| Scientific understanding of many natural systems, particularly in the field of hydrology, can be gained through mechanistic or conceptual modeling. Mechanistic models are often used to estimate the changes in a system under conditions different from those observed and may provide a more theoretically acceptable basis for extrapolation compared to empirical models. Mechanistic models of hydrological systems are frequently complex, deterministic, and require some of the model parameters to be estimated by calibration. However, estimates of the uncertainties in model output and calibrated parameter values, which are necessary to draw statistical inferences from data, are not available from such calibration. In this dissertation, the problem of uncertainty estimation was addressed by adding a random error term to the output of a deterministic model of canopy transpiration. Markov chain simulations were used for uncertainty analysis of the modified model following a Bayesian statistical approach. To test the methodology, a simple model based on the Penman-Monteith equation was chosen and parameters associated with canopy conductance and its response to specific environmental variables were estimated using half-hourly transpiration data. The results indicate that the Bayesian approach is useful for uncertainty analysis of deterministic models modified by adding a random error to their output. A Bayesian approach was also used to compare a number of different canopy conductance sub-models evaluating the tradeoff between model fit and model complexity through the deviance information criterion (DIC). The results of the comparison indicate that the most complex model available is not necessarily the most appropriate for a given set of data. In addition, depending on the information in the data, some of the parameters may be poorly identified. |
