Modeling of streamflow processes at different time scales

Abstract

The analysis and modeling of streamflow processes has attracted the attention of water resources specialists for several decades. A number of models have been suggested in the past for representing seasonal and annual streamflow processes. The topic addressed in this paper centers around the compatibility of stochastic models of streamflow at different time scales. More specifically, given a model for monthly flows, the models for the processes obtained by aggregation, i.e., models for bimonthly, quarterly, etc., time scales, are derived. Likewise, parameter space and covariance properties of such derived processes as well as the relationship of such properties of different time scales are given. These concepts are applied to modeling streamflow of the Niger River. The developments are restricted to the family of periodic autoregressive moving average (PARMA) processes. For instance, it was found that monthly flows based on the PARMA(2, 1) process leads to PARMA(2, 2) bimonthly flows and stationary ARMA(2, 2) annual flows. Furthermore, applications to modeling the Niger River flows suggest that one can reproduce the seasonal and annual second‐order statistics without using disaggregation if PARMA models are used for modeling the seasonal flows.