Rainfall‐Runoff Transfer Function by ARMA Modeling

Abstract

Deterministic unit hydrographs have been used by hydrologists for more than fifty years. A unit hydrograph is essentially a watershed rainfall‐runoff linear transfer function. Determination of the deterministic unit hydrograph is very difficult due to the need for separation flows into surface and subsurface runoff components, elimination of noise present in the data series, and inherent inadequacies of the deterministic deconvolution methods being applied to data series “corrupted” by autocorrelation of the data and moving average random inputs. The paper presents a simple methodology for separation of the unit hydrograph function from rainfall and runoff time series which is based on autoregressive‐moving average (ARMA) transfer function modeling. By converting the nonlinear ARMA transfer function model into a linear extended autoregressive (AR) transfer function model, the coefficients of the model can easily be estimated by linear multiple regression followed by filtering the transfer function. The methodology is illustrated on actual time series of flows and rainfalls from two sewer systems.