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This paper develops a global precipitation rate retrieval algorithm for the advanced microwave sounding unit (AMSU), which observes 23-191 GHz. The algorithm was trained using a numerical weather prediction (NWP) model (MM5) for 106 globally distributed storms that predicted brightness temperatures consistent with those observed simultaneously by AMSU. Neural networks were trained to retrieve hydrometeor water-paths, peak vertical wind, and 15-min average surface precipitation rates for rain and snow at 15-km resolution at all viewing angles. Different estimators were trained for land and sea, where surfaces classed as snow or ice were generally excluded from this paper. Surface-sensitive channels were incorporated by using linear combinations [principal components (PCs)] of their brightness temperatures that were observed to be relatively insensitive to the surface, as determined by visual examination of global images of each brightness temperature spectrum PC. This paper also demonstrates that multiple scattering in high microwave albedo clouds may help explain the observed consistency for a global set of 122 storms between AMSU-observed 50-191-GHz brightness temperature distributions and corresponding distributions predicted using a cloud-resolving mesoscale NWP model (MM5) and a two-stream radiative transfer model that models icy hydrometeors as spheres with frequency-dependent densities. The AMSU/MM5 retrieval algorithm developed in Part I of this paper is evaluated in Part II on a separate paper.