Quickstart: Load and Plot MMS Data

author: Louis Richard

Sets up the local MMS data path, loads the magnetic field (FGM survey), the electric field (EDP fast) and the ion and electron moments and omnidirectional energy spectra (FPI fast) of MMS1, and plots an overview. Then loads the magnetic field and position (MEC) of the four spacecraft and plots the magnetic field components measured by each spacecraft.

Getting started

To get up and running with Python, virtual environments and pyrfu, see:

https://pyrfu.readthedocs.io/en/latest/getting_started.html#installation

Python 3.12 or later is required.

Virtual environments

It is best to set up and use a virtual environment with Python: it avoids common dependency problems when you install several packages. To create one:

python -m venv pyrfu-tutorial

Then, to activate the virtual environment on macOS and Linux:

source pyrfu-tutorial/bin/activate

To exit the virtual environment, type deactivate.

Install pyrfu

pip install pyrfu ### Upgrade pyrfu pip install pyrfu --upgrade ### Local data directory The local data directory is the root data directory of the MMS files. It is set with mms.db_init (see below). For example, with local="/Volumes/mms", your data are stored in /Volumes/mms.

The supported load routines include: - Fluxgate Magnetometer (FGM) - Search-coil Magnetometer (SCM) - Electric field Double Probe (EDP) - Fast Plasma Investigation (FPI) - Hot Plasma Composition Analyzer (HPCA) - Energetic Ion Spectrometer (EIS) - Fly’s Eye Energetic Particle Sensor (FEEPS) - Ephemeris and Coordinates (MEC)

Import MMS routines

from pyrfu import mms

Load IGRF coefficients ...

Define time interval

tint = ["2019-09-14T07:54:00.000", "2019-09-14T08:11:00.000"]

Set up the MMS data path

The MMS data path is set up with mms.db_init.

mms.db_init(default="local", local="/Volumes/mms")

Download data from the MMS Science Data Center

help(mms.download_data)

Help on function download_data in module pyrfu.mms.download_data:

download_data(var_str, tint, mms_id, login: str = '', password: str = '', data_path: str = '')
    Downloads files containing field `var_str` over the time interval
    `tint` for the spacecraft `mms_id`. The files are saved to `data_path`.

    Parameters
    ----------
    var_str : str
        Input key of variable.
    tint : list of str
        Time interval.
    mms_id : str or int
        Index of the target spacecraft.
    login : str, Optional
        Login to LASP MMS SITL. Default downloads from
        https://lasp.colorado.edu/mms/sdc/public/
    password : str, Optional
        Password to LASP MMS SITL. Default downloads from
        https://lasp.colorado.edu/mms/sdc/public/
    data_path : str, Optional
        Path of MMS data. If None use `pyrfu/mms/config.json`

help(mms.download_ancillary)

Help on function download_ancillary in module pyrfu.mms.download_ancillary:

download_ancillary(product, tint, mms_id, login: str = '', password: str = '', data_path: str = '')
    Downloads files containing field `var_str` over the time interval
    `tint` for the spacecraft `mms_id`. The files are saved to `data_path`.

    Parameters
    ----------
    product : {"predatt", "predeph", "defatt", "defeph"}
        Ancillary type.
    tint : list of str
        Time interval
    mms_id : str or int
        Spacecraft index
    login : str, Optional
        Login to LASP MMS SITL. Default downloads from
        https://lasp.colorado.edu/mms/sdc/public/
    password : str, Optional
        Password to LASP MMS SITL. Default downloads from
        https://lasp.colorado.edu/mms/sdc/public/
    data_path : str, Optional
        Path of MMS data. If None use `pyrfu/mms/config.json`

Load data

The keywords to access the data are listed in the help of mms.get_data.

help(mms.get_data)

Help on function get_data in module pyrfu.mms.get_data:

get_data(var_str, tint, mms_id, verbose: bool = True, data_path: str = '')
    Load a variable. var_str must be in var (see below)

    Parameters
    ----------
    var_str : str
        Key of the target variable (use mms.get_data() to see keys.).
    tint : list of str
        Time interval.
    mms_id : str or int
        Index of the target spacecraft.
    verbose : bool, Optional
        Set to True to follow the loading. Default is True.
    data_path : str, Optional
        Path of MMS data. If None use `pyrfu/mms/config.json`

    Returns
    -------
    out : xarray.DataArray or xarray.Dataset
        Time series of the target variable of measured by the target
        spacecraft over the selected time interval.

    See also
    --------
    pyrfu.mms.get_ts : Read time series.
    pyrfu.mms.get_dist : Read velocity distribution function.

    Examples
    --------
    >>> from pyrfu import mms

    Define time interval

    >>> tint_brst = ["2019-09-14T07:54:00.000", "2019-09-14T08:11:00.000"]

    Index of MMS spacecraft

    >>> ic = 1

    Load magnetic field from FGM

    >>> b_xyz = mms.get_data("B_gse_fgm_brst_l2", tint_brst, ic)

Load magnetic field (FGM)

b_xyz = mms.get_data("b_gse_fgm_srvy_l2", tint, 1)

[21-Jul-23 09:26:54] INFO: Loading mms1_fgm_b_gse_srvy_l2...

Time series are xarray.DataArray objects

b_xyz

<xarray.DataArray (time: 16320, represent_vec_tot: 3)>
array([[-2.1031418 , -1.6935391 ,  2.835863  ],
       [-2.1007674 , -1.7059438 ,  2.8462613 ],
       [-2.1185403 , -1.6850468 ,  2.8634877 ],
       ...,
       [-0.7177708 ,  1.81181   ,  5.15961   ],
       [-0.75993973,  1.8259526 ,  5.165373  ],
       [-0.7561481 ,  1.8053148 ,  5.204192  ]], dtype=float32)
Coordinates:
  * time               (time) datetime64[ns] 2019-09-14T07:54:00.006946627 .....
  * represent_vec_tot  (represent_vec_tot) <U1 'x' 'y' 'z'
Attributes: (12/17)
    CATDESC:            Magnetic field vector in Geocentric Solar Ecliptic (G...
    COORDINATE_SYSTEM:  GSE
    DEPEND_0:           Epoch
    DISPLAY_TYPE:       time_series
    FIELDNAM:           Magnetic field vector in GSE plus Btotal (8 or 16 S/s)
    FILLVAL:            -1e+31
    ...                 ...
    SI_CONVERSION:      1.0e-9>T
    TENSOR_ORDER:       1
    UNITS:              nT
    VALIDMAX:           [17000. 17000. 17000. 17000.]
    VALIDMIN:           [-17000. -17000. -17000.      0.]
    VAR_TYPE:           data

xarray.DataArray

• time: 16320
• represent_vec_tot: 3

• -2.103 -1.694 2.836 -2.101 -1.706 ... 1.826 5.165 -0.7561 1.805 5.204

  array([[-2.1031418 , -1.6935391 ,  2.835863  ],
         [-2.1007674 , -1.7059438 ,  2.8462613 ],
         [-2.1185403 , -1.6850468 ,  2.8634877 ],
         ...,
         [-0.7177708 ,  1.81181   ,  5.15961   ],
         [-0.75993973,  1.8259526 ,  5.165373  ],
         [-0.7561481 ,  1.8053148 ,  5.204192  ]], dtype=float32)

• Coordinates: (2)
  • time
    (time)
    datetime64[ns]
    2019-09-14T07:54:00.006946627 .....

    CATDESC :

    Interval centered time tag (TBC)

    DELTA_MINUS_VAR :

    mms1_fgm_bdeltahalf_srvy_l2

    DELTA_PLUS_VAR :

    mms1_fgm_bdeltahalf_srvy_l2

    FIELDNAM :

    Time since Jan 1, 1958

    FILLVAL :

    -9223372036854775808

    LABLAXIS :

    mms1_fgm_srvy_Epoch

    MONOTON :

    INCREASE

    REFERENCE_POSITION :

    Rotating Earth Geoid

    SCALETYP :

    linear

    SI_CONVERSION :

    1.0e-9>s

    TIME_BASE :

    J2000

    TIME_SCALE :

    Terrestrial Time

    UNITS :

    ns

    VALIDMAX :

    946728069183000000

    VALIDMIN :

    315576066184000000

    VAR_TYPE :

    support_data

    array(['2019-09-14T07:54:00.006946627', '2019-09-14T07:54:00.069447445',
           '2019-09-14T07:54:00.131948263', ..., '2019-09-14T08:10:59.832789092',
           '2019-09-14T08:10:59.895289910', '2019-09-14T08:10:59.957790728'],
          dtype='datetime64[ns]')

  • represent_vec_tot
    (represent_vec_tot)
    <U1
    'x' 'y' 'z'

    CATDESC :

    representation for vector plus total

    FIELDNAM :

    representation for vector plus total

    FORMAT :

    A2

    LABLAXIS :

    represent_vec_tot

    VAR_TYPE :

    metadata

    array(['x', 'y', 'z'], dtype='<U1')

• Indexes: (2)
  • time
    PandasIndex

    PandasIndex(DatetimeIndex(['2019-09-14 07:54:00.006946627',
                   '2019-09-14 07:54:00.069447445',
                   '2019-09-14 07:54:00.131948263',
                   '2019-09-14 07:54:00.194449080',
                   '2019-09-14 07:54:00.256949898',
                   '2019-09-14 07:54:00.319450716',
                   '2019-09-14 07:54:00.381951533',
                   '2019-09-14 07:54:00.444452351',
                   '2019-09-14 07:54:00.506953169',
                   '2019-09-14 07:54:00.569453986',
                   ...
                   '2019-09-14 08:10:59.395283368',
                   '2019-09-14 08:10:59.457784186',
                   '2019-09-14 08:10:59.520285004',
                   '2019-09-14 08:10:59.582785821',
                   '2019-09-14 08:10:59.645286639',
                   '2019-09-14 08:10:59.707787457',
                   '2019-09-14 08:10:59.770288274',
                   '2019-09-14 08:10:59.832789092',
                   '2019-09-14 08:10:59.895289910',
                   '2019-09-14 08:10:59.957790728'],
                  dtype='datetime64[ns]', name='time', length=16320, freq=None))

  • represent_vec_tot
    PandasIndex

    PandasIndex(Index(['x', 'y', 'z'], dtype='object', name='represent_vec_tot'))

• Attributes: (17)

  CATDESC :

  Magnetic field vector in Geocentric Solar Ecliptic (GSE) cartesian coordinates plus Btotal (8 or 16 S/s)

  COORDINATE_SYSTEM :

  GSE

  DEPEND_0 :

  Epoch

  DISPLAY_TYPE :

  time_series

  FIELDNAM :

  Magnetic field vector in GSE plus Btotal (8 or 16 S/s)

  FILLVAL :

  -1e+31

  FORMAT :

  E13.5

  GLOBAL :

  {'Project': ['STP>Solar-Terrestrial Physics'], 'Source_name': ['MMS1>MMS Satellite Number 1'], 'Discipline': ['Space Physics>Magnetospheric Science'], 'Data_type': ['srvy_l2'], 'Descriptor': ['FGM>Flux Gate Magnetometer'], 'File_naming_convention': ['source_descriptor_datatype_yyyyMMdd'], 'Data_version': ['5.211.0'], 'PI_name': ['J. Burch, C. Russell, W. Magnus'], 'PI_affiliation': ['SWRI, UCLA, IWF'], 'TEXT': ['The Fluxgate Magnetometers (FGM) on Magnetospheric Multiscale consist of a traditional Analog Fluxgate Magnetometer (AFG), and a Digital Fluxgate magnetometer (DFG). The dual magnetometers are operated as a single instrument providing a single intercalibrated data product. Range changes occur at different times on the two instruments so the gains checked each periapsis can be carried out unambiguously to apoapsis. Cross correlation of calibration parameters can separate causes of the any apparent calibration changes. Use of Electron Drift Instrument (EDI) to determine the field along the rotation axis allows accurate monitoring of the zero levels along the rotation axis. Prior to launch the magnetometers were calibrated at the Technical University, Braunschweig, except for the AFG magnetometers on MMS3 and MMS4, which were calibrated at UCLA. Both sets of sensors are operated for the entire MMS orbit, with slow survey (8 samples per second) outside of the Region of Interest (ROI), and fast survey (16 samples per second) inside the ROI. Within the ROI burst mode data (128 samples per second) are also acquired. A detailed description of the MMS fluxgate magnetometers, including science objectives, instrument description, calibration, magnetic cleanliness program, and data flow can be found at http://link.springer.com/article/10.1007%2Fs11214-014-0057-3 (DOI 10.1007/s11214-014-0057-3).Additional information can also be found at http://www-spc.igpp.ucla.edu/ssc/mms (UCLA),and http://www.iwf.oeaw.ac.at (IWF, Graz).', 'The Fluxgate Magnetometers (FGM) on Magnetospheric Multiscale consist of a traditional Analog Fluxgate Magnetometer (AFG), and a Digital Fluxgate magnetometer (DFG). The dual magnetometers are operated as a single instrument providing a single intercalibrated data product. Range changes occur at different times on the two instruments so the gains checked each periapsis can be carried out unambiguously to apoapsis. Cross correlation of calibration parameters can separate causes of the any apparent calibration changes. Use of Electron Drift Instrument (EDI) to determine the field along the rotation axis allows accurate monitoring of the zero levels along the rotation axis. Prior to launch the magnetometers were calibrated at the Technical University, Braunschweig, except for the AFG magnetometers on MMS3 and MMS4, which were calibrated at UCLA. Both sets of sensors are operated for the entire MMS orbit, with slow survey (8 samples per second) outside of the Region of Interest (ROI), and fast survey (16 samples per second) inside the ROI. Within the ROI burst mode data (128 samples per second) are also acquired. A detailed description of the MMS fluxgate magnetometers, including science objectives, instrument description, calibration, magnetic cleanliness program, and data flow can be found at http://link.springer.com/article/10.1007%2Fs11214-014-0057-3 (DOI 10.1007/s11214-014-0057-3).Additional information can also be found at http://www-spc.igpp.ucla.edu/ssc/mms (UCLA),and http://www.iwf.oeaw.ac.at (IWF, Graz).'], 'Instrument_type': ['Magnetic Fields (space)'], 'Mission_group': ['MMS'], 'Logical_source': ['mms1_fgm_srvy_l2'], 'Logical_file_id': ['mms1_fgm_srvy_l2_20190914_v5.211.0'], 'Logical_source_description': ['Level2 Flux Gate Magnetometer Combined Fast/Slow Survey DC Magnetic Field for MMS Satellite Number 1'], 'Time_resolution': ['0.0625 to 0.125 sec'], 'Rules_of_use': ['See MMS Data Rights and Rules for Use https://lasp.colorado.edu/galaxy/display/mms/MMS+Data+Rights+and+Rules+for+Data+Use'], 'Generated_by': ['UCLA'], 'Generation_date': ['20191026'], 'MODS': ["version X=5: * Y-version number comes from cal file entries. \n * Ensures there are 2 ephemeris points before/after data to enable proper spline. \n * Fix to depend_0 of rdeltahalf: fixes bug when reading position data.\n * L-vector for DMPA2GSE transformation is smoothed with a gaussian filter, instead \n of using a single average value for the day. This short-term filter avoids \n introduding artificial jumps at 00:00 UTC and removes 7-minute 'wobble' after \n maneuvers in the GSE result. \n * Fixes error with DEFATT file selection found when choosing the \n daily DEFATT files to be used in Phase 2.\n * Fixed bug where reference Etemp was used for high range gain. Now uses measured Etemp.\nversion X=4: First version for public release of L2.\n Renamed variables to conform with new MMS variable name guidelines \n (obs_instr_paramName[_coordSys]_mode_level): \n Mag field parameters include 'b' for paramName. \n Use 'r' instead of 'pos' for S/C position paramName. \n Eliminated 'rate', replaced with 'bdeltahalf'. Added 'rdeltahalf'.\n l1a_mode is now just 'mode'.\nversion X=3: fixed removal of overlap between modes.\n fixed a bug that caused stemp and etemp to be empty.\nversion X=2: flag parameter name corrected: was 'status'\n added bits 4, 5, 6 to flag saturation on B1, B2, and B3, respectively\n added bit 7 to flag bad data at range changes\n Added etemp and l1a_mode parameters. \n rate, hirange, and stemp parameters now comply with MMS CDF Guidlelines, e.g.\n FILLVAL now defined for stemp and etemp, and is set to !values.f_nan\n No longer use Var_Parents attribute in stemp -- see Parents instead\n In this version, temperature-corrected gains are applied. Reference temperatures are used when \n stemp or etemp are set to FILLVAL. \n Non-linearity correction is applied to high rage DFG data.\nversion X=1: added 'flag', rate and hirange parameters (but 'flag' is actually called 'status')"], 'LINK_TEXT': ['MMS home page', 'MMS home page', 'MMS home page', 'MMS home page', 'MMS home page'], 'LINK_TITLE': ['at GSFC', 'at GSFC', 'at GSFC', 'at GSFC', 'at GSFC'], 'HTTP_LINK': ['http://mms.gsfc.nasa.gov/', 'http://mms.gsfc.nasa.gov/', 'http://mms.gsfc.nasa.gov/', 'http://mms.gsfc.nasa.gov/', 'http://mms.gsfc.nasa.gov/'], 'Parents': ['CDF>mms1_afg_fast_l1a_20190914_v1.7.5', 'CDF>mms1_afg_fast_l1a_20190914_v1.7.5', 'CDF>mms1_afg_fast_l1a_20190914_v1.7.5', 'CDF>mms1_afg_fast_l1a_20190914_v1.7.5', 'CDF>mms1_afg_fast_l1a_20190914_v1.7.5', 'CDF>mms1_afg_fast_l1a_20190914_v1.7.5', 'CDF>mms1_afg_fast_l1a_20190914_v1.7.5', 'CDF>mms1_afg_fast_l1a_20190914_v1.7.5', 'CDF>mms1_afg_fast_l1a_20190914_v1.7.5']}

  LABL_PTR_1 :

  label_b_gse

  REPRESENTATION_1 :

  represent_vec_tot

  SCALETYP :

  linear

  SI_CONVERSION :

  1.0e-9>T

  TENSOR_ORDER :

  1

  UNITS :

  nT

  VALIDMAX :

  [17000. 17000. 17000. 17000.]

  VALIDMIN :

  [-17000. -17000. -17000. 0.]

  VAR_TYPE :

  data

Load ion and electron density, bulk velocity and DEF (FPI)

# Number density
n_i, n_e = [mms.get_data(f"n{s}_fpi_fast_l2", tint, 1) for s in ["i", "e"]]

# Bulk velocity
v_xyz_i, v_xyz_e = [mms.get_data(f"v{s}_gse_fpi_fast_l2", tint, 1) for s in ["i", "e"]]

# Omnidirectional differential energy flux
def_omni_i, def_omni_e = [
    mms.get_data(f"def{s}_fpi_fast_l2", tint, 1) for s in ["i", "e"]
]

[21-Jul-23 09:26:55] INFO: Loading mms1_dis_numberdensity_fast...
[21-Jul-23 09:26:55] WARNING: /usr/local/lib/python3.10/site-packages/pyrfu/mms/get_ts.py:58: UserWarning: Epoch_plus_var/Epoch_minus_var units are not clear, assume s
  warnings.warn(message)

[21-Jul-23 09:26:55] INFO: Loading mms1_des_numberdensity_fast...
[21-Jul-23 09:26:55] INFO: Loading mms1_dis_bulkv_gse_fast...
[21-Jul-23 09:26:55] WARNING: /usr/local/lib/python3.10/site-packages/pyrfu/mms/get_ts.py:58: UserWarning: Epoch_plus_var/Epoch_minus_var units are not clear, assume s
  warnings.warn(message)

[21-Jul-23 09:26:55] INFO: Loading mms1_des_bulkv_gse_fast...
[21-Jul-23 09:26:55] WARNING: /usr/local/lib/python3.10/site-packages/pyrfu/mms/get_ts.py:58: UserWarning: Epoch_plus_var/Epoch_minus_var units are not clear, assume s
  warnings.warn(message)

[21-Jul-23 09:26:55] WARNING: /usr/local/lib/python3.10/site-packages/pyrfu/mms/get_ts.py:58: UserWarning: Epoch_plus_var/Epoch_minus_var units are not clear, assume s
  warnings.warn(message)

[21-Jul-23 09:26:55] INFO: Loading mms1_dis_energyspectr_omni_fast...
[21-Jul-23 09:26:55] WARNING: /usr/local/lib/python3.10/site-packages/pyrfu/mms/get_ts.py:58: UserWarning: Epoch_plus_var/Epoch_minus_var units are not clear, assume s
  warnings.warn(message)

[21-Jul-23 09:26:55] INFO: Loading mms1_des_energyspectr_omni_fast...

Load electric field (EDP)

e_xyz = mms.get_data("e_gse_edp_fast_l2", tint, 1)

[21-Jul-23 09:26:55] INFO: Loading mms1_edp_dce_gse_fast_l2...

Plot overview

Import matplotlib and define backend

%matplotlib inline
import matplotlib.pyplot as plt

Import pyrfu plotting routines

from pyrfu.plot import plot_line, plot_spectr

legend_options = dict(frameon=True, loc="upper right")

f, axs = plt.subplots(7, sharex="all", figsize=(9, 13))
f.subplots_adjust(hspace=0, left=0.1, right=0.88, bottom=0.05, top=0.97)

# Magnetic field
plot_line(axs[0], b_xyz)
axs[0].legend(["$B_x$", "$B_y$", "$B_z$"], ncol=3, **legend_options)
axs[0].set_ylabel("$B$ [nT]")

# Electric field
plot_line(axs[1], e_xyz)
axs[1].legend(["$E_x$", "$E_y$", "$E_z$"], ncol=3, **legend_options)
axs[1].set_ylabel("$E$ [mV.m$^{-1}$]")

# Number density
plot_line(axs[2], n_i, color="tab:red")
plot_line(axs[2], n_e, color="tab:blue")
axs[2].legend(["$Ions$", "$Electrons$"], ncol=2, **legend_options)
axs[2].set_ylabel("$n$ [cm$^{-3}$]")

# Ion bulk velocity
plot_line(axs[3], v_xyz_i)
axs[3].legend(["$V_{i,x}$", "$V_{i,y}$", "$V_{i,z}$"], ncol=3, **legend_options)
axs[3].set_ylabel("$V_i$ [km.s$^{-1}$]")

# Ion DEF
axs[4], caxs4 = plot_spectr(
    axs[4], def_omni_i, yscale="log", cscale="log", cmap="Spectral_r"
)
axs[4].set_ylabel("$E_i$ [eV]")
caxs4.set_ylabel("DEF" + "\n" + "[kev/(cm$^2$ s sr keV)]")

# Electron bulk velocity
plot_line(axs[5], v_xyz_e)
axs[5].legend(["$V_{e,x}$", "$V_{e,y}$", "$V_{e,z}$"], ncol=3, **legend_options)
axs[5].set_ylabel("$V_e$ [km.s$^{-1}$]")

# Electron DEF
axs[6], caxs6 = plot_spectr(
    axs[6], def_omni_e, yscale="log", cscale="log", cmap="Spectral_r"
)
axs[6].set_ylabel("$E_e$ [eV]")
caxs6.set_ylabel("DEF" + "\n" + "[kev/(cm$^2$ s sr keV)]")

f.align_ylabels(axs)
f.savefig("../../_static/quick-overview_nb_thumbnail.png", dpi=100)

Load data for all spacecraft

Spacecraft position (MEC)

r_mms = [mms.get_data("r_gse_mec_srvy_l2", tint, i) for i in range(1, 5)]

[21-Jul-23 09:27:00] INFO: Loading mms1_mec_r_gse...
[21-Jul-23 09:27:00] INFO: Loading mms2_mec_r_gse...
[21-Jul-23 09:27:01] INFO: Loading mms3_mec_r_gse...
[21-Jul-23 09:27:01] INFO: Loading mms4_mec_r_gse...

Magnetic field (FGM)

b_mms = [mms.get_data("b_gse_fgm_srvy_l2", tint, i) for i in range(1, 5)]

[21-Jul-23 09:27:01] INFO: Loading mms1_fgm_b_gse_srvy_l2...
[21-Jul-23 09:27:01] INFO: Loading mms2_fgm_b_gse_srvy_l2...
[21-Jul-23 09:27:01] INFO: Loading mms3_fgm_b_gse_srvy_l2...
[21-Jul-23 09:27:02] INFO: Loading mms4_fgm_b_gse_srvy_l2...

Plot

f, axs = plt.subplots(3, sharex="all", figsize=(9, 6))
f.subplots_adjust(hspace=0, left=0.1, right=0.82, bottom=0.05, top=0.95)

labels = ["MMS{:d}".format(i + 1) for i in range(4)]

for ax, j, c in zip(axs, [0, 1, 2], ["x", "y", "z"]):
    for i, b in enumerate(b_mms):
        plot_line(ax, b[:, j])

    ax.set_ylabel("$B_{}$ [nT]".format(c))

f.legend(labels, loc="upper center", borderaxespad=0.1, ncol=4, frameon=False)

<matplotlib.legend.Legend at 0x1360c2ce0>