The challenges of modelling phosphorus in a headwater catchment: Applying a ‘limits of acceptability’ uncertainty framework to a water quality model

There is a need to model and predict the transfer of phosphorus (P) from land to water, but this is challenging because of the large number of complex physical and biogeochemical processes involved. This study presents, for the first time, a ‘limits of acceptability’ approach of the Generalized Likelihood Uncertainty Estimation (GLUE) framework to the Soil and Water Assessment Tool (SWAT), in an application to a water quality problem in the Newby Beck Catchment (12.5km2), Cumbria, United Kingdom (UK). Using high frequency outlet data (discharge and P), individual evaluation criteria (limits of acceptability) were assigned to observed discharge and P loads for all evaluation time steps, identifying where the model was performing well/poorly and to infer which processes required improvement in the model structure. Initial limits of acceptability were required to be relaxed by a substantial amount (by factors of between 5.3 and 6.72 on a normalized scale depending on the evaluation criteria used) in order to gain a set of behavioral simulations (1001 and 1016, respectively out of 5,000,000). Of the 39 model parameters tested, the representation of subsurface processes and associated parameters, were consistently shown as critical to the model not meeting the evaluation criteria, irrespective of the chosen evaluation metric. It is therefore concluded that SWAT is not an appropriate model to guide P management in this catchment. This approach highlights the importance of high frequency monitoring data for setting robust model evaluation criteria. It also raises the question as to whether it is possible to have sufficient input data available to drive such models so that we can have confidence in their predictions and their ability to inform catchment management strategies to tackle the problem of diffuse pollution from agriculture