In hydrologic modeling and forecasting applications, many steps are needed. The steps that are relevant to this thesis include watershed discretization, model calibration, and data assimilation. Watershed discretization separates a watershed into homogeneous computational units for depiction in a distributed hydrologic model. Objective identification of an appropriate discretization scheme remains challenging in part because of the lack of quantitative measures for assessing discretization quality, particularly prior to simulation. To solve this problem, this thesis contributes to develop an a priori discretization error metrics that can quantify the information loss induced by watershed discretization without running a hydrologic model. Informed by the error metrics, a two-step discretization decision-making approach is proposed with the advantages of reducing extreme errors and meeting user-specified discretization error targets.

In hydrologic model calibration, several uncertainty-based calibration frameworks have been developed to explicitly consider different hydrologic modeling errors, such as parameter errors, forcing and response data errors, and model structure errors. This thesis focuses on climate and flow data errors. The common way of handling climate and flow data uncertainty in the existing calibration studies is perturbing observations with assumed statistical error models (e.g., addictive or multiplicative Gaussian error model) and incorporating them into parameter estimation by integration or repetition with multiple climate and (or) flow realizations. Given the existence of advanced climate and flow data uncertainty estimation methods, this thesis proposes replacing assumed statistical error models with physically-based (and more realistic and convenient) climate and flow ensembles. Accordingly, this thesis contributes developing a climate-flow ensemble based hydrologic model calibration framework. The framework is developed through two stages. The first stage only considers climate data uncertainty, leading to the climate ensemble based hydrologic calibration framework. The framework is parsimonious and can utilize any sources of historical climate ensembles. This thesis demonstrates the method of using the Gridded Ensemble Precipitation and Temperature Estimates dataset (Newman et al., 2015), referred to as N15 here, to derive precipitation and temperature ensembles. Assessment of this framework is conducted using 30 synthetic experiments and 20 real case studies. Results show that the framework generates more robust parameter estimates, reduces the inaccuracy of flow predictions caused by poor quality climate data, and improves the reliability of flow predictions.

The second stage adds flow ensemble to the previously developed framework to explicitly consider flow data uncertainty and thus completes the climate-flow ensemble based calibration framework. The complete framework can work with likelihood-free calibration methods. This thesis demonstrates the method of using the hydraulics-based Bayesian rating curve uncertainty estimation method (BaRatin) (Le Coz et al., 2014) to generate flow ensemble. The continuous ranked probability score (CRPS) is taken as an objective function of the framework to compare the scalar model prediction with the measured flow ensemble. The framework performance is assessed based on 10 case studies. Results show that explicit consideration of flow data uncertainty maintains the accuracy and slightly improves the reliability of flow predictions, but compared with climate data uncertainty, flow data uncertainty plays a minor role of improving flow predictions.

Regarding streamflow forecasting applications, this thesis contributes by improving the treatment of measured climate data uncertainty in the ensemble Kalman filter (EnKF) data assimilation. Similar as in model calibration, past studies usually use assumed statistical error models to perturb climate data in the EnKF. In data assimilation, the hyper-parameters of the statistical error models are often estimated by a trial-and-error tuning process, requiring significant analyst and computational time. To improve the efficiency of climate data uncertainty estimation in the EnKF, this thesis proposes the direct use of existing climate ensemble products to derive climate ensembles. The N15 dataset is used here to generate 100-member precipitation and temperature ensembles. The N15 generated climate ensembles are compared with the carefully tuned hyper-parameter generated climate ensembles in ensemble flow forecasting over 20 catchments. Results show that the N15 generated climate ensemble yields improved or similar flow forecasts than hyper-parameter generated climate ensembles. Therefore, it is possible to eliminate the time-consuming climate relevant hyper-parameter tuning from the EnKF by using existing ensemble climate products without losing flow forecast performance.

After finishing the above research, a robust hydrologic modeling approach is built by using the thesis developed model calibration and data assimilation methods. The last contribution of this thesis is validating such a robust hydrologic model in ensemble flow forecasting via comparison with the use of traditional multiple hydrologic models. The robust single-model forecasting system considers parameter and climate data uncertainty and uses the N15 dataset to perturb historical climate in the EnKF. In contrast, the traditional multi-model forecasting system does not consider parameter and climate data uncertainty and uses assumed statistical error models to perturb historical climate in the EnKF. The comparison study is conducted on 20 catchments and reveal that the robust single hydrologic model generates improved ensemble high flow forecasts. Therefore, robust single model is definitely an advantage for ensemble high flow forecasts. The robust single hydrologic model relieves modelers from developing multiple (and often distributed) hydrologic models for each watershed in their operational ensemble prediction system.