We have analyzed space weather throughout the heliosphere using the three-dimensional (3D) timedependent magnetohydrodynamic (MHD) Hybrid Heliospheric Modeling System with Pickup Protons (HHMS-PI) [1] out to Voyager 2 (V2) and beyond by comparing the HHMS-PI model results with the available spacecraft data. We also have analyzed space weather throughout the heliosphere through in-depth analyses of the available simultaneous data from a number of instruments on spacecraft at various locations. In this paper we focus on our HHMS-PI modeling (starting at the Sun) of the Halloween 2003 solar events by comparing the model results with spacecraft data at ACE and Ulysses. For the Halloween 2003 solar events we also summarize our inter-comparisons of the in-situ V2 data from many of the V2 instruments. These analyses of the comparisons ("benchmarking") of HHMS-PI simulations and the various spacecraft data and of our in-depth analyses of the V2 particle and field data indicate that particle acceleration and other important physical processes are associated with the heliospheric propagation of these large solar cycle 23 space weather events. We conclude that space weather, originating at the Sun, can have important affects throughout the heliosphere to distances as great as 73 AU and beyond.

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