Distributed lag models for hydrological data

The distributed lag model (DLM), used most prominently in air pollution studies, finds application wherever the effect of a covariate is delayed and distributed through time. We explore the use of modified formulations of DLMs to provide flexible varying-coeficient models with smoothness constraints, applicable in any setting in which lagged covariates are regressed on a time-dependent response. The models are applied to simulated flow and rainfall data and to flow data from a Scottish mountain river, with particular emphasis on approximating the relationship between environmental covariates and flow regimes in order to detect the influence of unobserved processes. It was found that under certain rainfall conditions some of the variability in the influence of rainfall on flow arises through a complex interaction between antecedent ground wetness and the time-delay in rainfall. The models are able to identify subtle changes in rainfall response, particularly in the location of peak influence in the lag structure and offer a computationally attractive approach for fitting DLMs