I.1.3.1. Overview

For trapped radiation and all earth orbits, the best known and most widely used models of radiation belt energetic particles are the AE-8 and AP-8 models for electrons [RN.10] and protons [RN.11], respectively. They were developed at Aerospace Corporation for the NSSDC at NASA/GSFC based on data from satellites flown in the 1960s and early 1970s. The models give omnidirectional fluxes as functions of idealized geomagnetic dipole coordinates B/B₀ and L. The user defines an orbit, generates a trajectory, transforms it to geomagnetic coordinates and access the radiation belt models to compute flux spectra, using the same geomagnetic field as used to develop the model. Apart from separate versions for solar maximum and solar minimum, there is no description of the temporal behaviour of fluxes. At high altitudes in particular (e.g. around geostationary orbit) fluxes vary by orders of magnitude over short times and exhibit significant diurnal variations; the models do not describe these. In addition, the models do not contain any explicit flux directionality.

At low altitudes, on the inner edge of the radiation belts, particle fluxes rise very steeply with altitude and small errors in computing locations can give rise to large errors in particle fluxes. This is a problem since the geomagnetic field is shifting and decaying so that the situation is no longer the same as when the model data were acquired. Use of a geomagnetic field model other than the one used in generating the model can result in large flux errors at low altitude.

Although use of an old field model and epoch can reduce errors in the magnitudes of fluxes, it does not model the spatial locations of radiationbelt features (e.g. the position of the South Atlantic anomaly), or particle fluxes, as they are today.

The AP-8 model for protons gives proton fluxes from 0,1 to 400 MeV while the AE-8 model for electrons covers electrons from 0,04 to 7 MeV. Figure I-1 shows contour plots of AE-8 and AP-8 model omnidirectional, integral fluxes for energies above 1 MeV and 10 MeV, respectively, in idealized dipole space.

Figure I-2 shows values of energetic electron and proton particle fluxes as stored in these models, for positions on the geomagnetic equator (B=B₀), as functions of L for both solar maximum and solar minimum. This shows that as far as the models are concerned, the solar activity only affects electron fluxes in the midL range and protons at low altitude where the higher neutral atmospheric density at solar maximum leads to reduced proton fluxes because of enhanced loss. Solar cycle effects on electrons appear to differ from this behaviour in reality [RD.58].

I.1.3.2. Uncertainties in trapped particle models

The accuracy of the predicted fluxes is within a factor of 2 for AP8 and within a factor depending on the location and incident electron energy for AE8. In [RN.10], a reasonable limit of the error on AE8 is a factor of 2, however, in some regions (L=3) this can increase to a factor of 4.5 and is energy dependent, the error is higher for the higher energies. In other regions, such as geostationary orbits, the AE8 models are pessimistic.

For short term estimates the models can underpredict by a considerable amount – instantaneous fluxes measured at specific locations in the electron belts have been measured to be several orders of magnitude higher than the long term model fluxes.

I.1.3.3. Specific orbits

For electron fluxes in geostationary orbit a great number of measurements exist_.The standard model IGE 2006 (International GEO Electron model version 2006) developed by ONERA & LANL [RN.12], is a statistical model based on more than 2 solar cycles of electron flux data from radiation monitors on-board different international GEO satellites (mainly US and Japan) see Figure I-4_.This model is available in the SPENVIS [RD.59] or OMERE [RD.60] space environment tools.

The accuracy of IGE 2006 is included in the model as the upper case takes into account uncertainties in the measurements, in the duration and strength of the solar cycle.

For MEO altitude, the electron environment is very hard, intense and dynamic. The model developed at ONERA [RN.13] and given in Table B-4 and Table B-5, is based on GPS data acquired from Los Alamos, covering from the early nineties to 2007. Data have been analysed in terms of saturation, contamination and global coherence to ensure high fidelity. This MEO model provides energetic electrons fluxes in the energy spectral range 0,28 MeV–2,24 MeV and gives three spectra: an average case, a lower case and an upper case. The accuracy of MEO-V2 is included in the model as the upper case takes into account uncertainties in the measurements, in the duration and the strength of the solar cycle.

The electron fluxes obtained in the mean case of MEO model are very close to electron fluxes deduced from NASA/AE8 model over a full solar cycle (7 years MAX and 4 years MIN for AE8), see Figure I-5. Similarly, the electron fluxes from the MEO mean model propagated to near geostationary orbit are in agreement with electron fluxes deduced from IGE06 model.

I.1.3.4. Other trapped radiation models

Other trapped radiation models exist. Amongst them, the main known are:

Those based on CRRES data :

CRRESELE: The Combined Radiation and Release Effects Satellite (CRRES) electron flux model specifies the location and intensity of electron omni-directional flux over the energy range 0,5-6,6 MeV for a range of geomagnetic activity levels [RD.61].

CRRESPRO: The Combined Radiation and Release Effects Satellite (CRRES) proton flux model specifies the location and intensity of proton omni-directional flux over the energy range 1-100 MeV for quiet, average, or active geophysical conditions [RD.62].

TPM1 (Trapped Proton model) [RD.25] which provides a solar-cycle dependent low-altitude extension to the CRRESPRO trapped energetic proton model based on NOAA/TIROS data from 1,5 to 81 MeV (but it is ITAR restricted).

These models are available in the AF-GEOSPACE tool, see: http://www.kirtland.af.mil/library/factsheets/factsheet.asp?id=7899

Other models are also listed and available in http://modelweb.gsfc.nasa.gov/