Magnetic models for the United States for 1985

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CONTENTS

Abstract Introduction Acknowledgment 1985.0 models Secular-variation models Coefficients Charts and "GEOMAG" References cited Appendix

1. Graph showing magnetic declination recorded at the Tucson (Arizona)
2. Map showing the three regions for which 1985.0 models were derived,

3-11. Maps showing locations of measurements and model values (fig. 11) used

12-18. Small-scale magnetic charts for the United States, 1985:

1. Boundaries of the modeled regions
2. Overall root-mean-square residual
3. Spherical harmonic coefficients

Magnetic Observatory since 1910

regions shown on U.S. magnetic charts, and locations of the magnetic observatories, repeat stations, and fill-in values used to derive the secular-variation models

to derive the 1985.0 models:

3. Land survey
4. Marine-survey vector
5. Marine-survey total intensity
6. Pre-1975 Project MAGNET aerial-survey vector
7. Aerial-survey vector (other than Project MAGNET)
8. 1976-1977 Project MAGNET aerial-survey total intensity
9. 1980-1983 Project MAGNET aerial-survey vector
10. Canadian aerial-survey vector
11. International Geomagnetic Reference Field 1985 vector values
12. Declination
13. Inclination
14. Horizontal intensity
15. North component
16. East component
17. Vertical intensity
18. Total intensity

INTRODUCTION

We developed a set of five new models of the magnetic field in the United States that describe the direction and intensity of the field at 1985.0 (that is, the beginning of 1985) and the annual change expected during the next few years. They form the basis of a new set of magnetic charts (Peddie and Zunde, 1988a, b, c, d, e) that replace those of Fabiano and Jones (1976), Peddie and others (1976), Jones and Fabiano (1976), and Fabiano and Peddie (1980, 1981). Three of the models describe the 1985.0 field in the conterminous (48) States, Alaska, and Hawaii-the three regions shown in separate plates on the charts. The other two models describe annual change-one for the conterminous States and Alaska and the other for Hawaii. This report describes the development of the models and includes the model coefficients and simplified small-scale charts.

Revision of magnetic models and charts is necessary because the geomagnetic field undergoes continual change, called secular variation, that is commonly irregular and not yet predictable. The

The new models were derived by ordinary spherical harmonic analysis (SHA), a method commonly used for modeling the global field. They represent the scalar magnetic potential as a series of 3-dimensional spherical harmonics, from which the field components are derived by differentiation. The earlier U.S. models were derived by polynomial analysis and represented the field elements themselves as polynomial functions of latitude and longitude.

The new method has some advantages over the older one. For example, now all the field elements are represented by one set of coefficients and the elements are mutually consistent. The model field now varies with elevation in a way that is consistent with observation and theory, and, like the real field, it is curl-free. The new models are compatible with widely available programs used for generating field values from global spherical harmonic models, such as those of the International Geomagnetic Reference Field (IGRF).

Before deciding to use SHA we considered two other methods: magnetic dipole analysis and spherical cap harmonic analysis (Haines, 1985). We tested the former method by fitting grids of dipoles, with unconstrained magnetic moment, to the Hawaii data using a nonlinear least-squares technique. We found that the fit did not match that achievable with SHA (using a comparable number of coefficients) and that it improved as the depth of the dipoles was increased, (thus making the set of dipoles more like the multipoles of SHA). The latter method, as presently implemented, could not be applied iteratively and thus would not have allowed us to utilize the many D- and F-only measurements, and, as it requires removal and later addition of a global field, it seemed less efficient than ordinary SHA (L.R. Alldredge, oral commun., 1986).

Acknowledgment

We thank Susan McLean of the National Geophysical Data Center in Boulder, Colorado, for providing the 1980-1983 Project MAGNET data and for helping us to update our repeat station data file.

1985.0 MODELS

The three models of the field at 1985.0 were derived from data selected from the three regions whose boundaries are given in table 1 and indicated by the heavier lines in figure 2 (the lighter lines indicate the regions actually shown on the charts). Data were taken from the following sets (figs. 3-11, which relate to these sets, follow "References Cited"): Data Center, 1984, p. 8).-This set comprises several hundred thousand measurements taken on land, sea, and in the air since 1900. We used a subset, created in 1975 for the development of the global model AWC/75 (Peddie and Fabiano, 1976), consisting of all records dated 1939.0 or later that include values of either D, or F, or the X (north), Y (east), and Z (vertical) field components. These measurements were already adjusted for the secular variation between the measurement date and 1975.0. The measurement locations are in five classes (figs. 3-7): land survey, marine-survey vector, marine-survey total intensity, pre-1975 Project MAGNETsurvey vector, and non-Project MAGNET aerial-survey vector.

United States (National Geophysical Data Center, 1984, p. 10).-The survey comprised 44 north-south and 7 east-west lines flown at an altitude of 600 meters over flat land and 1220 meters over mountainous areas (see fig. 8).

MAGNET aerial sUJveys (National Geophysical Data Center, 1984, p. 10).-Although these were not intended primarily as surveys of the United States, they did produce some measurements in the chart regions (see fig. 9).

Newitt, unpub. data).-These data were especially useful for promoting agreement with the charts of Canada (see fig. 10).

1985.0.-These values were derived by linear extrapolation of recent observatory annual means and repeat station measurements (see fig. 2).

The great number of original Project MAGNET measurements was reduced by retaining only every 50th intensity measurement and every 25th vector measurement. Of these we used only those taken when Kp (a geomagnetic disturbance index) was less than 3. To fill gaps in the coverage we included values computed from the International Geomagnetic Reference Field (IGRF) 1985 main-field model (International Association of Geomagnetism and Aeronomy, Division I, Working Group 1, 1986), a global model based mainly on data from the MAG SAT satellite survey of 1979-1980 (Langel and others, 1982). These were computed for a grid of points at 500-kilometer altitude and spaced one degree in latitude and longitude (see fig. 11).

The data were analyzed using the method of iterative SHA (for example, Cain and others, 1965). The resulting overall root-mean-square residuals, for maximum degree and order (n *) ranging from 1 to 5 for the conterminous States and Alaska and from 1 to 3 for

Figure 2. Map showing the three regions for which 1985.0 models were derived (heavy boundary lines), and the regions actually shown on the 1985 U.S. magnetic charts (light boundary lines). Also shown are the locations of the magnetic observatories (solid circles) and repeat stations (solid squares) whose data, along with fill-in values (solid triangles), were used to derive the secular-variation models.

Alaska of n * = 4 (24 coefficients each) and for Hawaii of

States n*

. ,r.·.

COEFFICIENTS

h

h

h

h

h

h

h

e

h

h

h

4 3 4 3 4 4 4 4 1985.0 field

(nT/yr)

-7.0 -1.8 -14.3 -2.1 Hawaii

REFERENCES CITED Figures 3-18

Figure 3. Locations (solid squares) of land-survey measurements used to derive the 1985.0 models.

go• w too• w ao• w

Figure 4. Locations (solid squares) of marine-survey vector measurements used to deriv.e the 1985.0 models.

Figure 5. Locations (solid squares, thinned out for clarity) of marine-suNey total-intensity measurements used to derive the 1985.0 models.

Figure 6. Locations (solid squares, thinned out for clarity) of pre-1975 Project MAGNET aerial-survey vector measurements used to derive the 1985.0 models.

·' • • • t'·.·

Figure 7. Locations (solid squares, thinned out for clarity) of non-Project MAGNET aerial-survey vector measurements used to derive the 1985.0 models.

Figure 8. Locations (solid squares, thinned out for clarity) of Project MAGNET aerial survey total-intensity measurements taken during 1976-1977 used to derive the 1985.0 models.

Figure 9. Locations (solid squares, thinned out for clarity) of Project MAGNET aerial-survey vector measurements taken during 1980-1983 used to derive the 1985.0 models.

Figure 10. Locations (solid squares) of Canadian aerial-survey vector measurements used to derive the 1985.0 models.

go• w too• w

tao• w tao• w

I . " . "· : v. .............

Figure 12. Magnetic declination in the United States, 1985.

Figure 13. Magnetic inclination in the United States, 1985.

uo• w too• w

Figure 15. Magnetic north component in the United States, 1985.

\ )0. \c:f1fil·.

Figure 17. Magnetic vertical intensity in the United States, 1985.

I I

Figure 18. Magnetic total intensity in the United States, 1985.

B_aker Lake , Canada Barrow Boulder Cambridge Bay, Canada -------- Cape Wellen, USSR ------------

College Del Rio Fort Churchill, Canada ------- Fredericksburg Fresno

Godhavn, Greenland Great Whale River, Canada ---- Guam, u.s. Honolulu Kakioka, Japan

Magadan, USSR Meanook, Canada Mould Bay, Canada Narssarssuaq, Greenland ------ Newport

Ottawa, Canada Petropavlovsk, USSR Resolute Bay, Canada San Juan, Puerto Rico -------- Sitka

------------------- AK 57.058 -135.325

Saint John's, Canada Thule (II), Greenland -------- Tucson Victoria, Canada ------------- Yellowknife, Canada

---------- VA 38.205

--------- 47.600 -52.683 Lat St (degrees)

co 40.138 -105.?38 69.200 -105.000 66.163 -169.835

48.517 -123.417 62.400 -114.500 Lon

-69.167 Elev (m)

(nanotesla per year)

z

-83.6 -22.2 -53.8 -41.6 -35.8 APPENDIX: Secular-variation data- Continued

Majuro (new airport) ---------

Midway (1980) ---------------- Wake -------------------------

Anchorage (NBS) --------- Bethel (airport 2) ------

Fort Yukon (IGY) ----·--· Homer (1) Kodiak (1975) ----------- Kotzebue (1975) --------- Nome (airport 3) --------

Northway (IGY) ---------- Unalakleet (1975) ------- Marion (forest) --------- Castle Rock ------------- Lompoc

Fort Myers -------------- Key West (golf aux 2) --- Spruce Creek (1958) ----- Bainbridge (1958) Milledgeville (golf) ----

Waycross (airport) ------ Bangor (Broadway) ------- Bangor (Griffin) -------- Fort Kent (hosp. B) ----- Fort Kent (pasture) -----

Detroit (River Rouge) --- Detroit (park) Marquette (golf 1947) --- Marquette (golf 2) ------ Brooklyn ----------------

Grenada (1971) Lamar (B 1981) Goldsboro (airport) ----- Bowbells Syracuse (Drumlins B) ---

Syracuse (Drumlins) ----- Indiantow-n Gap (airf) --- Indiantown Gap (lake) --- Kingston (campus) ------- Kingston (turf) ---------

--------------- AK 59.640 -151.493

-··-----·- MI 42.355 -83.262

---------· MS 33.750 -89.797

63.018 -141.797 63.890 -160.797 AL 32.657 CA 37.240 -122.130 CA 34.637 -120.532

26.610 FL 24.573 FL 29.077 FL 30.907 GA 33.095 GA

31.255 GA 44.828 ME 44.825 ME ME 47.268 ME 47.247

46.538 MI 46.538 MI 31.030

30.925 MS NC 35.385 48.800 -102.242 ND 43.017

NY 43.017 PA 40.453 PA 40.417 RI 41.480 RI 41.488 Lat (degrees)

(nanotes1a per year)

z

Fort Jackson ------------ Fort Jackson (2) -------- Brownsville (golf 2) ---- Dallas (observatory) ---- Orange· (C)

-----·-------- TX 30.063

Van Horn (airport) ------ Salt Lake City (hill) --- Burlington (LP) --------- Burlington (RS) --------- Eau Claire

sc sc

Model fill-in values Lat (degrees)

10.000 10.000 -105.000 10.000 -120.000 10.000 -135.000 75.000 0.000 Elev Lon

(nanotesla per year)

z

Catalogs

Maps t'eaa1e ana Lunae-MAL.NI:IIL MODELS FOR THE UNITEO STATES FOR 1985-U.S. Geological Survey Circular 1039

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