The recently-developed hybrid EnVE method for data assimilation in meteorological systems incorporates successive adjoint optimizations to update the initial conditions of a flow model, over various horizons of interest, in order to reconcile this model with recent measurements. Such adjoint optimizations typically require the trajectory to be saved over the entire interval over which the optimization is performed. In high-dimensional systems, this can lead to significant storage problems, which can be partially alleviated via checkpointing.

In the EnVE framework, the requirement to either save the entire space/time trajectory over the optimization window or to perform checkpointing is eliminated, and supplanted by a requirement to march the state of the system backward in time simultaneously with the adjoint. If the system is derived from a PDE with a diffusive component, this backward-in-time state march is ill conditioned, and requires regularization/smoothing to prevent errors from accumulating rapidly at the small scales. The present talk focuses specifically on this peculiar requirement of the EnVE algorithm. As the forecasting problem may itself be considered as a smoothing problem, it is, in fact, expected to find a ``smoothing'' ingredient at the heart of an algorithm of this sort.

Note that the large-scale meteorological systems of interest are essentially in the high-Reynolds-number limit, and that we are interested in forecasting large-scale meteorological phenomena. In this limit, the effect of the particular regularization method used to smooth the small length scales over short-time marches is anticipated to be relatively insignificant on the large-scale physics of interest.

Various strategies are proposed and tested for accomplishing the required smoothing in the EnVE setting, and are tested on both a chaotic 1D PDE (the Kuramoto-Sivashinsky equation) as well as our in-house spectral 3D DNS/LES code, diablo.