Modelling macronutrient dynamics in the Hampshire Avon river: A Bayesian approach to estimate seasonal variability and total flux.

The macronutrients nitrate and phosphate are aquatic pollutants that arise naturally, however, in excess concentrations they can be harmful to human health and ecosystems. These pollutants are driven by river currents and show dynamics that are affected by weather patterns and extreme rainfall events. As a result, the nutrient budget in the receiving estuaries and coasts can change suddenly and seasonally, causing ecological damage to resident wildlife and fish populations. In this paper, we propose a statistical change-point model with interactions between time and river flow, to capture the macronutrient dynamics and their responses to river flow threshold behaviour. It also accounts for the nonlinear effect of water quality properties via nonparametric penalised splines. This model enables us to estimate the daily levels of riverine macronutrient fluxes and their seasonal and annual totals. In particular, we present a study of macronutrient dynamics on the Hampshire Avon River, which flows to the southern coast of the UK through the Christchurch Harbour estuary. We model daily data for more than a year during 2013-14 in which period there were multiple severe meteorological conditions leading to localised flooding. Adopting a Bayesian inference framework, we have quantified riverine macronutrient fluxes based on input river flow values. Out of sample empirical validation methods justify our approach, which captures also the dependencies of macronutrient concentrations with water body characteristics.