## 1. Introduction

[2] Hydrologic modeling is always plagued by various uncertainties associated with model parameters, driving force inputs, model structure, and output observations [*Ajami et al*., 2007; *Zhang*, 2002]. To reduce these uncertainties, model calibration that aims to minimize the discrepancy between simulated and observed model outputs is a mandatory element of a good modeling practice [*Refsgaard et al*., 2010]. For many years, a great effort has been directed toward calibration methods, including direct search optimization [e.g., *Duan et al*., 1992, 1993] and probabilistic estimation [e.g., *Beven and Binley*, 1992; *Beven and Freer*, 2001a].

[3] However, most of these methods attribute the underlying uncertainty in the input-output representation of the model to the uncertainty of parameter estimates [*Kavetski et al*., 2004; *Vrugt et al*., 2005]. A few studies based on the Bayesian theorem have tried to account for various sources of uncertainties (e.g., the Bayesian approach for total error analysis (BATEA)) [*Kavetski et al*., 2004], but such approaches are rarely used for nonlinear watershed models [*Vrugt et al*., 2005]. A comprehensive review on confronting modeling uncertainties can be found in *Kavetski et al*. [2004] and *Liu and Gupta* [2007].

[4] In a separate line of research, newly developed data assimilation methods, especially sequential data assimilation techniques, have demonstrated potential for explicitly dealing with various uncertainties and for optimally merging observations into uncertain model predictions [*Troch et al*., 2003]. One of these techniques is the particle filter that is suitable for non-Gaussian nonlinear dynamical models [*Han and Li*, 2008]. Particle filters have received much attention in hydrologic modeling [*DeChant and Moradkhani*, 2012; *Moradkhani et al*., 2005a; *Moradkhani and Sorooshian*, 2008]; however, they may impose a remarkable computational burden for obtaining accurate results [*Weerts and El Serafy*, 2006; *Han and Li*, 2008]. As a prototype of sequential data assimilation techniques, the Kalman filter (KF) [*Kalman*, 1960] and the ensemble Kalman filter (EnKF) [*Evensen*, 1994] recursively result in optimal estimation for linear dynamic models with Gaussian uncertainties. The EnKF has earned its popularity in hydrology due to its attractive features, such as real-time adjustment and ease of implementation [*Reichle et al*., 2002]. In some applications, it was mainly used for dynamic state estimation, while the parameters were fixed at predefined values, thereby explicitly ignoring the effects of parameter uncertainty and interaction [*Vrugt et al*., 2005]. That is partly attributable to the fact that the parameter estimation is more difficult than the state estimation in hydrology, since the relation between parameters and states are nonlinear for most hydrological models and model parameters cannot be directly measured like states.

[5] The EnKF also provides a general framework for state and parameter estimation. This joint estimation can be performed, typically, with two strategies. One is a hybrid strategy with simultaneous optimization and data assimilation [*Vrugt et al*., 2005]. Its implementation consists of an inner EnKF loop and an outer global-optimization loop. The former is for state estimation conditioned on an assumed parameter set, and the latter for batch estimation of parameters using an optimization method, such as the Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm [*Vrugt et al*., 2003]. The optimal set of parameters identified by this strategy, however, does not guarantee the best model forecasts when the data assimilation is not implemented or no state adjustments are allowed. The other is a state augmentation strategy, which extends the state vector to include the parameter set. Parameters are considered as part of the model state, and they are updated together with the dynamic states when observations are available [*Annan et al*., 2005]. So this technique is a simple extension of the EnKF in which the parameter estimation problem is generally formulated to find the joint probability density of parameters and model states, given a set of measurements and a dynamic model with known uncertainties [*Evensen*, 2009].

[6] For joint state-parameter estimation, the state augmentation technique with the EnKF has been successfully demonstrated in many areas, such as the earth system model [*Annan et al*., 2005], the hydrogeologic model [*Chen and Zhang*, 2006; *Liu et al*., 2008], and catchment-scale hydrologic models [*Young*, 2002; *Xie and Zhang*, 2010]. This technique is also undergoing improvement. One example is the constrained schemes that can be exerted on the EnKF to avoid violating physical principles in updating states and parameters [*Wang et al*., 2009]. Another example is the dual state-parameter estimation approach that can decrease the degree of freedom of the augmented state vector in the updating process [*Moradkhani et al*., 2005a, 2005b]. In addition to the EnKF, particle filtering has also been used for joint state-parameter estimation [*Moradkhani et al*., 2005a, 2005b]. However, most of these applications in rainfall-runoff characterizations aim at lumped hydrologic models with a small number of states and parameters.

[7] For distributed hydrologic models, this state augmentation technique may suffer from spurious or incorrect correlations between states and parameters, which would directly spoil parameter estimation during data assimilation. This is basically due to biased model error quantification and a large degree of freedom for high-dimensional vectors of the augmented state. This disadvantage will be transferred to the covariance matrix that is computed with the (biased) ensemble states within the framework of the EnKF. Especially for the nonlinear impulse response, such as the rainfall-runoff process, the correlations between dynamic states and parameters are easily overestimated or underestimated by the interference of parameters, since different types of parameters contribute differently to the impulse response in the alternate wet-dry seasons. Moreover, when the augmented state vector holds a high dimension, the joint estimation is possibly unstable and intractable [*Moradkhani et al*., 2005a, 2005b]. To better approximate the correlations, a localization scheme is capable of suppressing correlations beyond a certain separation distance [*Reichle and Koster*, 2003]. The localization scheme may be impractical for the joint state-parameter estimation, however, especially since observations (typically, of streamflow) are usually sparse in a watershed.

[8] To reduce the degree of freedom of high-dimensional states and achieve simultaneous state-parameter estimation, a partitioned update scheme based on the EnKF is proposed in this study. This scheme, inspired by the localization scheme [*Reichle and Koster*, 2003] and the dual state-parameter estimation approach [*Moradkhani et al*., 2005a, 2005b], partitions the parameter set according to the parameter types, and estimates the dynamic states and parameters by repeatedly assimilating observations after a separate forecast. Moreover, the parameters are artificially evolved at each time step using a kernel smoothing method to overcome the overdispersion of parameter samples [*Liu*, 2000]. This scheme is first examined with synthetic experiments and further evaluated with a distributed hydrologic model regarding a real case. Results show that this partitioned update scheme can strengthen and expand the robustness of the state augmentation technique due to the fact that it retrieves acceptable parameter values and captures the temporal patterns of dynamic states compared with the standard state augmentation technique. It should be noted that, in this paper, distributed hydrologic models hold a general definition [*Reed et al*., 2004; *Smith et al*., 2004] that includes conceptual distributed models (e.g., the Soil and Water Assessment Tool (SWAT) model used in this study) and fully physically based models [e.g., the SHE model, *Refsgaard et al*., 2010].

[9] The connotation of the parameter type is associated with the distributed hydrologic model in which each computational unit contains the target parameter to be estimated. For example, in SWAT, the parameter CN_{2} (see section 4.2) is related to the surface runoff generation in each hydrologic response unit (HRU). Since there are many CN_{2} parameters to be estimated for all HRUs in a watershed, “CN_{2}” is regarded as one parameter type. In a general sense, it is also reasonable that a parameter type contains only one parameter, as shown in section 3, for the synthetic experiments.

[10] This paper is organized as follows. In section 2, we present an overview of the EnKF framework and describe the new parameter update scheme with the kernel smoothing method for parameter evolution. In section 3, we examine the performance of the new algorithm by means of synthetic experiments with a simplified rainfall-runoff model. In section 4, we further demonstrate the scheme using a real case using a distributed hydrologic model, i.e., the SWAT. Finally, in section 5, we summarize the methodology and discuss the results.