Comment on RamaRao et al. [1995] and LaVenue et al. [1995]

A method for stochastic modeling of groundwater flow systems using a combination of pilot point parameterization and conditional simulation was presented by RamaRao et. al [1995] and LaVenue et. al [1995]. (We will collectively term these two papers RLMM and term the method developed in RLMM the CS method here.) RLMM (pp. 478-479) state that the CS method is intended to provide a frequency distribution of possible alternative spatial transmissivity T distributions that (1) are statistically similar to the observed T distribution, (2) are equally likely given the calibration data, and (3) closely reproduce the measured pressures. The frequency distribution of transmissivities is then used to form frequency distribution of derived functions, such as travel times, which are summarized in the form of uncertainty measures, such as (RLMM, p. 512) "confidence (or tolerance) intervals," on the actual values, which in the case of travels times, are values that could occur sometime in the future (RLMM, p.513). 

Cooley [2000] analyzes the RLMM method using linearization and bootstrap theory and concludes that that the method can yield accurate uncertainty estimates but only under some limited circumstances.  In this comment we use Cooley's analysis to critique the method. We also identify and discuss some statements made my by RLMM about model calibration and their methodology that appear to be misleading. 

It is unusual to comment on a paper so long after publication. Subsequent work has expanded the method of RLMM, and the method was used advantageously in the testing documented by Zimmerman et. al [1998], so it is clear the method has significant strengths. We go back to the 1995 papers for this comment, however, because they display most clearly the methodological difficulties with which we are concerned.