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Brief description of geomagnetism and observation systems

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Learn more about model derivation, uncertainties and magnetic poles

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Download model coefficients, software and documentation

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Calculate magnetic field values at or near the Earth surface

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Common applications of WMM

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WMM coefficient file format for developers


The World Magnetic Model coefficient file is named “WMM.COF”. Numerical values of the Gauss coefficients (g_nm, h_nm, g_dot_nm, h_dot_nm) at the base epoch, their corresponding predictive annual changes for the next 5 years and their associated degrees and orders are provided in this file. For more details about the WMM Gauss coefficients, see section 1.2 of the WMM Technical report. The World Magnetic Model coefficients are written to this file in a specific format. The WMM.COF file format is designed such that, if implemented correctly, an update to a new WMM is done by simply replacing the old “WMM.COF” file with the new “WMM.COF” file, without needing to make any changes to the software. The “WMM.COF” file is an ASCII file with one header line, 90 lines of coefficients data and 2 terminating lines. Each line has 48 characters, ending with a carriage return and a linefeed (\n\r).


 Line 1: “Header”

2020.0 WMM-2020 12/10/2019
^ ^ ^
Model Epoch Model-name Date of release

WMM is valid for 5 years from the "Model Epoch" parameter given in decimal years. The "Date of release" of the model has no significance in magnetic field calculation and is US style, MM/DD/YYYY.


 Lines 2 to 91: Model coefficients

1 0 -29404.5 0.0 6.7 0.0
^ ^ ^ ^ ^ ^
n m g_nm h_nm g_dot_nm h_dot_nm

 Lines 92 and 93: File terminators

  999999999999999999999999999999999999999999999999

  999999999999999999999999999999999999999999999999


A software implementation for reading WMM.COF should stop when reaching the terminator line.


WMM.COF file format is permanent and we do not anticipate making changes to it in the foreseeable future.


Example code

  1. FORTRAN
  2. 123456789012345678901234567890123456789012345678 (line length 48)
    2020.0              WMM-2020        12/10/2019
      OPEN (UNIT=9, FILE='WMM.COF')
      READ (9, 1) EPOCH,MODEL,RELEASEDATE
    1 FORMAT(F10.1,A20,A18)

    123123123456789012345678901234567890112345678901 (line length 48)
    1  0  -29404.5       0.0        6.7        0.0

      READ(9,4) N,M,GNM,HNM,DGNM,DHNM
    4 FORMAT(I3,I3,F10.1,F10.1,F11.1,F11.1)

  3. C
  4. 123456789012345678901234567890123456789012345678 (line length 48)
    2020.0              WMM-2020        12/10/2019

    fscanf(fp, "%4.1f %20s %02d/%02d/%04d", &epoch, model_name, &month, &day, &year);

    123123123456789012345678901234567890112345678901 (line length 48)
    1  0  -29404.5       0.0        6.7        0.0

    fscanf(fp,"%3d%3d%10.1f%10.1f%11.1f%11.1f", &n, &m, &g_nm, &h_nm, &g_dot_nm, &h_dot_nm);