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                    1
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                # -*- coding: utf-8 -*-  | 
            
            
                                                        
            
                                    
            
            
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                    2
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                """Pythonic wrappers for AACGM-V2 C functions that were depricated in the  | 
            
            
                                                        
            
                                    
            
            
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                    3
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                change from version 2.0.0 to version 2.0.2  | 
            
            
                                                        
            
                                    
            
            
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                    4
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                    5
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                Functions  | 
            
            
                                                        
            
                                    
            
            
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                    6
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                -------------------------------------------------------------------------------  | 
            
            
                                                        
            
                                    
            
            
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                    7
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                convert : Converts array location  | 
            
            
                                                        
            
                                    
            
            
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                    8
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                subsol : finds subsolar geocentric longitude and latitude  | 
            
            
                                                        
            
                                    
            
            
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                    9
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                gc2gd_lat : Convert between geocentric and geodetic coordinates  | 
            
            
                                                        
            
                                    
            
            
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                    10
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                igrf_dipole_axis : Get Cartesian unit vector pointing at the IGRF north dipole  | 
            
            
                                                        
            
                                    
            
            
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                    11
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                ------------------------------------------------------------------------------  | 
            
            
                                                        
            
                                    
            
            
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                    13
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                References  | 
            
            
                                                        
            
                                    
            
            
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                    14
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                -------------------------------------------------------------------------------  | 
            
            
                                                        
            
                                    
            
            
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                    15
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                Laundal, K. M. and A. D. Richmond (2016), Magnetic Coordinate Systems, Space  | 
            
            
                                                        
            
                                    
            
            
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                    16
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                 Sci. Rev., doi:10.1007/s11214-016-0275-y.  | 
            
            
                                                        
            
                                    
            
            
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                    17
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                -------------------------------------------------------------------------------  | 
            
            
                                                        
            
                                    
            
            
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                    18
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                """  | 
            
            
                                                        
            
                                    
            
            
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                    19
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                    20
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                from __future__ import division, absolute_import, unicode_literals  | 
            
            
                                                        
            
                                    
            
            
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                    21
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                import numpy as np  | 
            
            
                                                        
            
                                    
            
            
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                    22
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                import logbook as logging  | 
            
            
                                                        
            
                                    
            
            
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                    23
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                import warnings  | 
            
            
                                                        
            
                                    
            
            
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                    24
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                    25
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                def convert(lat, lon, alt, date=None, a2g=False, trace=False, allowtrace=False,  | 
            
            
                                                        
            
                                    
            
            
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                    26
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                            badidea=False, geocentric=False):  | 
            
            
                                                        
            
                                    
            
            
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                    27
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                    """Converts between geomagnetic coordinates and AACGM coordinates  | 
            
            
                                                        
            
                                    
            
            
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                    28
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                    29
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                    Parameters  | 
            
            
                                                        
            
                                    
            
            
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                    30
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                    ------------  | 
            
            
                                                        
            
                                    
            
            
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                    31
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                    lat : (float)  | 
            
            
                                                        
            
                                    
            
            
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                    32
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                        Input latitude in degrees N (code specifies type of latitude)  | 
            
            
                                                        
            
                                    
            
            
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                    33
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                    lon : (float)  | 
            
            
                                                        
            
                                    
            
            
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                    34
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                        Input longitude in degrees E (code specifies type of longitude)  | 
            
            
                                                        
            
                                    
            
            
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                    35
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                    alt : (float)  | 
            
            
                                                        
            
                                    
            
            
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                    36
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                        Altitude above the surface of the earth in km  | 
            
            
                                                        
            
                                    
            
            
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                    37
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                    date : (datetime)  | 
            
            
                                                        
            
                                    
            
            
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                    38
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                        Datetime for magnetic field  | 
            
            
                                                        
            
                                    
            
            
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                    39
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                    a2g : (bool)  | 
            
            
                                                        
            
                                    
            
            
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                    40
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                        True for AACGM-v2 to geographic (geodetic), False otherwise  | 
            
            
                                                        
            
                                    
            
            
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                    41
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                        (default=False)  | 
            
            
                                                        
            
                                    
            
            
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                    42
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                    trace : (bool)  | 
            
            
                                                        
            
                                    
            
            
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                    43
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                        If True, use field-line tracing, not coefficients (default=False)  | 
            
            
                                                        
            
                                    
            
            
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                    44
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                    allowtrace : (bool)  | 
            
            
                                                        
            
                                    
            
            
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                    45
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                        If True, use trace only above 2000 km (default=False)  | 
            
            
                                                        
            
                                    
            
            
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                    46
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                    badidea : (bool)  | 
            
            
                                                        
            
                                    
            
            
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                    47
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                        If True, use coefficients above 2000 km (default=False)  | 
            
            
                                                        
            
                                    
            
            
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                    48
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                    geocentric : (bool)  | 
            
            
                                                        
            
                                    
            
            
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                    49
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                        True for geodetic, False for geocentric w/RE=6371.2 (default=False)  | 
            
            
                                                        
            
                                    
            
            
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                    50
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                 | 
            
            
                                                        
            
                                    
            
            
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                    51
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                    Returns  | 
            
            
                                                        
            
                                    
            
            
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                    52
                 | 
                                    
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                    -------  | 
            
            
                                                        
            
                                    
            
            
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                    53
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                    lat_out : (float)  | 
            
            
                                                        
            
                                    
            
            
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                    54
                 | 
                                    
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                        Output latitude in degrees N  | 
            
            
                                                        
            
                                    
            
            
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                    55
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                    lon_out : (float)  | 
            
            
                                                        
            
                                    
            
            
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                    56
                 | 
                                    
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                        Output longitude in degrees E  | 
            
            
                                                        
            
                                    
            
            
                | 
                    57
                 | 
                                    
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                    """  | 
            
            
                                                        
            
                                    
            
            
                | 
                    58
                 | 
                                    
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                 | 
                    import aacgmv2  | 
            
            
                                                        
            
                                    
            
            
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                    59
                 | 
                                    
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                 | 
            
            
                                                        
            
                                    
            
            
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                    60
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                    dstr = "Deprecated routine, may be removed in future versions.  Recommend "  | 
            
            
                                                        
            
                                    
            
            
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                    61
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                    dstr += "using convert_latlon or convert_latlon_arr"  | 
            
            
                                                        
            
                                    
            
            
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                    62
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                 | 
                    warnings.warn(dstr, category=FutureWarning)  | 
            
            
                                                        
            
                                    
            
            
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                    63
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                 | 
            
            
                                                        
            
                                    
            
            
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                    64
                 | 
                                    
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                    if(np.array(alt).max() > 2000 and not trace and not allowtrace and  | 
            
            
                                                        
            
                                    
            
            
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                    65
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                       not badidea):  | 
            
            
                                                        
            
                                    
            
            
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                    66
                 | 
                                    
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                        estr = 'coefficients are not valid for altitudes above 2000 km. You'  | 
            
            
                                                        
            
                                    
            
            
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                    67
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                        estr += ' must either use field-line tracing (trace=True '  | 
            
            
                                                        
            
                                    
            
            
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                    68
                 | 
                                    
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                 | 
                        estr += 'or allowtrace=True) or indicate you know this is a bad idea'  | 
            
            
                                                        
            
                                    
            
            
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                    69
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                        estr += ' (badidea=True)'  | 
            
            
                                                        
            
                                    
            
            
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                    70
                 | 
                                    
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                        logging.error(estr)  | 
            
            
                                                        
            
                                    
            
            
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                    71
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                        raise ValueError(estr)  | 
            
            
                                                        
            
                                    
            
            
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                    72
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                 | 
            
            
                                                        
            
                                    
            
            
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                    73
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                    # construct a code from the boolian flags  | 
            
            
                                                        
            
                                    
            
            
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                    74
                 | 
                                    
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                    bit_code = aacgmv2.convert_bool_to_bit(a2g=a2g, trace=trace,  | 
            
            
                                                        
            
                                    
            
            
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                    75
                 | 
                                    
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                                                           allowtrace=allowtrace,  | 
            
            
                                                        
            
                                    
            
            
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                    76
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                                                           badidea=badidea,  | 
            
            
                                                        
            
                                    
            
            
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                    77
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                                                           geocentric=geocentric)  | 
            
            
                                                        
            
                                    
            
            
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                    78
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                 | 
            
            
                                                        
            
                                    
            
            
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                    79
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                    # convert location  | 
            
            
                                                        
            
                                    
            
            
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                    80
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                    lat_out, lon_out, _ = aacgmv2.convert_latlon_arr(lat, lon, alt, date,  | 
            
            
                                                        
            
                                    
            
            
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                    81
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                                                                     code=bit_code)  | 
            
            
                                                        
            
                                    
            
            
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                    82
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                 | 
            
            
                                                        
            
                                    
            
            
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                    83
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                    return lat_out, lon_out  | 
            
            
                                                        
            
                                    
            
            
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                    84
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                 | 
            
            
                                                        
            
                                    
            
            
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                    85
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                def subsol(year, doy, utime):  | 
            
            
                                                        
            
                                    
            
            
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                    86
                 | 
                                    
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                    """Finds subsolar geocentric longitude and latitude.  | 
            
            
                                                        
            
                                    
            
            
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                    87
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                 | 
            
            
                                                        
            
                                    
            
            
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                    88
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                    Parameters  | 
            
            
                                                        
            
                                    
            
            
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                    89
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                    ------------  | 
            
            
                                                        
            
                                    
            
            
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                    90
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                    year : (int)  | 
            
            
                                                        
            
                                    
            
            
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                    91
                 | 
                                    
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                        Calendar year between 1601 and 2100  | 
            
            
                                                        
            
                                    
            
            
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                    92
                 | 
                                    
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                    doy : (int)  | 
            
            
                                                        
            
                                    
            
            
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                    93
                 | 
                                    
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                        Day of year between 1-365/366  | 
            
            
                                                        
            
                                    
            
            
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                    94
                 | 
                                    
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                    utime : (float)  | 
            
            
                                                        
            
                                    
            
            
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                    95
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                        Seconds since midnight on the specified day  | 
            
            
                                                        
            
                                    
            
            
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                    96
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                 | 
            
            
                                                        
            
                                    
            
            
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                    97
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                    Returns  | 
            
            
                                                        
            
                                    
            
            
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                    98
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                    ---------  | 
            
            
                                                        
            
                                    
            
            
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                    99
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                    sbsllon : (float)  | 
            
            
                                                        
            
                                    
            
            
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                    100
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                        Subsolar longitude in degrees E for the given date/time  | 
            
            
                                                        
            
                                    
            
            
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                    101
                 | 
                                    
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                    sbsllat : (float)  | 
            
            
                                                        
            
                                    
            
            
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                    102
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                        Subsolar latitude in degrees N for the given date/time  | 
            
            
                                                        
            
                                    
            
            
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                    103
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                 | 
            
            
                                                        
            
                                    
            
            
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                    104
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                    Notes  | 
            
            
                                                        
            
                                    
            
            
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                    105
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                    --------  | 
            
            
                                                        
            
                                    
            
            
                | 
                    106
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                    Based on formulas in Astronomical Almanac for the year 1996, p. C24.  | 
            
            
                                                        
            
                                    
            
            
                | 
                    107
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                    (U.S. Government Printing Office, 1994). Usable for years 1601-2100,  | 
            
            
                                                        
            
                                    
            
            
                | 
                    108
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                    inclusive. According to the Almanac, results are good to at least 0.01  | 
            
            
                                                        
            
                                    
            
            
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                    109
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                    degree latitude and 0.025 degrees longitude between years 1950 and 2050.  | 
            
            
                                                        
            
                                    
            
            
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                    110
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                    Accuracy for other years has not been tested. Every day is assumed to have  | 
            
            
                                                        
            
                                    
            
            
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                    111
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                    exactly 86400 seconds; thus leap seconds that sometimes occur on December  | 
            
            
                                                        
            
                                    
            
            
                | 
                    112
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                    31 are ignored (their effect is below the accuracy threshold of the  | 
            
            
                                                        
            
                                    
            
            
                | 
                    113
                 | 
                                    
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                    algorithm).  | 
            
            
                                                        
            
                                    
            
            
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                    114
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                    After Fortran code by A. D. Richmond, NCAR. Translated from IDL  | 
            
            
                                                        
            
                                    
            
            
                | 
                    115
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                    by K. Laundal.  | 
            
            
                                                        
            
                                    
            
            
                | 
                    116
                 | 
                                    
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                 | 
                    """  | 
            
            
                                                        
            
                                    
            
            
                | 
                    117
                 | 
                                    
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                    dstr = "Deprecated routine, may be removed in future versions"  | 
            
            
                                                        
            
                                    
            
            
                | 
                    118
                 | 
                                    
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                    warnings.warn(dstr, category=FutureWarning)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    119
                 | 
                                    
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                 | 
            
            
                                                        
            
                                    
            
            
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                    120
                 | 
                                    
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                      | 
            
            
                                                        
            
                                    
            
            
                | 
                    121
                 | 
                                    
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                    yr2 = year - 2000  | 
            
            
                                                        
            
                                    
            
            
                | 
                    122
                 | 
                                    
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                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    123
                 | 
                                    
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                 | 
                    if year >= 2101:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    124
                 | 
                                    
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                 | 
                        logging.error('subsol invalid after 2100. Input year is:', year) | 
            
            
                                                        
            
                                    
            
            
                | 
                    125
                 | 
                                    
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                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    126
                 | 
                                    
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                 | 
                    nleap = np.floor((year - 1601) / 4)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    127
                 | 
                                    
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                 | 
                    nleap = nleap - 99  | 
            
            
                                                        
            
                                    
            
            
                | 
                    128
                 | 
                                    
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                 | 
                    if year <= 1900:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    129
                 | 
                                    
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                 | 
                        if year <= 1600:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    130
                 | 
                                    
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                 | 
                            print('subsol.py: subsol invalid before 1601. Input year is:', year) | 
            
            
                                                        
            
                                    
            
            
                | 
                    131
                 | 
                                    
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                 | 
                        ncent = np.floor((year - 1601) / 100)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    132
                 | 
                                    
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                 | 
                        ncent = 3 - ncent  | 
            
            
                                                        
            
                                    
            
            
                | 
                    133
                 | 
                                    
                                                     | 
                
                 | 
                        nleap = nleap + ncent  | 
            
            
                                                        
            
                                    
            
            
                | 
                    134
                 | 
                                    
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                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    135
                 | 
                                    
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                 | 
                    l_0 = -79.549 + (-0.238699 * (yr2 - 4 * nleap) + 3.08514e-2 * nleap)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    136
                 | 
                                    
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                 | 
                    g_0 = -2.472 + (-0.2558905 * (yr2 - 4 * nleap) - 3.79617e-2 * nleap)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    137
                 | 
                                    
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                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    138
                 | 
                                    
                                                     | 
                
                 | 
                    # Days (including fraction) since 12 UT on January 1 of IYR2:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    139
                 | 
                                    
                                                     | 
                
                 | 
                    dfrac = (utime / 86400 - 1.5) + doy  | 
            
            
                                                        
            
                                    
            
            
                | 
                    140
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    141
                 | 
                                    
                                                     | 
                
                 | 
                    # Mean longitude of Sun:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    142
                 | 
                                    
                                                     | 
                
                 | 
                    l_sun = l_0 + 0.9856474 * dfrac  | 
            
            
                                                        
            
                                    
            
            
                | 
                    143
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    144
                 | 
                                    
                                                     | 
                
                 | 
                    # Mean anomaly:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    145
                 | 
                                    
                                                     | 
                
                 | 
                    grad = np.radians(g_0 + 0.9856003 * dfrac)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    146
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    147
                 | 
                                    
                                                     | 
                
                 | 
                    # Ecliptic longitude:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    148
                 | 
                                    
                                                     | 
                
                 | 
                    lmrad = np.radians(l_sun + 1.915 * np.sin(grad) + 0.020 * np.sin(2 * grad))  | 
            
            
                                                        
            
                                    
            
            
                | 
                    149
                 | 
                                    
                                                     | 
                
                 | 
                    sinlm = np.sin(lmrad)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    150
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    151
                 | 
                                    
                                                     | 
                
                 | 
                    # Days (including fraction) since 12 UT on January 1 of 2000:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    152
                 | 
                                    
                                                     | 
                
                 | 
                    epoch_day = dfrac + 365.0 * yr2 + nleap  | 
            
            
                                                        
            
                                    
            
            
                | 
                    153
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    154
                 | 
                                    
                                                     | 
                
                 | 
                    # Obliquity of ecliptic:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    155
                 | 
                                    
                                                     | 
                
                 | 
                    epsrad = np.radians(23.439 - 4.0e-7 * epoch_day)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    156
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    157
                 | 
                                    
                                                     | 
                
                 | 
                    # Right ascension:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    158
                 | 
                                    
                                                     | 
                
                 | 
                    alpha = np.degrees(np.arctan2(np.cos(epsrad) * sinlm, np.cos(lmrad)))  | 
            
            
                                                        
            
                                    
            
            
                | 
                    159
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    160
                 | 
                                    
                                                     | 
                
                 | 
                    # Declination, which is the subsolar latitude:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    161
                 | 
                                    
                                                     | 
                
                 | 
                    sbsllat = np.degrees(np.arcsin(np.sin(epsrad) * sinlm))  | 
            
            
                                                        
            
                                    
            
            
                | 
                    162
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    163
                 | 
                                    
                                                     | 
                
                 | 
                    # Equation of time (degrees):  | 
            
            
                                                        
            
                                    
            
            
                | 
                    164
                 | 
                                    
                                                     | 
                
                 | 
                    etdeg = l_sun - alpha  | 
            
            
                                                        
            
                                    
            
            
                | 
                    165
                 | 
                                    
                                                     | 
                
                 | 
                    etdeg = etdeg - 360.0 * np.round(etdeg / 360.0)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    166
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    167
                 | 
                                    
                                                     | 
                
                 | 
                    # Apparent time (degrees):  | 
            
            
                                                        
            
                                    
            
            
                | 
                    168
                 | 
                                    
                                                     | 
                
                 | 
                    aptime = utime / 240.0 + etdeg    # Earth rotates one degree every 240 s.  | 
            
            
                                                        
            
                                    
            
            
                | 
                    169
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    170
                 | 
                                    
                                                     | 
                
                 | 
                    # Subsolar longitude:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    171
                 | 
                                    
                                                     | 
                
                 | 
                    sbsllon = 180.0 - aptime  | 
            
            
                                                        
            
                                    
            
            
                | 
                    172
                 | 
                                    
                                                     | 
                
                 | 
                    sbsllon = sbsllon - 360.0 * np.round(sbsllon / 360.0)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    173
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    174
                 | 
                                    
                                                     | 
                
                 | 
                    return sbsllon, sbsllat  | 
            
            
                                                        
            
                                    
            
            
                | 
                    175
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    176
                 | 
                                    
                                                     | 
                
                 | 
                def gc2gd_lat(gc_lat):  | 
            
            
                                                        
            
                                    
            
            
                | 
                    177
                 | 
                                    
                                                     | 
                
                 | 
                    """Convert geocentric latitude to geodetic latitude using WGS84.  | 
            
            
                                                        
            
                                    
            
            
                | 
                    178
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    179
                 | 
                                    
                                                     | 
                
                 | 
                    Parameters  | 
            
            
                                                        
            
                                    
            
            
                | 
                    180
                 | 
                                    
                                                     | 
                
                 | 
                    -----------  | 
            
            
                                                        
            
                                    
            
            
                | 
                    181
                 | 
                                    
                                                     | 
                
                 | 
                    gc_lat : (array_like or float)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    182
                 | 
                                    
                                                     | 
                
                 | 
                        Geocentric latitude in degrees N  | 
            
            
                                                        
            
                                    
            
            
                | 
                    183
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    184
                 | 
                                    
                                                     | 
                
                 | 
                    Returns  | 
            
            
                                                        
            
                                    
            
            
                | 
                    185
                 | 
                                    
                                                     | 
                
                 | 
                    ---------  | 
            
            
                                                        
            
                                    
            
            
                | 
                    186
                 | 
                                    
                                                     | 
                
                 | 
                    gd_lat : (same as input)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    187
                 | 
                                    
                                                     | 
                
                 | 
                        Geodetic latitude in degrees N  | 
            
            
                                                        
            
                                    
            
            
                | 
                    188
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                        
            
                                    
            
            
                | 
                    189
                 | 
                                    
                                                     | 
                
                 | 
                    dstr = "Deprecated routine, may be removed in future versions"  | 
            
            
                                                        
            
                                    
            
            
                | 
                    190
                 | 
                                    
                                                     | 
                
                 | 
                    warnings.warn(dstr, category=FutureWarning)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    191
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    192
                 | 
                                    
                                                     | 
                
                 | 
                      | 
            
            
                                                        
            
                                    
            
            
                | 
                    193
                 | 
                                    
                                                     | 
                
                 | 
                    wgs84_e2 = 0.006694379990141317 - 1.0  | 
            
            
                                                        
            
                                    
            
            
                | 
                    194
                 | 
                                    
                                                     | 
                
                 | 
                    return np.rad2deg(-np.arctan(np.tan(np.deg2rad(gc_lat)) / wgs84_e2))  | 
            
            
                                                        
            
                                    
            
            
                | 
                    195
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    196
                 | 
                                    
                                                     | 
                
                 | 
                def igrf_dipole_axis(date):  | 
            
            
                                                        
            
                                    
            
            
                | 
                    197
                 | 
                                    
                                                     | 
                
                 | 
                    """Get Cartesian unit vector pointing at dipole pole in the north,  | 
            
            
                                                        
            
                                    
            
            
                | 
                    198
                 | 
                                    
                                                     | 
                
                 | 
                    according to IGRF  | 
            
            
                                                        
            
                                    
            
            
                | 
                    199
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    200
                 | 
                                    
                                                     | 
                
                 | 
                    Parameters  | 
            
            
                                                        
            
                                    
            
            
                | 
                    201
                 | 
                                    
                                                     | 
                
                 | 
                    -------------  | 
            
            
                                                        
            
                                    
            
            
                | 
                    202
                 | 
                                    
                                                     | 
                
                 | 
                    date : (dt.datetime)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    203
                 | 
                                    
                                                     | 
                
                 | 
                        Date and time  | 
            
            
                                                        
            
                                    
            
            
                | 
                    204
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    205
                 | 
                                    
                                                     | 
                
                 | 
                    Returns  | 
            
            
                                                        
            
                                    
            
            
                | 
                    206
                 | 
                                    
                                                     | 
                
                 | 
                    ----------  | 
            
            
                                                        
            
                                    
            
            
                | 
                    207
                 | 
                                    
                                                     | 
                
                 | 
                    m_0: (np.ndarray)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    208
                 | 
                                    
                                                     | 
                
                 | 
                        Cartesian 3 element unit vector pointing at dipole pole in the north  | 
            
            
                                                        
            
                                    
            
            
                | 
                    209
                 | 
                                    
                                                     | 
                
                 | 
                        (geocentric coords)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    210
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    211
                 | 
                                    
                                                     | 
                
                 | 
                    Notes  | 
            
            
                                                        
            
                                    
            
            
                | 
                    212
                 | 
                                    
                                                     | 
                
                 | 
                    ----------  | 
            
            
                                                        
            
                                    
            
            
                | 
                    213
                 | 
                                    
                                                     | 
                
                 | 
                    IGRF coefficients are read from the igrf12coeffs.txt file. It should also  | 
            
            
                                                        
            
                                    
            
            
                | 
                    214
                 | 
                                    
                                                     | 
                
                 | 
                    work after IGRF updates.  The dipole coefficients are interpolated to the  | 
            
            
                                                        
            
                                    
            
            
                | 
                    215
                 | 
                                    
                                                     | 
                
                 | 
                    date, or extrapolated if date > latest IGRF model  | 
            
            
                                                        
            
                                    
            
            
                | 
                    216
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                        
            
                                    
            
            
                | 
                    217
                 | 
                                    
                                                     | 
                
                 | 
                    import datetime as dt  | 
            
            
                                                        
            
                                    
            
            
                | 
                    218
                 | 
                                    
                                                     | 
                
                 | 
                    import aacgmv2  | 
            
            
                                                        
            
                                    
            
            
                | 
                    219
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    220
                 | 
                                    
                                                     | 
                
                 | 
                    dstr = "Deprecated routine, may be removed in future versions"  | 
            
            
                                                        
            
                                    
            
            
                | 
                    221
                 | 
                                    
                                                     | 
                
                 | 
                    warnings.warn(dstr, category=FutureWarning)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    222
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    223
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    224
                 | 
                                    
                                                     | 
                
                 | 
                    # get time in years, as float:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    225
                 | 
                                    
                                                     | 
                
                 | 
                    year = date.year  | 
            
            
                                                        
            
                                    
            
            
                | 
                    226
                 | 
                                    
                                                     | 
                
                 | 
                    doy = date.timetuple().tm_yday  | 
            
            
                                                        
            
                                    
            
            
                | 
                    227
                 | 
                                    
                                                     | 
                
                 | 
                    year_days = int(dt.date(date.year, 12, 31).strftime("%j")) | 
            
            
                                                        
            
                                    
            
            
                | 
                    228
                 | 
                                    
                                                     | 
                
                 | 
                    year = year + doy / year_days  | 
            
            
                                                        
            
                                    
            
            
                | 
                    229
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    230
                 | 
                                    
                                                     | 
                
                 | 
                    # read the IGRF coefficients  | 
            
            
                                                        
            
                                    
            
            
                | 
                    231
                 | 
                                    
                                                     | 
                
                 | 
                    with open(aacgmv2.IGRF_COEFFS, 'r') as f_igrf:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    232
                 | 
                                    
                                                     | 
                
                 | 
                        lines = f_igrf.readlines()  | 
            
            
                                                        
            
                                    
            
            
                | 
                    233
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    234
                 | 
                                    
                                                     | 
                
                 | 
                    years = lines[3].split()[3:][:-1]  | 
            
            
                                                        
            
                                    
            
            
                | 
                    235
                 | 
                                    
                                                     | 
                
                 | 
                    years = np.array(years, dtype=float)  # time array  | 
            
            
                                                        
            
                                    
            
            
                | 
                    236
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    237
                 | 
                                    
                                                     | 
                
                 | 
                    g10 = lines[4].split()[3:]  | 
            
            
                                                        
            
                                    
            
            
                | 
                    238
                 | 
                                    
                                                     | 
                
                 | 
                    g11 = lines[5].split()[3:]  | 
            
            
                                                        
            
                                    
            
            
                | 
                    239
                 | 
                                    
                                                     | 
                
                 | 
                    h11 = lines[6].split()[3:]  | 
            
            
                                                        
            
                                    
            
            
                | 
                    240
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    241
                 | 
                                    
                                                     | 
                
                 | 
                    # secular variation coefficients (for extrapolation)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    242
                 | 
                                    
                                                     | 
                
                 | 
                    g10sv = np.float32(g10[-1])  | 
            
            
                                                        
            
                                    
            
            
                | 
                    243
                 | 
                                    
                                                     | 
                
                 | 
                    g11sv = np.float32(g11[-1])  | 
            
            
                                                        
            
                                    
            
            
                | 
                    244
                 | 
                                    
                                                     | 
                
                 | 
                    h11sv = np.float32(h11[-1])  | 
            
            
                                                        
            
                                    
            
            
                | 
                    245
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    246
                 | 
                                    
                                                     | 
                
                 | 
                    # model coefficients:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    247
                 | 
                                    
                                                     | 
                
                 | 
                    g10 = np.array(g10[:-1], dtype=float)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    248
                 | 
                                    
                                                     | 
                
                 | 
                    g11 = np.array(g11[:-1], dtype=float)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    249
                 | 
                                    
                                                     | 
                
                 | 
                    h11 = np.array(h11[:-1], dtype=float)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    250
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    251
                 | 
                                    
                                                     | 
                
                 | 
                    # get the gauss coefficient at given time:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    252
                 | 
                                    
                                                     | 
                
                 | 
                    if year <= years[-1]:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    253
                 | 
                                    
                                                     | 
                
                 | 
                        # regular interpolation  | 
            
            
                                                        
            
                                    
            
            
                | 
                    254
                 | 
                                    
                                                     | 
                
                 | 
                        g10 = np.interp(year, years, g10)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    255
                 | 
                                    
                                                     | 
                
                 | 
                        g11 = np.interp(year, years, g11)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    256
                 | 
                                    
                                                     | 
                
                 | 
                        h11 = np.interp(year, years, h11)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    257
                 | 
                                    
                                                     | 
                
                 | 
                    else:  | 
            
            
                                                        
            
                                    
            
            
                | 
                    258
                 | 
                                    
                                                     | 
                
                 | 
                        # extrapolation  | 
            
            
                                                        
            
                                    
            
            
                | 
                    259
                 | 
                                    
                                                     | 
                
                 | 
                        dyear = year - years[-1]  | 
            
            
                                                        
            
                                    
            
            
                | 
                    260
                 | 
                                    
                                                     | 
                
                 | 
                        g10 = g10[-1] + g10sv * dyear  | 
            
            
                                                        
            
                                    
            
            
                | 
                    261
                 | 
                                    
                                                     | 
                
                 | 
                        g11 = g11[-1] + g11sv * dyear  | 
            
            
                                                        
            
                                    
            
            
                | 
                    262
                 | 
                                    
                                                     | 
                
                 | 
                        h11 = h11[-1] + h11sv * dyear  | 
            
            
                                                        
            
                                    
            
            
                | 
                    263
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    264
                 | 
                                    
                                                     | 
                
                 | 
                    # calculate pole position  | 
            
            
                                                        
            
                                    
            
            
                | 
                    265
                 | 
                                    
                                                     | 
                
                 | 
                    B_0 = np.sqrt(g10**2 + g11**2 + h11**2)  | 
            
            
                                                        
            
                                    
            
            
                | 
                    266
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    267
                 | 
                                    
                                                     | 
                
                 | 
                    # Calculate output  | 
            
            
                                                        
            
                                    
            
            
                | 
                    268
                 | 
                                    
                                                     | 
                
                 | 
                    m_0 = -np.array([g11, h11, g10]) / B_0  | 
            
            
                                                        
            
                                    
            
            
                | 
                    269
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    270
                 | 
                                    
                                                     | 
                
                 | 
                    return m_0  | 
            
            
                                                        
            
                                    
            
            
                | 
                    271
                 | 
                                    
                                                     | 
                
                 | 
                 |