Nonlinear empirical modeling to estimate phosphorus exports using continuous records of turbidity and discharge

C. Minaudo, R. Dupas, C. Gascuel-Odoux, O. Fovet, P.-E. Mellander, P. Jordan, M. Shore, F. Moatar

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We tested an empirical modeling approach using relatively low-cost continuous records of turbidity and discharge as proxies to estimate phosphorus (P) concentrations at a subhourly time step for estimating loads. The method takes into account nonlinearity and hysteresis effects during storm events, and hydrological conditions variability. High-frequency records of total P and reactive P originating from four contrasting European agricultural catchments in terms of P loads were used to test the method. The models were calibrated on weekly grab sampling data combined with 10 storms surveyed subhourly per year (weekly+ survey) and then used to reconstruct P concentrations during all storm events for computing annual loads. For total P, results showed that this modeling approach allowed the estimation of annual loads with limited uncertainties (≈ −10% ± 15%), more reliable than estimations based on simple linear regressions using turbidity, based on interpolated weekly+ data without storm event reconstruction, or on discharge weighted calculations from weekly series or monthly series. For reactive P, load uncertainties based on the nonlinear model were similar to uncertainties based on storm event reconstruction using simple linear regression (≈ 20% ± 30%), and remained lower than uncertainties obtained without storm reconstruction on weekly or monthly series, but larger than uncertainties based on interpolated weekly+ data (≈ −15% ± 20%). These empirical models showed we could estimate reliable P exports from noncontinuous P time series when using continuous proxies, and this could potentially be very useful for completing time-series data sets in high-frequency surveys, even over extended periods.
Original languageEnglish
Pages (from-to)7590-7606
JournalWater Resources Research
Issue number9
Early online date1 Sept 2017
Publication statusPublished online - 1 Sept 2017


  • Phosphorus
  • non-linear empirical modelling
  • high-frequency monitoring
  • proxies
  • hysteresis


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