THE INFLUENCE OF DIFFUSION AND ASSOCIATED ERRORS ON THE ADJOINT DATA ASSIMILATION TECHNIQUE

We investigate the influence of diffusion, and errors associated with its representation, on the adjoint data assimilation technique. In ord er to determine how diffusion influences the retrieval of the initial state given a set of observations at later times, we perform a linear analysis of the one-dimensional diffusion equation and show that the r etrieved initial state will be amplified (smoothed) if the diffusion i n the prediction model is larger (smaller) than that present within th e observations. This amplification (smoothing) not only increases dram atically as the length scale of the feature under consideration decrea ses, but also plays a role in suggesting an appropriate time period wi thin which to assimilate observed data. These results are verified num erically for the simple case of a rising thermal in a neutrally-strati fied environment using simulated pseudo-observations from a dry, three -dimensional Boussinesq model and its adjoint.