A method for correcting the structural instability of time-dependent atmospheric trajectory models under perturbations of the mass balance

Lagrangian trajectory models of atmospheric fluid parcels have been used over a wide range of spatial scales to study the transport and dispersion of pollutants, radioactive materials, ash clouds produced by volcanic eruptions or modeling global carbon cycle. It was pointed out trajectory calculations have three error sources: error in the gridded data from measurements error or from approximations in Eulerian numerical models, error from the spatial and temporal resolution of data, and truncation error from numerical integration of the velocity field. In a recent work we showed that trajectory models can be structurally unstable under perturbations of the mass balance, e.g., the flow can go from hyperbolic to elliptic and vice versa. In this work we propose a mass-consistent approach to correct this structural instability. The orthogonal projection character of this approach guarantees the correction even for large perturbations of the mass-balance. This is illustrated by means of numerical examples. Mass-consistent models have been considered as diagnostic models of the wind field but the results of this work show that such a models can be used for four-dimensional data assimilation of nonstationary flows. (paper)