Electron/Ion Flux Model for Geosynchronous Orbit (GEO) and Outer Magnetosphere

Description : Model Outputs : Example Output : Future Work : Acknowledgements : Download : ReferencesContact

*NEW*:  Outer magnetosphere model is now available (see below)

Description: The flux models described here are purely empirical specifications of the ion flux and the electron flux at geosynchronous orbit (GEO) and in the outer magnetosphere (6 to 20 RE).  

For the GEO model  the energy range of the model fluxes is ~1 eV to ~40 keV.   This model is based on a total of 82 satellite-years of observations from the Magnetospheric Plasma Analyzer instruments on Los Alamos National Laboratory satellites at GEO.  These data are assigned to a fixed grid of 24 local-times, at all possible values of Kp or solar wind electric field (-vBz), with 40 energy bins at GEO.  Bi-linear (or tri-linear)  interpolation is used between grid points to provide the ion flux and the electron flux values at any energy and local-time, and for given values of geomagnetic activity (proxied by the 3-hour Kp index ) or solar-wind electric field.  The Kp version of the model  also provides flux values for given values of solar activity (proxied by the daily F10.7 index).  Initial comparison of the electron flux from the GEO model with out-of-sample data from a Compact Environmental Anomaly Sensor II (CEASE-II), also located at GEO, indicate a good match between model and observations during both quiet and disturbed periods.  

For the outer magnetosphere model (6 and 20 RE) the energy range covered is ~45 keV to 325 keV (electrons only).  This model is based on Cluster/RAPID electron fluxes (2001 to 2016).  These data are assigned to a fixed grid of 24 local-times, 14 radial distances (6-20 RE), six energy channels (~45-325 keV) and all possible values of Kp.  Although the data and grids in this model are quite sparse, comparison of the model with out-of-sample fluxes from THEMIS/SST data demonstrates a reasonable match between model and measured data.

All models are available for download below, and can be modified to suit user-requirements.

Kp version at GEO (example fluxes)

Figure 1. Plots showing example slices through the model dataset.  The left panel shows the mean electron flux as a function of energy and local-time, at Kp=2.  The right panel shows the mean ion flux as a function of energy and local time, at Kp=4.  Bi-linear interpolation is used to provide off-grid flux values.  The user is also supplied with the standard deviation from the mean, percentile fluxes, and a coarse parametization of the effects of solar-activity (F10.7 index).

Figure 2. Locations of 419 selected satellites on orbit at GEO.  Alternate satellites are coloured blue/yellow for clarity.

Figure 3. Binning scheme for -vBz model.

Figure 4. In-sample comparison of outer flux model predictions (blue) with actual Cluster/RAPID data (red).

Model Outputs: For the selected conditions of geomagnetic activity (Kp index), energy (eV) and Local Time (LT), the model provides the user with:
of the ion and electron fluxes, at three different solar-activity (F10.7 - Kp model only) levels, based on averaged fluxes from seven Los Alamos National Laboratory (LANL) satellites at GEO using flux data from 1989 to 2007.

Example Output: Model results for Kp=7-, Energy =5.28 keV, LT=7.00.  The model can easily be modified and called for any set of (Kp, E, LT) values.

Future Work: Future model development is planned in two areas:

1. Geomagnetic/Solar Conditions - While Kp is a good proxy for general geomagnetic activity, it would be useful to be able to drive the model with upstream solar-wind conditions, such as the solar-wind electric field (-vswBz).

2.(a) Extending the model in spatial extent (inwards and outwards of GEO);
PARTIALLY COMPLETE!  (model now extends from 6 to 20 RE - electrons only - based on Cluster/RAPID fluxes)

2.(b) Extending the energy range of the model (upwards from 40 keV);
PARTIALLY COMPLETE!  (outer magnetosphere model now covers 45-325 keV - electrons only - based on Cluster/RAPID fluxes)
We are working on extending the energy range at GEO using GOES/MAGED and GOES/MAGPD data.

2.(c) Extending the model to consider geomagnetic latitude (off-equator) effects.  

3. Add tool to calculate total dose over a specific time period

4. Add tool to predict spacecraft-surface charging likelihood (derived from LANL/MPA data).

5. Investigate how to include time-history into the model to improve flux forecasts (Note: this will be HARD!)

Acknowledgements:   Thanks to all those who contributed to the model, particularly Michelle Thomsen (LANL), my mentor during my time as a  postdoc at LANL, and Vania Jordanova(LANL), who first suggested I should work on such a model.  Thanks are also to Mike Henderson (PI for the LANL/MPA dataset), Joe Borovksy (for helpful conversations), Dave Pitchford (for access to the CEASE-II data, and boundless hospitality), Jo Denton (for help with figures and everything else), and Dave Hartley (for coffee, beer, and science...not necessarily in that order).  

Thanks also to Jonny Rae, Clare Watt, and Colin Forsyth for helpful discussions when I first presented the model during a visit to Mullard Space Science Laboratory in January 2015.

I also wish to thank all at ISR-1/LANL who have contriubuted to the MPA dataset over the years, and all members of the Cluster/RAPID instrument team.

Since Autumn 2017 work on the model has been funded by a NASA-Living With a Star (LWS) award : 80NSSC17K0682

Download: A tar-ball of the latest version of the models can be found below:

GEO Kp Model v0.1First versionApril 2015
GEO Kp Model v1.0Minor bug fixes from original v0.1 modelJune 2016
GEO -vBz Model v1.0First versionJune 2016
    OUTER MAG Kp Model v1.0 (6-20 RE)   First version30th April 2019
GEO, Kp, higher energies from GOESUnder Review...3rd Aug 2021

The models are all written in FORTRAN 77, and are freely available for download (GNU General Public License v3).  They can be modified as required, in accordance with GNU/GPL v3.  

If you are curious to know why I used FORTRAN then feel free to spend some quality time here :-)

References: A full description of the models can be found in the following papers:  

M. H. Denton, J. V. Rodriguez, and M. G. Henderson
An empirical flux model for electrons and protons at geosynchronous orbit based on GOES MAGED and MAGPD observations.
Journal of Space Weather and Space Climate,
2021 (under review),

J. V. Rodriguez, M. H. Denton, and M. G. Henderson
On-orbit calibration of geostationary electron and proton flux observations for augmentation of an existing empirical radiation model
Journal of Space Weather and Space Climate, 10, 28, doi:10.1051/swsc/2020031, 2020
. (open access link).

# M. H. Denton, M. G. G. T. Taylor, J. V. Rodriguez, and M. G. Henderson,
Extension of an empirical electron flux model from 6 to 20 Earth radii using CLUSTER/RAPID observations.
Space Weather
, 17, 778-792, doi:10.1029/2018SW002121, 2019.

A pre-print .pdf version of the manuscript can be found here.   Selected as a Editors Highlight (https://eos.org/editor-highlights/extending-the-envelope-for-known-safe-locations-in-space)

# M. H. Denton, M. G. Henderson, V. K. Jordanova, M. F. Thomsen, J. E. Borovsky, J. Woodroffe, D. P. Hartley, and D. Pitchford, 
An improved empirical model of electron and ion fluxes at geosynchronous orbit based on upstream solar wind conditions.
Space Weather, 14, 511–523, doi:10.1002/2016SW001409, 2016.
A pre-print .pdf version of the manuscript can be found here.

M. H. Denton, M. F. Thomsen, V. K. Jordanova, M. G. Henderson, J. E. Borovsky, J. S. Denton, D. Pitchford, and D. P. Hartley,
An empirical model of electron and ion fluxes derived from observations at geosynchronous orbit.
Space Weather, 13, 233–249, doi:10.1002/2015SW001168, 2015.

A pre-print .pdf version of the manuscript can be found here.


Feel free to contact me regarding the model.

   Space Science Institute
   4765 Walnut Street (Suite B)
   CO 80301
   Email: mdenton(at)spacescience.org

I also keep a mailing list to notify people about new versions of the model, etc.  If you would like to be added to the list, simply drop me an email.

Description : Model Bounds : Model Outputs : Example Output : Future Work : Acknowledgements : Download : ReferencesContact
Web page created 19th April 2015.
Last update: 3rd August 2021.

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