DOI: 10.5281/zenodo.2538169
title: Derivation of Hemispheric Ionospheric Current Functions From Ground-Level Magnetic Fields

description: These files provide the input and output data for the Figures shown in the paper "Derivation of<br>
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<br>
versions are included, readable with any NetCDF software library. These NetCDF files have the same<br>
names as the ".xdr" files, except they have the extension ".nc".  Scalar variables (length 1) are put<br>
into the Global Attributes in these files.

The files in this archive are:

Figures:<br>
    Figure_1.PDF<br>
    Figure_2.PDF<br>
    Figure_3.PDF<br>
    Figure_4.PDF<br>
    Figure_5.PDF<br>
    Figure_6.PDF

IDL Programs:<br>
    spherical_cap_90_fits.pro : Routines for fitting magnetic field data on a hemispheric cap (90<br>
        degrees), using spherical harmonics having both internal and external sources (or external alone),<br>
        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<br>
    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),<br>
        shown in Figure 1, and used to calculate the coefficients used to make Figures 2, 3, and 4.<br>
        Contents:<br>
            ALLLATS         FLOAT     = Array[8640] , array of latitude values, degrees<br>
            ALLMLTS         FLOAT     = Array[8640] , array of Magnetic Local Time (MLT) values, hours<br>
            DBNS            FLOAT     = Array[8640] , array of northward magnetic field values<br>
            DBES            FLOAT     = Array[8640] , array of eastward magnetic field values<br>
            DBVS            FLOAT     = Array[8640] , array of vertical (downward) magnetic field values<br>
            NLATS           FLOAT     =       180.000<br>
            NMLTS           INT       =       48<br>
            empirical model inputs:<br>
            BT              FLOAT     =       10.0000 , magnitude of the IMF<br>
            ANGLE           FLOAT     =       180.000 , IMF clock angle<br>
            F107            FLOAT     =       120.000 , F10.7 solar index<br>
            SWVEL           FLOAT     =       400.000 , solar wind velocity<br>
            TILTA           FLOAT     =       0.00000 , dipole tilt angle

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

    Figures_3_4_dB_ModelData-Dst.xdr : Magnetic field values, after subtraction of the ring current<br>
        magnetic field, used to calculate the coefficients to make Figures 3 and 4.<br>
        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<br>
      that had the ring current subtracted, used to make Figures 3, and 4.<br>
        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<br>
      ring current magnetic field, used to calculate the coefficients to generate Figure 5.<br>
        Contents: Similar variables as in file Figures_1_2_3_4_dB_ModelData.xdr, except that TILTA is<br>
          replaced by TILTS, an array with the eight dipole tilt angles.  The magnetic field values are<br>
          replaced by these arrays:<br>
                DBN3X           FLOAT     = Array[180, 48, 3] , northward magnetic field, eight sets<br>
                DBE3X           FLOAT     = Array[180, 48, 3] , eastward magnetic field, eight sets<br>
                DBV3X           FLOAT     = Array[180, 48, 3] , vertical magnetic field, eight sets

    Figure_5_SCHA90FitResultsTilt3x-Dst.xdr : eight sets of coefficients obtained from fitting the<br>
        magnetic field, used to make Figure 5.<br>
        Contents: Same variables as in file Figures_2_3_4_SCHA90FitResults.xdr, except for these arrays:<br>
            SPHCE3X         DOUBLE    = Array[115, 3] , external spherical harmonic coefficients, eight sets<br>
            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<br>
        the ring current magnetic field, used to calculate the coefficients to generate Figure 6.<br>
        Contents: Similar variables as in file Figures_1_2_3_4_dB_ModelData.xdr, except that ANGLE is<br>
          replaced by ANGLES, an array with the eight IMF clock angles.  The magnetic field values are<br>
          replaced by these arrays:<br>
            DBN8X           FLOAT     = Array[180, 48, 8] , northward magnetic field, eight sets<br>
            DBE8X           FLOAT     = Array[180, 48, 8] , eastward magnetic field, eight sets<br>
            DBV8X           FLOAT     = Array[180, 48, 8] , vertical magnetic field, eight sets

    Figure_6_SCHAFitResultsClock8x-Dst.xdr : Eight sets of coefficients obtained from fitting the<br>
        magnetic field, used to make Figure 6.<br>
        Contents:  Same variables as in file Figures_2_3_4_SCHA90FitResults.xdr, except for these arrays:<br>
            SPHCE8X         DOUBLE    = Array[115, 8] , external spherical harmonic coefficients, eight sets<br>
            SPHCI8X         DOUBLE    = Array[115, 8] , internal spherical harmonic coefficients, eight sets<br>
description: Abstract
The horizontal currents in the high-latitude ionosphere are the primary driver of the magnetic field perturbations that are observed at the surface of the Earth.  These currents and their ground effects are an important aspect of the magnetosphere-ionosphere coupling process.  This paper discusses the method of inversion that uses spherical harmonic potential function, in which magnetic field measurements on the ground can be used to derive maps of the ``ionospheric equivalent currents,'' a mathematical representation of the horizontal currents flowing on a thin shell.  It is shown that the use of both internal, telluric and external current sources is required when fitting the spherical harmonic series, otherwise the ionospheric currents will be overestimated. Furthermore, the inversion needs to compensate for magnetic effects of the magnetospheric ring current, otherwise this current is projected onto the ionosphere. The amplification of the surface horizontal magnetic field and the suppression of the vertical magnetic field is demonstrated. The equivalent currents may be useful for estimating the ionospheric conductivity values. Additionally, these currents can be compared with the results from simulation models as as means of validation.