A COMPARISON BETWEEN COMPUTER DERIVED (FMI METHOD) AND HAND SCALED K INDICES AT PORT AUX FRANCAIS AND PORT ALFRED FRENCH OBSERVATORIES

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1 A COMPARISON BETWEEN COMPUTER DERIVED (FMI METHOD) AND HAND SCALED K INDICES AT PORT AUX FRANCAIS AND PORT ALFRED FRENCH OBSERVATORIES M. BITTERLY 1, M. MENVIELLE 2,4, J. BITTERLY 1 and A. BERTHELIER 3,4 1 E.O.P.G., 5 rue René Descartes, F STRASBOURG CEDEX, FRANCE 2 Equipe de Physique de la Terre et des Planètes (URA CNRS 1369), Bat Université Paris Sud, F ORSAY CEDEX, FRANCE 3 C.E.T.P., 4 Avenue de Neptune, F SAINT MAUR DES FOSSES CEDEX, FRANCE 4 International Service of Geomagnetic Indices, c/o C.E.T.P., SAINT MAUR, FRANCE The algorithms developed for computer derivation of K indices have been extensively tested under the responsability of the IAGA Working Group V-5, `Geophysical indices'. The comparison of computer derived K indices with a one month long reference data set of K indices hand-scaled strictly following the Bartels-Mayaud rules showed that the FMI method follows very satisfactorily the Bartels-Mayaud rules. We present here study of the K indices derived with the FMI method for on a one year sample ( ) at the Kerguelen and Crozet magnetic observatories. We computed K indices with the FMI method using digital recordings available for the same period (minute values), and compared them with reference K indices scaled during the visit of P.N. Mayaud at the observatories of the am network. The comparison between hand-scaled and computer derived K indices for this one year sample at two observatories confirm the results obtained with the one month reference sample: about 70% of indices are in agreement, less than 1% differ by more than one unit, and a fairly negligeable LT effect (less than +/-8%) are observed. A K effect is also observed. It is fairly negligeable, except for the 3-hour intervals corresponding to hand-scaled K equal to 0 (less than 45% of indices in agreement in that case). 1. INTRODUCTION The question of the derivation of geomagnetic indices from digital data arose with the apparition of digital magnetometers at the end of the seventies. It became a key question at the end of the eighties (Menvielle, 1990; Coles and Menvielle, 1991), when the increasing performances of telecommunication facilities (file transfer) and the use of automated stations and satellite links [e.g. INTERMAGNET (Coles et al., 1990)] made possible a real time dissemination of data from a planetary network of digital observatories. According to the I.A.G.A. regulations, the K indices are to be hand-scaled from analog magnetograms. In the case of digital observatories, it implies the production of computer plots of digital data with scale values similar to those of photographic magnetograms (about 2 cm/h and 5 nt/mm). K hand-scaling thus induces delays and K indices are generally circulated some weeks after the end of the month. Computation and circulation of IAGA K- derived indices within a short time delay clearly require computer derivation of K indices. A lot of algorithms that claim to derive K indices from digital data have been proposed for several years now (e.g. Van Wijk and Nagtegaal, 1977; Riddick and Stuart, 1984; Hopgood, 1986; Walker, 1987; Wilson, 1987; Jankowski et al., 1988; Hattingh et al., 1989; Golovkov et al., 1989; Pirjola et al., 1990). In order to compare the proposed algorithms for computer derivation of K indices and decide which of them were suitable, a test was organized by the IAGA Working Group `Geophysical Indices. The test was made with a common data set consisting in hand-scaled K indices and digital minute values provided by a selected network of observatories for a one year

2 period (March February 1986). Four methods were thus accredited, and recommended by the Working Group during the Vienna IUGG General Assembly, in The results of this test are summarized in a short report which appeared in IAGA News (IAGA News N 32, p.27, 1993), and extensively presented in Menvielle et al. (1995). Menvielle et al. (1995) also compared the computer produced K indices to a reference set of hand-scaled K indices (one month at three observatories). They showed that only two accredited methods [the FMI method (Pirjola et al., 1990; Sucksdorff et al., 1991) and the ASm method (Jankowski et al., 1988; Nowozynski et al., 1991)] provide computer produced K indices in good agreement with reference hand-scaled K indices. In particular, the K indices computer produced with the FMI method and the reference hand-scaled K indices were found to be equal in about 80% of the cases, and to differ by more than one unit in less than 0.2% of the cases. Furthermore, a fairly negligeable LT effect (+/-5%), and a small K effect (+/-8%) were evidenced in the computer produced indices. The reference set of hand-scaled indices used by Menvielle et al. (1995) was fairly small, and the results established by these authors should be confirmed by further studies on other data sets from observatories representing different areas of the world. We present here a comparison between reference hand-scaled and computer produced (FMI method) K indices for a one year data set at two observatories located in the Indian Ocean. The data we used for this test are described in section 2, and the FMI method for computer derivation of K indices is presented in section 3. The results we obtained are presented and discussed in section THE DATA A quantitative estimate of the performances of an algorithm for computer derivation of K indices requires to have K hand-scaled on classical analog magnetograms by a well trained observer at stations where high quality digital data are available for the same period. It is the case for the French Port-aux-Français (PAF, Kerguelen Islands) and Port Alfred (CZT, Crozet Archipelago) subantarctic observatories, where these data are available for the one year period July June The geographic and geomagnetic coordinates of these two observatories are given in Table 1. TABLE 1 Geographic Geomagnetic PAF S E -57,3 131,7 CZT S E -51,5-111,9 Geographic and geomagnetic coordinates of the Port-aux-Français (PAF) and Port Alfred (CZT) observatories. 2.1 The reference K indices At the end of the seventies, P.N. Mayaud visited the observatories of the am network. During this visit, K indices for a one year period (July 1976 to June 1977) were carefully scaled at each observatory by P.N. Mayaud and the observer in charge of the station (Mayaud and Menvielle, 1980). The K indices were scaled on classical analog magnetograms, even at observatories where digital recordings were already available. The resulting data set is in fact a reference K data set well suited for systematic studies on K and K-derived planetary indices. We therefore digitized the K hand-scaled during the Mayaud s visit. We used this data set in the present evaluation of K indices computer produced with the FMI method. 2.2 The digital data Digital recording of magnetic data started as early as 1972 at the French subantarctic observatories. Continuous recording of variations in the Earth s magnetic field was routinely carried out at these observatories from that time. The equipment consists in a triaxial variometer and a proton precession magnetometer, with digital recording of sampled minute values. The triaxial fluxgate magnetometer is a VFO 31, developed in collaboration with Thomson Cintra D.A.S.M. Corporation. Its functioning and performances are extensively described in Bitterly et al. (1988). Let us only recall here that it is a parallel type sensor with two saturated mu-metal core, with a resolution of 0.1 nt, a noise of 0.1 nt peak-peak from DC to 0.5 Hz, and a long term stability on the order of 1 nt per month. The performances of the VFO 31 variometer are comparable with those of other fluxgate recently developed. The comparison between K indices derived by computer from the digital recordings and those hand-scaled

3 from analog magnetogram during the Mayaud s visit will therefore provide a relevant characterization of computer produced K indices. We used this data set to characterize the performances of the FMI method. 3. The FMI Method The K indices are computed in two steps. The S R variations in the two horizontal components of the magnetic field are first estimated. They are then removed from the observed variations, and the K indices are deduced from the 3-hour ranges on the residuals. The S R curves are computed on 24 hours long time windows corresponding to the LT days. For each component, the 24 points used in the production of the S R -curve are the means of all data points inside a UT hour and m+n minutes on both sides of the hour. The mean is thus the same as the middle point of a line fitted to the values in question. m depends on the local time, and n depends on the magnetic activity (n=k 3.3 minutes, where K is a preliminary value). The method has two steps. In the first step, the preliminary K values used for the calculation of n are simply determined from differences maximum minus minimum. The S R curve is then produced by performing a 5 th degree harmonic fit to the means described above. In the second step, the K values produced in the first step are used to determine n, and the final S R curve is then produced by performing a 5 th degree harmonic fit to the middle point of each window centered on LT hours. The program is exactly the same for all observatories. 4. THE RESULTS Let us call K(HS) the hand-scaled K indices, and K(FMI) the K indices computer produced with the FMI method. In order to characterize the results obtained with the FMI method, we first compared the K(HS) and K(FMI) distributions for the one year period. We then studied the distribution of the differences DK = K(FMI) - K(HS) between computer derived and hand-scaled K indices, for the whole year and for each season separately. 4.1 Study of the global distribution Figure 1 shows the observed K(FMI) and K(HS) distributions At the two stations, they are both single peaked, with a maximum observed at K=1. Significant differences are however observed at each station between the K(FMI) and K(HS) distributions. Taking the K(HS) distribution as a reference distribution, it thus appears that the FMI method overestimates the number of K=1 and tends to compensate in underestimating the number of K=2 and K=3 at Port-aux-Français while, on the contrary, it underestimates the number of K=0, and tends to compensate in overestimating the number of K=1 and K=2 at Port Alfred. There is therefore a systematic bias in the K indices computer produced with the FMI method, but this bias is not the same at the two stations. Figure 1 also presents the distributions of the differences DK = K(FMI) - K(HS) between computer derived and hand-scaled K indices. Consider first the whole data set. The distributions observed at Port-aux-Français and Port Alfred have almost the same percentage of differences equal to 0 (69% at Port-aux- Français, and 68% at Port Alfred), and a very low percentage of differences equal to ±2 (less than 1% at each stations). These results are consistent with those observed by Menvielle and al. (1995) for their reference data set. However, the observed differences have not the same distribution at Port Alfred and at Port-aux- Français: that observed at Port Alfred is almost symmetric while that observed at Port-aux- Français is very disymmetric, with a number of differences equal to -1 (19%) almost twice as large as that of the differences equal to +1 (11%). The percentage of differences equal to 0 slightly varies with the season at the two stations (between 63% and 72% at Port-aux-Français, and between 64% and 73% at Port Alfred). On the contrary, the ratio between the percentages of differences equal to +1 and -1 (which determine the symmetric character of the distribution) significantly depends on the season. It varies between 0.18 (equinox) and 0.75 (summer) at Port-aux-Français, and between 0.90 (winter) and 2.06 (summer) at Port Alfred. There is therefore a clear seasonal effect in the K values determined with the FMI method, Following Menvielle et al. (1995) and taking the number of differences equal to 0 and greater than 1 as key parameters in the evaluation of the the global performance of the FMI method, this effect remains however

4 acceptable. On the other hand, this effect is not the same at the two stations, that gives further evidence that the bias introduced by the FMI method depends on the station. 4.2 Hand-scaled K value dependance Figures 2 and 3 present the dependance of the differences DK with hand-scaled K values. They clearly show that the agreement between computer derived and hand-scaled indices depends on the K value. Consider first the whole data set. The percentage of differences equal to 0 is dramatically low for K(HS) equal to 0, in particular at Port Alfred where it is on the order of 55%. On the contrary, it is rather high and remains fairly constant (68% ± 5% at Port-aux- Français, and 74% ± 7% at Port Alfred) for K(HS) greater than 0. Another feature worth noticing is the dependance on the K value of the symmetry of the distribution of the differences DK, in particular at Port Alfred. These effects are present for each season with a similar pattern. The percentage of differences equal to 0 varies with the season, but, for a given season, it does not significantly depends on K(HS) for K(HS) greater than 0. On the contrary, the number of differences equal to 0 is very low for K(HS) equal to 0, and it varies dramatically with the season. It is minimum in summer during which it becomes as low as 47% at Port-aux-Français and 33% at Port Alfred, and maximum in winter (76% at Portaux-Français, and 71% at Port Alfred). These results demonstrate a clear effect of the level of the activity on the K(FMI) determination. The K values corresponding to disturbed 3-hour intervals tends to be underestimated. The comparison between the S R curves and the magnetograms clearly show that this results from a contamination of the S R curve by long period variations in the irregular activity which are not completely filtered out. On the contrary, the K values corresponding to very quiet 3-hour intervals are overestimated by the FMI method. That might indicate a significant discrepancy between the S R definition used by Mayaud for hand-scaling, and that adopted by the FMI method. In particular, the frequency cut-off used in the FMI method may lead to disregarding some short period variations which might have been taken as S R variations by Mayaud. This question deserves further considerations. 4.3 UT dependance Figures 2 and 3 also present the dependance of the differences DK with the UT 3-hour interval. The percentage of differences equal to 0 varies with the UT interval, between 60% and 78% at Port-aux-Français and between 60% and 75% at Port Alfred. There is a clear UT effect in the K(FMI) determination at the two stations. The evolution with the UT 3-hour interval of the observed DK distribution is similar at the two stations. The percentages of differences equal to 0 are minimum during the 03-06, 06-09, and UT intervals, and maximum during the last four 3-hour intervals of the UT day. Given the longitudes of the two stations (see Table 1), the UT interval is roughly centered in both cases on the local noon. The number of differences equal to 0 is thus more important during the period of the day characterized by fairly slow variations in the S R intensity. This UT effect is present during the three seasons. It is more important in summer and less important in winter, that strongly suggests that the bias in the S R estimate tends to increase with increasing S R intensity. The observed UT effect demonstrates that rapid changes the S R intensity might not be correctly accounted for by the FMI method. The comparison between the S R curves and the magnetograms clearly show that the FMI method always provides good S R determinations during very quiet days. The observed UT effect therefore results from erroneous discrimination between rapid variations in the S R intensity and irregular activity. 5. CONCLUSION The results of the present study can be summarized as follows: - the K(FMI) and K(HS) values are equal for about 70% of the 3-hour intervals at each station (68% and 69% respectively), and they differ by more than one unit for less than 1% of the 3-hour intervals; - the ratio between the percentages of differences equal to +1 and -1 (which determine the symmetric character of the distribution of the differences) significantly depends on the season; - the percentage of 3-hour intervals for which K(FMI) = K(HS) is rather high and remains fairly constant (68% ± 5% at Port-aux-Français, and 74% ± 7% at Port Alfred) for hand-scaled K

5 greater than 0. On the contrary, it is dramatically low for hand-scaled K equal to 0, in particular at Port Alfred where it is on the order of 55%; - the percentage of 3-hour intervals for which K(FMI) = K(HS) has fairly negligeable variations with the season (about ± 5%) for hand-scaled K different from 0. On the contrary, it significantly varies with the season for handscaled K equal to 0 (between 47% and 76% at Port-aux-Français, and between 33% and 71% at Port Alfred); - the percentage of 3-hour intervals for which K(FMI) = K(HS) varies with the UT interval. It is minimum (about 60% at each station) around LT noon, and maximum (78% at Port-aux- Français and 75% at Port Alfred) around LT midnight. These results are in good agreement with those obtained by Menvielle et al. (1995) on their reference data set. They confirm that although it does not provide K determinations that are as good as those hand-scaled by real specialists, the FMI method follows the Mayaud rules better than the observers at many observatories [see for instance the results obtained by Mayaud and Menvielle (1980) or Menvielle et al. (1995) with hand-scalings made at the observatories]. The distribution of the differences between the hand-scaled K values and those computed with the FMI method depends on the station This gives further evidence that the FMI method is good enough for the continuation of the long tradition of producing K-indices and K-derived planetary magnetic indices without any serious jump in the statistics. The results of this study also confirm the existence of a significant discrepancy between the hand-scaled K values and those computed with the FMI method during very quiet 3-hour intervals. It is in particular the case at Port Alfred, where the percentage of K=0 values in the indices computed with the FMI method is actually significantly lower than that observed in the hand-scaled K indices. This difference can be accounted for neither by the systematic bias introduced in the computer produced indices by the 60 seconds sampling rate (Niblett et al. 1984), nor by the uncertainties in the K determination for the very quiet 3-hour intervals. Our results therefore gives further evidence for the existence of a systematic difference between the S R definition used by Mayaud for hand-scaling, and that adopted by the designers of the FMI method. REFERENCES Bitterly, J., Cantin, J.M., Burdin, J., Schlich, R., Folques, J. and Gilbert, D., Digital recording of variations in the Earth's magnetic field in French observatories: description of equipment and results for the period , in Proceedings of the international workshop on magnetic observatory instruments, Coles, R.L. editor, 59-66, Geomagnetic series N 32, Geological Survey of Canada, Ottawa. Coles, R., Green, A.W., Le Mouël, J.L. and Stuart, W.F., Intermagnet, in Proceedings of International Workshop on Observatory Data Acquisition and Processing, Kauristie, K., Sucksdorff, C. and Nevanlinna, H. editors, , Geophysical Publications N 15, Finnish Meteorological Institute, Helsinki. Coles, R. and Menvielle, M., Some thoughts concerning new digital magnetic indices, Geophysical Transactions, 36, Golovkov, V.P., Papitashvili, V.O. and Papitashvili, N.E., Calculations of K-index using the Method of Natural Orthogonal Components, Geomagn. Aeron., 29, Hattingh, M., Loubser, L. and Nagtegaal, D., Computer K-index estimation by a new linear-phase, robust, non-linear smoothing method, Geophys. J. Int., 99, Hopgood, P.A., On the computer generation of geomagnetic K-indices from digital data, J. Geomagn. Geoelectr., 38, Jankowski, J.A., Ernst, T., Sucksdorff, C., Pirjola, R. and Ryno, J., Experiences of a filter method and a standard curve method for determining K-indices, Annales Geophysicae, 6, Mayaud, P.N. and Menvielle, M., A report on Km observatories visit, IAGA Bulletin N 32i, Menvielle, M., About the derivation of geomagnetic indices from digital data, in Proceedings of International Workshop on Observatory Data Acquisition and Processing, Kauristie, K., Sucksdorff, C. and Nevanlinna, H. editors, , Geophysical Publications N 15, Finnish Meteorological Institute, Helsinki. Menvielle, M., Papitashvili, N.E., Häkkinen, L. and Sucksdorff, C., Computer production of K indices: review and comparison of methods, Geophys. J. Int., 123, in press.

6 Niblett, E.R., Loomer, E.I., Coles, R. and Jansen Van Beek, G., Derivation of K- indices using magnetograms constructed from digital data, Geophysical Surveys, 6, Nowozynski, K., Ernst, T. and Jankowski, J.A., Adaptive smoothing method for computer derivation of K-indices, Geophys. J. Int., 104, Pirjola, R., Ryno, J. and Sucksdorff, C., Computer production of K-indices by a simple method based on linear elimination, in Proceedings of International Workshop on Observatory Data Acquisition and Processing, Kauristie, K., Sucksdorff, C. and Nevanlinna, H. editors, , Geophysical Publications N 15, Finnish Meteorological Institute, Helsinki. Riddick, J.C. and Stuart, W.F., The generation of K-indices from digitally recorded magnetic data, Geophysical Surveys, 6, Sucksdorff, C., Pirjola, R. and Häkkinen, L., Computer production of K-values based on linear elimination, Geophysical Transactions, 36, Van Wijk, A.M. and Nagtegaal, D., K measurements by computer, J. Atmos. Terr. Phys., 39, Walker, J.K., Adaptive separation of regular and irregular magnetic activity for K indices, J. Atmos. Terr. Phys., 49, Wilson, L.R., An evaluation of digitally derived K-indices, J. Geomagn. Geoelectr., 39,

7 Figure 1 Observed distributions of the hand-scaled, K(HS), and computer produced, K(FMI), K values, and of the differences K(FMI) - K(HS) at Port Alfred (top) and Port-aux-Français (bottom). Annual: July 1976 to June 1977; summer: November 1976 to February 1977; equinox: September-October 1976 and March-April 1977; winter: July-August 1976 and May-June 1977.

8 Figure 2 Observed distributions of the differences K(FMI) - K(HS) with hand-scaled K values (left) and UT intervals (right) at Port-aux-Français. Note that in each vertical bar the differences are arranged from top to bottom according to increasing values. Annual: July 1976 to June 1977; summer: November 1976 to February 1977; equinox: September-October 1976 and March-April 1977; winter: July-August 1976 and May-June 1977.

9 Figure 3 Observed distributions of the differences K(FMI) - K(HS) with hand-scaled K values (left) and UT intervals (right) at Port Alfred. Note that in each vertical bar the differences are arranged from top to bottom according to increasing values. Annual: July 1976 to June 1977; summer: November 1976 to February 1977; equinox: September-October 1976 and March-April 1977; winter: July-August 1976 and May-June 1977.