It is often easy to see when an atmospheric model disagrees with data. It is usually much harder to locate the ultimate sources of model error.

It is particularly difficult to diagnose errors in a model's structure, that is, errors in the functional form of the model equations. One technique that may help is parameter estimation, that is, the optimization of model parameter values. Typically, parameter estimation is used solely to improve the fit between a model and observational data. In the process, however, parameter estimation may cover up structural model errors.

In a quite opposite application, parameter estimation may be used to uncover the ways in which a model is wrong. The basic idea is to separately optimize model parameters to two different data sets, and then identify parameter values that differ between the two optimizations. When no single value of a particular parameter fits both datasets, then there must exist a related structural error.

The parameter estimation method that we use is akin to an ensemble Bayesian technique. It produces an entire multi-variate distribution of parameter values. It may prove useful for a wide range of parameterizations. We apply the method to a parameterization of boundary layer clouds, uncover the presence of a structural model error, revise the model structure, and obtain improved results.