## 1. Introduction

[2] Within the hydrologic modeling community, there are many new and developing perspectives on the methods through which uncertainty should be estimated. The newest techniques were developed due to a recent shift in focus of model calibration from simple optimization to probabilistic characterization of model parameters [*Beven and Freer*, 2001]. With the recognition of multiple different uncertainty sources (i.e., forcing data, observation, model structure, and parameters), much of the community has tried to account for these uncertainties at varying levels [e.g., *Bulygina and Gupta*, 2009; *Kavetzki et al.*, 2006; *Moradkhani et al.*, 2006; *Moradkhani and Meskele*, 2009; *Vrugt et al.*, 2008]. This has led to an array of different probabilistic techniques to estimate the uncertainty in a given modeling framework. Through an analysis of the uncertainty in a model prediction, the ultimate goal is to produce an accurate probabilistic forecast of a given hydrologic variable. An accurate probabilistic forecast is necessary to allow for effective decision making in the management of water resources. Some examples of attempts in the literature to analyze the uncertainty in hydrologic prediction include the generalized likelihood uncertainty estimator (GLUE) [*Beven and Freer*, 2001; *Stedinger et al.*, 2008], Markov chain Monte Carlo (MCMC) [*Jeremiah et al.*, 2011; *Smith and Marshall*, 2008; *Vrugt et al.*, 2008], Bayesian total error analysis [*Kavetski et al.*, 2002], data assimilation [*DeChant and Moradkhani*, 2011b; *Liu and Gupta*, 2007; *Moradkhani et al.*, 2005a, 2005b; *Moradkhani*, 2008], combined data assimilation and Bayesian model averaging [*Parrish et al.*, 2012], and hierarchical Bayesian [*Wu et al.*, 2010] methods. With this collection of methods at hand, there is great potential for improving the handling of uncertainty in hydrologic modeling and improving the accuracy of probabilistic forecasts.

[3] The study presented here focuses on the use of data assimilation techniques to manage the uncertainty in the modeling framework. Of the above-mentioned methods, data assimilation is attractive for a number of reasons. First, the data assimilation framework provides a methodology for handling all sources of modeling error simultaneously. Second, data assimilation is performed sequentially and therefore has potential in an operational framework, where the estimation of hydrologic quantities is desired at regular intervals. The last benefit of data assimilation is that it does not rely on the assumption of stationarity. Through a sequential estimation of parameters, data assimilation has the potential to handle changes in hydrologic flow patterns.

[4] In the hydrologic data assimilation literature, recent studies have examined the estimation of uncertainty in parameters of a hydrologic model, in addition to the more traditional state estimation [*Moradkhani and Sorooshian*, 2008]. Through the inclusion of parameters in the data assimilation process, it is hypothesized that the total uncertainty in the prediction can be more accurately characterized. Several recent studies of state-parameter estimation in hydrologic models have utilized the popular EnKF [*DeChant and Moradkhani*, 2011a; *Franssen and Kinzelbeck*, 2008; *Leisenring and Moradkhani*, 2011; *Moradkhani et al.*, 2005b; *Wang et al.*, 2009]. In addition to the EnKF, particle filters (PF) have been increasing in popularity for both state and state-parameter estimation [*DeChant and Moradkhani*, 2011a; *Leisenring and Moradkhani*, 2011; *Montzka et al.*, 2010; *Mordakhani et al.*, 2005a; *Nagarajan et al.*, 2010; *Rings et al.*, 2010; *Salamon and Feyen*, 2009; *Smith et al.*, 2008; *Weerts and El Serafy*, 2006]. Of the recent attention that has been paid to state-parameter estimation in the EnKF and PF, little has been shown as to the robustness of these two techniques. It is necessary for the hydrologic data assimilation community to address the effectiveness of both techniques for state-parameter estimation over different scenarios to prove the applicability of the techniques, and relate the results back to the statistical theory and their inherent assumptions. This study aims to perform such an analysis with two conceptual rainfall-runoff models of differing complexities. Throughout this analysis, the importance of examining the behavior of techniques over many different scenarios is highlighted. This study is organized as follows. Section 2 discusses the formulation of the data assimilation techniques and the study basin. Section 3 discusses the experimental setup, including the hydrologic models, time-lagged replicates of the experiment, and the methods through which these replicates are validated. Section 4 presents the results of the data assimilation techniques followed by a discussion of the results and the conclusion in section 5.