Nordkapp, using the three baseline procedures.One feature of difference between these curves is seen between B x = −50 and +50 nT: the distribution of the disturbance field is wider spread when the quiet day averages are used as baseline than for the other two methods.This is obviously due to the S q variations, which occur every day, and in this case are included in the resulting field.The effect of this on the pdf is that near-zero values of B x become smeared out over the range between ±50 nT.This feature is seen in the distributions for all stations.Introduction

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Full The distribution using the smoothed curves of the quiet days is also more spread for small values than the one using the harmonic baseline, but not quite as much as the one using the quiet-day averages.This must be due to variations in the S q field from day to day (such as the tidal variations described in Sect.7).These variations are excluded from the baseline if the same daily curve is used for the entire month, and are therefore included in the disturbance field, which again causes the pdf to spread small values over a larger range.
Apart from that, some other features are seen in the graph, which are most pronounced in those stations which are relatively little monitored.In particular, the pdf of the B x -field in Nordkapp shows some unrealistic peaks at B x = −55, 90 and 200 nT, both when the quiet-day averages are used as baseline and when the LPF-filtered quiet-day curves are used.Apparently, some extended periods exist in the database where the disturbance field varies unrealistically around a nonzero value, obviously due to the fact the the quiet day is not realistic as a baseline, either averaged or smoothed.The pdf of the disturbance field using the harmonic baseline as described in this paper does not show these artifacts, and presents a realistic function all the way.
As another example, the pdf of the B x -field in Karmøy is shown in Fig. 12 using the same three methods.This figure shows an even stronger peak around −130 nT when the quiet day averages or the smoothed quiet-day curves are used as baselines, due to the same cause as above.
It should be emphasised here, that the baseline methods by Janzhura and Troshichev (2008), Stauning (2011), andGjerloev (2011) are all better than the two methods used here for comparison.They would likely include all diurnal S q and longerterm variations in the baseline, resulting in an equally sharp peak around zero for the pdf of the disturbed field as the blue line in Figs.11 and 12.However, these methods are not likely to deal with equipment effects efficiently, which makes it likely that the resulting pdf of the disturbance field would show similar unrealistic peaks as the red and green curves in the graphs of this section.(In addition, these methods would leave Introduction

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Full discontinuities in the disturbance field, as explained in Sect.1.4; this is a feature which does not show up in the pdf curve.)

Other applications
Now that the harmonic coefficients X h (in e.g.Eq. 1) and Y h of the magnetometer baselines have been derived over 10 yr and for 32 magnetometer stations, these can be used to examine their long-term behaviour, which represent the Solar quiet-time (S q ) diurnal variation of the magnetic field B x and B y .Like the disturbance field, also this field is mainly caused by currents in the ionosphere.However, unlike the disturbance field, this field varies with diurnal variations of electron density in the ionosphere, which in turn depends on solar radiation.
Several statistical studies of the harmonic coefficients of S q diurnal variations, dependent on season, year, location and solar activity, have already been made throughout the 20th century, revealing information about the long-term dependencies of the geomagnetic field, see e.g. the overviews by Matsushita (1968) andCampbell (1989).The results obtained in the study of the current paper can help to verify those studies, and help to improve prediction models of the S q magnetic field.This will be the subject of a later paper.

Conclusions
A novel method of determining the baselines of magnetometer data has been presented.The full baseline is composed of three components: disturbed ones; a procedure is included to ensure that these median values are unaffected by disturbances.
-A diurnal baseline, interpolated between "templates", i.e. diurnal baselines of the nearest two quiet days.These templates consist of the first seven harmonics of the diurnal variation of the magnetic field of the quiet days.This method ensures a smooth baseline at all times, avoiding any discontinuities at transitions between days or months.
More than the traditional method of using the average of the nearest quiet day as a baseline, the baseline derived according to this method is able to follow medium-tolong-term variations in the measured magnetic field, such as tidal and secular variations, as well as equipment drifts of individual instruments.The procedure avoids many problems associated with other existing baseline procedures, and makes magnetometer data suitable for the calculation of ionospheric equivalent currents.Even data from remote unmanned magnetometers, which exhibit significant equipment effects, can be made suitable with this method, which can give valuable contributions to the equivalent current database.Introduction

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Full  Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | other hand components caused by Coronal Mass Ejections and other disturbances in Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Figure 3
Figure 3 demonstrates this procedure, showing B x in Ouluj ärvi on three different days in March 2002.The day shown in the bottom two graphs, 28 March, resulted from this procedure as the quietest day of this month (note that the actual procedure also Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | figure shows that the baseline derived for this period follows the equipment drift well, making this data reasonably usable for equivalent current calculations.
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A jump baseline, which contains only the artificial jumps in the data and is otherwise constant.-A long-term baseline, interpolated between daily median values of the raw data of most days.The daily median values are calculated for all days except the most 108 Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Table 1 .
Threshold values of σ H max and σ H med for each IMAGE station.• ) σ H max (nT) σ H med , B x (nT) σ H med , B y (nT)