Time Series Separation of Non-Stationary Hydrologic Data with Empirical Mode Decomposition

Stationarity is one of the most important assumptions in the general stochastic time series analysis. In the actual aspect, however, it is very hard that general hydrologic data satisfy the stationarity assumption. Huang et al. (1998) proposed the new method, empirical mode decomposition (EMD), to decompose the non-stationary time series into the stationary and non-stationary components. EMD can decompose the no-stationary time series into several stationary components, Intrinsic Mode Function (IMF), and one non-stationary component, a long-term trend. In this study, EMD was applied to remove the non-stationary component from the observed hydraulic head data and identify the efficiencies of the atmospheric pressure and earth tide component. The monitoring period of applied data is from 2003. 12. 25 to 2004. 1. 27, and monitoring interval is 30 minutes. Hydraulic heads and atmospheric pressures were directly measured with the pressure transducers and the earth tide potential was synthesized with Longman equation. The long-term trend of temporal variations in hydraulic heads include the two different components; seasonal variations in groundwater recharges and seasonal changes in the atmospheric pressure. When I tried to identify contributions of short-term variations in atmospheric pressure and earth tide to the changes in hydraulic potential, both components of trend are generally eliminated from the monitoring data with moving average method and band-pass filter in the frequency domain, comparing results from EMD method. Generally, moving average method is one of the powerful methods in smoothing and reducing the white noise in time domain. But, moving average is one of the worst methods in frequency separation. Especially in the case of earth tide signal and the head variation induced by the earth tide, moving average shows the poor performance. Actually, it is very difficult to separate the non-stationary component from the whole signal with the moving average method. On the other hand, band-pass filter is a very powerful method in the frequency separation, but there are some serious boundary problems in time domain. Among three methods, band-pass filters show the worst performance and moving average show similar results with EMD method. EMD can be a robust method to separate the non-stationary signal from the measured time series in this study.