The largest explosive volcanic eruptions produce umbrella clouds that drive ash radially outward, enlarging the area that impacts aviation and ground-based communities. Models must consider the effects of umbrella spreading when forecasting hazards from these eruptions. In this paper we test a version of the advection–dispersion model Ash3d that considers umbrella spreading by comparing its simulations with observations from three well-documented umbrella-forming eruptions: (1) the 15 June 1991 eruption of Pinatubo (Philippines); (2) the 13 February 2014 eruption of Kelud (Indonesia); and (3) phase 2 of the 22–23 April 2015 eruption of Calbuco (Chile). In volume, these eruptions ranged from several cubic kilometers dense-rock equivalent (DRE) for Pinatubo to about one tenth for Calbuco. In mass eruption rate (MER), they ranged from 10⁸–10⁹ kg s⁻¹ at Pinatubo to 9–16 × 10⁶ kg s⁻¹ at Calbuco. For each case we ran simulations that considered umbrella growth and ones that did not. All umbrella-cloud simulations produced a cloud whose area was within ~25% of the observed cloud by the end of the eruption. By the eruption end, the simulated areas of the Pinatubo, Kelud, and Calbuco clouds were 851, 53.2, and 100 × 10³ km² respectively. These areas were 2.2, 2.2, and 1.5 times the areas calculated in simulations that ignored umbrella growth. For Pinatubo and Kelud, the umbrella simulations provided better agreement with the observed cloud area than the non-umbrella simulations. Each of these simulations extended 24 h from the eruption start. After the eruption ended, the difference in cloud area (umbrella minus non-umbrella) at Pinatubo persisted for many hours; at Kelud it diminished and became negative after 14 h and at Calbuco it became negative after ~23 h. The negative differences were inferred to result from the fact that non-umbrella simulations distributed ash over a wider vertical extent in the plume, and that wind shear spread the cloud out in multiple directions. Thus, for some smaller eruptions, wind shear can produce a larger cloud than might be produced by umbrella spreading alone.