Comment on "An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction'' by Newsha K. Ajami et al.

Uncertainty in the rainfall inputs, which constitute a primary forcing of hydrological systems, considerably affects the calibration and predictive use of hydrological models. In a recent paper, Ajami et al. [2007] proposed the Integrated Bayesian Uncertainty Estimator (IBUNE) to quantify input, parameter and model uncertainties. This comment analyzes two interpretations of the IBUNE method and compares them to the Bayesian Total Error Analysis (BATEA) method [Kavetski et al., 2002, 2006a]. It is shown that BATEA and IBUNE are based on the same hierarchical conceptualization of the input uncertainty. However, in interpretation A of IBUNE, the likelihood function, and hence the posterior distribution, are random functions of the inferred variables, which violates a standard requirement for probability density functions (pdf). A synthetic study shows that IBUNE-A inferences are inconsistent with the correct parameter values and model predictions. In the second interpretation, IBUNE-B, it is shown that a specific implementation of IBUNE is equivalent to a special Metropolis-Hastings sampler for the full Bayesian posterior, directly including the rainfall multipliers as latent variables (but not necessarily storing their samples). Consequently, IBUNE-B does not reduce the dimensionality of the sampling problem. Moreover, the jump distribution for the latent variables embedded in IBUNE-B is computationally inefficient and leads to prohibitively slow convergence. Modifications of these jump rules can cause convergence to incorrect posterior distributions. The primary conclusion of this comment is that, unless the hydrological model and the structure of data uncertainty allow specialized treatment, Bayesian hierarchical models invariably lead to high-dimensional computational problems, whether working with the full posterior (high-dimensional sampling problem) or with the marginal posterior (high-dimensional integration problem each time the marginal posterior is evaluated).