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r <br /> Author-produced version of the article published in Water and Environment Journal,2015,29(3),360-364. <br /> The original publication is available at:hftp://onlinelibrary.wiley.com/doi/l 0.1111/wej.12114/pdf doi:10.1111/wej.12114 <br /> 99 The value of Qi„(t)is an input while the value of Qa,,,(t)needs to be estimated(except for the initial <br /> 100 value).This is carried out by minimizing the objective function(11)at time t.Figure 3 schematizes the <br /> 101 basic computation steps. <br /> Initial conditions <br /> Qin(t11).Qout(to).h(ta) <br /> r>.rp <br /> Compute hit-.\t) <br /> Eq. 12 <br /> t=t+4t <br /> nput hydrogram <br /> %M <br /> Compute hc(t) <br /> Eq.10 <br /> Compute Q_t(t) <br /> Eq.1 <br /> 102 <br /> 103 Figure 3.Computation steps <br /> 104 Model implementation <br /> 105 The model was implemented in R(R Core Team,2013).The method used for minimizing the <br /> 106 objective function is a combination of golden section search and successive parabolic interpolation <br /> 107 (Brent, 1973).Accuracy was set to 1 x 10-10 m. <br /> 108 Practical test cases <br /> 109 This technical note presents three test cases.(1)It is often assumed that the largest inflow rate for a <br /> 110 septic tank(if properly disconnected from rainwater)corresponds to the emptying of a bath(200 litres <br /> 111 in 3 minutes).(2)In France,new treatment systems require authorization before being <br /> 112 commercialized. Since 2009,this authorization is given based on the results of normalized <br /> 113 experiments(AFNOR,2013)carried out by accredited laboratories.Feeding of the wastewater <br /> 114 treatment system during these normalized experiments is carried out according to a distribution of the <br /> 115 daily hydraulic load that is based on the assumed consumption of a typical household. Based on this <br /> 116 distribution,a synthetic hydrograph was generated,corresponding to a two person-household. Daily <br /> 117 hydraulic load was estimated at 84 L/pers./day according to Cauchi&Vignolles(2012).(3)Butler& <br /> 118 Graham(1995)and Butler&Gatt(1996)presented synthetic hydrographs of wastewater discharge in <br /> 119 person-equivalents. Despite the fact that these studies were done on sewage,they are often cited as a <br /> 120 benchmark for on-site wastewater treatment systems due to the lack of input hydrographs in this <br />