Solving underdetermined tracer inverse problems by spatial smoothing and cross validation

Abstract

A parameter estimation technique known as generalized cross-validation is used to determine the degree of smoothing based on optimizing the prediction of withheld information. The method is tested for the case of steady flow containing a range of spatial scales in a two-dimensional channel with a spatially varying diffusion coefficient. It is shown that the correct flow field and diffusivity may be reproduced relatively accurately from a knowledge of the distribution of two tracers for a variety of flow configurations. The impact on the solution of errors in the equations and errors in the tracer data is studied. -from Authors