Tephra fallout hazard assessment relies on accurate reconstruction of eruption source parameters (ESPs) from tephra deposits. Models of tephra transport and sedimentation from a volcanic plume use ESPs (e.g. erupted mass, column height, mass eruption rate, total grain size distribution) that characterize the processes and the properties of the plume, particles and the atmosphere. We use Tephra2, an Eulerian model of tephra dispersion that simplifies atmospheric dynamics to reconstruct ESPs from mapped deposits. Tephra2 works well in reconstructing ESPs for some deposits, however it does not account for the geometry (i.e. shape) of umbrella clouds of large explosive eruptions. Since the accumulation of particles on the ground is calculated with respect to their release point in the atmosphere, we hypothesize that a modification of Tephra2 that accounts for umbrella clouds would better explain the deposit variations observed in the field associated with some large eruptions. We developed a Python version of Tephra2 that uses the advection – diffusion equation to calculate the mass accumulation of tephra released from an umbrella cloud. We tested three different geometries (i.e. point, vertical line and horizontal disk) against field data from the deposit of the 2450 BP Pululagua (Ecuador) eruption that occurred in absence of wind. Our preliminary results indicate three important aspects of tephra modeling: i) a disk geometry characterizing an umbrella cloud fits the data better than the line and point sources, the last two being highly sensitive to the atmospheric diffusion coefficient; ii) a disk geometry is sensitive to the volume of tephra and the radius of the disk and, iii) different discretization of disk geometries show little sensitivity in deposit geometry with change in the release height, suggesting that disk radius is a more sensitive parameter in modeling large umbrella clouds than the release point or release height. Since large explosive eruptions are characterized by large laterally spreading umbrella clouds even when advected by wind and the umbrella diameter is controlled by eruption rate, as is plume height in vertical plumes,, we suggest the modeling of large deposits with alternative models of the cloud geometries is an important step in analysis of ESPs associated with mapped deposits.