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\title{Virtual magnetograms -- a tool for the study  of geomagnetic response to the solar wind/IMF driving}

\author{O. V. Kozyreva$^{1}$, V. A. Pilipenko$^{2,3}$, A.~A.~Soloviev$^{1.2}$, M. J. Engebretson$^{3}$}

\affil{1}{Schmidt Institute of Physics of the Earth  RAS, Moscow, Russia}
\affil{2}{Geophysical Center RAS, Moscow, Russia}
\affil{3}{Augsburg University, Minneapolis, MN, USA}

\abstract{Processes of the solar-wind/magnetosphere interaction can be monitored by magnetic records on the
ground from the worldwide array of stations. However, a serious drawback of the analysis of ground-based
magnetograms is the inevitable variation of the magnetic response due to continual changes of
the station location. An ideal, but impossible, solution of this difficulty, that will help to discriminate
temporal and spatial variations, would be the deployment of a ``stationary'' in situ observatory with a
fixed position in the solar-magnetospheric coordinate system. However, the desired result can be
obtained with the proposed technique of ``virtual magnetograms'' (VMs). This technique has been
implemented for key magnetospheric domains (midnight auroral and noon cusp regions) as an
additional tool for monitoring the response of the geomagnetic field to solar wind\linebreak\newpage}

\noindent\centerline{\parbox{100mm}{ and interplanetary
magnetic field forcing. A VM is reconstructed by 2D gridding and interpolation of 1-min
magnetograms from $>200$ magnetic stations distributed worldwide. VMs have been produced for the
period since 1994 up to the current year for both Northern and Southern hemispheres. A wide range
of space physics studies, such as the solar wind-magnetosphere interaction, dayside-nightside
coupling, etc. will benefit from the introduction of the VMs. The VMs for the dayside cusp and
midnight auroral regions in both hemispheres, as well as simultaneous interplanetary parameters
(solar wind density, electric field $E_y$) and geomagnetic indices ($AE$, SYMH, and PC), are combined
in one plot. These quick-look plots and corresponding digital files are freely available via the web
site  \href{http://vm.gcras.ru}{http://vm.gcras.ru}
for all interested researchers for testing and validation. Here we present
examples of VMs for the following phenomena: a sawtooth event, modulation of the dayside cusp by
IMF variations, and coupling between the dayside cusp ULF activity and substorms. VM database
may make the selection of events for subsequent in-depth analysis much easier.}}

\section{1. Introduction}

\fitopen{.95}
\begin{sloppypar}
The interaction between the solar wind with embedded interplanetary magnetic field (IMF) and the
terrestrial magnetosphere is the main driver of many processes and phenomena occurring in the
near-Earth environment. Magnetic disturbances on the ground, being the images of dynamic processes of
solar-wind/magnetosphere interaction, can be monitored in the time domain by magnetic records. The
number of permanently operating magnetic stations now exceeds 200 and continues to grow. A recent
trend in the geomagnetism community implies the transition from studying data from a single
magnetometer (L2-type data) to construction of models based on data from the global magnetometer
array (L3-type products). Examples of such higher order products recently introduced in the
geomagnetism are the new geomagnetic indices SMU/SML/SME of auroral electrojet strength
(\href{http://supermag.jhuapl.edu}{http://supermag.jhuapl.edu}),
the IMAGE electrojet indicators
(\href{http://space.fmi.fi/image/www}{http://space.fmi.fi/image/www}),
 and
ultra-low-frequency (ULF) wave power index
(\href{http://ulf.gcras.ru}{http://ulf.gcras.ru}).
Various techniques for constructing
global maps of geomagnetic disturbances are being developed
[\itc{Waters et al.,} \reflink{Wate15}{2015};
\itc{Weimer et al.,} \reflink{Weim10}{2010}].
\end{sloppypar}


      However, a serious drawback of the analysis of ground-based magnetograms is the inevitable
variation of the magnetic response due to continual changes of the station location in local time regarding
the direction of the solar wind flow. An ideal, but impossible, solution of this difficulty would be the
deployment of a ``stationary'' in-situ observatory with a fixed position in the solar-magnetospheric
coordinate system. This will help to distinguish between temporal and spatial variations. However, the
desired result can be obtained with the ``virtual magnetometer'' technique proposed here. A virtual
magnetogram (VM) for a fixed reference system is reconstructed by interpolation of 1-min magnetograms
from worldwide distributed magnetic stations. The availability of pre-calculated VMs for the ionospheric
projections of key magnetospheric domains, such as the dayside cusp and midnight auroral oval, will
facilitate enormously the quick-look analysis, event selection, and study of the ground response to various
space weather events. Here we outline the production method of VMs, describe the structure of database
with VMs for the period since 1994, and present several examples of VMs for different space weather
events.\fitclose

\section{2. \!Database for the Virtual Magnetograms}

VM for ionospheric projections of key magnetospheric domains with fixed latitude/MLT geomagnetic
coordinates is reconstructed from the data of the worldwide array of magnetic stations: INTERMAGNET,
Greenland Coastal Chains, MAGDAS, MACCS, IMAGE,\linebreak CARISMA/CANMOS, AARI network, and
others in the Northern and Southern hemispheres. Most of these data are compiled in a unified 1-min
database at the SuperMAG portal
(\href{http://supermag.jhuapl.edu}{http://supermag.jhuapl.edu}).

      VMs have been generated for the following fixed locations in the Northern and Southern
hemispheres:
\begin{itemize}
\item
 at noon (MLT $=12$:00) for cusp geomagnetic latitudes $\Phi_0 =75\deg \pm 5\deg$ in the Northern hemisphere, and
$\Phi_0= - [70\deg \div 80\deg]$ in the Southern hemisphere;
\item
 at midnight (MLT$=00$:00) for auroral geomagnetic latitudes
 $\Phi_0 = \pm [65\deg \pm 5\deg]$.
\end{itemize}
Data from the stations located within these latitudinal ranges only have been used for the VM
construction. In the data from the SuperMAG database the baseline was subtracted using the algorithm
described in
[\itc{Gjerloev,} \reflink{Gjer12}{2012}].


\begin{sloppypar}
      The raw data quality can be verified using the stacked magnetograms from all contributing
stations. These plots have been included in the database.
\end{sloppypar}


      The VM plots have been augmented with the basic interplanetary and geomagnetic parameters.
Because of the limited format of the plots only the following information can be presented:
\begin{itemize}
\item
 space weather parameters from the OMNI database
(\href{https://omniweb.gsfc.nasa.gov}{https://omniweb.gsfc.nasa.gov}):
solar wind density
$N_p$ (or dynamic pressure $P$) and electric field
$E_y= -V_x \times B_z$  %%% ???
(where $V_x$ is the solar wind velocity, and $B_z$
 is % in
the vertical IMF component). The southward IMF~$B_z$ corresponds to the positive $E_y$;
\item
\begin{sloppypar}
 geomagnetic indices: SYMH index
(\href{http://swdcwww.kugi.kyoto-u.ac.jp/}{http://swdcwww.kugi.kyoto-u.ac.jp/}), %http://wdc.kugi.kyoto-u.ac.jp/ %%% ???
 cha\-racterizing magnetic storm
intensity; PCN/PCS indices
(\href{http://pcindex.org}{http://pcindex.org}),
characterizing the energy supply into the high-latitude
ionospheres; and the $AE$~index
(\href{http://wdc.kugi.kyoto-u.ac.jp/}{http://wdc.kugi.kyoto-u.ac.jp/}),     % http://wdc.kugi.kyoto-u.ac.jp/ %%% ???
 characterizing the auroral activity.
\end{sloppypar}
\end{itemize}

\section{3. Algorithm of VM Construction and Database Availability}
	

\begin{sloppypar}
A VM for a fixed reference system is constructed by 2D fitting and interpolation of 1-min magnetograms
from the worldwide array of irregularly distributed magnetic stations. The ``inverse distance'' interpolation
algorithm has been applied. From available world-wide stations, those are chosen that are within the
pre-selected latitudinal range indicated in the section~2. Then, three nearest stations to a given MLT (00:00 or 12:00)
are selected. If number of selected stations is less than 3, VM is not calculated. A current VM amplitude
$A_0$ of each magnetic field components $\{X,Y,Z\}$ is calculated as follows
\end{sloppypar}


\begin{eqnarray*}
A_0 = \frac{\sum_{i=1}^3 A_i d_i}{\sum_{i=1}^3 |d_i|}
\end{eqnarray*}
\begin{equation}\label{1}
d_i^{-1} =
\sqrt{(\mathrm{MLT}_i - \mathrm{MLT}_0)^2 + (\Phi_i - \Phi_0)^2}
\end{equation}  % (1)
where $A_i=\{X,Y,Z\}$ is the amplitude at site ($i$), the ``distance''
 $d_i$ is the weight coefficient depending on the
MLT/latitude $(\Phi)$ difference between the VM location (index 0) and a selected station (index $i$). In
\eqref{1}  % (1)
the
latitude difference $\Delta \Phi$ is measured in degrees, while the longitudinal difference $\Delta $(MLT) is measured in
hours. Thus, $\Delta \Phi =1\deg$ ($\sim 111$~km) provides the same contribution to the ``inverse distance'' as $\Delta $(MLT)$=1$~h
(that is at auroral latitudes 15\deg $\sim \!670$~km). This asymmetry takes into account a strong inhomogeneity of
the geomagnetic disturbance field where a latitudinal gradient is much larger than a gradient in the
longitudinal direction.


\begin{sloppypar}
	A VM plot combines both noon and midnight virtual magnetograms of geomagnetic response for
the Northern and Southern hemispheres. Also, VM magnetograms are written in output multi-column
ASCII files comprising $X,Y,Z$~components, interplanetary parameters, and geomagnetic indices.
A freely-available database of VMs has been uploaded for validation and testing at the web site
\href{http://vm.gcras.ru/}{http://vm.gcras.ru/}.
Examples of VM plots will be presented below for several space weather events.
\end{sloppypar}


\section{4. Examples of VM for Various Space Weather Events}


\begin{sloppypar}
The VM technique was applied for the description of substorm activations during the ``St. Patrick's day''
geomagnetic storm on 17 March  2015
[\itc{Kozyreva et al.,} \reflink{Kozy18a}{2018a}].
 This peculiar magnetic storm was
initiated by an interaction between high-speed solar wind streams in a corotating interaction region (CIR)
and two coronal mass ejections (CMEs). During the very long ($\sim 17$~hours) main phase several isolated
substorms took place. The VM provides more detailed fine structure of the substorm activity and more
clearly indicates the onsets of each substorm than the $AE$ or PC indices do.
\end{sloppypar}


      Here we demonstrate the possibility to apply the derived VMs to examine, on a case-by-case
basis, such effects as:
\begin{itemize}
\item
	sawtooth oscillations;
\item
	the near-cusp ionosphere response to IMF va\-riations;  % and
\item
	dayside-nightside coupling during substorm growth and explosive phases.
\end{itemize}

\subsection{4.1. Sawtooth Event}

In addition to substorms, response modes of the magnetosphere include sawtooth events, which share
common features with isolated substorms. A sawtooth event consists of a series of gradual decrease and
rapid increases in energetic particle flux at geosynchronous orbit (i.e., particle injections), while an
isolated substorm has one variation cycle. In fact, sawtooth oscillations are a sequence of storm-time
substorms with an intrinsic occurrence periodicity of 2--3~hours, when nearly simultaneous energetic
particle flux enhancements and magnetic field variations occur at all MLTs for each sawtooth cycle. It
was suggested that the sawtooth oscillations are directly driven by a series of solar wind pressure $P$
enhancements, whereas even a modest dynamic pressure enhancement can result in significant changes in
the magnetosphere when the IMF stays strongly southward for a long interval
 [\itc{Lee et al.,} \reflink{Lee04}{2004}].
Alternatively, it was suggested that the sawtooth oscillations are a repetitive internal magnetospheric
response to sustained solar wind energy input
 [\itc{Cai and Clauer,} \reflink{Cai13}{2013};
 \itc{Fung et al.,} \reflink{Fung16}{2016}].



\begin{figure}                     % Fig 1
\figurewidth{115mm}
\setimage{}{}{}{125mm}{2019es000654-f01}
\fcaplabel{\footnotesize A plot of the VM showing the basic space weather parameters: solar wind dynamic pressure $P$, electric field $E_y=-V \times B_z$, SYMH-index, PCN/PCS indices, $AE$-index, and the $X$ component of virtual magnetograms of the geomagnetic response at the noon-cusp region (12:00 MLT) and the midnight auroral region (00:00 MLT) for the Northern (blue line) and Southern (red line) hemispheres during the sawtooth event of 14 October 2000 (01:00--23:00~UT).}
\end{figure}

 \begin{sloppypar}
      The plot from the VM database for the event of 14 October 2000
 (\figref{1})           % (Figure 1)
  clearly reveals the
 quasi-periodic character of the nightside magnetosphere response during this sawtooth event (panel VM
00:00~MLT) during a weak magnetic storm \mbox{($|$SYMH$|$}    %%% ???+
 up to 100~nT) driven by persistent (more than 17
hours) southward IMF~$B_z$ (positive $E_y$). The VM time series indicates 8 substorms with magnetic bay
amplitudes from $\sim 200$~nT to \mbox{$\sim 700$~nT} during 01:00--23:00~UT. Each substorm intensification is more evident in
the VM, than in $AE$ or PC~indices. Comparison of dynamic pressure $P$ and the midnight VM shows that
sawtooth substorms during this event are triggered by the solar wind density enhancements (sometimes
rather weak).
\end{sloppypar}

\subsection{4.2. Response of the Dayside Ionosphere Current System to Solar Wind Alfv\'{e}nic Variations}

Extensive studies with global arrays of magnetometers involved showed that dayside ionospheric
convection and current systems at high latitudes are driven by the IMF variations
 [\itc{Cai et al.,} \reflink{Cai09}{2009}, \reflink{Cai06}{2006};
 \itc{Murr and Hughes,} \reflink{Murr01}{2001};
 \itc{Milan et al.,} \reflink{Mila18}{2018}].
  This effect can be clearly seen with the VM technique, as was
demonstrated in
[\itc{Kozyreva et al.,} \reflink{Kozy18b}{2018b}].
Comparison of IMF variations with VMs confirmed that the
dayside ionospheric convection is indeed predominantly controlled by the
IMF~$B_z$.

      A specific type of the space weather events is the high-speed solar wind streams (HSSs). A very
important aspect of the HSSs is that they are embedded within large-amplitude Alfv\'{e}n waves. These
Alfv\'{e}n waves propagating along the solar wind away from the Sun are believed to be remnants of heating
processes in the solar atmosphere. The HSS-associated Alfv\'{e}n waves, with intermittent negative IMF~$B_z$
and large IMF~$B_y$~component, may lead to significantly enhanced magnetospheric convection.

\begin{figure}                     % Fig 2
\figurewidth{100mm}
\setimage{}{}{}{140mm}{2019es000654-f02}
\fcaplabel{A plot of the VM for the HSS event with solar wind Alfv\'{e}nic waves on 17 September  2003 (04:00--24:00~UT). The format is the same as in
\figref{1}.}
\end{figure}

      Indeed,
\itc{Echer et al.} [\reflink{Eche17}{2017}]
followed the coupling from the solar wind to the Earth's magnetotail,
geosynchronous orbit, auroral zone and to the ground, during periods of Alfv\'{e}nic fluctuations in HSS on
September--October 2003, and found a range of periodic responses from 1.8 to 3.1~h. The VM for one of
the period of HSS with solar wind Alfv\'{e}nic waves on 17 September 2003 is shown in
 \figref{2}.           % Figure 2.
 Each blip of
positive $E_y$ (up to 6~mV/m) produces a corresponding negative geomagnetic disturbance (up to $\sim 1000$~nT)
in the cusp region, as evident from VM for Northern hemisphere (panel VM 12:00~MLT). A significant
magnetic response on the ground to IMF variations (about two orders of magnitudes amplification) may
be due to convergence of near-magnetopause field lines into narrow cusp region
[\itc{Pilipenko et al.,} \reflink{Pili00}{2000}].

\subsection{4.3. Coupling Between the Cusp-Associated ULF Activity and Nighttime Substorms}

Very intense activity in the ULF range (from fractions of mHz to few Hz) is persistently observed at high
latitudes during day time
[\itc{Bolshakova et al.,} \reflink{Bols75}{1975}, \reflink{Bols89}{1989};
\itc{Troitskaya and Bolshakova,} \reflink{Troi88}{1988}].
Dynamic irregular
long-period magnetic pulsations are observed almost every day over a wide period range (3--20~min) when
a ground-based magnetic station happens to be within several hours from local noon. These high-latitude
disturbances were denoted IPCL (Irregular Pulsations at Cusp Latitudes) or broad-band Pc5-6 pulsations.
The issue of whether these pulsations are characteristic of some dayside boundary domain/boundary is
still unresolved
[e.g., \itc{Pilipenko et al.,} \reflink{Pili18}{2018}],
and the driver of these broadband dayside Pc5-6 pulsations
has not been firmly established. They may be associated with pressure pulses
[\itc{Kleimenova et al.,} \reflink{Klei99}{1999}],
plasma intrusions
 [\itc{Pilipenko et al.,} \reflink{Pili17}{2017}],
  or intermittent bursts in the turbulent magnetosheath
[\itc{Kurazkovskaya and Klain,} \reflink{Kura90}{1990}].
The high latitude broadband wave activity on the dayside cannot be
simply associated with cusp proximity, but, instead, shows persistent activity across several hours of local
time
[\itc{Engebretson et al.,} \reflink{Enge95}{1995}].

      Much less is known about the relationships between nightside substorm activity and ULF
disturbances in the dayside cusp region, and possible physical mechanisms for such coupling processes.
Although there are some indications that such coupling between cusp-associated ULF activity and
substorms may exist.
\itc{Samson et al.} [\reflink{Sams92}{1992}]
suggested a wave channel for energy transmission across the
magnetosphere which may provide an essential input to substorm energetics. It is feasible that ULF
activity at high latitudes on the dayside is an indicator of an enhanced rate of turbulent energy supply into
the magnetosphere during the growth phase of a substorm, and thus can be a substorm precursor.

      Determination of the sequence of events leading to substorm onset is the long-standing problem.
Dayside auroral and magnetic activity appearing shortly before substorm onset has gained attention
because it may provide means to predict substorms for space weather forecasting purposes. However,
controversy still exists regarding the existence of such coupling between dayside and nightside
phenomena. Auroral observations by
\itc{Elphinstone et al.} [\reflink{Elph13}{2013}]
suggested that dayside events are affected
by the same solar wind disturbances, which later affect nightside magnetospheric dynamics.
 \itc{Lyons et al.} [\reflink{Lyon11}{2011}]
  proposed that enhanced mesoscale flows from well within the region of open polar cap field lines
may cross the nightside polar cap boundary and contribute to the triggering of poleward boundary
intensifications (PBIs) and auroral streamers, eventually leading to substorm onset. Other researchers
concluded that substorms are not likely to be triggered by a solar wind disturbance, which propagates in a
visible manner from dayside to nightside.
\itc{Sandholt et al.} [\reflink{Sand85}{1985}]
presented examples showing the
disconnection of dayside auroral arcs from the nightside aurora.


\begin{sloppypar}
      Nonetheless, observational evidences of dayside-nightside coupling are mounting, though most of
them remain not well understood and validated. According to
\itc{Eather et al.} [\reflink{Eath79}{1979}]
all substorms result in
equatorward shifts of the dayside aurora. Statistics of the IPCL bursts shows that $>80$\%
of bursts in the
dayside cusp
[\itc{Kurazkovskaya and Klain,} \reflink{Kura09}{2009}]
 occur at the background of developing substorm in the
nightside auroral oval. Just before break-up
\itc{Vorobiev et al.} [\reflink{Voro92}{1992}]         %%% ???
observed a decrease of the intensity of
dayside aurora with duration 3--8~min, most evident in the ``green'' (557.7~nm) line, whereas the ``red''
(630.0~nm) line intensity remained practically unchanged. ULF pulsation precursors of substorms in the
polar cap were found using data from Vostok station in Antarctica: long-period pulsation amplitudes
became higher at last pre-substorm hours in comparison with non-substorm days
[\itc{Yagova et al.,} \reflink{Yago00}{2000}].
\itc{Rostoker et al.} [\reflink{Rost84}{1984}]
 noticed that statistically southward turning IMF~$B_z$ nearly 2 hours before onset is
accompanied by an apparent peak in daytime Pc5 power.
\itc{Yagodkina and Vorobiev} [\reflink{YaVo00}{2000}]
found that the
expansive phase of a nightside auroral substorm was accompanied by a short-lived ($\sim 10$~min)
enhancement in the daytime pulsation power in 3--8~s (Pc1-2) and 30--80~s (Pc3-4) period ranges.
\end{sloppypar}


      Here we present examples of other effects of the dayside-nightside coupling during substorms, not
thoroughly examined yet.



\subsubsection{4.3.1. Dayside ULF precursor of substorm and suppression of cusp-related ULF activity by onset.}
An effect evidencing the coupling between the dayside ULF activity and substorm is suppression of
cusp-related ULF activity by substorm onset
[\itc{Kleimenova et al.,} \reflink{Klei98}{1998};
\itc{Pilipenko et al.,} \reflink{Pili98}{1998}].
 A relevant effect
was observed with SuperDARN radars that detected a mesoscale convection vortex in the afternoon
sector, which abruptly disappeared with the onset of a midnight substorm
[\itc{Greenwald et al.,} \reflink{Gree96}{1996}].
 The
authors attributed the vortex disappearance to a redirection of magnetospheric closure currents as
consequence of a significant increase in the nightside conductivity during a substorm expansion.
\itc{Bolshakova et al.} [\reflink{Bols97}{1997}]
 interpreted the occurrence of daytime IPCL pulsations and their disappearance
during nighttime substorm as the manifestation of ULF precursor of a substorm. Indeed, an enhanced
reconnection at the dayside magnetopause provides energy for an impending substorm, and this turbulent
process may reveal itself in an enhancement of cusp-related ULF disturbances.

\begin{figure}                     % Fig 3
\figurewidth{100mm}
\setimage{}{}{}{137mm}{2019es000654-f03}
\fcaplabel{A plot of the VM showing dayside IPCL pulsation suppression during a nightside substorm on 7 March  2015 (10:00--19:00~UT). The format is the same as in
\figref{1}.}
\end{figure}


\begin{sloppypar}
      The effect of dayside IPCL suppression during nightside substorm on 7 March 2015 (10:00--19:00~UT)
can be seen in VM
(\figref{3}).           % (Figure 3).
 The substorm with maximum $AE>1200$~nT and PC~$\sim 4$~mV/m develops
during 16:00--17:00~UT. Since 10:00~UT persistent monochromatic Pc5 pulsations are observed at dayside in both
Northern and Southern hemispheres. The gradual substorm onset which started around 16:00~UT results in
the suppression of dayside Pc5 pulsations. Formally, this event may be interpreted as an occurrence of the
cusp ULF precursor of nighttime substorm.
\end{sloppypar}


      To illustrate the content of the VM database, for this event we present an example of stacked
magnetograms from stations used for the construction of the cusp VM
(\figref{4}).           % (Figure 4).
 This plot enables one to
check the data quality, and to examine a contribution of particular stations into a combined VM.

\begin{figure}                    % Fig 4
\figurewidth{100mm}
\setimage{}{}{}{130mm}{2019es000654-f04}
\fcaplabel{The stacked magnetograms from stations used for the construction of the cusp VM (upper panel) on 7 March 2015 (10:00 -- 19:00 UT). Station’s codes and geomagnetic coordinates are indicated near the right-hand ordinate. Empty triangles denote MLT noon, and black rhombs denote MLT midnight.}
\end{figure}

\subsubsection{4.3.2. Triggering of dayside ULF waves by nightside substorm.}
\itc{Rostoker et al.} [\reflink{Rost84}{1984}]
found that total power in the Pc5 band at auroral latitudes close to dawn (06:00--09:00~LT)
appears to be elevated during a large substorm expansive phase. They proposed that these pulsations are
caused by a Kelvin-Helmholtz (KH) instability in the interface between the sunward convecting
plasmasheet plasma and the anti-sunward flowing low-latitude boundary layer (LLBL) plasma.
According to their model the northward turning of IMF~$B_z$ triggers a substorm expansive phase and
thinning of LLBL. The latter reduces the width of the shear zone and leads to stimulation of the KH
instability.

\begin{figure}                     % Fig 5
\figurewidth{100mm}
\setimage{}{}{}{137mm}{2019es000654-f05}
\fcaplabel{A plot of the VM showing triggering of dayside cusp-related ULF activity during a nightside substorm on 22 March 2015 (03:00--15:00 UT). The format is the same as in \figref{1}.}
\end{figure}

\figref{5}           % Figure 5
      shows dayside cusp-related ULF activity during various phases of nightside substorm on
22 March  2015. Southward oriented IMF~$B_z$ (and correspondingly positive $E_y$) causes two adjacent
substorm expansions (with peak of $AE \sim 1400$~nT) at $\sim $06:30--07:40~UT. At the substorm recovery phase
intense IPCL pulsations emerge in the Northern cusp region for nearly 6~hours, from $\sim 08$:00 until $\sim 14$:00~UT.
At the same time, in the Southern cusp region monochromatic Pc5 waves are stimulated.

\subsubsection{4.3.3. Change of dayside pulsation dominant frequency during nighttime substorm onset.}
\itc{Samson and Rostoker} [\reflink{Sams81}{1981}]
found that large amplitude dayside Pc5 pulsations seemed to disappear with
the onset of a substorm expansive phase and were replaced by higher frequency pulsations in the Pc3-4
range. They proposed that sudden inward ring current motion causes changes in the magnetic field in the
equatorial plane of the magnetosphere and, respectively, in the Alfv\'{e}n period.

\begin{figure}                     % Fig 6
\figurewidth{100mm}
\setimage{}{}{}{135mm}{2019es000654-f06}
\fcaplabel{An example of a Samson-Rostoker event -- a change of the dominant dayside pulsation frequency during a nighttime substorm onset, on 13 December 2015 (07:00--16:00 UT). The format is the same as in \figref{1}.}
\end{figure}

      An example of the Samson-Rostoker event is shown in
\figref{6}.           % Figure 6.
      For $\sim 3$ hours before a moderate
substorm ($AE \sim 400$~nT) at $\sim \ $10:30~UT on 13 December 2015, IPCL pulsations with predominant period $\sim 10-15$~min
 are observed. After substorm, since $\sim 11$:00~UT, monochromatic Pc5 waves with periods $\sim 3-4$~min
last for about 4~hours.

\subsection{4.4. Polar Substorms}

Substorms can be divided into ``polar'' and ordinary ``high latitude'' substorms
 [\itc{Despirak et al.,} \reflink{Desp14}{2014}].
During ``polar'' substorms all disturbances are concentrated in a narrow latitude region near the polar cap
($\Phi >70$\deg), and usually occur, when the auroral oval is contracted and poleward shifted. During ``high
latitude'' substorms, a disturbance starts at auroral latitudes, then propagates poleward, whereas the
westward electrojet moves to high geomagnetic latitudes ($>75$\deg)
 [\itc{Despirak et al.,} \reflink{Desp08}{2008};
 \itc{Mende et al.,} \reflink{Mend99}{1999}].
  It is not yet clear whether mechanisms of high-latitude and polar substorms are the same.

\begin{figure}                    % Fig 7
\figurewidth{100mm}
\setimage{}{}{}{140mm}{2019es000654-f07}
\fcaplabel{An example of a polar substorm event on 31 October 2007 (05--17 UT). The format is the same as in \figref{1}.}
\end{figure}

      An example of a polar substorm is the event on  31 October 2007
 (\figref{7}).           % (Figure 7).
  A weak southward IMF~$B_z<0$ (positive $E_y$) after 09:00~UT causes geomagnetic activity activation as evident from the elevated level
of $AE$~index from 10:00~UT until 16:00~UT. No clear signatures of an isolated substorm are evident in the $AE$-
or PC-index behavior. At the same time, VM evidently reveals a weak substorm onset (magnetic bay
$>150$~nT) at $\sim $13:50~UT. This weak substorm develops on the background of elevated IPCL/Pc5 activity.
Such kind of weak substorm accompanied by intense dayside ULF activity may be a result of ``thermal
catastrophe'' substorm, stimulated by the wave heating of the plasmasheet plasma
[\itc{Goertz and Smith,} \reflink{Goer89}{1989}].







\section{5. Concluding Remarks}

We have developed a provisional database (of L3-type) of ``virtual'' 1-min magnetograms for two fixed
locations: noon and midnight meridian at typical cusp and auroral latitudes, using the data from
worldwide magnetometers. The noon and midnight VMs from both Northern and Southern hemispheres
are combined in one plot, together with the solar wind and IMF data and geomagnetic indices.
Several
examples presented here are intended to demonstrate that the usage of pre-calculated VMs significantly
facilitates quick-look selection and analysis of space weather events. An analysis of one combined VM is
far easier than the standard analysis of numerous magnetograms from a global array of stations with
unavoidable time-space ambiguity. This technique might be useful to reveal a ground response to
IMF/SW discontinuities, dayside-nightside coupling, triggering and precursors of substorms, sawtooth
events, etc. Moreover, VM data provides a possibility to easily estimate the time response between IMF
variations and dayside ionospheric convection, without space-time ambiguity.

      To illustrate usefulness of the VM technique, we have presented some interesting events with a
probable substorm/cusp coupling. These events demonstrate that a substorm is not a localized nightside
phenomenon, but a global process influencing the entire magnetosphere. A substorm onset was found to
impact the ULF wave generation process at dayside high latitudes, causing either suppression or
stimulation of ULF activity. However, the number of events is too small so far to discuss the reliability of
the effects listed above. Here we deliberately do not discuss any physical conclusions, because our main
goal is to present a new tool for event selection and analysis, and to discuss its possible applications for
the geophysical community.

      The VM database for the period since 1994 up to nowadays is available for validation and testing
at the web site
\href{http://vm.gcras.ru}{http://vm.gcras.ru}.
 The IDL program for plotting VM for any desired time interval from
VM database is enclosed, too. Any suggestions or corrections are appreciated and will be taken into
account in further updates.

      The technique of VM construction can be updated and modified. Sometimes jumps are observed,
which may be caused by several reasons: interference in raw data from a contributing station or lack of
stations in some regions. The rarity of stations in some low-populated regions with harsh weather
conditions (e.g., Russian Arctic, Antarctica) and oceans is the main issue in any attempt to construct a
global characteristic of geomagnetic field variations. We are permanently working on upgrade of the
magnetometer database and adding new data whenever they become available. So far, VM for the
Southern hemisphere is less reliable because of a much worse station coverage. In further studies, we plan
to test other algorithms of gridding and interpolation, e.g., polynomial regression. In further versions we
plan to use the SuperMAG SME index instead of $AE$.

\acknowledgement{This study is supported by grant \# 16-17-00121 from the Russian Science
Foundation (OVK, AAS), and grant AGS-1651263 from the U.S. National Science Foundation (MJE,
VAP).  Useful comments of both reviewers are appreciated.\vspace*{-1pc}}

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\end{references}

\end{document}

