Highlights 1. The fundamental currency of data informativeness under model misspecification is not the Fisher but the Godambe information 2. The asymptotically valid sandwich variance substantially enlarges hydrologic parameter uncertainty 3. The sandwich covariance matrix is invariant to elastic stretching of the likelihood function as practiced by the GLUE method 4. Markov chain Monte Carlo sampling methods provide an incorrect (naive) characterization of parameter uncertainty 5. Distribution-adaptive likelihood functions help reduce information-bias