To understand, reduce, and quantify the uncertainty with which mathematically based models predict behavior of field systems, we need to: (1) provide clear consideration and accounting of the errors in data used for model development, (2) consider alternative model representations developed with data-based constraints (generally hydrogeologic information and analyses), (3) use local and(or) global sensitivity analysis methods to understand the strengths and limitations of the available data in the context of model construction choices, (4) calibrate each model with optimization methods that take advantage of gradient or global methods as execution times allow, (5) define and quantify prediction uncertainty related to parameters (including parameters not estimated during the calibration process but important to predictions) using inferential statistics such as linear and nonlinear confidence intervals and sampling techniques such as Monte Carlo methods, (6) average the predictions and associated uncertainty for the alternative models, and (7) identify additional data that are likely to reduce prediction uncertainty based on sensitivity analysis of the calibrated models in the prediction scenarios.  It is important to examine the alternative models carefully for parameter correlation, parameter insensitivity, and unrealistic parameter values and model structure. When applying some types of data-based constraints, prior information needs to be accounted for in the nonlinear regression rather than as prior model probability in a Bayesian sense.  Strengths and weaknesses of these and alternative methods will be discussed.