A time-varying parameter estimation approach using split-sample calibration based on dynamic programming

Abstract

Abstract. Although the parameters of hydrological models are usually regarded as constant, temporal variations can occur in a changing environment. Thus, effectively estimating time-varying parameters becomes a significant challenge. Following a survey of existing estimation methodologies, this paper describes a new method that combines (1) the basic concept of split-sample calibration (SSC), whereby parameters are assumed to be stable for one sub-period, and (2) the parameter continuity assumption, i.e., the differences between parameters in consecutive time steps are small. Dynamic programming is then used to determine the optimal parameter trajectory by considering two objective functions: maximization of simulation accuracy and maximization of parameter continuity. The efficiency of the proposed method is evaluated by two synthetic experiments, one with a simple two-parameter monthly model and the second using a more complex 15-parameter daily model. The results show that the proposed method is superior to SSC alone, and outperforms the ensemble Kalman filter if the proper sub-period length is used. An application to the Wuding River basin indicates that the soil water capacity parameter varies before and after 1972, which can be interpreted according to land use and land cover changes. Further application to the Xun River basin shows that parameters are generally stationary on an annual scale, but exhibit significant changes over seasonal scales. These results demonstrate that the proposed method is an effective tool for identifying time-varying parameters in a changing environment.

A Differentiable Hydrology Approach for Modeling With Time‐Varying Parameters

“…The primary disadvantage to this approach is that it does not, in general, encourage TVP estimates with continuous or incremental variation which may be a desirable condition for parameter estimates. Recent work has been done in attempts to identify corrections to the split‐sample procedure to help rectify this issue, however (Zhang & Liu, 2021).…”