geomag.c

// March 2020: Made to work as a small and easy to use library for GNU/Linux C programs by M. Wirth
// Original notes provided below
/* PROGRAM MAGPOINT (GEOMAG DRIVER) */
/************************************************************************

     Contact Information

     Software and Model Support
     	National Geophysical Data Center
     	NOAA EGC/2
     	325 Broadway
     	Boulder, CO 80303 USA
		Attn: Manoj Nair or Stefan Maus
		Phone:  (303) 497-4642 or -6522
		Email:  Manoj.C.Nair@Noaa.gov or Stefan.Maus@noaa.gov
		Web: http://www.ngdc.noaa.gov/geomag/WMM/

	 Sponsoring Government Agency
	   National Geospatial-Intelligence Agency
    	   PRG / CSAT, M.S. L-41
    	   3838 Vogel Road
    	   Arnold, MO 63010
    	   Attn: Craig Rollins
    	   Phone:  (314) 263-4186
    	   Email:  Craig.M.Rollins@Nga.Mil

      Original Program By:
        Dr. John Quinn
        FLEET PRODUCTS DIVISION, CODE N342
        NAVAL OCEANOGRAPHIC OFFICE (NAVOCEANO)
        STENNIS SPACE CENTER (SSC), MS 39522-5001

		3/25/05 Version 2.0 Stefan Maus corrected 2 bugs:
         - use %c instead of %s for character read
		 - help text: positive inclination is downward
		1/29/2010 Version 3.0 Manoj Nair
		Converted floating variables from single precision to double
		Changed : height above AMSL (WGS84) to Height above WGS84 Ellipsoid
		Removed the NaN forcing at the geographic poles
		A new function "my_isnan" for improved portablility

*/

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

#define NaN log(-1.0)

static char **wmm_lines;
static char *wmm_string;
static int wmm_index;
static int maxdeg;
static double epochlowlim,epochuplim,epoch;
char decd[7], dipd[7],modl[20];

static char* goodbye = "\n -- End of WMM Point Calculation Program -- \n\n";

static int my_isnan(double d)
{
    return (d != d);              /* IEEE: only NaN is not equal to itself */
}

static int geomag_E0_init(int *maxdeg);
static char geomag_introduction(double epochlowlim);

int geomag_destroy() {
    return 0;
}

int geomag_init()
{

    // hard code WMM2020, this can easily enough be replaced
    // i don't like having to read a file, better to have the data in the source code.
    // when replacing this, make sure to add \n\ at the end of each line to the text from the WMM.COF
    // also make sure the indentation stays as it is ... some code depends on that.

    wmm_string = strdup("\
    2020.0            WMM-2020        12/10/2019\n\
  1  0  -29404.5       0.0        6.7        0.0\n\
  1  1   -1450.7    4652.9        7.7      -25.1\n\
  2  0   -2500.0       0.0      -11.5        0.0\n\
  2  1    2982.0   -2991.6       -7.1      -30.2\n\
  2  2    1676.8    -734.8       -2.2      -23.9\n\
  3  0    1363.9       0.0        2.8        0.0\n\
  3  1   -2381.0     -82.2       -6.2        5.7\n\
  3  2    1236.2     241.8        3.4       -1.0\n\
  3  3     525.7    -542.9      -12.2        1.1\n\
  4  0     903.1       0.0       -1.1        0.0\n\
  4  1     809.4     282.0       -1.6        0.2\n\
  4  2      86.2    -158.4       -6.0        6.9\n\
  4  3    -309.4     199.8        5.4        3.7\n\
  4  4      47.9    -350.1       -5.5       -5.6\n\
  5  0    -234.4       0.0       -0.3        0.0\n\
  5  1     363.1      47.7        0.6        0.1\n\
  5  2     187.8     208.4       -0.7        2.5\n\
  5  3    -140.7    -121.3        0.1       -0.9\n\
  5  4    -151.2      32.2        1.2        3.0\n\
  5  5      13.7      99.1        1.0        0.5\n\
  6  0      65.9       0.0       -0.6        0.0\n\
  6  1      65.6     -19.1       -0.4        0.1\n\
  6  2      73.0      25.0        0.5       -1.8\n\
  6  3    -121.5      52.7        1.4       -1.4\n\
  6  4     -36.2     -64.4       -1.4        0.9\n\
  6  5      13.5       9.0       -0.0        0.1\n\
  6  6     -64.7      68.1        0.8        1.0\n\
  7  0      80.6       0.0       -0.1        0.0\n\
  7  1     -76.8     -51.4       -0.3        0.5\n\
  7  2      -8.3     -16.8       -0.1        0.6\n\
  7  3      56.5       2.3        0.7       -0.7\n\
  7  4      15.8      23.5        0.2       -0.2\n\
  7  5       6.4      -2.2       -0.5       -1.2\n\
  7  6      -7.2     -27.2       -0.8        0.2\n\
  7  7       9.8      -1.9        1.0        0.3\n\
  8  0      23.6       0.0       -0.1        0.0\n\
  8  1       9.8       8.4        0.1       -0.3\n\
  8  2     -17.5     -15.3       -0.1        0.7\n\
  8  3      -0.4      12.8        0.5       -0.2\n\
  8  4     -21.1     -11.8       -0.1        0.5\n\
  8  5      15.3      14.9        0.4       -0.3\n\
  8  6      13.7       3.6        0.5       -0.5\n\
  8  7     -16.5      -6.9        0.0        0.4\n\
  8  8      -0.3       2.8        0.4        0.1\n\
  9  0       5.0       0.0       -0.1        0.0\n\
  9  1       8.2     -23.3       -0.2       -0.3\n\
  9  2       2.9      11.1       -0.0        0.2\n\
  9  3      -1.4       9.8        0.4       -0.4\n\
  9  4      -1.1      -5.1       -0.3        0.4\n\
  9  5     -13.3      -6.2       -0.0        0.1\n\
  9  6       1.1       7.8        0.3       -0.0\n\
  9  7       8.9       0.4       -0.0       -0.2\n\
  9  8      -9.3      -1.5       -0.0        0.5\n\
  9  9     -11.9       9.7       -0.4        0.2\n\
 10  0      -1.9       0.0        0.0        0.0\n\
 10  1      -6.2       3.4       -0.0       -0.0\n\
 10  2      -0.1      -0.2       -0.0        0.1\n\
 10  3       1.7       3.5        0.2       -0.3\n\
 10  4      -0.9       4.8       -0.1        0.1\n\
 10  5       0.6      -8.6       -0.2       -0.2\n\
 10  6      -0.9      -0.1       -0.0        0.1\n\
 10  7       1.9      -4.2       -0.1       -0.0\n\
 10  8       1.4      -3.4       -0.2       -0.1\n\
 10  9      -2.4      -0.1       -0.1        0.2\n\
 10 10      -3.9      -8.8       -0.0       -0.0\n\
 11  0       3.0       0.0       -0.0        0.0\n\
 11  1      -1.4      -0.0       -0.1       -0.0\n\
 11  2      -2.5       2.6       -0.0        0.1\n\
 11  3       2.4      -0.5        0.0        0.0\n\
 11  4      -0.9      -0.4       -0.0        0.2\n\
 11  5       0.3       0.6       -0.1       -0.0\n\
 11  6      -0.7      -0.2        0.0        0.0\n\
 11  7      -0.1      -1.7       -0.0        0.1\n\
 11  8       1.4      -1.6       -0.1       -0.0\n\
 11  9      -0.6      -3.0       -0.1       -0.1\n\
 11 10       0.2      -2.0       -0.1        0.0\n\
 11 11       3.1      -2.6       -0.1       -0.0\n\
 12  0      -2.0       0.0        0.0        0.0\n\
 12  1      -0.1      -1.2       -0.0       -0.0\n\
 12  2       0.5       0.5       -0.0        0.0\n\
 12  3       1.3       1.3        0.0       -0.1\n\
 12  4      -1.2      -1.8       -0.0        0.1\n\
 12  5       0.7       0.1       -0.0       -0.0\n\
 12  6       0.3       0.7        0.0        0.0\n\
 12  7       0.5      -0.1       -0.0       -0.0\n\
 12  8      -0.2       0.6        0.0        0.1\n\
 12  9      -0.5       0.2       -0.0       -0.0\n\
 12 10       0.1      -0.9       -0.0       -0.0\n\
 12 11      -1.1      -0.0       -0.0        0.0\n\
 12 12      -0.3       0.5       -0.1       -0.1\n\
999999999999999999999999999999999999999999999999\n\
999999999999999999999999999999999999999999999999\n\
");

    wmm_lines = malloc(sizeof(char*) * 256);
    if (!wmm_lines) {
        fprintf(stderr, "malloc fail in geomag.c\n");
        return -1;
    }
    wmm_index = 0;

    char *saveptr = NULL;
    wmm_lines[wmm_index] = strtok_r(wmm_string, "\n", &saveptr);
    while (wmm_lines[wmm_index]) {
        wmm_index++;
        wmm_lines[wmm_index] = strtok_r(NULL, "\n", &saveptr);
    }


    if (wmm_lines[0] == NULL || sscanf(wmm_lines[0],"%lf%s",&epochlowlim,modl) < 2)
    {
        fprintf(stderr, "Invalid header in model wmm_string in geomag.c\n");
        return -1;
    }

    /* INITIALIZE GEOMAG ROUTINE */

    maxdeg = 12;
    int result = geomag_E0_init(&maxdeg);
    free(wmm_lines);
    wmm_lines = NULL;
    free(wmm_string);
    wmm_string = NULL;
    return result;
}

/*************************************************************************/

static int E0000(int IENTRY, int *maxdeg, double alt, double glat, double glon, double time, double *dec, double *dip, double *ti, double *gv)
{
    static int maxord,i,icomp,n,m,j,D1,D2,D3,D4;
    static double c[13][13],cd[13][13],tc[13][13],dp[13][13],snorm[169],
    sp[13],cp[13],fn[13],fm[13],pp[13],k[13][13],pi,dtr,a,b,re,
    a2,b2,c2,a4,b4,c4,gnm,hnm,dgnm,dhnm,flnmj,
    dt,rlon,rlat,srlon,srlat,crlon,crlat,srlat2,
    crlat2,q,q1,q2,ct,st,r2,r,d,ca,sa,aor,ar,br,bt,bp,bpp,
    par,temp1,temp2,parp,bx,by,bz,bh;
    static char model[20], c_new[5];
    static double *p = snorm;

    switch(IENTRY){case 0: goto INIT; case 1: goto CALC;}

INIT:

    /* INITIALIZE CONSTANTS */
    maxord = *maxdeg;
    sp[0] = 0.0;
    cp[0] = *p = pp[0] = 1.0;
    dp[0][0] = 0.0;
    a = 6378.137;
    b = 6356.7523142;
    re = 6371.2;
    a2 = a*a;
    b2 = b*b;
    c2 = a2-b2;
    a4 = a2*a2;
    b4 = b2*b2;
    c4 = a4 - b4;

    /* READ WORLD MAGNETIC MODEL SPHERICAL HARMONIC COEFFICIENTS */
    c[0][0] = 0.0;
    cd[0][0] = 0.0;

    wmm_index = 0;
    if (wmm_lines[wmm_index] == NULL || sscanf(wmm_lines[wmm_index],"%lf%s",&epoch,model) < 2) 
    {
        fprintf(stderr, "Invalid header in model wmm_string in geomag.c\n");
        return -1;
    }

S3:
    wmm_index++;
    if (wmm_lines[wmm_index] == NULL) goto S4;

    /* CHECK FOR LAST LINE IN FILE */
    for (i=0; i<4 && (wmm_lines[wmm_index][i] != '\0'); i++)
    {
        c_new[i] = wmm_lines[wmm_index][i];
        c_new[i+1] = '\0';
    }
    icomp = strcmp("9999", c_new);
    if (icomp == 0) goto S4;
    /* END OF FILE NOT ENCOUNTERED, GET VALUES */
    sscanf(wmm_lines[wmm_index], "%d%d%lf%lf%lf%lf",&n,&m,&gnm,&hnm,&dgnm,&dhnm);

    if (n > maxord) goto S4;
    if (m > n || m < 0.0) 
    {
        fprintf(stderr, "%d\n", wmm_index);
        fprintf(stderr, "Corrupt record in model wmm_string in geomag.c\n");
        return -1;
    }

    if (m <= n)
    {
        c[m][n] = gnm;
        cd[m][n] = dgnm;
        if (m != 0)
        {
            c[n][m-1] = hnm;
            cd[n][m-1] = dhnm;
        }
    }
    goto S3;

    /* CONVERT SCHMIDT NORMALIZED GAUSS COEFFICIENTS TO UNNORMALIZED */
S4:
    *snorm = 1.0;
    fm[0] = 0.0;
    for (n=1; n<=maxord; n++)
    {
        *(snorm+n) = *(snorm+n-1)*(double)(2*n-1)/(double)n;
        j = 2;
        for (m=0,D1=1,D2=(n-m+D1)/D1; D2>0; D2--,m+=D1)
        {
            k[m][n] = (double)(((n-1)*(n-1))-(m*m))/(double)((2*n-1)*(2*n-3));
            if (m > 0)
            {
                flnmj = (double)((n-m+1)*j)/(double)(n+m);
                *(snorm+n+m*13) = *(snorm+n+(m-1)*13)*sqrt(flnmj);
                j = 1;
                c[n][m-1] = *(snorm+n+m*13)*c[n][m-1];
                cd[n][m-1] = *(snorm+n+m*13)*cd[n][m-1];
            }
            c[m][n] = *(snorm+n+m*13)*c[m][n];
            cd[m][n] = *(snorm+n+m*13)*cd[m][n];
        }
        fn[n] = (double)(n+1);
        fm[n] = (double)n;
    }
    k[1][1] = 0.0;

    return 0;

    /*************************************************************************/

CALC:

    dt = time - epoch;

    pi = 3.14159265359;
    dtr = pi/180.0;
    rlon = glon*dtr;
    rlat = glat*dtr;
    srlon = sin(rlon);
    srlat = sin(rlat);
    crlon = cos(rlon);
    crlat = cos(rlat);
    srlat2 = srlat*srlat;
    crlat2 = crlat*crlat;
    sp[1] = srlon;
    cp[1] = crlon;

    /* CONVERT FROM GEODETIC COORDS. TO SPHERICAL COORDS. */
    q = sqrt(a2-c2*srlat2);
    q1 = alt*q;
    q2 = ((q1+a2)/(q1+b2))*((q1+a2)/(q1+b2));
    ct = srlat/sqrt(q2*crlat2+srlat2);
    st = sqrt(1.0-(ct*ct));
    r2 = (alt*alt)+2.0*q1+(a4-c4*srlat2)/(q*q);
    r = sqrt(r2);
    d = sqrt(a2*crlat2+b2*srlat2);
    ca = (alt+d)/r;
    sa = c2*crlat*srlat/(r*d);

    for (m=2; m<=maxord; m++)
    {
        sp[m] = sp[1]*cp[m-1]+cp[1]*sp[m-1];
        cp[m] = cp[1]*cp[m-1]-sp[1]*sp[m-1];
    }

    aor = re/r;
    ar = aor*aor;
    br = bt = bp = bpp = 0.0;
    for (n=1; n<=maxord; n++)
    {
        ar = ar*aor;
        for (m=0,D3=1,D4=(n+m+D3)/D3; D4>0; D4--,m+=D3)
        {
            /*
               COMPUTE UNNORMALIZED ASSOCIATED LEGENDRE POLYNOMIALS
               AND DERIVATIVES VIA RECURSION RELATIONS
               */
            if (n == m)
            {
                *(p+n+m*13) = st**(p+n-1+(m-1)*13);
                dp[m][n] = st*dp[m-1][n-1]+ct**(p+n-1+(m-1)*13);
                goto S50;
            }
            if (n == 1 && m == 0)
            {
                *(p+n+m*13) = ct**(p+n-1+m*13);
                dp[m][n] = ct*dp[m][n-1]-st**(p+n-1+m*13);
                goto S50;
            }
            if (n > 1 && n != m)
            {
                if (m > n-2) *(p+n-2+m*13) = 0.0;
                if (m > n-2) dp[m][n-2] = 0.0;
                *(p+n+m*13) = ct**(p+n-1+m*13)-k[m][n]**(p+n-2+m*13);
                dp[m][n] = ct*dp[m][n-1] - st**(p+n-1+m*13)-k[m][n]*dp[m][n-2];
            }
S50:
            /*
               TIME ADJUST THE GAUSS COEFFICIENTS
               */
            tc[m][n] = c[m][n]+dt*cd[m][n];
            if (m != 0) tc[n][m-1] = c[n][m-1]+dt*cd[n][m-1];
            /*
               ACCUMULATE TERMS OF THE SPHERICAL HARMONIC EXPANSIONS
               */
            par = ar**(p+n+m*13);
            if (m == 0)
            {
                temp1 = tc[m][n]*cp[m];
                temp2 = tc[m][n]*sp[m];
            }
            else
            {
                temp1 = tc[m][n]*cp[m]+tc[n][m-1]*sp[m];
                temp2 = tc[m][n]*sp[m]-tc[n][m-1]*cp[m];
            }
            bt = bt-ar*temp1*dp[m][n];
            bp += (fm[m]*temp2*par);
            br += (fn[n]*temp1*par);
            /*
               SPECIAL CASE:  NORTH/SOUTH GEOGRAPHIC POLES
               */
            if (st == 0.0 && m == 1)
            {
                if (n == 1) pp[n] = pp[n-1];
                else pp[n] = ct*pp[n-1]-k[m][n]*pp[n-2];
                parp = ar*pp[n];
                bpp += (fm[m]*temp2*parp);
            }
        }
    }
    if (st == 0.0) bp = bpp;
    else bp /= st;
    /*
       ROTATE MAGNETIC VECTOR COMPONENTS FROM SPHERICAL TO
       GEODETIC COORDINATES
       */
    bx = -bt*ca-br*sa;
    by = bp;
    bz = bt*sa-br*ca;
    /*
       COMPUTE DECLINATION (DEC), INCLINATION (DIP) AND
       TOTAL INTENSITY (TI)
       */
    bh = sqrt((bx*bx)+(by*by));
    *ti = sqrt((bh*bh)+(bz*bz));
    *dec = atan2(by,bx)/dtr;
    *dip = atan2(bz,bh)/dtr;
    /*
       COMPUTE MAGNETIC GRID VARIATION IF THE CURRENT
       GEODETIC POSITION IS IN THE ARCTIC OR ANTARCTIC
       (I.E. GLAT > +55 DEGREES OR GLAT < -55 DEGREES)

       OTHERWISE, SET MAGNETIC GRID VARIATION TO -999.0
       */
    *gv = -999.0;
    if (fabs(glat) >= 55.)
    {
        if (glat > 0.0 && glon >= 0.0) *gv = *dec-glon;
        if (glat > 0.0 && glon < 0.0) *gv = *dec+fabs(glon);
        if (glat < 0.0 && glon >= 0.0) *gv = *dec+glon;
        if (glat < 0.0 && glon < 0.0) *gv = *dec-fabs(glon);
        if (*gv > +180.0) *gv -= 360.0;
        if (*gv < -180.0) *gv += 360.0;
    }
    return 0;
}

/*************************************************************************/

static int geomag_E0_init(int *maxdeg)
{
    return E0000(0,maxdeg,0.0,0.0,0.0,0.0,NULL,NULL,NULL,NULL);
}

/*************************************************************************/

int geomag_calc(double alt, double glat, double glon, double time, double *dec, double *dip, double *ti, double *gv)
{
    return E0000(1,NULL,alt,glat,glon,time,dec,dip,ti,gv);
}

/*************************************************************************/

static char geomag_introduction(double epochlowlim)
{
    char help;
    static char ans;
    int res = 0;
    res++;

    printf("\n\n Welcome to the World Magnetic Model (WMM) %4.0lf C-Program\n\n", epochlowlim);
    printf("            --- Version 3.0, January 2010 ---\n\n");
    printf("\n This program estimates the strength and direction of ");
    printf("\n Earth's main magnetic field for a given point/area.");
    printf("\n Enter h for help and contact information or c to continue.");
    printf ("\n >");
    res = scanf("%c%*[^\n]",&help);
    getchar();

    if ((help == 'h') || (help == 'H'))
    {
        printf("\n Help information ");

        printf("\n The World Magnetic Model (WMM) for %7.2lf", epochlowlim);
        printf("\n is a model of Earth's main magnetic field.  The WMM");
        printf("\n is recomputed every five (5) years, in years divisible by ");
        printf("\n five (i.e. 2010, 2015).  See the contact information below");
        printf("\n to obtain more information on the WMM and associated software.");
        printf("\n ");
        printf("\n Input required is the location in geodetic latitude and");
        printf("\n longitude (positive for northern latitudes and eastern ");
        printf("\n longitudes), geodetic altitude in meters, and the date of "); 
        printf("\n interest in years.");

        printf("\n\n\n The program computes the estimated magnetic Declination");
        printf("\n (D) which is sometimes called MAGVAR, Inclination (I), Total");
        printf("\n Intensity (F or TI), Horizontal Intensity (H or HI), Vertical");
        printf("\n Intensity (Z), and Grid Variation (GV). Declination and Grid");
        printf("\n Variation are measured in units of degrees and are considered"); 
        printf("\n positive when east or north.  Inclination is measured in units");
        printf("\n of degrees and is considered positive when pointing down (into");
        printf("\n the Earth).  The WMM is reference to the WGS-84 ellipsoid and");
        printf("\n is valid for 5 years after the base epoch.");

        printf("\n\n\n It is very important to note that a  degree and  order 12 model,");
        printf("\n such as WMM, describes only the long  wavelength spatial magnetic ");
        printf("\n fluctuations due to  Earth's core.  Not included in the WMM series");
        printf("\n models are intermediate and short wavelength spatial fluctuations ");
        printf("\n that originate in Earth's mantle and crust. Consequently, isolated");
        printf("\n angular errors at various  positions on the surface (primarily over");
        printf("\n land, incontinental margins and  over oceanic seamounts, ridges and");
        printf("\n trenches) of several degrees may be expected.  Also not included in");
        printf("\n the model are temporal fluctuations of magnetospheric and ionospheric");
        printf("\n origin. On the days during and immediately following magnetic storms,");
        printf("\n temporal fluctuations can cause substantial deviations of the geomagnetic");
        printf("\n field  from model  values.  If the required  declination accuracy  is");
        printf("\n more stringent than the WMM  series of models provide, the user is");
        printf("\n advised to request special (regional or local) surveys be performed");
        printf("\n and models prepared. Please make requests of this nature to the");
        printf("\n National Geospatial-Intelligence Agency (NGA) at the address below.");

        printf("\n\n\n Contact Information");

        printf("\n  Software and Model Support");
        printf("\n	National Geophysical Data Center");
        printf("\n	NOAA EGC/2");
        printf("\n	325 Broadway");
        printf("\n	Boulder, CO 80303 USA");
        printf("\n	Attn: Susan McLean or Stefan Maus");
        printf("\n	Phone:  (303) 497-6478 or -6522");
        printf("\n	Email:  Susan.McLean@noaa.gov or Stefan.Maus@noaa.gov ");

        printf("\n\n\n Continue with program? (y or n) ");
        res = scanf("%c%*[^\n]", &ans);
        getchar();
    }
    else
    {
        ans = 'y';      
    }

    return(ans);
}

void geomag_interactive() {

    int warn_H, warn_H_strong, warn_P;
    double warn_H_val, warn_H_strong_val;
    char answer;
    double x1,x2,y1,y2,z1,z2,h1,h2;
    double altm, dlat, dlon;
    double ati, adec, adip;
    double alt, time, dec, dip, ti, gv;
    double time1, dec1, dip1, ti1;
    double dec2, dip2, ti2;
    double ax,ay,az,ah;
    double rTd=0.017453292;
    double epochrange = 5.0;
    double dmin, imin, ddeg, ideg;
    int res = 0;
    res++;

    char ans = geomag_introduction(epochlowlim);
    if ((ans == 'y') || (ans == 'Y'))

S1:

    maxdeg = 12;
    warn_H = 0;
    warn_H_val = 99999.0;
    warn_H_strong = 0;
    warn_H_strong_val = 99999.0;
    warn_P = 0;

    printf("\n\n\nENTER LATITUDE IN DECIMAL DEGREES ");
    printf("\n(North latitude positive, South latitude negative \n");
    printf("i.e. 25.5 for 25 degrees 30 minutes north.) \n");
    res = scanf("%lf%*[^\n]", &dlat);
    getchar();

    printf("ENTER LONGITUDE IN DECIMAL DEGREES");
    printf("(East longitude positive, West negative \n"); 
    printf("i.e.- 100.0 for 100.0 degrees west.)\n");
    res = scanf("%lf%*[^\n]", &dlon);
    getchar();

    printf("ENTER ALTITUDE IN KILOMETERS ABOVE WGS84 ELLIPSOID\n");
    res = scanf("%lf%*[^\n]", &altm);
    getchar();
    alt = altm;

    epochuplim = epochlowlim + epochrange;
    printf("ENTER TIME IN DECIMAL YEAR (%-7.2lf - %-7.2lf)\n",epochlowlim,epochuplim);
    res = scanf("%lf%*[^\n]",&time);
    getchar();

    double dt = time - epoch;
    printf("%.1f %.1f\n", time, epoch);
    if (time < 0.0 || (dt < 0.0 || dt > 5.0))
    {      
        printf("\n\n WARNING - TIME EXTENDS BEYOND MODEL 5-YEAR LIFE SPAN");
        printf("\n CONTACT NGDC FOR PRODUCT UPDATES:");
        printf("\n         National Geophysical Data Center");
        printf("\n         NOAA EGC/2");
        printf("\n         325 Broadway");
        printf("\n         Boulder, CO 80303 USA");
        printf("\n         Attn: Manoj Nair or Stefan Maus");
        printf("\n         Phone:  (303) 497-4642 or -6522");
        printf("\n         Email:  Manoj.C.Nair@Noaa.Gov");
        printf("\n         or");
        printf("\n         Stefan.Maus@noaa.gov");
        printf("\n         Web: http://www.ngdc.noaa.gov/geomag/WMM/");
        printf("\n\n EPOCH  = %.3lf",epoch);
        printf("\n TIME   = %.3lf",time);
        printf("\n Do you wish to continue? (y or n) ");

        res = scanf("%c%*[^\n]",&answer);
        getchar();
        if ((answer == 'n') || (answer == 'N'))
            goto MORE;
    }

    geomag_calc(alt,dlat,dlon,time,&dec,&dip,&ti,&gv);
    time1 = time;
    dec1 = dec;
    dip1 = dip;
    ti1 = ti;
    time = time1 + 1.0;

    geomag_calc(alt,dlat,dlon,time,&dec,&dip,&ti,&gv);
    dec2 = dec;
    dip2 = dip;
    ti2 = ti;

    /*COMPUTE X, Y, Z, AND H COMPONENTS OF THE MAGNETIC FIELD*/

    x1=ti1*(cos((dec1*rTd))*cos((dip1*rTd)));
    x2=ti2*(cos((dec2*rTd))*cos((dip2*rTd)));
    y1=ti1*(cos((dip1*rTd))*sin((dec1*rTd)));
    y2=ti2*(cos((dip2*rTd))*sin((dec2*rTd)));
    z1=ti1*(sin((dip1*rTd)));
    z2=ti2*(sin((dip2*rTd)));
    h1=ti1*(cos((dip1*rTd)));
    h2=ti2*(cos((dip2*rTd)));

    /*  COMPUTE ANNUAL CHANGE FOR TOTAL INTENSITY  */
    ati = ti2 - ti1;

    /*  COMPUTE ANNUAL CHANGE FOR DIP & DEC  */
    adip = (dip2 - dip1) * 60.;
    adec = (dec2 - dec1) * 60.;


    /*  COMPUTE ANNUAL CHANGE FOR X, Y, Z, AND H */
    ax = x2-x1;
    ay = y2-y1;
    az = z2-z1;
    ah = h2-h1;


    if (dec1 < 0.0) { 
        strcpy (decd,"(WEST)");
    }
    else 
    { 
        strcpy(decd,"(EAST)");
    }

    if (dip1 < 0.0) 
    {
        strcpy(dipd,"(UP)  ");
    }
    else 
    {
        strcpy(dipd,"(DOWN)");
    }

    /* deal with geographic and magnetic poles */

    if (h1 < 100.0) /* at magnetic poles */
    {
        dec1 = NaN;
        adec = NaN;
        strcpy(decd,"(VOID)");
        /* while rest is ok */
    }

    if (h1 < 1000.0) 
    {
        warn_H = 0;
        warn_H_strong = 1;
        warn_H_strong_val = h1;
    }
    else if (h1 < 5000.0 && !warn_H_strong) 
    {
        warn_H = 1;
        warn_H_val = h1;
    }


    /* convert D and I to deg and min */
    if (my_isnan(dec1)) ddeg = dec1; else ddeg=(int)dec1;
    dmin=(dec1-(double)ddeg)*60;
    if (dec1 > 0 && dmin >= 59.5)
    {
        dmin -= 60.0;
        ddeg++;
    }
    if (dec1 < 0 && dmin <= -59.5)
    {
        dmin += 60.0;
        ddeg--;
    }
    if(ddeg!=0) dmin=fabs(dmin);

    if (my_isnan(dip1)) ideg = dip1; else ideg=(int)dip1;
    imin=(dip1-(double)ideg)*60;
    if (dip1 > 0 && imin >= 59.5)
    {
        imin -= 60.0;
        ideg++;
    }
    if (dip1 < 0 && imin <= -59.5)
    {
        imin += 60.0;
        ideg--;
    }
    if(ideg!=0) imin=fabs(imin);

    printf("\n Results For \n");
    if (dlat < 0)
        printf("\n LATITUDE:     %7.2lfS",-dlat);
    else
        printf("\n LATITUDE:     %7.2lfN",dlat);
    if (dlon < 0)
        printf("\n LONGITUDE:    %7.2lfW",-dlon);
    else
        printf("\n LONGITUDE:    %7.2lfE",dlon);

    printf("\n ALTITUDE:    %8.2lf KM ABOVE WGS84 ELLIPSOID",altm);
    printf("\n DATE:         %6.1lf\n",time1);


    printf("\n     Main Field    \t\t\t      Secular Change");

    printf("\n F      =    %-9.1lf nT\t\t   dF  = %-8.1lf nT/yr",ti1,ati);
    if (my_isnan(h1))
        printf("\n H      =    NaN         \t\t   dH  = NaN");
    else
        printf("\n H      =    %-9.1lf nT\t\t   dH  = %-8.1lf nT/yr",h1,ah);
    if (my_isnan(x1))
        printf("\n X      =    NaN         \t\t   dX  = NaN");
    else
        printf("\n X      =    %-9.1lf nT\t\t   dX  = %-8.1lf nT/yr ",x1,ax);
    if (my_isnan(y1))
        printf("\n Y      =    NaN         \t\t   dY  = NaN");
    else
        printf("\n Y      =    %-9.1lf nT\t\t   dY  = %-8.1lf nT/yr ",y1,ay);
    printf("\n Z      =    %-9.1lf nT\t\t   dZ  = %-8.1lf nT/yr ",z1,az);
    if (my_isnan(dec1))
        printf("\n D      =    NaN         \t\t   dD  = NaN");
    else
        printf("\n D      = %4.0lf Deg %3.0lf Min  %s\t   dD  = %-8.1lf Min/yr",ddeg,dmin,decd,adec); 
    printf("\n I      = %4.0lf Deg %3.0lf Min  %s\t   dI  = %-8.1lf Min/yr",ideg,imin,dipd,adip); 

    if (warn_H)
    {
        printf("\n\nWarning: The horizontal field strength at this location is only %6.1lf nT\n",warn_H_val);
        printf("         Compass readings have large uncertainties in areas where H is\n");
        printf("         smaller than 5000 nT\n");
    } 
    if (warn_H_strong)
    {
        printf("\n\nWarning: The horizontal field strength at this location is only %6.1lf nT\n",warn_H_strong_val);
        printf("         Compass readings have VERY LARGE uncertainties in areas where H is\n");
        printf("         smaller than 1000 nT\n");
    }
    if (warn_P)
    {
        printf("\n\nWarning: Location is at geographic pole where X, Y, and Decl are undefined\n");
    } 

MORE:

    printf("\n\nDO YOU NEED MORE POINT DATA? (y or n) ");
    res = scanf("%c%*[^\n]", &answer);
    getchar();

    if ((answer =='y')||(answer == 'Y')) goto S1;
    else 
    {
        printf("%s",goodbye);
    }

}