Estimation of state variables of Hymod hydrologic model by applying data assimilation methods

Conceptual Soil moisture rainfall runoff models (RRM) can be applied for simulation and forecasting daily stream flow based on their developed relations. There is an inherent uncertainty in the outputs of RRM. Data assimilation (DA) is an approach that can help to not only estimate the state variable, but also to calculate the uncertainty of outputs. DA can be used in order to reduce the state uncertainty via updating the model states by fusing observations and model outputs to obtain an estimate of the model states. Sequential DA techniques provide a general framework for explicitly taking into account input uncertainty, model uncertainty, and output uncertainty. DA approach is the process through which the available information is used to estimate the state of the conceptual hydrologic model, as accurate as possible. There are several different DA methods available. State-space filtering methods based on variations of the kalman filter (KF) approach have been proposed and implemented because of their potential ability to explicitly handle uncertainties in hydrologic predictions. Kalman filtering is a popular tool in the research community for estimating non-stationary processes when it is possible to model the system dynamics by linear behavior and Gaussian statistics. The first sequential DA method called Kalman filter that was employed for optimizing control of linear developed systems. KF has not used in hydrologic investigations because of its limitation to linear models. In hydrologic studies the Ensemble Kalman filter (EnKf) has been developed in order to estimate state variables, as well as parameters. DA is useful in state estimation and making the forecasts more accurate. In EnKf, the hydrologic model being run and gone forward temporally with a specified number of state variables. HyMod was used in this research. Hymod is a non-linear RRM. It relates the mean areal precipitation and the potential evapotranspiration, for a certain catchment, to the discharge. The model consists of a slow flow and quick flow components. The slow flow component consists of one linear tank. It represents the water that flows through the ground and eventually empty to the river. While the quick flow component consists of three identical quick flow tanks, representing the portion of water that flows directly into the river. It is a parsimonious model, which consists of five parameters. By applying EnKf method, the amounts of soil moisture in rapid and slow tanks of HyMod model are estimated by updating the forecasted steamflow based on the observations. Hence, the forecasted flow will be corrected with updated soil moisture in daily step. In the present study, parameters were estimated by applying the shuffled complex evolution method (SCE-UA). This method was applied in many studies and has been highly recommended by multiple scholars. As the procedure needs that the equations to be written in state space format, therefore the HyMod equations changed to matrix form to be calculated. The equations have written down in a matrix form and the state and measurement equations have been related. Different ensemble members also assessed in order to check the capability of the EnKf based on Nash-Sutcliffe measure in kassilian river basin. Kassilian watershed is located in the northern part of Iran. Its discharge area covers a surface of 67.2 km2 and its average slope is 16.4%. It is a mountainous watershed with 65% of its total area covered with forests. A gauging station, operated since 1970, is located at the outlet of the basin. An Ensemble with 25 members was selected as the elite results. To show the merits of the proposed method; first, the model was used in an open loop way without data assimilation and updating. Afterwards, the EnKf has been implemented. The Nash-Suttclife measure has been employed to show, which method performs better.The results revealed that by using EnKf and updating the soil moisture of the Hymod model the accuracy of forecasted streamflow improves and the Nash-Suttclife criteria increases by 31%. It reaches 0.72. This study has introduced the theory and concepts of EnKf as a DA methodology for inference of state variables in a RRM. As models besides the parameters have state variables, therefore, they can simultaneously be estimated with EnKf. So, we suggest that the dual combination of state and parameters can be explored in a complementary study.