應用即時校正方法與非線性Volterra模式於水文預報

Applications of Real-Time Corrective Method and Nonlinear Volterra Model to Hydrological Forecasting

周建明(Chien-Ming Chou) ； 洪君伯(Chun-Po Hung) ； 洪光廷(Koung-Ting Hung)

《水保技術》 6卷4期 (2011/12) Pp. 191-198

https://doi.org/10.30040/JSWCT.201112.0002

摘要

非線性系統廣泛存在，幾乎所有實際系統（包括降雨－逕流歷程）都是非線性，因此研究非線性系統之模擬十分必要。因Volterra模式可視為非線性系統之通用表示式，其為一種多項式模式，且其輸出與核心之間為線性關係，因此，本研究採用非線性之二階Volterra模式來模擬非線性降雨－逕流歷程。另套配Kalman濾波以即時校正Volterra模式參數，可更進一步模擬非線性降雨－逕流歷程之時變特性。上述方法經應用於鹽水溪流域豐化橋上游集水區之降雨－逕流歷程分析，研究結果顯示，具時變性之二階Volterra模式，普遍優於非時變性之二階Volterra模式。此乃因為套配線性Kalman濾波於模式參數，可使其具有時變性，能進一步地模擬及反應非線性降雨－逕流歷程之時變特性，進而提高水文預報之精確度。

關鍵字

Volterra模式 ； 非線性降雨－逕流歷程 ； Kalman濾波 ； 水文預報

並列摘要

Almost all practical systems, including rainfall-runoff processes, are nonlinear. The modeling of a nonlinear system must be studied. The Volterra model, which is one kind of the polynomial models, offers an important general representation of a nonlinear time-invariant system. One benefit of Volterra filters is that the output of the systems is linearly related to the Volterra kernels. The nonlinear second-order Volterra model is adopted for approximating nonlinear rainfall-runoff processes herein. Kalman filters are then utilized to online estimate the parameters of the Volterra kernels and thus model the time-varying nonlinear rainfall-runoff processes. To demonstrate the feasibility of applying Kalman filters and the Volterra model to the modeling of rainfall-runoff processes, the Feng-Hua Bridge watershed in the Yan-Shui River basin is selected as the study area. The average of validation results indicates that the developed time-varying second-order Volterra model outperforms the time-invariant one, because the time-variation of parameters is associated with the adoption of a Kalman filter, and thus simulate and respond to the time-variation of nonlinear rainfall-runoff processes. Validation results also reveal that the resulting method improves the accuracy of hydrological forecasting.

並列關鍵字

Volterra Model ； Nonlinear Rainfall-Runoff Processes ； Kalman Filter ； Hydrological Forecasting