Variational coupling of Plinian column models and data: Application to El Chichón volcano

Many efforts have been done in the modelling of Plinian columns. However, until now, the inverse problem of the reconstruction of a Plinian event from observed data has been only roughly tackled. This paper discusses the efficient variational data assimilation (VDA) that manages the optimization iterate sequence by means of gradient computations. Theoretical developments of VDA are presented for both the Woods equations and a generic system allowing for the modelling of the Navier–Stokes equations. Two- and three-dimensional unsteady Plinian models being based on the latters, VDA could be clearly performed on their differentiable subset of equations.Although no column data are available for the 1982 El Chichón eruptions, identical twin experiments were used to check the abilities of the VDA approach. VDA experiments coupled with a tephra tephra-fall model could be used to obtain isopach and isopleth maps of past eruptions. Performing VDA experiments with a Plinian model coupled to a tephra-fall model could be an interesting solution to exploit isopach and isopleth maps of the past eruptions of El Chichón.Some of the numerical experiments presented in this paper are downloadable in the PliniAD package which is freely available from the author's webpage.