Identification and prediction of nonlinear hydrologic systems by the filter-separation autoregressive (AR) method: Extension to hourly hydrologic data

Abstract In this paper, our method — from the hydrologic inverse detection method originally proposed for daily runoff data analysis — is extended to hourly hydrologic data analysis. A few modifications of the original inverse method (filter separation and autoregressive (AR) method) are necessary in order to apply it to hourly data. 1. (1) The cut-off frequency to separate the total runoff time series into component runoffs was determined by the slope of the semi-logarithmic plot of the recession curve. 2. (2) Coefficients of the autoregressive moving average (ARMA) model applied to each of the subsystems were determined by the least-squares criterion from the recession period data when rainfall stopped; thus the ARMA model is reduced to the AR model with a white-noise error. A remaining coefficient to be multiplied by the rainfall (input) is obtained by the continuity condition of effective rainfall and runoff. The conclusions of this analysis are as follows: 1. (1) Nonlinear hourly hydrologic systems are easily and precisely identified and predicted by the present method. 2. (2) Each subsystem of surface runoff, interflow and groundwater runoff is linear; the nonlinearity of the rainfall-runoff system is caused mainly by the nonlinearity of the separation of rainfall into component rainfalls. The nonlinear separation rule of rainfall into rainfall components is derived from inversely estimated rainfalls. 3. (3) Time series of hourly rainfalls can be inversely estimated from hourly runoff by this method and it compares well with the observed effective precipitation time series regardless of the size of watershed.