MAGNETIC POTENTIAL PLOTS OVER THE NORTHERN HEMISPHERE FOR 26-28 MARCH 1976 April 1979 World Data Center A consists of the Coordination Office and seven Subcenters: World Data Center A Coordination Office National Academy of Sciences 2101 Constitution Avenue, N.W. 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World Data Centers conduct international exchange of geophysical observations in accordance with the principles set forth by the International Council of Scientific Unions. WDC-A is established in the United States under the auspices of the National Academy of Sciences. 2. Communications regarding data interchange matters in general and World Data Center A as a whole should be addressed to: World Data Center A, Coordination Office (see address above). 3. Inquiries and communications concerning data in specific disciplines should be addressed to the appropriate subcenter listed above. # TABLE OF CONTENTS | PART 1 | |--------| | I. Introduction | 1 | | II. Data Processing | 1 | | III. Derived Parameters | 1 | | IV. Acknowledgments | 4 | | V. References | 4 | | VI. Appendix | 5 | | PART 2 | |--------| | The 10-Minute Plots for 26 - 28 March 1976 | 7 | MAGNETIC POTENTIAL PLOTS OVER THE NORTHERN HEMISPHERE FOR 26-28 MARCH 1976 by A. D. Richmond¹, H. W. Kroehl², M. A. Henning³, and Y. Kamide⁴ National Geophysical and Solar-Terrestrial Data Center NOAA, Boulder, CO 80303 PART I I. Introduction The magnetic storm of 26-28 March 1976 has been the subject of considerable scientific interest, being part of a Retrospective World Interval, a Study of Traveling Interplanetary Phenomena Interval II and a Special International Magnetospheric Study Interval [e.g., Coffey and McKinnon, 1977]. This report presents contour maps of magnetic potential variations over the Northern Hemisphere at 10-min intervals between 0000 UT, 26 March and 0550 UT, 28 March 1978 as an aid to further study of this event. These are excerpts from a larger data set, with plots every minute, which were used to make a data moving picture. An analysis of these maps for several magnetic substorms occurring during this period is presented in Kroehl and Richmond [1979]. A geomagnetic variation field $B$ at ground level can be described as the negative gradient of a scalar magnetic potential $V$, if the magnetic effects of electrical currents within the lower atmosphere are negligible. The magnetic potential is closely related to the so-called "equivalent" ionospheric current often discussed in the literature. For many purposes, it is sufficient to make the approximation that 1 T-m of magnetic potential variation at ground level represents $10^6$ A of equivalent overhead current, a relation that takes into account the contribution of induced earth currents to $B$. For example, if the magnetic potential is increasing toward the north at the rate of $10^{-6}$ Tesla-meters per meter (a 1,000-nT southward magnetic variation), the equivalent overhead ionospheric current is approximately 1 Ampere per meter toward the west. In reality the actual currents responsible for the ground-based magnetic variations are not confined to the ionosphere but extend far out into the magnetosphere. II. Data Processing The magnetic potentials are derived from observed magnetic variation data at the 52 observatories listed in Table 1 and shown in Figure 1. From the 1-min digitized H and D (or X and Y) magnetogram traces on 26-28 March 1976, the corresponding values on 25 March 1976 (a quiet day) are subtracted in an attempt to remove Sq effects. For intervals when data gaps or unusable data occur, the problem station or stations are excluded from the magnetic potential derivation. The computerized procedure used to obtain the potentials, as outlined by Kroehl and Richmond [1979], is reproduced in the Appendix. This procedure differs from one used by Kamide et al. [1976] in a report presenting magnetic potential maps for 8-9 November 1969. Because ring current effects are strong throughout most of the storm period, it is useful to remove these effects in order to reveal other features of the potential patterns more clearly. This is done as described in the Appendix. In this report we present maps of the total potential $V$ and the potential with symmetric ring current effects removed $V'$. III. Derived Parameters Several parameters have been extracted from the potential plots, and the time variations of some of these are shown in Figure 2. "Dst" is derived as explained in the Appendix. "Potential maximum (with Dst)" is the maximum value of $V$ in the northern geomagnetic hemisphere, while "potential maximum (without Dst)" is the maximum value of $V'$. "AU(13)" and "AL(13)" are defined in a similar manner to the standard AE indices, except that we have used our own digitizations of auroral-zone magnetic data in their derivations. Present Addresses: 1 Space Environment Laboratory, Environmental Research Laboratories, NOAA, Boulder, Colorado 2 Data Studies Division, NOAA/EDIS/NGSDC, Boulder, Colorado 3 Lockheed Missiles and Space Co., Aurora, Colorado 4 Kyoto Sangyo University, Kyoto, Japan | STATION | GEOMAG LAT | GEOMAG EAST LONG | |------------------|------------|------------------| | Thule | 89.0 | 3.6 | | Alert | 85.9 | 167.3 | | Resolute Bay | 83.1 | 290.2 | | Godhavn | 79.8 | 33.3 | | Mould Bay | 79.3 | 256.4 | | Cambridge | 77.4 | 290.0 | | New Alesund | 76.4 | 131.0 | | Baker Lake | 73.8 | 316.0 | | Heiss Island | 71.3 | 156.3 | | Narssarssuaq | 71.1 | 37.4 | | Leirvogur | 70.1 | 71.5 | | Yellowknife | 69.1 | 294.3 | | Fort Churchill | 68.7 | 323.5 | | Point Barrow | 68.6 | 241.6 | | Great Whale River| 66.6 | 348.1 | | Cape Chelyuskin | 66.3 | 176.7 | | Abisko | 65.9 | 115.3 | | College | 64.7 | 257.0 | | Dixon Island | 63.0 | 161.8 | | Meanook | 61.9 | 301.6 | | Tixie Bay | 60.5 | 191.7 | | St. Johns | 58.4 | 21.8 | | Ottawa | 56.8 | 352.1 | | Newport | 55.2 | 300.8 | | Wingst | 54.3 | 95.3 | | Dourbes | 51.9 | 88.2 | | Minsk | 51.4 | 111.0 | | Fredericksburg | 49.5 | 350.4 | | Boulder | 49.0 | 317.0 | | Furstenfeldbruck | 48.7 | 93.8 | | Sverdlovsk | 48.5 | 141.1 | | Tihany | 46.2 | 99.8 | | Logrono | 46.0 | 77.7 | | Petropavlosk | 44.8 | 219.3 | | Toledo | 43.8 | 75.1 | | Odessa | 43.6 | 111.5 | | Almeria | 40.5 | 75.8 | | Tucson | 40.5 | 312.7 | | Karanganda | 40.3 | 148.7 | | Tbilisi | 36.6 | 122.5 | | Memambetsu | 34.1 | 208.8 | | Vladivostock | 32.9 | 198.5 | | Tashkent | 32.3 | 144.4 | | San Juan | 29.6 | 3.6 | | Kakioka | 26.1 | 206.4 | | Honolulu | 21.2 | 267.0 | | M'Bour | 21.2 | 55.5 | | Kanoya | 20.6 | 198.5 | | Fuquene | 16.9 | 355.6 | | Bangui | 4.7 | 89.0 | | Guam | 4.0 | 213.4 | | Davao | -4.0 | 195.3 | Fig. 1. Station locations in geomagnetic latitude and geomagnetic local time (MLT) at 0000 UT. The geomagnetic prime meridian (0° geomagnetic longitude) is at 1920 MLT. Fig. 2. The geomagnetic history of 26-28 March 1976 is shown by indices of magnetic activity, i.e. "Dst", maximum values of V and V', "AU" and "AL". "Dst", "AU", and "AL" are comparable to the standard magnetic indices though they were derived from our techniques and data. Note that the 600-nT range of "AU" is plotted in the same vertical displacement as the 2,300-nT range of "AL". IV. Acknowledgments This work was done when two of us (A.D. Richmond and Y. Kamide) were guest workers at NGSDC/World Data Center A for Solar-Terrestrial Physics, and another (M.A. Henning) was a work-study employee. A.D. Richmond was supported in part by a Resident Research Associateship from the National Research Council. We wish to express our gratitude to P.R. Yotka for preparation of the data and to J.H. Allen and A.H. Shapley for their financial support and encouragement. V. References COFFEY, H. E. and J. A. MCKINNON, eds. 1977 Collected Data Reports for STIP Interval II, 20 March - 5 May 1976, World Data Center-A for Solar-Terrestrial Physics, Report UAG-61. KAMIDE, Y., H. W. KROEHL, M. KANAMITSU, J. H. ALLEN, and S.-I. AKASOFU 1976 Equivalent Ionospheric Current Representations by a New Method, Illustrated for 8-9 November 1969 Magnetic Disturbances, World Data Center-A for Solar-Terrestrial Physics, Report UAG-55. KROEHL, H. W., and A. D. RICHMOND 1979 Magnetic Substorm Characteristics Described by Magnetic Potential Maps for 26-28 March 1976, Space Sci. Rev., in press. VI. Appendix The magnetic variation potential $V$ at any given time is expressed as a spherical harmonic series as a function of geomagnetic colatitude $\theta$ and east longitude $\phi$: $$ V(\theta, \phi) = \sum_{m=0}^{12} \sum_{n} (a_n^m \cos m\phi + b_n^m \sin m\phi) P_n^m(\cos \theta) $$ (1) The values of $n$ to be included in this series are determined from the following considerations. First, the spacing of our stations permits resolution of features down to scales of a few hundred kilometers at some high-latitude locations. It is found that including values of $n$ up to 34 gives the desired resolution in the potential. Because this degree of spatial resolution is required only at colatitudes less than 30 degrees, and because the associated Legendre polynomials $P_n^m$ for $m > 12$ and $n < 35$ are insignificant at these colatitudes, it is unnecessary to include in the series values of $m$ greater than 12. Second, since our data are only from the northern hemisphere and since an infinite series including only terms with $(n-m)$ odd would form a complete set of orthonormal functions over one hemisphere, most of the terms for which $(n-m)$ is even are omitted from our series. The exception is when $n=m>0$, which terms are included in our series in order to allow magnetic potential contours to intersect the equator in our finite series representation. Because those coefficients $b_n^m$ with $m=0$ are indeterminate, we have in total 377 coefficients $a_n^m$ and $b_n^m$ to be determined in our series. Two fundamental criteria guided our selection of a principle from which to determine the 377 coefficients. First, the negative gradient of the potential should match up reasonably well to the observed magnetic variation vectors at each station. An exact fit could be required, but in practice is not necessary nor perhaps even desirable. Some data error should be allowed for; and, probably even more importantly, allowance should be made for the fact that an observation at a given station may be unduly influenced by a localized feature in the ionospheric currents and therefore may not accurately represent mean conditions over a spatial scale characteristic of inter-station distances, an implicit assumption of any global mapping procedure. Our second fundamental criterion is that the potential vary smoothly between stations. The principle we selected to determine the coefficients is the minimization of the following function $\Psi$ with respect to variations of the coefficients $a_n^m$ and $b_n^m$: $$ \Psi(V) = \sum_j \left[ \alpha_j \left( X_j - \frac{1}{R_E} \frac{\partial V}{\partial \theta} (\theta_j, \phi_j) \right)^2 + \beta_j \left( Y_j + \frac{1}{R_E \sin \theta} \frac{\partial V}{\partial \phi} (\theta_j, \phi_j) \right)^2 \right] $$ $$ + \frac{\Gamma}{2\pi R_E} \int_0^{\pi/2} \sin \theta \, d\theta \int_0^{2\pi} d\phi \, \Theta(\theta) \left\{ \frac{1}{\sin \theta} \frac{\partial}{\partial \theta} \left[ \sin \theta \frac{\partial V}{\partial \theta} \right] + \frac{1}{\sin^2 \theta} \frac{\partial^2 V}{\partial \phi^2} \right\}^2 $$ $$ + \frac{\gamma}{2\pi R_E} \int_0^{2\pi} d\phi \left[ \frac{\partial^2 V}{\partial \phi^2}(\pi/2, \phi) \right]^2 $$ (2) where $R_E$ is the radius of the earth (6371 km); $X_j$ and $Y_j$ are the observed geomagnetic north and east variations at the $j$th station; $\alpha_j$, $\beta_j$, $\Gamma$, and $\gamma$ are prechosen weighting factors, and $\Theta(\theta)$ is a latitudinal weighting function defined by $$ \Theta(\theta) = 1 - 12 \cos^6 \theta + 19.078125 \cos^8 \theta - 8.0625 \cos^{10} \theta $$ (3) The choice of weighting factors determines the relative importance of each of the constraints in (2). Because the measurement errors and spatial variability are generally much greater at high latitudes than at low latitudes, the weighting factors $\alpha_j$ and $\beta_j$ are chosen to increase with decreasing geomagnetic latitude, being generally 0.25 above 56 degrees, 0.5 at 50 - 56 degrees, 1.0 at 45 - 50 degrees, 2.0 at 40 - 45 degrees, and 4.0 below 40 degrees. At the magnetic equator (Davao) $\alpha_j$ is set equal to zero in order to avoid influencing the global pattern by the localized feature of the equatorial electrojet. The term in (2) containing $\Gamma$ is a weighted hemispherical integral of the hori- zontal Laplacian of $V$, which represents a measure of roughness of the potential. The weighting function $\Theta$ is small at high latitudes and large at low latitudes, so that this constraint for $V$ to be smooth operates more strongly at low latitudes, where spatial structure is expected to be much smoother than at high latitudes. The resultant potential patterns are found to be fairly insensitive to the choice of $\Gamma$; a value of 2.0 is used. Finally, initial computations with $\gamma = 0$ often yielded unrealistic wavy patterns around the equator. This can occur because certain types of structure are not suppressed by the constraint on the Laplacian (for example, functions like $\tan^m(\theta/2)\cos(m\theta)$ have a zero Laplacian in the northern hemisphere, but their importance increases with $\theta$). This structure is suppressed by constraining potential contours to tend not to cross the equator, accomplished by use of a non-zero value (4.0) for $\gamma$. In order to solve for $V$, partial derivatives of $\Psi(V)$ with respect to each of the $a_n^m$ and $b_n^m$ are set equal to zero, yielding 377 linear equations with 377 unknowns. An iterative procedure is used to solve for the coefficients. After $V$ is determined, the computed magnetic variation components at each station are compared with the observed values. Typically, the root-mean-square difference for all stations is about 8% of the root-mean-square observed variation. However, at certain times the average discrepancy rises to as much as 20%. An important practical advantage of comparing the computed and observed variations at each station is that it permits us to locate easily bad data sets, for which the fit is consistently poor. We define the ring current component of the potential as $$V_{rc}(\theta) = Dst R_E \cos \theta$$ (4) in which $Dst$ is chosen such that $V_{rc}$ at 60 degrees colatitude equals the average value of $V$ around the 60 degrees colatitude circle. (Note that both $V_{rc}$ and the average value of $V$ around the equator are zero). The magnetic variation potential with longitudinally symmetric ring current effects removed $V'$ is then defined simply as $$V'(\theta,\phi) = V(\theta,\phi) - V_{rc}(\theta)$$ (5) PART 2 The 10-Minute Plots for 26-28 March 1976 Two magnetic potential contour plots for the northern geomagnetic hemisphere are presented for each time. On the left is shown the total potential $V$ and on the right is shown the potential $V'$ which has symmetric ring current effects removed. Coordinates are geomagnetic latitude and geomagnetic local time. At 0440 UT the geomagnetic prime meridian extends straight down from the pole; for any later (earlier) time the contours are rotated clockwise (counterclockwise) by 2.5 degrees per 10 minutes. Thus geomagnetic local midnight is always at the bottom of the plot. The contour interval is 0.1 T·m corresponding to approximately $10^5$ Amperes of equivalent overhead current. Station locations are indicated by small crosses. The positions of the maximum and minimum potentials are shown by a plus and minus sign, respectively. To the left are shown the AU and AL indices (whose difference gives the AE index) for a 24-hour period, with time increasing downwards. The horizontal bar across the middle of the AE plot marks the time of the contour plot to the right. UAG Series of Reports UAG Reports are issued on an irregular basis, with 6 to 12 reports being issued each year. Subscriptions may be ordered through the National Geophysical and Solar-Terrestrial Data Center, Environmental Data and Information Service, NOAA, Boulder, CO 80303, USA. The annual subscription price is $25.20 ($17.30 additional for foreign mailing). In years when the single price copies are less than $25.20, arrangements will be made to extend the subscription duration. Single issues are also available at the prices shown below. Some of the issues are now out of print and are available only on microfiche. 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Kamide, Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado 80302 and Geophysical Institute, University of Alaska, Fairbanks, Alaska 99701 (currently Guest worker at Data Studies Division, NOAA/EDS/NGSDC, Boulder, Colorado 80302), April 1976, 37 pages, price $1.39. UAG-57 "Manual on Ionospheric Absorption Measurements", edited by K. Rawer, Institut für Physikalische Weltraumforschung, Freiburg, G.F.R., June 1976, 202 pages, price $4.27. UAG-58 "ATS6 Radio Beacon Electron Content Measurements at Boulder, July 1974 - May 1975", by R. B. Fritz, Space Environment Laboratory (currently with Wave Propagation Laboratory), NOAA, Boulder, Colorado 80302 USA, September 1976, 61 pages, price $1.04. UAG-59 "Auroral Electrojet Magnetic Activity Indices AE(11) for 1974", by Joe Haskell Allen, Carl C. Abston and Leslie D. Morris, National Geophysical and Solar-Terrestrial Data Center, Environmental Data Service, December 1976, 144 pages, price $2.16. UAG-60 "Geomagnetic Data for January 1976 (AE(7) Indices and Stacked Magnetograms)" by J. H. Allen, C. C. Abston and L. D. Morris, NGSDC/EDS/NOAA, July 1977, 57 pages, price $1.07. UAG-61 "Collected Data Reports for STIP Interval II 20 March - 5 May 1976", edited by Helen E. Coffey and John A. McKinnon, National Geophysical and Solar-Terrestrial Data Center, Environmental Data Service, August 1977, 313 pages, price $2.95. UAG-62 "Geomagnetic Data For February 1976 (AE(7) Indices and Stacked Magnetograms)" by J. H. Allen, C. C. Abston and L. D. Morris, NGSDC/EDS/NOAA, September 1977, 55 pages, price $1.11. UAG-63 "Geomagnetic Data for March 1976 (AE(7) Indices and Stacked Magnetograms)" by J. H. Allen, C. C. Abston and L. D. Morris, NGSDC/EDS/NOAA, September 1977, 57 pages, price $1.11. UAG-64 "Geomagnetic Data for April 1976 (AE(8) Indices and Stacked Magnetograms)" by J. H. Allen, C. C. Abston and L. D. Morris, NGSDC/EDS/NOAA, February 1978, 55 pages, price $1.00. UAG-65 "The Information Explosion and Its Consequences for Data Acquisition, Documentation, and Processing" by G. K. Hartmann, Max-Planck-Institut für Aeronomie, D-3411 Katlenburg-Lindau 3, GFR, May 1978, 36 pages, price 75 cents. UAG-66 "Synoptic Radio Maps of the Sun at 3.3mm 1970-1973" by Earle B. Mayfield, Space Science Lab., and Fred I. Shimabukuro Electronics Res. Lab., The Ivan A. Getting Laboratories, The Aerospace Corp., El Segundo, California 90245, May 1978, 30 pages, price 75 cents. UAG-67 "Ionospheric D-Region Profile Data Base, A Collection of Computer-Accessible Experimental Profiles of the D and Lower E Regions", by L. F. McNamara, Ionospheric Prediction Service, Sydney, Australia, August 1978, 30 pages, price 88 cents. UAG-68 "A Comparative Study of Methods of Electron Density Profile Analysis", by L. F. McNamara, Ionospheric Prediction Service, Sydney, Australia, September 1978, 56 pages, price $1.41. UAG-69 "Selected Disturbed D-Region Electron Density Profiles. Their relation to the undisturbed D region", by L. F. McNamara, Ionospheric Prediction Service, Sydney, Australia, October 1978, 50 pages, price $1.29. UAG-70 "Annotated Atlas of Hα Synoptic Charts for Solar Cycle 20 (1964-1974) Carrington Solar Rotations 1487-1616", by Patrick S. McIntosh, Space Environment Laboratory, ERL/NOAA, February 1979, 327 pages, price $3.50.