relatively simple system and use the resulting covariance statistics in a suboptimal data assimilation scheme for a more detailed model? In general, how might the hierarchical approach suggested in the section above on data assimilation (also cf., NRC 1992a) be implemented?
When should one statistical method be applied as opposed to another? What diagnostics are there to help make decisions on suitable methods? Answers to such questions could be compiled in a handbook on statistical analysis of oceanographic and atmospheric data, could include such things as definitions and methods of statistical parameter estimation, and could discuss such questions as, e.g., What do these parameters convey?
What statistical methods can be used for cross-validating data that take inherent averaging errors into account, and that provide estimates of their magnitude? With the advent of remote sensing, data comparison (Chapter 7) is not limited merely to measurements and model verification, but involves cross-validation of different sensors or assimilation of data into models for quality assessment (see NRC, 1991a). In such analyses, each data set contains errors that are inherent to the averaging process. As Dickey (1991, p. 410) has noted:
One of the major challenges from both the atmospheric and ocean sciences is to merge and integrate in situ and remotely sensed interdisciplinary data sets which have differing spatial and temporal resolution and encompass differing scale ranges…. Interdisciplinary data assimilation models, which require subgrid parametrizations based on higher resolution data, will need to utilize these data sets for applications such as predicting trends in the global climate.