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An investigation into the impact of nine catchment characteristics on the accuracy of two phosphorus load apportionment models

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Phosphorus (P) load apportionment models (LAMs), requiring only spatially and temporally paired P and flow (Q) measurements, provide outputs of variable accuracy using long-term monthly datasets. Using a novel approach to investigate the impact of catchment characteristics on accuracy variation, 91 watercourses’ Q-P datasets were applied to two LAMs, BM and GM, and bootstrapped to ascertain standard errors (SEs). Random forest and regression analysis on data pertaining to catchments’ land use, steepness, size, base flow and sinuosity were used to identify the individual relative importance of a variable on SE. For BM, increasing urban cover was influential on raising SEs, accounting for c.19% of observed variation, whilst analysis for GM found no individually important catchment characteristic. Assessment of model fit evidenced BM consistently outperformed GM, modelling P values to ±10% of actual P values in 85.7% of datasets, as opposed to 17.6% by GM. Further catchment characteristics are needed to account for SE variation within both models, whilst interaction between variables may also be present. Future research should focus on quantifying these possible interactions and should expand catchment characteristics included within the random forest. Both LAMs must also be tested on a wide range of high temporal resolution datasets to ascertain if they can adequately model storm events in catchments with diverse characteristics.

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Availability of data and material

Data were sourced from the National River Flow Archive and the EA historical river water quality. These were obtained under licence and are unavailable for distribution without the express permission of NRFA or the EA.


No funding was provided for this study aside from supervisory support through Harper Adams University.

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The primary author completed the majority of analyses of data, interpretation of findings and production of manuscript. Second author provided expertise in model and method development. Third author provided expertise in data analysis and development of methods. Fourth author provided supervisory support, aid in interpretation of data, and final manuscript preparation for submission.

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Correspondence to L. Crockford.

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R packages used for data analysis were nortest, quantreg, phlosam, randomForest, hydroGOF and base. The code for this is available on request.

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Stevenson, J.L., O’Riordain, S., Harris, W.E. et al. An investigation into the impact of nine catchment characteristics on the accuracy of two phosphorus load apportionment models. Environ Monit Assess 193, 142 (2021).

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