Multi-input single-output (MISO) nonlinear autoregressive moving average with
exogenous inputs (NARMAX) models have been derived to forecast the

The configuration of the magnetic field in the region of the terrestrial
radiation belts allows for charged particles to be trapped. As such, the
radiation belts contain energetic electron from tens of

Although the radiation belts were discovered more than half a century ago

Despite the complexity of the particle acceleration within the radiation
belts, there are a number of proposed models that explain the dynamics

An alternative approach to developing a model based on first principles is
to deduce a forecasting model for the radiation belt electron fluxes directly
from data

Nonlinear autoregressive moving average with exogenous inputs (NARMAX) models
have the advantage of providing accurate results and at the same time are
very easy to interpret. The NARMAX algorithm was initially developed for
complex engineering and biological systems but has since been employed in
many other fields, such as space weather. In solar–terrestrial physics, the
NARMAX methodology was first employed to develop forecasting models for the
Dst index using solar wind inputs

The main aim of this study was to develop two NARMAX models for the

The NARMAX approach, first developed by

There are three stages to identify a NARMAX model. The first stage, model
structure detection, is to identify the most significant model terms by
evaluating all the possible combinations of the past inputs, past outputs and
past noise values with the use of the ERR. An advantage of the ERR in
selecting input terms is that ERR is independent of the possible nonlinear
and correlated noise

The NARMAX algorithm requires both input and output data for the system to
deduce a model. In this study, the output for each of the two models is the
daily averaged

As discussed in the Introduction, previous data-based models have used
geomagnetic indices and the solar wind velocity to forecast the electron
fluxes at GEO. The recent study by

The NARMAX algorithm was then employed to obtain the two models for both the

The

The

The final models for both energies only included terms of past output,

Model forecast showing measured electron flux in blue and the model
estimate in red for

Model performance analysis was used to validate the model and test whether the model would be accurate enough for real-time online forecasts of the 1-day-ahead electron flux at GEO. This was achieved using past data intervals to investigate how accurate the 1-day forecasts would have been compared to the electron flux observed by the GOES spacecraft.

Electron flux data from GOES 13 were used to evaluate the performance of the
model. GOES 13 became the primary GOES satellite for the Energetic Proton
Electron and Alpha Detector (EPEAD) on 14 April 2010. Thus, the period of
data to analyse the

The previous GOES satellites measured the channel for

The 1-day forecasts were calculated using the

In addition to simply inspecting the figures showing the difference between
the forecast and observed electron flux at GEO, the statistics of how the
model 1-day forecast relates to the measurement needs to be
calculated. Here, the performance of the models were statistically analysed
using the prediction efficiency (PE) (Eq.

The

The aim of this study was to derive electron flux models that provide a high
accuracy for the 1-day forecast and implement them online in real time.
The CC and the PE show that the models are accurate; however, since a high
accuracy is relative, the

The SWPC provides a forecast of the

The main aim of this study was to produce two electron flux models at GEO:
for energies of

The NARMAX

Thus, the goal to implement the models online to deliver a real-time forecast
for the next day using the real-time data provided by the NOAA NWS Space
Weather Prediction Center has been achieved and the online forecast of
SNB

The authors would like to acknowledge the financial support from EPSRC and ERC. The authors would also like to thank the OMNIWeb service for providing the past solar wind data and the NOAA NWS Space Weather Prediction Center for the use of the real-time data from both ACE and GOES. Topical Editor V. Fedun thanks two anonymous referees for their help in evaluating this paper.