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