The last paper of this three‐part series illustrates and explores various features of the methodology we have proposed in papers 1 and 2 (J. Carrera and S. P. Neuman, this issue (a, b)) by applying it to a synthetic test case and to a set of field data from the southwestern United States. In addition to demonstrating the ability of our method to estimate model parameters under a variety of conditions, the synthetic example is used to investigate the relative worth of transient and steady state data in terms of their ability to bring about an improvement in the quality of the estimates. A similar investigation is performed with regard to the role that prior information may play in reducing the variance of the estimation errors. The paper demonstrates the potential utility of our inverse methodology to the optimum design of observation and measurement networks in space and time. Based on a synthetic example, the paper shows that the model structure identification criteria introduced in paper 1 (J. Carrera and S. P. Neuman, this issue (a)) can be used successfully to choose the best parameter zonation pattern among a number of given alternatives. In particular, a criterion due to R. L. Kashyap (1982) is found to be the most adequate for this purpose because it responds in the most convincing manner to noise in the data. The field example illustrates a case where one must account for temporal autocorrelation between water level data at a given observation point. By validating the model against data which have not been used for parameter estimation, one finds that the validation results improve when the temporal error structure of the water level data is represented by a lag‐one autocorrelation model. Both the synthetic and the field examples are used to obviate the advantages of performing the analysis of the estimation errors in the eigenspace instead of the original parameter space and to relate the results of this analysis to the fundamental questions of identifiability, uniqueness, and stability where appropriate.
ASJC Scopus subject areas
- Water Science and Technology