Fitting models to inadequate data by enforcing spatial and temporal smoothness


  • William Carlisle Thacker


When observations are too sparse to determine the state of a dynamical model, it is necessary to make use of prior knowledge or prejudice. The approach discussed here is to require that the model state be the best smooth fit to the sparse data. The requirement of smoothness is enforced by introducing bogus data, which correspond to hypothetical observations that properties such as slope, curvature, or temporal tendency of model fields have zero values within some specified accuracy. The bogus data serve to increase the effective ratio of data to model degrees of freedom. The concept of bogus data allows a bias toward smoothness to be incorporated easily into the adjoint method for fitting time-dependent models to asynoptic data. Computational examples using a simple three-wave model show that reasonable fits can be obtained even when the number of real data is considerably less than the number of model degrees of freedom.