Derivation of Hemispheric Ionospheric Current Functions From Ground-Level Magnetic Fields

These files provide the input and output data for the Figures shown in the paper "Derivation of
Hemispheric Ionospheric Current Functions From Ground-Level Magnetic Fields" by Daniel Weimer, published in the Journal of Geophysical Research, Space Physics, paper number 2018JA026191, doi:10.1029/2018JA026191

Two IDL program files and the original, PDF versions of the figures are included.

The data are provided as IDL "SAVE" files, readable in IDL with the "RESTORE" command. NetCDF
versions are included, readable with any NetCDF software library. These NetCDF files have the same
names as the ".xdr" files, except they have the extension ".nc".  Scalar variables (length 1) are put
into the Global Attributes in these files.

The files in this archive are:

Figures:
    Figure_1.PDF
    Figure_2.PDF
    Figure_3.PDF
    Figure_4.PDF
    Figure_5.PDF
    Figure_6.PDF

IDL Programs:
    spherical_cap_90_fits.pro : Routines for fitting magnetic field data on a hemispheric cap (90
        degrees), using spherical harmonics having both internal and external sources (or external alone),
        and functions for evaluating the results as equivalent currents, or the magnetic field components.

    AllLegendre.pro : Required by spherical_cap_90_fits.pro, provides computations of Associated
    Legendre Polynominals as arrays, for all combinations of l and m, up to Lmax and Mmax, as well as first derivatives.

Data Files:

    Figures_1_2_3_4_dB_ModelData.xdr : Magnetic field values (output from the 2013 empirical model),
        shown in Figure 1, and used to calculate the coefficients used to make Figures 2, 3, and 4.
        Contents:
            ALLLATS         FLOAT     = Array[8640] , array of latitude values, degrees
            ALLMLTS         FLOAT     = Array[8640] , array of Magnetic Local Time (MLT) values, hours
            DBNS            FLOAT     = Array[8640] , array of northward magnetic field values
            DBES            FLOAT     = Array[8640] , array of eastward magnetic field values
            DBVS            FLOAT     = Array[8640] , array of vertical (downward) magnetic field values
            NLATS           FLOAT     =       180.000
            NMLTS           INT       =       48
            empirical model inputs:
            BT              FLOAT     =       10.0000 , magnitude of the IMF
            ANGLE           FLOAT     =       180.000 , IMF clock angle
            F107            FLOAT     =       120.000 , F10.7 solar index
            SWVEL           FLOAT     =       400.000 , solar wind velocity
            TILTA           FLOAT     =       0.00000 , dipole tilt angle

    Figures_2_3_4_SCHA90FitResults.xdr : The coefficients obtained from the fits, used to generate
         Figures 2, 3, and 4.
        Contents:
            SPHCE           DOUBLE    = Array[115] , external spherical harmonic coefficients
            SPHCI           DOUBLE    = Array[115] , interal spherical harmonic coefficients
            NOINT_SPHCE     DOUBLE    = Array[115] , external spherical harmonic coefficients,
                derived without using the internal terms in the fitting of the magnetic potential
            The following variables are documented in the IDL program spherical_cap_90_fits.pro:
            MAXL            INT       =       34
            MAXM            INT       =        3
            ODD             INT       =        1
            EVEN            INT       =        0
            CSIZE           INT       =      115
            LS              INT       = Array[115]
            MS              INT       = Array[115]
            AB              BYTE      = Array[115]

    Figures_3_4_dB_ModelData-Dst.xdr : Magnetic field values, after subtraction of the ring current
        magnetic field, used to calculate the coefficients to make Figures 3 and 4.
        Contents:  Same variables as in file Figures_1_2_3_4_dB_ModelData.xdr

    Figures_3_4_SCHA90FitResults-Dst.xdr : The coefficients obtained from fitting the magnetic field
      that had the ring current subtracted, used to make Figures 3, and 4.
        Contents: Same variables as in file Figures_2_3_4_SCHA90FitResults.xdr

    Figure_5_dB_ModelDataTilt3x-Dst.xdr : eight sets of magnetic field values, after subtraction of the
      ring current magnetic field, used to calculate the coefficients to generate Figure 5.
        Contents: Similar variables as in file Figures_1_2_3_4_dB_ModelData.xdr, except that TILTA is
          replaced by TILTS, an array with the eight dipole tilt angles.  The magnetic field values are
          replaced by these arrays:
                DBN3X           FLOAT     = Array[180, 48, 3] , northward magnetic field, eight sets
                DBE3X           FLOAT     = Array[180, 48, 3] , eastward magnetic field, eight sets
                DBV3X           FLOAT     = Array[180, 48, 3] , vertical magnetic field, eight sets

    Figure_5_SCHA90FitResultsTilt3x-Dst.xdr : eight sets of coefficients obtained from fitting the
        magnetic field, used to make Figure 5.
        Contents: Same variables as in file Figures_2_3_4_SCHA90FitResults.xdr, except for these arrays:
            SPHCE3X         DOUBLE    = Array[115, 3] , external spherical harmonic coefficients, eight sets
            SPHCI3X         DOUBLE    = Array[115, 3] , internal spherical harmonic coefficients, eight sets

    Figure_6_dB_ModelDataClock8x-Dst.xdr : Eight sets of magnetic field values, after subtraction of
        the ring current magnetic field, used to calculate the coefficients to generate Figure 6.
        Contents: Similar variables as in file Figures_1_2_3_4_dB_ModelData.xdr, except that ANGLE is
          replaced by ANGLES, an array with the eight IMF clock angles.  The magnetic field values are
          replaced by these arrays:
            DBN8X           FLOAT     = Array[180, 48, 8] , northward magnetic field, eight sets
            DBE8X           FLOAT     = Array[180, 48, 8] , eastward magnetic field, eight sets
            DBV8X           FLOAT     = Array[180, 48, 8] , vertical magnetic field, eight sets

    Figure_6_SCHAFitResultsClock8x-Dst.xdr : Eight sets of coefficients obtained from fitting the
        magnetic field, used to make Figure 6.
        Contents:  Same variables as in file Figures_2_3_4_SCHA90FitResults.xdr, except for these arrays:
            SPHCE8X         DOUBLE    = Array[115, 8] , external spherical harmonic coefficients, eight sets
            SPHCI8X         DOUBLE    = Array[115, 8] , internal spherical harmonic coefficients, eight sets