Estimating Parameters in Real-Time Under Changing Conditions Via the Ensemble Kalman Filter Based Method

Hydrological model performance is usually not as acceptable as expected due to limited measurements and imperfect parameterization which is attributable to the uncertainties from model parameters and model structures. In applications, a general assumption is hold that model parameters are constant in a stationary condition during the simulation period, and the parameters are generally prescribed though calibration with observed data. In reality, but the model parameters related to the physical or conceptual characteristics of a catchment will travel in nonstationary conditions in response to climate transition and land use alteration. The travels or changes of parameters are especially evident for long-term hydrological simulations. Therefore, the assumption of using constant parameters under nonstationary condition is inappropriate, and it will deliver errors from the parameters to the outputs during the simulation and prediction. Even though a few of studies have acknowledged the parameter travel or change, little attention has been paid on the estimation of changing parameters.

In this study, we employ an ensemble Kalman filter (EnKF) based method to trace parameter changes in real time. Through synthetic experiments, the capability of the EnKF-based is demonstrated by assimilating runoff observations into a rainfall-runoff model, i.e., the Xinanjing Model. In addition to the stationary condition, three typical nonstationary conditions are considered, i.e., the leap, linear and Ω-shaped transitions. To examine the robustness of the method, different errors from rainfall input, modelling and observations are investigated. The shuffled complex evolution (SCE-UA) algorithm is applied under the same conditions to make a comparison.

The results show that the EnKF-based method is capable of capturing the general pattern of the parameter travels even for high levels of uncertainties. It provides better estimates than the SCE-UA method does by taking advantages of real-time tracing and accounting for various sources of uncertainties in hydrologic simulations. Therefore, the EnKF-based method is suitable for hydrological modelling in a changing environment.

Keywords: Parameter estimation; Nonstationary condition; Xinanjiang model; ensemble Kalman filter, data assimilation.