UC Irvine

Bayesian methods are finding increasing application and use in environmental modeling. Bayes law states that the posterior, P(θ|D) is proportional to the product of the prior, P(θ) and likelihood, L(θ|D), or in mathematical form, P(θ|D) / P(θ)L(θ|D). The main crux in the application of such methods relies in the definition of the likelihood function, L(θ|D) used to summarize the distance between the n model simulated values,D' and corresponding data, D. Under ideal conditions, the residuals exhibit normality and standard likelihood functions will suffice. Yet, in real-world modeling studies the residuals are dominated by model and input data errors with probabilistic properties that are not easy to capture in the construction of a likelihood function. Recent contributions therefore use latent variables to parameterize model input and structural errors and estimate these variables jointly with the model parameters, θ. We caution against this approach in the present thesis and demonstrate that the posterior values of the latent variables strongly depend on the (hydrologic) model structure being used. Although strong priors can be used to somewhat alleviate this problem, this requires explicit information about the size and space/time correlation of the input data errors. An alternative viewpoint emerges that model structural errors are relative and only meaningfully interpreted on a model comparative basis.