Distributed lag models for hydrological data
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Updated: May 14, 2026

Visualizing Hyporheic Flow Through Bedforms Using Dye Experiments and Simulation
Published on: November 18, 2015
Alastair M Rushworth1, Adrian W Bowman, Mark J Brewer
1School of Mathematics and Statistics, University of Glasgow, G12 8QQ, UK. a.rushworth.1@research.gla.ac.uk
Abstract:
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 specify modified formulations of DLMs to provide computationally attractive, flexible varying-coefficient models that are applicable in any setting in which lagged covariates are regressed on a time-dependent response. We investigate the application of such models to rainfall and river flow and in particular their role in understanding the impact of hidden variables at work in river systems. We apply two models to data from a Scottish mountain river, and we fit to some simulated data to check the efficacy of our model approach. During heavy rainfall conditions, changes in the influence of rainfall on flow arise through a complex interaction between antecedent ground wetness and a time-delay in rainfall. The models identify subtle changes in responsiveness to rainfall, particularly in the location of peak influence in the lag structure.
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