# Plots and Discussion of the Forecast Models

## Li [2004]

This model uses real-time data from ACE as the only input for the
standard radial diffusion equation. The radial diffusion equation
is solved after making the diffusion coefficient a function of the
solar wind velocity and interplanetary magnetic field, with appropriate
boundary conditions. The solar wind velocity is the most important
parameter in the
variation of relativistic electron fluxes at geostationary orbit.
The model is described in
[Li, 2004] and
[Li et al., 2001a].

Prediction Efficiencies for Day 1 Forecast:
Persistence: 0.288
Li [2004]: 0.258
Prediction Efficiencies for Day 2 Forecast:
Persistence: -0.390
Li [2004]: -0.599

## Li [2004] with Source

This model is Li [2004], with the addition of a source term.
The source term represents internal heating mechanisms like wave-particle
interactions. The source term's amplitude is a function of the AL index,
which is forecast in real-time
here.

Prediction Efficiencies for Day 1 Forecast:
Persistence: 0.288
Li [2004] with Source: 0.211
Prediction Efficiencies for Day 2 Forecast:
Persistence: -0.390
Li [2004] with Source: -0.781

## Turner and Li [2008]

This model uses low-energy electron flux to forecast relativistic flux,
taking advantage of the fact that changes in the low-energy electron
population are followed at a later time by similar changes in the
high-energy population. The day 2 forecast is based on persistence of
the day 1 forecast. This model is described in
Turner and Li [2008].

Prediction Efficiencies for Day 1 Forecast:
Persistence: 0.288
Turner and Li [2008]: 0.186
Prediction Efficiencies for Day 2 Forecast:
Persistence: -0.390
Turner and Li [2008]: -0.530

## Best Combination of Models

This shows the best combination of the three models, using a weighted average
which gives the maximum PE for the last 30 days. The weights indicate how
well each model's forecast matched the measured data. The weights are then
applied to the 1 and 2 day forecasts of each model.
This ensemble most often outperforms the individual models.

Prediction Efficiencies for Day 1 Forecast:
Persistence: 0.288
Li [2004]: 0.258
Li [2004] with Source: 0.211
Turner and Li [2008]: 0.186
Best Combination: 0.273
Weighting coefficients for maximum PE:
Li [2004]: 0.67
Li [2004] with Source: 0.00
Turner and Li [2008]: 0.33
Prediction Efficiencies for Day 2 Forecast:
Persistence: -0.390
Li [2004]: -0.599
Li [2004] with Source: -0.781
Turner and Li [2008]: -0.530
Best Combination: -0.530
Weighting coefficients for maximum PE:
Li [2004]: 0.00
Li [2004] with Source: 0.00
Turner and Li [2008]: 1.00