Comparison of Polar Cap (PC) index calculations. P. Stauning Danish Meteorological Institute ( Abstract. The Polar Cap (PC) index introduced by Troshichev and Andrezen (1985) is derived from polar magnetic variations and is mainly a measure of the intensity of the transpolar ionospheric currents. These currents relate to the polar cap antisunward ionospheric plasma convection driven by the dawn-dusk electric field, which in turn is generated by the interaction of the solar wind with the Earth's magnetosphere. Coefficients to calculate PCN and PCS index values from polar magnetic variations recorded at Thule and Vostok, respectively, have been derived by several different procedures in the past. The first published set of coefficients for Thule was derived by Vennerstrøm, 1991 and is still in use for calculations of PCN index values by DTU Space. Errors in the program used to calculate index values were corrected in 1999 and again in In 2005 DMI adopted a unified procedure proposed by Troshichev for calculations of the PCN index. Thus there exists 4 different series of PCN index values. Similarly, at AARI three different sets of coefficients have been used to calculate PCS indices in the past. The presentation discusses the principal differences between the various PC index procedures and provides comparisons between coefficient and index values derived using the different procedures. Examples from published papers are examined to illustrate the differences. 1. Basics. A high degree of correlation exists between polar cap horizontal magnetic field variations ΔF and the ”Geo-effective” (or “merging”) Electric Field, E m, that controls the global energy input from the Solar wind to the Earth’s Magnetosphere (Kan and Lee, 1979): E m = V SW B T sin 2 (  /2)(1) B T = (B Y 2 + B Z 2 ) 1/2 : IMF transverse magnetic field component  = arctan(B Y /B Z ) : IMF polar angle with respect to the GSM Z-axis We may increase the correlation by projecting ΔF to an “optimum” direction in a polar cap coordinate system fixed with respect to the Sun-Earth direction (the X-axis in the GSM system). The optimum direction is characterized by the angle, φ, between the equivalent horizontal transverse current and the direction to the Sun and varies with local time and season. Now ΔF PROJ is a scalar quantity. A further increase in the correlation is obtained by displacing the projected horizontal variation by an amount, β (intercept), which also varies with local time and season. Hence we are looking for the correlation between the modified polar cap horizontal magnetic field variations ΔF* and the Solar Wind ”Geo-effective Electric Field” E m of the form: ΔF* = ΔF PROJ – β = α E m (2) where β (e.g. in units of nT) is the baseline shift (“intercept”), while the proportionality constant α is the “slope” (e.g. in units of nT/(mV/m)). The parameters are calculated on a statistical basis from cases of measured values through an extended epoch. From equivalence with Em the dimensionless Polar Cap Index PC is defined by: PC == (ΔF PROJ – β)/α(3) The PC index is a measure of the polar geomagnetic activity but also a proxy for the geo-effective electric field E m measured in mV/m Comparison of reported values of PCN (DMI#2) and PCS (Lukianova) from Lee, Lyons and Yumoto, JGR, 2004, (Fig.5a) with PCN and PCS based on the unified procedure and geo-effective electric field based on IMP8 and ACE satellite data (Fig.5b below). Note the large differences between PCN (lower grey line) and PCS (black line) in the upper diagram, (Lee et al., 2004]. Unified indices and electric field are shown in the diagram Fig.5b below for the same time interval. Comparisons through of yearly averages of PCN and PCS calculated by DMI#4 procedure, and the ”geo-effective” (or ”merging”) electric field based on IMP8 and ACE satellite data are shown below. There are good agreement between the data sets Comparison of PCN (DMI#2) and PCS (Lukianova). Note again the large differences between PCN (grey line) up to ~10 and PCS (black line) up to ~35 in the diagram (note different scales). (from Lee et al., 2004). 3. PC indices used in publications in the past. PC indices have been issued in different versions. For the same magnetic data the calculated index values are often quite different depending on the supplier. Here is a list of PC index procedures, their data bases and software, and their availability. 1. AARI#1: PCS index based on Vostok data. (i). Published description: Troshichev et al., (ii) Programmer: V. G. Andrezen (iii) Data base and software for coefficients: Not available (iv) PC index values: Available in WDC-B2 report. Possibly available AARI. 2. AARI#2: PCS index based on Vostok data. (i) Published description: Not available (ii) Programmer: R. Yu. Lukianova (iii) Data base for coefficients: 1992, 1995, Available (iv) PC index values: 1992, 1995, Available. (v) Comment: PCN and PCS values are very different 3. AARI#3: PCS and PCN indices based on Vostok and Thule data (i) Published description: Troshichev et al., 2006 (Unified PC indices) (ii) Programmer: A. Janzhura (iii) Data base and software for coefficients: Available. (iv) PCS index values: calculated for Supplied on request. (v) Comment: PCN and PCS values are similar 4. Lukianova: PCS and PCN indices based on Vostok and Thule data (i) Published description: Not available (ii) Programmer: R. Yu. Lukianova (iii) Data base and software for coefficients: Not available (iv) PC index values: were supplied on request (v) Comment: PCN and PCS values are very different. 5. DMI#1: PCN indices based on Thule data (i) Published description: Vennerstrøm, 1991; Vennerstrøm et al., 1991 (ii) Programmer: S. Vennerstrøm (iii) Data base and software for coefficients: Not available (iv) PCN index values: calculated for Available in WDC-A- report. (Report UAG-103) (v) Comment: Principal error in coefficient calculations. Software error corrected in Previously issued PCN data are incorrect. 6. DMI#2 = DTU-S#1: PCN indices based on Thule data (i) Published description: Vennerstrøm, 1991; Vennerstrøm et al., (ii) Programmers: V. O. Papitashvili and O. Rasmussen based on S. Vennerstrøm’s software. Now: Jürgen Matzka, DTU-Space (iii) Data base and software for coefficients: (same as above). Not available. (iv) PC index values: re-calculated for Available from DTU- Space (v) Comments: Software error corrected in Previously issued PCN data incorrect. Principal error in coefficient calculations not corrected. 7. DMI#3: PCN indices based on Thule data (i) Published description: Papitashvili et al., 2001 (DMI report 01-01) (ii) Programmers: V. O. Papitashvili and O. Rasmussen based on S. Vennerstrøms software (iii) Data base and software for coefficients: Not available (iv) PC index values: calculated for Not available (v) Comment: Coefficient tables for PCN index values were derived yearly through for analyses of solar cycle effects. (vi) Use in publications: DMI Report DMI# 4: PCN indices based on Thule data (i) Published description: Troshichev et al., 2006 (Unified PC indices); Stauning et al., (ii) Programmer: P. Stauning (iii) Data base and software for coefficients: Available. (iv) PC index values: Available on request. (v) Comment: The extended data base for calculation of coefficients, small differences in QDC calculations and handling of reverse convection give some deviations from values calculated by AARI (cf. above #3 ). 7. Examples of similar and different PC indices Conclusions. It is highly desirable to reach agreement on the procedures used to calculate PCN and PCS index values. It is evident that the situation was particularly bad before the attempt to unify the procedures by Troshichev et al., (2006). With the unified procedure (subtraction of QDC) the results from the different calculations by AARI#3 and DMI#4 procedures match much better. There are still a few details to be finalized like the precise handling of the magnetic recordings with respect to baseline, QDC calculations, solar wind sector structure, and, in particular, reverse convection cases. The calculation of coefficients for the DTUS#1 (DMI#2) procedure has a principal error (Stauning, JASTP, 2011) and DTU-S#1 PCN indices should be discarded. All numerical relations between Polar Cap voltage, Joule heating, Auroral Power, etc. and PCN or PCS published prior to 2005 should be discarded. 5. PC index coefficients at AARI, DTUS and DMI The calculations of PC index series during gave quite different results for PCN values calculated by DMI#2 (DTUS#1) and PCS calculated by AARI#2 procedures. An example is shown in Fig.2 to the right. PCS is generally much larger than PCN. DMI and AARI have since 2005 modified their procedures and developed the ”Unified PC index” concept. The PC indices derived by the AARI#3 and DMI#4 procedures agree much better. They give nearly the same values when used on data from the same hemisphere (Fig.3a). Used on separate hemispheres (Fig.3b) they give closely symmetrical values. The reason for the ”horns” in the lower part of the diagram is the preferred occurrence of negative PC index values around local noon in the local summer season. 2. Definition of magnetic variation vector. In the calculation of magnetic variations, three variants have developed to derive the magnetic variation vector, ΔF, from the observed magnetic data, F OBS, which could be described by the following defining equations: ΔF = F OBS - F BL ….. DTUS#1 (formerly DMI#2)(4a) ΔF = (F OBS - F BL ) - F QDC.…..DMI#4(4b) ΔF = (F OBS – F BL - ΔF Y ) - F QDC..... AARI#4 (4c) In these expressions F BL is the slowly (secularly) varying baseline vector for the day in question; F QDC is the quiet day (QDC) variation vector for the time in question; ΔF Y is an IMF By-related (solar wind sector dependent) correction vector for the day in question. F BL and ΔF Y could be combined. In the DMI#4 method the IMF By-related (solar wind sector related) contribution is included in the calculation of the QDC vector. In the AARI#3 version the QDC is found by averaged over an interval much longer than the sector structure and the IMF By-related contribution is calculated separately. The different ways to calculate magnetic variations is not the only difference between the three current PC index variants (AARI#3, DTUS#1, and DMI#4). In the DTUS#1 version there is a fundamental error in the calculation of coefficients. Furthermore, the DTUS#1 (DMI#2) and the AARI#3 versions include reverse convection cases in the calculation of coefficients, which is why the intercept values tend to become strongly negative during local summer days (see Fig.1c). The DMI#4 version excludes reverse convection cases in the calculation of coefficients (not in the calculation of PC index values). The coefficients: optimum angle, slope, and intercept values derived for PCN in the three versions are displayed below. Each monthly segment (1/12 of the diagram width) displays the monthly averaged daily variation in the selected parameter. 5. PC index calculations at AARI and DMI Fig.1 a Fig.1 b Fig.1 c Fig.2 Fig.3a b Fig.4 Fig.5a Fig.5b Fig.6