A supply-based concentration rating curve to predict total phosphorus concentrations in the Rhine River

Abstract

Concentration rating curves are useful for the analysis of the responseof sediment or solute concentrations to changes in stream discharge orfor the interpolation of infrequent concentration measurements in timewith discharge as auxiliary variable, for example to estimate annualsediment or solute loads. A known limitation of rating curves is thattheir performance is generally poor, which can be partly attributed tothe fact that rating curve methods neglect the hysteresis effects in theconcentration response to changes in discharge. To enhance theperformance of rating curve models, they should account for thesehysteresis effects. Here, we present a supply-based concentrationrating curve for total phosphorus concentrations in the Rhine River, theNetherlands, which does account for the above hysteresis effects. Thesupply-based concentration rating curve has four components: 1) Thetraditional power law rating curve of the form C = a Qb where C is thephosphorus concentration [M L-3], Qis the river discharge [L T-1], and aand b are constants [-]; 2) A long-term linear trend; 3) Aseasonal trend of the form C(t) = Acos [2π(t - Tk)/T] where A is theconcentration amplitude [M L-3], t is the time (T), Tk is the phaseshift (T), and T is the period [T] (365.25 d). 4) A dischargedependent supply or loss term of the form C = -ΔS/(QΔt),where S is the phosphorus stock [M]. The phosphorus stock was assumed toincrease linearly during periods of deposition, i.e. the discharge isbelow a critical discharge. If the discharge is greater than thecritical discharge during a sufficiently long period (> 16 days), thedecrease in phosphorus stock was assumed to be proportional to theexcess discharge above the critical discharge. For modelparameterization and calibration, we used the daily Aqualarm data oftotal phosphorus concentrations and the Waterbase data of waterdischarge measured daily by Rijkswaterstaat (Dutch Ministry ofInfrastructure and the Environment) at the Lobith-Bimmen monitoringstation at the German-Dutch border between 1 April 2004 and 20 July2010. The model parameters were calibrated by a step-wise procedurewhich involved in some steps visual calibration (e.g. concentrationamplitude, critical discharge for erosion/deposition) and in other stepsregression analysis (e.g. long-term linear trend, power law ratingcurve). The total phosphorus concentrations show a long-term lineardecrease of 1.0 - 10-5 mg l-1 d-1. The amplitude of the seasonalfluctuation in phosphorus concentration was estimated to be 0.03 mg l-1.The critical discharge for erosion and deposition was estimated to be1900 m s-1, the increase in phosphorus stock during deposition periods9300 kg d-1, and the supply from the phosphorus stock to the river water32 kg d-1per m3 s excess discharge. The squared Pearson's correlationcoefficient between the observed and predicted total phosphorusincreased from 0.16 for the traditional power-law concentration ratingcurve (Nash's efficiency coefficient = 0.13) to 0.36 for thesupply-based rating curve (Nash's efficiency coefficient = 0.34). Thisimplies that inclusion of the long-term and seasonal trends and adischarge dependent supply and loss term considerably enhances theperformance and predictive power of the concentration rating curvemodel. As the response to changes in discharge is different fordissolved and particulate total phosphorus, a further improvement ofmodel performance can likely be achieved by deriving separateconcentration rating curves for dissolved total phosphorus andsediment-associated phosphorus.