Hydrologic models are twofold: models for understanding physical processes and models for prediction. This study addresses the latter, which modelers use to predict, for example, streamflow at some future time given knowledge of the current state of the system and model parameters. In this respect, good estimates of the parameters and state variables are needed to enable the model to generate accurate forecasts. In this paper, a dual state–parameter estimation approach is presented based on the Ensemble Kalman Filter (EnKF) for sequential estimation of both parameters and state variables of a hydrologic model. A systematic approach for identification of the perturbation factors used for ensemble generation and for selection of ensemble size is discussed. The dual EnKF methodology introduces a number of novel features: (1) both model states and parameters can be estimated simultaneously; (2) the algorithm is recursive and therefore does not require storage of all past information, as is the case in the batch calibration procedures; and (3) the various sources of uncertainties can be properly addressed, including input, output, and parameter uncertainties. The applicability and usefulness of the dual EnKF approach for ensemble streamflow forecasting is demonstrated using a conceptual rainfall-runoff model.

Two elementary issues in contemporary Earth system science and engineering are (1) the specification of model parameter values which characterize a system and (2) the estimation of state variables which express the system dynamic. This paper explores a novel sequential hydrologic data assimilation approach for estimating model parameters and state variables using particle filters (PFs). PFs have their origin in Bayesian estimation. Methods for batch calibration, despite major recent advances, appear to lack the flexibility required to treat uncertainties in the current system as new information is received. Methods based on sequential Bayesian estimation seem better able to take advantage of the temporal organization and structure of information, so that better compliance of the model output with observations can be achieved. Such methods provide platforms for improved uncertainty assessment and estimation of hydrologic model components, by providing more complete and accurate representations of the forecast and analysis probability distributions. This paper introduces particle filtering as a sequential Bayesian filtering having features that represent the full probability distribution of predictive uncertainties. Particle filters have, so far, generally been used to recursively estimate the posterior distribution of the model state; this paper investigates their applicability to the approximation of the posterior distribution of parameters. The capability and usefulness of particle filters for adaptive inference of the joint posterior distribution of the parameters and state variables are illustrated via two case studies using a parsimonious conceptual hydrologic model.

Data assimilation (DA) holds considerable potential for improving hydrologic predictions as demonstrated in numerous research studies. However, advances in hydrologic DA research have not been adequately or timely implemented in operational forecast systems to improve the skill of forecasts for better informed real-world decision making. This is due in part to a lack of mechanisms to properly quantify the uncertainty in observations and forecast models in real-time forecasting situations and to conduct the merging of data and models in a way that is adequately efficient and transparent to operational forecasters. The need for effective DA of useful hydrologic data into the forecast process has become increasingly recognized in recent years. This motivated a hydrologic DA workshop in Delft, the Netherlands in November 2010, which focused on advancing DA in operational hydrologic forecasting and water resources management. As an outcome of the workshop, this paper reviews, in relevant detail, the current status of DA applications in both hydrologic research and operational practices, and discusses the existing or potential hurdles and challenges in transitioning hydrologic DA research into cost-effective operational forecasting tools, as well as the potential pathways and newly emerging opportunities for overcoming these challenges. Several related aspects are discussed, including (1) theoretical or mathematical aspects in DA algorithms, (2) the estimation of different types of uncertainty, (3) new observations and their objective use in hydrologic DA, (4) the use of DA for real-time control of water resources systems, and (5) the development of community-based, generic DA tools for hydrologic applications. It is recommended that cost-effective transition of hydrologic DA from research to operations should be helped by developing community-based, generic modeling and DA tools or frameworks, and through fostering collaborative efforts among hydrologic modellers, DA developers, and operational forecasters.

The aim of this paper is to foster the development of an end‐to‐end uncertainty analysis framework that can quantify satellite‐based precipitation estimation error characteristics and to assess the influence of the error propagation into hydrological simulation. First, the error associated with the satellite‐based precipitation estimates is assumed as a nonlinear function of rainfall space‐time integration scale, rain intensity, and sampling frequency. Parameters of this function are determined by using high‐resolution satellite‐based precipitation estimates and gauge‐corrected radar rainfall data over the southwestern United States. Parameter sensitivity analysis at 16 selected 5° × 5° latitude‐longitude grids shows about 12–16% of variance of each parameter with respect to its mean value. Afterward, the influence of precipitation estimation error on the uncertainty of hydrological response is further examined with Monte Carlo simulation. By this approach, 100 ensemble members of precipitation data are generated, as forcing input to a conceptual rainfall‐runoff hydrologic model, and the resulting uncertainty in the streamflow prediction is quantified. Case studies are demonstrated over the Leaf River basin in Mississippi. Compared with conventional procedure, i.e., precipitation estimation error as fixed ratio of rain rates, the proposed framework provides more realistic quantification of precipitation estimation error and offers improved uncertainty assessment of the error propagation into hydrologic simulation. Further study shows that the radar rainfall‐generated streamflow sequences are consistently contained by the uncertainty bound of satellite rainfall generated streamflow at the 95% confidence interval.