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:                0.556
Li [2004]:                  0.512

Prediction Efficiencies for Day 2 Forecast:
Persistence:               -0.016
Li [2004]:                 -0.231

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:                0.556
Li [2004] with Source:      0.544

Prediction Efficiencies for Day 2 Forecast:
Persistence:               -0.016
Li [2004] with Source:     -0.081

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:                0.556
Turner and Li [2008]:       0.577

Prediction Efficiencies for Day 2 Forecast:
Persistence:               -0.016
Turner and Li [2008]:      -0.043

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:                0.556
Li [2004]:                  0.512
Li [2004] with Source:      0.544
Turner and Li [2008]:       0.577
Best Combination:           0.577

Weighting coefficients for maximum PE:
Li [2004]:                   0.02
Li [2004] with Source:       0.00
Turner and Li [2008]:        0.98

Prediction Efficiencies for Day 2 Forecast:
Persistence:               -0.016
Li [2004]:                 -0.231
Li [2004] with Source:     -0.081
Turner and Li [2008]:      -0.043
Best Combination:          -0.036

Weighting coefficients for maximum PE:
Li [2004]:                   0.03
Li [2004] with Source:       0.00
Turner and Li [2008]:        0.97