P. Stauning: The Polar Cap (PC) Index for Space Weather Forecasts 1/5 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. Sketches of polar and auroral current systems 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.

Basics of the PC index. 2/5 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.

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

PCN index in Space Weather forecasts 4/5 PCN index in Space Weather forecasts 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

The use of PC indices in Space Weather Forecast Systems 5/5 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.