Parameter and Predictive Uncertainty Analysis of a Spatially Distributed Watershed

12 Uncertainty quantification is currently receiving a surge in attention in hydrology as researchers 13 are trying to better understand characteristics of the watersheds being studied and as decision 14 makers are keen to better quantify accuracy and precision of model predictions. Informal and 15 formal Bayesian approaches have been documented for assessment of parameter and model 16 predictive uncertainty. These methods differ in their underlying assumptions, mathematical rigor, 17 and how the various sources of error are treated. In this paper, we implement a formal Bayesian 18 approach for inference of parameter uncertainty and predictive uncertainty in a spatially 19 distributed hydrologic model using streamflow data from five different locations in the 20 watershed. Posterior parameter distributions are inferred using the recently presented 21 DREAM (ZS) algorithm using a simple least squares (SLS) and generalized likelihood (GL) 22 function. Our most important conclusions are as follows: (1) the parameter uncertainty identified 23 by DREAM (ZS) showed significant sensitivity to the likelihood function (i.e., SLS or GL); (2) 24 when used with GL, DREAM (ZS) generated fairly accurate predictive uncertainty estimates at all 25 five streamflow gages available in the study watershed. The predictive uncertainty obtained 26 using SLS significantly underestimated the predictive intervals; (3) most of the predictive 27 uncertainty quantified for the watershed has been attributed to model structure and input/output 28 data. Parameter uncertainty alone explained only about five percent of the streamflow observed 29 2 at the watershed outlet; (4) the model parameters exhibited significant seasonal sensitivity as 30 demonstrated by the parameter uncertainty obtained using both SLS and GL.