Application of wavelet‐based multi‐model Kalman filters to real‐time flood forecasting

Abstract

Abstract:This paper presents the application of a multimodel method using a wavelet-based Kalman filter (WKF) bank to simultaneously estimate decomposed state variables and unknown parameters for real-time flood forecasting. Applying the Haar wavelet transform alters the state vector and input vector of the state space. In this way, an overall detail plus approximation describes each new state vector and input vector, which allows the WKF to simultaneously estimate and decompose state variables. The wavelet-based multimodel Kalman filter (WMKF) is a multimodel Kalman filter (MKF), in which the Kalman filter has been substituted for a WKF. The WMKF then obtains M estimated state vectors. Next, the M state-estimates, each of which is weighted by its possibility that is also determined on-line, are combined to form an optimal estimate. Validations conducted for the Wu-Tu watershed, a small watershed in Taiwan, have demonstrated that the method is effective because of the decomposition of wavelet transform, the adaptation of the time-varying Kalman filter and the characteristics of the multimodel method. Validation results also reveal that the resulting method enhances the accuracy of the runoff prediction of the rainfall-runoff process in the Wu-Tu watershed.

Post-Processing of Stream Flows in Switzerland with an Emphasis on Low Flows and Floods

“…In the work of Bogner and Kalas [16], an error-correcting method was developed combining wavelet transformations (e.g., Beylkin and Saito [17], Chou and Wang [18]) and Vector AutoRegressive Models with eXogeneousinput (Wave-VARX). The idea was to incorporate not only the most recent information of the error in the correction model, but also information with time lags of several hours and days.…”

Daily river flow forecasting using wavelet ANN hybrid models

“…Some recent studies reported that integration of wavelet transformation technique with ANN yields superior results compared to simple ANN and regression models (Anctil & Tape 2004;Chou & Wang 2004;Zhou et al 2006;Partal & Kisi 2007;Nourani et al 2008;Kisi 2008bKisi , 2009aRemesan et al 2009). This advanced pre-processing of raw data to capture the non-stationary behaviour of the time series data by decomposing the original series into wavelet coefficients of different frequency bands has been effectively applied by site is shown in Figure 1.…”

Piecewise‐quadratic Harmut basis functions and their application to problems in digital signal processing

“…Here k = number of Harmut's functions. hrm(r ) is Harmut's function of r , both of these functions have been established by the Harmut matrix [10]. x is the argument value and p is the order of Haar's functions such as (p = 1, 2, .…”

“…The Walsh functions, the mathematical functions, and the ramp function belong to this class [9,10,12]. (2) Local basis functions-for which nonzero values are chosen on the enclosed intervals.…”

“…It is found that the current approach is not suitable due to weak convergence of approximation, discontinuity, and others [5,10,11]. To eliminate the previous problems, a new algorithm has been proposed in this paper to make suitable signal-based applications.…”