Conceptually-based multivariate simulation of monthly runoff

This paper presents a multivariate extension of a parsimonious conceptually-based AutoRegressive-Moving Average (ARMA) stochastic model for monthly runoff. The multi-station model is aContemporaneous-ARMA (CARMA), which considers separately the serial and space correlation of runoff.Serial correlation is reproduced in individual series by an ARMA model. The ARMA model residuals areuncorrelated in time but correlated in space. Spatial correlation of runoff is then reproduced by generatingcorrelated series of residuals and using them to generate runoff through the individual ARMA models. In theconceptual framework, stochastic ARMA parameters are related to the parameters of a linear system, whichrepresents the watershed filter that produces runoff. The system input is the effective rainfall, which isinversely estimated through the ARMA model residual. Application of the CARMA model in the conceptualframework consists in reproducing the spatial correlation on the effective rainfall rather than on the residuals.A suitable technique is also proposed for estimation of correlation in matrices with gaps. The performances ofthe model are discussed with regard to its application on a 9-station system in Southern Italy.