Variational assimilation of simulated acoustic tomography data and point observations: A comparative study

Abstract

A simple advection‐diffusion model is used to generate synthetic acoustic tomography data and local temperature observations which are then assimilated by a numerical model. The data are assimilated using the following two methods: a variational adjoint method and a sequential assimilation technique formulated as a minimization problem. The “success” of the analyses are gauged by comparing them to the true fields and, in the adjoint assimilation experiments, by also performing analysis of error and resolution. Results show that with the same number of acoustic rays and point observations the initial temperature field is well reproduced whether acoustic data or local temperature data are used. Model and observation errors are introduced in the main assimilation experiments by adding random noise to the velocities of the model that generates the data but not into the assimilation model (model error). On top of that, extra random noise is added directly to the “observations” (observation error). The results are compared to experiments where only one source of error is introduced and to “identical twin” experiments in which there are neither model nor observation errors and therefore model and data are perfectly compatible. The effect of model error is to produce analyses whose error grows with time even in the presence of diffusion which tends to reduce such errors, whereas observation errors produce analyses similar to the identical twin experiments. The detrimental effect of model (and observation) errors can be reduced by weighting properly the background or a priori information which is used to regularize the analyses. It is found that the analyses from sequential assimilation methods are more sensitive to this weight. Adjoint‐variational assimilation is used to determine other model parameters (in this case, one of the advective velocities of the model) as a method to correct model deficiencies from data.