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A two-dimensional, time-dependent numerical model is used to calculate themodulation of cosmic rays in the heliosphere. Computations are compared tospacecraft observations in the inner and outer heliosphere. It is shown thatthe model produces cosmic ray proton intensities compatible to differentspacecraft observations on a global scale, at Earth and along both Voyagerspacecraft trajectories. The study reveals that when the same modulationparameters, which resulted in compatible intensities along Voyager 1, wereassumed along the Voyager 2 trajectory, the model failed to reproduce theobservations. The study also found that any change in diffusion parametersalone could not reproduce the cosmic ray observations along Voyager 2 so thatchanges to the heliospheric geometry were necessary i.e the computedintensities along both Voyager trajectories suggest that the heliosphere isasymmetric. Furthermore, $E >$ 70 MeV and 133-242 MeV proton intensities alongVoyager 1 and 2 trajectories are predicted from end of 2012 onwards. It isshown that the computed intensities along Voyager 1 increase with an almostconstant rate up to the heliopause. However, the model shows that Voyager 2 isstill under the influence of temporal solar activity changes because of itsrelatively large distance to the heliopause. Along the Voyager 2 trajectory,the intensities remained generally constant for some time and should soon startto increase steadily.

Time-dependent cosmic ray modulation in the outer heliosphere:  Signatures of a heliospheric asymmetry and model predictions along Voyager 1  and 2 trajectories