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:                0.310
Li [2004]:                  0.353

Prediction Efficiencies for Day 2 Forecast:
Persistence:               -0.328
Li [2004]:                 -0.331

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:                0.310
Li [2004] with Source:      0.358

Prediction Efficiencies for Day 2 Forecast:
Persistence:               -0.328
Li [2004] with Source:     -0.404

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:                0.310
Turner and Li [2008]:       0.274

Prediction Efficiencies for Day 2 Forecast:
Persistence:               -0.328
Turner and Li [2008]:      -0.564

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:                0.310
Li [2004]:                  0.353
Li [2004] with Source:      0.358
Turner and Li [2008]:       0.274
Best Combination:           0.378

Weighting coefficients for maximum PE:
Li [2004]:                   0.04
Li [2004] with Source:       0.57
Turner and Li [2008]:        0.39

Prediction Efficiencies for Day 2 Forecast:
Persistence:               -0.328
Li [2004]:                 -0.331
Li [2004] with Source:     -0.404
Turner and Li [2008]:      -0.564
Best Combination:          -0.330

Weighting coefficients for maximum PE:
Li [2004]:                   1.00
Li [2004] with Source:       0.00
Turner and Li [2008]:        0.00