Modeling the 1913 eruption of Colima volcano, Mexico, based on data collected by Jim Luhr and colleagues

Jim Luhr and colleagues spent more than a decade characterizing the explosive eruptions of Colima volcano, particularly the January 20, 1913 Plinian eruption that sent a tephra cloud to the NNE of the volcano, by some reports depositing tephra up to 725 km from the volcano. Their data are modeled using TEPHRA2, a computer model that calculates the expected accumulation of tephra at specific geographical locations as a result of a volcanic eruption with specific input parameters using the advection diffusion equation. TEPHRA2 has numerous input parameters so it is literally impossible to find a best-fit solution using brute force iteration. Instead, we use nonlinear inversion techniques to explore best-fit solutions. Here we use a downhill simplex inversion algorithm. No parameter correlations (for example between eruption column height and eruption mass) are assumed a priori in the inversion. Overall, it appears from inversion results that acceptable solutions for total eruption mass lie between 0.8 x 1011 kg and 1.3 x 1011 kg and acceptable solutions for eruption column height lie between about 20 and 38 km above mean sea-level. In order to better understand the solution space, we ran the inversion numerous times, each time limiting the ranges of eruption column height and erupted mass. All other eruption parameters are allowed to vary over wide ranges to identify best-fit solutions. These results show that best-fit solutions for total erupted mass are constrained between approximately 0.6 x 1011 kg and 1.6 x 1011 kg. Best-fit solutions of essentially equal quality are identified for a wide range of eruption column heights (20-40 km). The plot of best-fit solutions suggests that slightly better results are obtained by the model in the region of 30-38 km and 1.4 x 1010 to 1.8 x 1011 kg, with all other parameters allowed to vary over their entire ranges. We note that eruption physics places some additional constraints on the maximum column height. For an instantaneous explosion, and 1.3 x 1011 kg mass in the plume, and the maximum column height above sea level should be approximately 36 km. Given that the entire plume was not likely released instantaneously, we regard this to be an approximate maximum possible plume height.