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P. Stauning: The Polar Cap (PC) Index for Space Weather Forecasts
Sketches of polar and auroral current systems
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The Polar Cap (PC) indices may assist to predict the
occurrence and the intensity of substorms, that might
pose threaths to technological systems like power grids
and satellite systems.
Substorms are characterized a.o. by strong magnetic
disturbances in the auroral zone particularly near local
midnight, intense energetic particle fluxes in the
Magnetosphere, and increases in the equatorial Ring Current.
The interaction of the Solar Wind with the Earth’s magnetosphere
generates convection-related current systems in the polar
ionospheres like sketched in the figure. They comprise the basic
transpolar ”forward” convection system, DP2, when the IMF BZ
component is negative or just weak, and the ”reverse” convection
system, DP3, when the IMF BZ is strongly positive.
The DP4 (or ”DPY”) Cusp convection system is driven by the IMF BY
component. The DP1 current and convection system relate to the
occurrence of Substorms.
The magnetic variations related to the Polar Cap ionospheric convection systems can be used to indicate the
varying intensities of the solar wind encounter with the Magnetosphere.
However, the amplitudes of the magnetic variations observed in the Polar Cap depend strongly on
observatory local time, season and location. This complicates their use in Space Weather applications.
To be useful for Space Weather issues, the magnetic variations should be converted into values that are
independent of local time, season and observatory. This is the basis for developing a PC index.
ESWW13. P. Stauning
Basics of the PC index.
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The Solar Wind ”Merging” (or ”Geo-effective”) Electric Field, EM, (=MEF) that controls the
global energy input to the Magnetosphere is defined by (Kan and Lee, 1979):
EM = VSW • BT • sin2(/2)
(1)
where: VSW is solar wind velocity, BT = (BY2 + BZ2)1/2 is the IMF transverse magnetic field
component, and θ = arctan(BY/BZ) is IMF polar angle with respect to GSM Z-axis.
The Polar Cap index is based on the assumption that polar magnetic variations over the
quiet variation (the QDC) are proportional to the merging electric field through the relation:
ΔFPROJ = EM • α + β
(2)
Where ΔFPROJ (in units of nT) is the magnetic variation projected to the “optimum
(correlation) direction” in a polar cap coordinate system fixed with respect to the Sun-Earth
direction. The proportionality constant α is the “slope” (e.g. in units of nT/(mV/m)) and the
baseline shift β (nT) is the “intercept”.
The Polar Cap Index PC is now derived from the projected magnetic variations calibrated by
α and β to statistically equal the merging electric field:
PC = (ΔFPROJ – β)/α
(== EM )
(3)
The scaling parameters, i.e. projection angle, slope and intercept, are found from statistical
analyses of corresponding polar geomagnetic observations and interplanetary satellite
measurements to make PC and EM values statistically equal. The parameters vary with local
time and season but are kept invariant through the solar cycle. Defined this way, the PC
index, in principle, is invariant to observatory local time, season, and location. There is a
PCN (North) index based on Thule data and PCS (South) index based on Vostok data.
ESWW13. P. Stauning
Relations of Polar Cap indices to further magnetic indices and to Auroral Power
The PC index is a ”master index” for the input of energy from the solar wind to the magnetosphere.
This energy is later converted or dissipated to provide basis for other ground-based magnetic indices.
Thus, the other magnetic indices relate to the PC index as demonstrated in the figures, where the
PCC index is the average of the PCN and PCS index values.
APN = 13 PCN + 10 [GW]
For PCN>0
AE = 110 PCC + 60 [nT]
Q = 4.6 PCC + 1.2 [nT/hr]
Kp = PCC + 1.0
The PC indices have been averaged over
the 3-hr Kp interval with a small time shift
Q is the source function for the Dst index
ESWW13. P. Stauning
PCN index in Space Weather forecasts
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Statistics of PCN indices around powerline cuts
PC indices can provide Space Weather
monitoring, and could give warning of
substorms that could endanger electric
power grids and cause disruptions of power
lines (black triangles). Note in the figure
below the sudden substorm onset following
an hour of PCN>10 units (mV/m).
Note in the figure that the powerline cuts marked by the
red vertical line occur at PCN index values between 15
and 25 following an hour’s interval of PCN>10.
Yearly number of hours with enhanced PCN values
ESWW13. P. Stauning
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The use of PC indices in Space Weather Forecast Systems
A Space Weather forecast system must start with observations and analysis of activity at the Sun
like Earth-directed Coronal Mass Ejections (CMEs).
With a delay of 1 – 3 days such ejecta could be observed at satellites like ACE or WIND near the
L1 position. A CME detected here will reach the Earth within around 20 to 60 min. Depending
particularly on the magnetic properties in the CME cloud, preliminary forecasts could be issued.
With a delay of around 15 min, the effects from a solar wind change at the front of the
Magnetosphere will reach the Polar Cap ionosphere and modify the convection-related current
systems thereby changing the magnetic variations from which the PC indices are derived.
The PC index level, preferably comprising both PCN and PCS index values, should be monitored.
Solar wind enhancement will cause increases in the PC indices within 15 min after impinging on
the Magnetosphere. Enhanced PC index values provide early warning of substorm activity.
PC index values sustained at a level above 10 mV/m during more than 30 min indicate an
immediate risk for violent substorm activity, which could endanger power grids located in
the local night region .
In order to improve the reliability of a warning
system, PC index values should be derived with
a simplified algoritm omitting the determination of
the quiet level (QDC) (cf . Stauning, JGR 2013).
Furthermore, data from other than the standard
observatories could be monitored.
Thus, magnetic data from e.g. Resolute (RES) in
Canada, using special coefficients, provide PCN
index values close to those derived from Thule
data. Further potential locations for providing
data for a preliminary PCN index are ALE, EQA,
SVS, and KUV marked in the map.
ESWW13. P. Stauning