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。

Almost all practical systems, including rainfall-runoffprocesses, are nonlinear. The modeling of a nonlinear system must bestudied. The Volterra model, which is one kind of the polynomial models,offers an important general representation of a nonlinear time-invariantsystem. One benefit of Volterra filters is that the output of the systems islinearly related to the Volterra kernels. The nonlinear second-orderVolterra model is adopted for approximating nonlinear rainfall-runoffprocesses herein. Kalman filters are then utilized to online estimate theparameters of the Volterra kernels and thus model the time-varyingnonlinear rainfall-runoff processes. To demonstrate the feasibility ofapplying Kalman filters and the Volterra model to the modeling ofrainfall-runoff processes, the Feng-Hua Bridge watershed in the Yan-ShuiRiver basin is selected as the study area. The average of validation resultsindicates that the developed time-varying second-order Volterra modeloutperforms the time-invariant one, because the time-variation ofparameters is associated with the adoption of a Kalman filter, and thussimulate and respond to the time-variation of nonlinear rainfall-runoffprocesses. Validation results also reveal that the resulting methodimproves the accuracy of hydrological forecasting.