Notes: Abstract Gas accumulation in magma may be aided by coalescence of bubbles because large coalesced bubbles rise faster than small bubbles. The observed size distribution of gas bubbles (vesicles) in lava flows supports the concept of post-eruptive coalescence. A numerical model predicts the effects of rise and coalescence consistent with observed features. The model uses given values for flow thickness, viscosity, volume percentage of gas bubbles, and an initial size distribution of bubbles together with a gravitational collection kernel to numerically integrate the stochastic collection equation and thereby compute a new size spectrum of bubbles after each time increment of conductive cooling of the flow. Bubbles rise and coalesce within a fluid interior sandwiched between fronts of solidification that advance inward with time from top and bottom. Bubbles that are overtaken by the solidification fronts cease to migrate. The model predicts the formation of upper and lower vesicle-rich zones separated by a vesicle-poor interior. The upper zone is broader, more vesicular, and has larger bubbles than the lower zone. Basaltic lava flows in northern California exhibit the predicted zonation of vesicularity and size distribution of vesicles as determined by an impregnation technique. In particular, the size distribution at the tops and bottoms of flows is essentially the same as the initial distribution, reflecting the rapid initial solidification at the bases and tops of the flows. Many large vesicles are present in the upper vesicular zones, consistent with expected formation as a result of bubble coalescence during solidification of the lava flows. Both the rocks and model show a bimodal or trimodal size distribution for the upper vesicular zone. This polymodality is explained by preferential coalescence of larger bubbles with subequal sizes. Vesicularity and vesicle size distribution are sensitive to atmospheric pressure because bubbles expand as they decompress during rise through the flow. The ratio of vesicularity in the upper to that in the lower part of a flow therefore depends not only on bubble rise and coalescence, but also on flow thickness and atmospheric pressure. Application of simple theory to the natural basalts suggests solidification of the basalts at 1.0±0.2 atm, consistent with the present atmospheric pressure. Paleobathymetry and paleoaltimetry are possible in view of the sensitivity of vesicle size distributions to atmospheric pressure. Thus, vesicular lava flows can be used to crudely estimate ancient elevations and/or sea level air pressure.