sustainability Article
Synthetic Pollutograph by Prediction Indices: An Evaluation in Several Urban Sub-Catchments Juan T. García * Luis G. Castillo
ID
, Pablo Espín-Leal, Antonio Vigueras-Rodríguez
ID
, José M. Carrillo
ID
and
ID
Hidr@m Group, Department of Civil Engineering, Universidad Politécnica de Cartagena, Paseo Alfonso XIII, 52, 30203 Cartagena, Spain;
[email protected] (P.E.-L.);
[email protected] (A.V.-R.);
[email protected] (J.M.C.);
[email protected] (L.G.C.) * Correspondence:
[email protected]; Tel.: +34-968-327-026; Fax: +34-968-325-435 Received: 1 July 2018; Accepted: 25 July 2018; Published: 26 July 2018
Abstract: A generalized methodology applicable to any urban sub-catchment to calculate the pollution curve due to combined sewer overflows would help to implement integrated management policies to reduce urban impacts on the environment. An existing methodology to predict the pollutographs associated to rainfall events is tested in five different sub-catchments with very different pluviometry. Ninety-three rainfall events have been considered by measuring the in-sewer turbidity along the runoff episodes. Such data is then evaluated to obtain two prediction indices: the time to peak of pollutograph ITPP , and the maximum turbidity concentration ICMAX . These indices may be used with linear regressions to calculate the characteristics of pollutographs, such as the time to the peak, TPP, the maximum concentration of turbidity, CMAXtb , and the time to descent, TDP. These parameters allow to estimate the pollutographs of a sub-catchment. The comparison between pollutographs measured in the Ensanche sub-catchment and those calculated with the methodology shows a good agreement in terms of the root mean square deviation between samples and estimated values with the model proposed. Hence, the methodology could be a key way to find synthetic pollutographs for any sub-catchment. Keywords: combined sewer overflow (CSO); sewer system; turbidity; pollution prediction indices; synthetic pollutographs
1. Introduction Combined sewer overflows (CSOs) constitute a source of diffuse urban pollution that impacts the environment and human health. The CSO systems are referred to in Directive 91/271/EEC, the Urban Waste Water Treatment Directive (UWWTD), and indirectly in others, such as the Water Framework Directive (WFD, 2000/60/EC), Bathing Water Directive (BWD, 2006/7/EC), the Groundwater Directive (GWD, 2006/118/EC), and the Environmental Quality Standards Directive (EQS, 2008/105/EC). These European Union (EU) directives require that Member States include measurements in their plans for the conservation or restoration of the environment. The UWWTD sets mandatory limits for specific polluting substances and specific requirements for storm water overflows. These legislations require the monitoring and the assessment of emissions to water that should be addressed through combined sewer overflow integrated planning [1–5]. To achieve this, the knowledge on storm water quality is needed based on time-continuous sampling campaigns and laboratory analyses to understand the dynamic of pollutographs. Time-continuous water quality monitoring based on turbidity measurements offer correlations between several pollutants, such as particles and organic matter [6–11]. Other methods, like ultraviolet–visible (UV–VIS) spectrometric sensors, present better correlations between spectrophotometric measurements Sustainability 2018, 10, 2634; doi:10.3390/su10082634
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and organic matter and nitrogen. In-sewer sensors are interesting and useful tools to measure water pollution during dry and wet weather conditions and long-term operational scenarios [12]. Once field data is available, the next step is to establish accurate models to simulate runoff pollution. Here we can distinguish, on the one hand, the physically-based models, that generally simulate surface accumulation, wash-off, sediment erosion, and pollutant transport in sewer systems [13,14]. In case of physically-based models Di Modugno et al. [15] present pollution cumulative curves as a function of total runoff volume, also named M(V) curves, and the adjustment of pollution mobilization to a build-up and wash-off model in Storm Water Management Model (SWMM) software [13]. Others like Willems [16] study uncertainty associated to quality models that are integrated in hydraulic models. On the other hand, are those stochastic methods where different parameters of the pollutograph curve, like the maximum turbidity concentration CMAXtb , or other global parameters in combined sewer overflows, like the event mean concentration of a pollutant, EMC, among others, have been adjusted by statistical approaches from samples taken during rainfall events [17–25]. Lee and Bang [17] present M(V) curves for different events in nine sub-catchments. Additionally, they calculate the EMC, and propose a linear regression to obtain the annual rate of pollution associated to a sub-catchment. Nazahiya et al. [18], from urban runoff samples in a small catchment, analyze EMC and M(V) curves, too. Gupta and Saul [19] present specific regression relationships to predict the first flush load of suspended solids in a combined sewer flow for pollutant-suspended solids, SS. LeBoutillier and Putz [20] also propose global volume indicators of pollution per event by linear regressions. Gromaire et al. [21] compare different pollutants, like heavy metals, at different sub-catchments with a predomination of different surfaces, such as roofs, yards, or streets. They calculated the total volume of pollution and concluded that erosion of in-sewer pollutant stocks was found to be mainly of particles and of organic matter in wet weather runoff flows. Lau et al. [22] studied the frequency of volume of CSO spills as an indicator of receiving water pollution impact. Francey [23] presents global event parameters and also the maximum event concentration of pollutant, CMAX . Harremoës [24] checks that EMC of pollutants adjusts to a log-normal function as a function of rainfall volume. Logarithmic overall mean concentration plus standard deviation for characteristic land uses and characteristic properties of the sewer system are proposed by this author to be a key factor of pollution. Suarez and Puertas [25] present the adjustment of CMAX and EMC to a log-normal base 10 function for different pollutants, like chemical organic matter, COD, and SS. In summary, authors [17–25] presented several statistics methods to characterize pollution associated to overflows from sewer networks that are not still addressed to build the pollutograph associated to each rainy event. For instance, the M(V) curves describe how pollution is distributed along the episode in percentage. However, these curves do not quantify the pollution mobilized with time. The first attempts to obtain a pollutograph associated to a rainy event based on statistics were presented by Garcia et al. [26]. From this curve of pollution, it would be possible to evaluate the efficiency of techniques to reduce pollution such as construction of ponds. Stochastic models allow forecasting the water pollution parameters associated to CSOs. The possibility of application stochastic models to any sub-catchment with enough accuracy is an important objective, taking into account the large differences observed in pollution patterns at different sub-catchments. Definitely, achieving a generalized methodology for defining synthetic pollutographs would be very helpful in the CSOs integrated planning [1,3,22]. If we look into the prediction of design storms in urban catchments, the depth-duration-frequency (DDF) curves at each precipitation station point are widely used [27]. From this, the construction of a synthetic unit hydrograph is a useful and implemented tool for runoff studies [28,29]. For instance, the Soil Conservation Service (SCS) and Clark unit hydrographs are used in ungauged watersheds with little available information. Those methods only need three parameters: the area of the catchment, its time of concentration, and the rainfall characteristics. These techniques enable the estimation of the runoff at any outfall point of the sub-catchments with good accuracy despite the sparse input
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Intensity (mm/h)
Measured rainfall or calculated synthetic hyetograph
Rainfall (mm)
Sustainability 2018, 10, x FOR PEER REVIEW of 17 data. In the same way, being able to have a generalized catchment-independent methodology3that would allow obtaining the pollution curve over time would be of great help when establishing CSO independent methodology that would allow obtaining the pollution curve over time would be of integrated planning. great help when establishing CSO integrated planning. Based on time-continuous turbidity measurements in two urban sub-catchments, García et al. [26] Based on time-continuous turbidity measurements in two urban sub-catchments, García et al. proposed a stochastic methodology which allowed the prediction of the event maximum turbidity [26] proposed a stochastic methodology which allowed the prediction of the event maximum concentration (CMAXtb ), the time to the peak of the pollutograph TPP, and the time to the descent of turbidity concentration (CMAXtb), the time to the peak of the pollutograph TPP, and the time to the pollutograph TDP, from intermediate stochastic predictor indices. This procedure is summarized in descent of pollutograph TDP, from intermediate stochastic predictor indices. This procedure is Figure 1. In this work, the statistical prediction indices proposed by García et al. [26] are evaluated for summarized in Figure 1. In this work, the statistical prediction indices proposed by García et al. [26] different sub-catchments: Saint-Mihiel and Cordon-Bleu, from data collected in Hannouche [30]; are evaluated for different sub-catchments: Saint-Mihiel and Cordon-Bleu, from data collected in Ensanche, from data of Del Río [6]. Moreover, three new rainfall events were considered in Hannouche [30]; Ensanche, from data of Del Río [6]. Moreover, three new rainfall events were sub-catchments S1 and San Félix, besides the events from previous works [26]. A total of ninety considered in sub-catchments S1 and San Félix, besides the events from previous works [26]. A total three events were considered in present work, of which seventy four are new, and the others were of ninety three events were considered in present work, of which seventy four are new, and the others considered from previous adjustments of the proposed stochastic model in García et al. [26]. were considered from previous adjustments of the proposed stochastic model in García et al. [26].
Hydrograph (measured, simulated or synthetic)
Flow (m3/s)
Duration of the rainfall (minutes)
Time (hours)
Start and end of the hydrograph Definition of hydrological and hydraulic parameters
Catchment area, A, slope, S, and time of concentration, Tc Time to peak of the pollutograph, TPH Total rainfall, PTOTAL Dry weather period, DWP
Calculation of prediction indexes
Index of maximum turbidity concentration, ICMAX
Maximum concentration of turbidity, CMAXtb
Index of time to peak of the pollutograph, ITTP
Time to peak of the pollutograph, TPP
Dry weather pollutograph
Construction of pollutograph
Line of ascent of the pollutograph Time to descent, TDP, and line of descent of the pollutograph 1000
Pollutograph
Dry weather pollutograph TDP
TPP
Graph of the pollutograph
Turbidity (NTU)
800
CMAXtb
600 400 200 Dry weather concentration
0 22:40
23:52
1:04 Time (hh:mm)
2:16
Figure 1. Methodology proposed for the construction of pollutographs [26]. Figure 1. Methodology proposed for the construction of pollutographs [26].
Discussion of the adjustment achieved with the index of maximum turbidity concentration, ICMAX, in case of the five sub-catchments, is presented. In the case of the stochastic predictor index of the time to peak of the pollutograph, ITPP, due to the information available, is presented in the case of sub-catchments Ensanche [6], S1, and San Félix [26]. Finally, the measured pollutographs for rainfall
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Discussion of the adjustment achieved with the index of maximum turbidity concentration, ICMAX , in case of the five sub-catchments, is presented. In the case of the stochastic predictor index of the time2018, to peak of the ITPP , due to the information available, is presented in Sustainability 10, x FOR PEERpollutograph, REVIEW 4 ofthe 17 case of sub-catchments Ensanche [6], S1, and San Félix [26]. Finally, the measured pollutographs for events the Ensanche sub-catchment [6] are also with thosewith obtained the proposed rainfallinevents in the Ensanche sub-catchment [6]compared are also compared thosewith obtained with the methodology. proposed methodology. 2. Materials Materialsand andMethods Methods 2. 2.1. Description DescriptionofofSub-Catchments Sub-Catchments Areas Areas 2.1. 2.1.1. San Félix and S1 at Murcia, South East of Spain 2.1.1. San Félix and S1 at Murcia, South East of Spain Murcia is a southeastern Spanish city with an equivalent population of 525,027 (Figure 2). This Murcia is a southeastern Spanish city with an equivalent population of 525,027 (Figure 2). This study site included two urban sub-catchments, called San Félix and S1. Both catchments were study site included two urban sub-catchments, called San Félix and S1. Both catchments were residential areas, their impervious areas being 47% and 21%, respectively (Table 1). The sewer system residential areas, their impervious areas being 47% and 21%, respectively (Table 1). The sewer system is combined, incorporating storm water. is combined, incorporating storm water.
Figure 2. View of the location of the five evaluated sub-catchments. Figure 2. View of the location of the five evaluated sub-catchments. Table 1. S1 and San Félix sub-catchments descriptions. Table 1. S1 and San Félix sub-catchments descriptions. Sub-Catchment San Félix S1 2 Area of catchment (km ), A 14.89 Sub-Catchment San Félix 47.53 S1 2) Population density (inh/km 14,250 2685 2 14.89 47.53 Area of catchment (km ), A 2/m2) 0.47 0.21 2685 Ratio of imperviousness (m 2 14,250 Population density (inh/km ) Mean slope (m/m), S 2) 0.0043 0.00130.21 0.47 Ratio of imperviousness (m2 /m Catchment flow length 10.75 17.000.0013 Mean slope (m/m), S (km), L 0.0043 Length combined sewerage 513.15 616.8417.00 Catchment flow length (km), L(km) 10.75 Length combined sewerage (km) 513.15 616.84
2.1.2. Ensanche Sub-Catchment at Santiago de Compostela Sub-Catchments, Northwest Spain 2.1.2.The Ensanche Sub-Catchment at Santiago de in Compostela Northwest SpainAll the Ensanche sub-catchment is located Santiago Sub-Catchments, de Compostela (Galicia–Spain). information of this sub-basin was obtained from Río [6].deIt Compostela is one of the (Galicia–Spain). 13 main sub-catchments The Ensanche sub-catchment is located in Del Santiago All the of the city’s of sanitation and drainage system. Ensanche hasItaispredominantly unitary urban sewer information this sub-basin was obtained from Del Río [6]. one of the 13 main sub-catchments of network that serves an approximate population of 25,000 inhabitants and its approximate surface area is 38 ha. The instrumentation equipment could not be located at the outfall point of the subcatchment network. However, it covers approximately half of the total area of Ensanche (around 20 ha and a population of 13,000 inhabitants). Table 2 shows the main details of the sub-catchment.
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the city’s sanitation and drainage system. Ensanche has a predominantly unitary urban sewer network that serves an approximate population of 25,000 inhabitants and its approximate surface area is 38 ha. The instrumentation equipment could not be located at the outfall point of the sub-catchment network. However, it covers approximately half of the total area of Ensanche (around 20 ha and a population of 13,000 inhabitants). Table 2 shows the main details of the sub-catchment. Table 2. Ensanche sub-catchment description (Del Río [6]). Sub-Catchment
Ensanche
(km2 ),
0.20 65,000 0.0042 1.40 -
Area of catchment A Population density (inh/km2 ) Ratio of imperviousness (m2 /m2 ) Mean slope (m/m), S Catchment flow length (km), L Length combined sewerage (km)
2.1.3. Saint-Mihiel and Cordon-Bleu Sub-Catchments, South of France The Saint-Mihiel sub-catchment has an area of 100 ha and it is located upstream of the central area of the city of Nantes (Figure 2). It is entirely unitary. The Cordon-Bleu sub-catchment is much larger (5000 ha) and it is located downstream of the main collector of the Nantes agglomeration (right bank of the Loire River) near to the Tougas wastewater treatment plant and serving approximately 500,000 equivalents inhabitants. Although only half sub-catchment is unitary, the measurement point is located in an accessible unitary manifold of ovoid section. The slope of this sewer is 0.04%. Table 3 shows the details of the two sub-catchments obtained by Hannouche [30]. Table 3. Saint-Mihiel and Cordon-Bleu sub-catchments description (Hannouche [30]). Sub-Catchment
Saint-Mihiel
Cordon-Bleu
1.00 0.0010 2.50 -
50.00 10,000 0.0004 25.00 -
(km2 ),
Area of catchment A Population density (inh/km2 ) Ratio of imperviousness (m2 /m2 ) Mean slope (m/m), S Catchment flow length (km), L Length combined sewerage (km)
2.2. Monitoring Equipment in the Evaluated Sub-Catchments S1 and San Félix sub-catchments have a water gauge to continuously monitor the flow, while two different probes measure turbidity, conductivity, and temperature. The turbidity data is obtained with an infra-red nephelometric turbidimeter Endress+Hauser CUS 42 measuring at a wavelength of 880 nm according to the standard NF EN 27027, associated to a data logger. A backwash process with clear water is automatized each hour to avoid disturbing measurements. Turbidimeters are calibrated with formazine solution. A technique for the removal of these outliers has been implemented. In the Ensanche sub-catchment, a continuous sampler was installed with intervals of five and ten minutes between samples. This also allowed the characterization of the turbidity of the sample in Nephelometric Turbidity Units, NTUs. Flow depth, flow velocity, and flow meters were installed at the measurement point located in the Ensanche sub-catchment. Ten rain events with values of turbidity are available (Del Río [6]). In Saint-Mihiel and Cordon-Bleu sub-catchments the rainfall was measured with the nearest rain gauges. Time-continuous turbidity was also measured during dry and wet weather by a turbidity probe in Formazin Attenuation Units, FAUs. In rainy weather in Cordon-Bleu, 35 events were sampled to establish total suspended solids TSS/turbidity relationships. For Saint-Mihiel, 27 rain events were
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sampled for SS/turbidity relationships. Detailed values are collected in Hannouche [30]. Hydrological characteristics of the rainfall events at both sites, like precipitated height, previous dry time, rain duration and maximum intensities in 5 and 60 min, Imax5 and Imax60 are also included in this work. Some hydraulic parameters, such as the time to peak of the hydrograph, TPH, could not be obtained due to the lack of instrumentation to measure the flow. In case of turbidity determinations, the optical method of measurement for FAU is different than the NTU all measurements were calibrated with formazine solution. This allowed Sustainabilitymethod. 2018, 10, xHowever, FOR PEER REVIEW 6 of 17 for considering that thePEER value for each of these units are equivalent. Sustainability 2018, 10, x FOR REVIEW 6 of 17 In intervals of of five minutes, thethe estimated hydrograph andand the In Figure Figure3,3,the themeasured measuredrainfall rainfallinin intervals five minutes, estimated hydrograph measured time-continuous turbidity are presented novel events in sub-catchments S1 and the measured time-continuous turbidity are presented for two novel events inhydrograph sub-catchments S1 In Figure 3, the measured rainfall in intervals offor fivetwo minutes, the estimated and the San-Félix. Figure 4 shows the measured rainfall, measured flow rate by and San-Félix. Figure 4 shows the measured rainfall, measured flow rateand and turbiditycalculated calculated by measured time-continuous turbidity are presented for two novel events in turbidity sub-catchments S1 and sample in 4the Ensanche sub-catchment in two events, as presented in Del Rio Remarkable sample analysis analysis the Ensanche sub-catchment presented Rio [6]. [6]. Remarkable San-Félix. Figure shows the measured rainfall, measured flow rate and turbidity calculated by differences in duration are observed totwo thethe concentration time of sub-catchment: 15 differences in event event duration are observeddue due to concentration time of each sub-catchment: sample analysis in the Ensanche sub-catchment in events, as presented in each Del Rio [6]. Remarkable min in the Ensanche sub-catchment; 193.75 min S1S1sub-catchment; and 87.14 min 15 min in the sub-catchment; 193.75 min inthe the sub-catchment; and 87.14 minin in the the San San differences inEnsanche event duration are observed due tointhe concentration time of each sub-catchment: 15 Félix sub-catchment. Félixin sub-catchment. min the Ensanche sub-catchment; 193.75 min in the S1 sub-catchment; and 87.14 min in the San Félix sub-catchment. Rainfall (mm)
Turbidity (NTU)
2500 2000 2000 1500
SF 13/02/2017 Rainfall (mm) (L/s) Hydrograph (L/S) SF 13/02/2017 1200 0.0 Rainfall (mm) (L/s) Hydrograph (L/S) 0.5 1200 0.0 1000 1.0 0.5 1000 800 1.5 1.0 800 600 2.0 1.5 2.5 2.0
1500 1000
3.0 2.5
1000 500
3.5 3.0
500 0 17:16 0 17:16
22:04
4.0 3.5 7:40 4.0 7:40
2:52
Time (hh:mm)
22:04
2:52
Turbidity (NTU) Turbidity (NTU)
600 400 400 200 200 0 15:21 0 15:21
16:33 16:33
(L/s) Hydrograph (L/S) 0.0 (L/s) Hydrograph (L/S) 0.1 0.0 0.2 0.1 0.3 0.2 0.4 0.3 0.5 0.4 0.6 0.5 0.7 0.6 0.8 0.7 0.9 0.8 1.0 0.9 21:21 22:33 1.0 21:21 22:33
Rainfall Rainfall (mm)(mm)
3000 2500
Turbidity (NTU)
Rainfall Rainfall (mm)(mm)
Turbidity (NTU) - Q (L/s) Turbidity (NTU) - Q (L/s)
S1 20/10/2016 3000
Rainfall (mm)
Turbidity (NTU) - Q (L/s) Turbidity (NTU) - Q (L/s)
S1 20/10/2016
17:45
18:57
20:09
Time (hh:mm)
17:45
18:57
20:09
Time (hh:mm)
(hh:mm) Figure 3. Rainfall, Time hydrograph, and turbidity-pollutograph for the events dated 20/10/2016 in the S1 Figure 3. Rainfall, hydrograph, and turbidity-pollutograph for the events dated 20/10/2016 in the S1 sub-catchment andhydrograph, 13/02/2017 inand the turbidity-pollutograph San Félix sub-catchment. Figure 3. Rainfall, for the events dated 20/10/2016 in the S1 sub-catchment and 13/02/2017 in the San Félix sub-catchment. sub-catchment and 13/02/2017 in the San Félix sub-catchment.
700 800 600 700
Rainfall (mm)
Turbidity (NTU)
Rainfall (mm)
Turbidity (NTU)
Hydrograph (L/s) (L/S) 0 Hydrograph (L/s) (L/S) 10 21
500 600 400 500
32
300 400 200 300 100 200 0 100 7:30 0 7:30
43 54 65 7:57
8:24
8:52
9:19
7:57
8:24
Time (hh:mm) 8:52
9:19
6
EN 23/05/2009 EN 23/05/2009
700
Rainfall (mm)
Turbidity (NTU)
Rainfall (mm)
Turbidity (NTU)
600 700 500 600
Hydrograph (L/s) (L/S) 0 Hydrograph (L/s) (L/S) 0 0.4
400 500
0.4 0.8
300 400
0.8 1.2
200 300
1.2 1.6
100 200 0 100 18:00 0 18:00
Rainfall Rainfall (mm)(mm)
Turbidity (NTU)Q (L/s) Turbidity (NTU)Q (L/s)
EN 21/10/2008 800
Rainfall Rainfall (mm)(mm) Turbidity (NTU)Q (L/s) Turbidity (NTU)Q (L/s)
EN 21/10/2008
1.6 2 18:28 18:28
18:57
19:26
19:55
Time (hh:mm) 19:26 18:57
19:55
2
Time (hh:mm)
Time (hh:mm) Figure 4. Rainfall, hydrograph, and turbidity-pollutograph for the events dated 21/10/2008 and 23/05/2009 in the Ensanche sub-catchment [6]. Figure 4. Rainfall, hydrograph, and turbidity-pollutograph for the events dated21/10/2008 21/10/2008 and Figure 4. Rainfall, hydrograph, and turbidity-pollutograph for the events dated and 23/05/2009 in the Ensanche sub-catchment [6]. 23/05/2009 in the Ensanche sub-catchment [6].
3. Results and Discussion 3. Results and Discussion 3. Results and Discussion 3.1. Variables Definition from Wet Weather Measured Events 3.1. Definition Wet Weather Measured Events Events 3.1. Variables Variables Definition from from Weathervariables Measured Table 4 summarizes theWet required for the calculation of the predictor indices and the application the methodology [26]. These data have been obtained of from Table summarizes the variables for calculation the predictor Table 44ofsummarizes the required required variables for the the calculation of the[6,26,30]. predictor indices indices and and the the application of the methodology [26]. These data have been obtained from [6,26,30]. application of the methodology [26]. These data have been obtained from [6,26,30]. Table 4. Variables measured at each sub-catchment in wet weather events.
Table 4. Variables measured at each sub-catchment in wet weather events. Sub-Catchment S1 San_Félix Saint-Mihiel Cordon-Bleu Ensanche Years of study 2014–2017 2014–2017 2002–2007 1998–2006 2008–2009 Sub-Catchment S1 San_Félix Saint-Mihiel Cordon-Bleu Ensanche Number of events 11 10 27 35 10 Years of study 2014–2017 2014–2017 2002–2007 1998–2006 2008–2009 TOTAL (mm) X X X X X P Number of events 11 10 27 35 10 IPmean (mm/h) X X X X X TOTAL (mm)
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Table 4. Variables measured at each sub-catchment in wet weather events. Sub-Catchment
S1
San_Félix
Saint-Mihiel
Cordon-Bleu
Ensanche
Years of study Number of events
2014–2017 11
2014–2017 10
2002–2007 27
1998–2006 35
2008–2009 10
Hydrology
PTOTAL (mm) Imean (mm/h) Imax5–10 (mm/h) DWP (days) A (ha) TC (h)
X X X X X X
X X X X X X
X X X X X -
X X X X X -
X X X X X X
Hydraulic
Qmax (L/s) Qmean (L/s) TPH (min)
X X X
X X X
-
-
X X X
Quality
CMAXtb (NTU) EMCtb (NTU) TPP (min)
X X X
X X X
X X X
X X X
X X X
Where X represents that this information is available, PTOTAL is the total event rainfall, Imean is the mean rainfall intensity, Imax5–10 is the maximum 5, 10 min rainfall intensity, DWP is the proportion of consecutive dry weather days previous to the event in the last month, TC is the time of concentration of urban catchment, Qmax is the maximum event inflow, and Qmean is the mean event inflow.
3.2. Pollution Prediction Indices. Statistical Model The maximum concentration index ICMAX , and the time to peak of the pollutograph index ITPP are calculated in order to adjust afterwards (i) the maximum concentration of turbidity during each event, CMAXtb ; and (ii) the time elapsed from the beginning of the event until the maximum peak of the pollutograph TPP. 3.2.1. Maximum Concentration Index ICMAX The maximum concentration index ICMAX arises with the objective of estimating the maximum concentration of turbidity CMAXtb , from predictor variables quantified in rainfall events. Together with the ITPP , they allow the estimation of both the magnitude of the pollutograph and the location in time of the highest turbidity. The equation for ICMAX was previously defined as [26]: ICMAX =
PTOTAL PTOTAL ANNU AL
0.3 S
(DWR)0.3 Fshape
(1)
where PTOTAL is the rainfall volume of each event (mm); PTOTALANNUAL is the total precipitation expected in a year, adopting 350 mm for the cases of sub-catchments S1 and San Félix, 800 mm for Saint-Mihiel and Cordon-Bleu, and 1300 mm for the Ensanche sub-catchment; DWR is the proportion of consecutive dry weather days previous to the event in the last month (DWP/30); and S is the mean slope of the sub-catchment (m/m). Equation (1) is dimensionless and represents the power of the event. It is multiplied by the time without precipitation, accounting for the effect of the possible sedimentation during the dry weather period. Fshape is a shape factor of the sub-catchment defined as: Fshape =
10A L2
(2)
where A is the area of the sub-catchment (km2 ) and L is the catchment flow length (km). Table 5 summarizes the shape factors obtained in the sub-catchments analyzed. Figure 5 presents the values of ICMAX , calculated by Equation (1) for each rainfall event, and the maximum measured turbidity in each event CMAXtb . A linear relation between the later variable and the index is obtained through a least squares adjustment. The values are mainly explained by such a common line except for four events in sub-catchments S1 and San Félix out of their 21 events. Those
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different cases are due to very low precipitation episodes or anomalously high registered values for the maximum turbidity that should be studied in more depth. In Sain-Mihiel sub-catchment, two values from the 27 existing values were not considered. In the Cordon-Bleu sub-catchment, two of the thirty-five existing values were omitted. In the sub-catchment of Ensanche three of the 10 values were not used in the adjustment. To sum up, 11 cases were omitted from a total of 93. The relationship between CMAXtb and ICMAX fit to a line with a coefficient of determination R2 = 0.73. Figure 5 also presents the values omitted from the adjustment. Table 6 shows the regression coefficients and the coefficient of determination obtained for each sub-catchment independently and considering all the Sustainability 2018,data. 10, x FOR PEER REVIEW 8 of 17 non-omitted Table5.5.Catchments’ Catchments’shape shapefactors. factors. Table
Sub-Catchment Sub-Catchment
Slope Slope(m/m) (m/m)
S1 S1 San Félix San Félix Saint-Mihiel Saint-Mihiel Cordon-Bleu Cordon-Bleu Ensanche Ensanche
0.0013 0.0013 0.0043 0.0043 0.0010 0.0010 0.0004 0.0004 0.0042 0.0042
S1
SAN FÉLIX
CLICHY
Sub-Catchment Sub-CatchmentFlow FlowLength, Length, Sub-Catchment Sub-CatchmentArea, Area, Fshape (-) Fshape (-) 2 L L(km) SS(km (km) (km)2 ) 17.00 47.53 1.65 17.00 47.53 1.65 10.75 14.89 1.29 10.75 14.89 1.29 2.50 1.00 1.60 2.50 1.00 1.60 25.00 50.00 0.80 25.00 50.00 0.80 1.40 0.20 1.02 1.40 0.20 1.02 SAINT MIHIEL
CORDON BLEU
ENSANCHE
omitted values
Linear regression
1800.0 1600.0 1400.0
CMAXtb (NTU)
1200.0 1000.0 800.0 600.0 400.0
CMAXtb = 6,784.30ICMAX + 274.38 R² = 0.73
200.0 0.0 0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.140
ICMAX
Figure 5. Linear adjustment of CMAXtb withthe theprediction predictionindex indexICMAX. ICMAX. MAXtb with
Table Table6.6.Regression Regressionparameters. parameters. Sub-Catchment m (Slope) Sub-Catchment m (Slope) S1 6678.70 S1 San-Félix 6678.70 4864.70 San-Félix 4864.70 Saint-Mihiel 8800.30 Saint-Mihiel 8800.30 Cordon-Bleu 5699.10 Cordon-Bleu 5699.10 Ensanche 13,682.00 Ensanche 13,682.00 All Data 6784.30 All Data 6784.30
R2 n (Intercept) n (Intercept) 269.50 0.94 269.50 0.91 398.95 398.95 0.45 232.79 232.79 282.06 0.05 282.06 52.16 0.91 52.16 274.38 0.73 274.38
R2 0.94 0.91 0.45 0.05 0.91 0.73
The fitted line of the adjustment between the maximum concentration index, ICMAX, and the The fitted line of the between the maximum concentration index, ICMAX , and the maximum concentration of adjustment turbidity, CMAXtb , is given by a linear regression: maximum concentration of turbidity, CMAXtb , is given by a linear regression: (3) MAXtb = 6784.30 CMAX + 274.38 C MAXtb = 6784.30I + 274.38 proposed in Equation (3) may (3) In the case of the Ensanche sub-catchment, the linear CMAXadjustment be improved by using two additional alternatives: Alternative 2, i.e., adopting the regression equation In theincase of the Ensanche sub-catchment, the Ensanche linear adjustment proposed in Equation (3) may presented Table 6 considering only data of the sub-catchment, with a coefficient of be improved by using two additional alternatives: Alternative 2, i.e., adopting the regression equation determination R2 = 0.91, or the named Alternative 3, changing the power factors in Equation (1) to presented in0.43 Table 6 considering only(second data ofterm), the Ensanche with a coefficient the values of (first term) and 0.85 while thesub-catchment, exponent of Fshape remains constant,of reaching the following regression adjustment. MAXtbEnsanche
= 75,867.00
CMAX
+ 200.27
(4)
with R2 = 0.99. These three alternatives will be evaluated in the following sections. Equation (3) and (4) could be dimensionless dividing both sides of each equation by the 90th percentile of CMAXtb,
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determination R2 = 0.91, or the named Alternative 3, changing the power factors in Equation (1) to the values of 0.43 (first term) and 0.85 (second term), while the exponent of Fshape remains constant, reaching the following regression adjustment. C MAXtbEnsanche = 75, 867.00ICMAX + 200.27
(4)
with R2 = 0.99. These three alternatives will be evaluated in the following sections. Equation (3) and (4) could be dimensionless dividing both sides of each equation by the 90th percentile of CMAXtb , calculated from the adjustment to a lognormal distribution of the 82 validated values of CMAXtb . This distribution was already proposed by Suarez and Puertas [25] and by Butler and Davies [31]. This dimensionless procedure does not change the values of CMAXtb obtained with previous Equations (3) and (4). The lognormal fit graphic of CMAXtb values have been included in the text through Figure 6. Lognormal parameters, such as location, scale, p-value for 0.05 significance, and the Anderson–Darling Sustainability 2018, 10, x FOR PEER REVIEW 9 of 17 statistic are presented [32]. Figure 6 includes the fitted line and the 95% confidence intervals. In summary, the 90th percentile of CMAXtb could be used as the variable for dimensionless. Results of In summary, the 90th percentile of CMAXtb could be used as the variable for dimensionless. Results of CMAXtb obtained through Equations (3) and (4) by proposed dimensionless would not change the CMAXtb obtained through Equations (3) and (4) by proposed dimensionless would not change the previously obtained results. previously obtained results. 99 95
Percent
90 80 70 60 50 40 30 20 10 Location 6.024 Scale 0.4392 Number of data 82 A-D test 0.252 P-value 0.729
5 1 0.1
100
1000 CMAXtb (NTU) CMAX
distribution for for the the fivefive sub-catchments Figure 6. Probability variable CMAXtb fit Figure 6. Probability plotplot forfor variable CMAXtb fitto toaalognormal lognormal distribution sub-catchments evaluated. evaluated.
to Peak the Peak of PollutographIndex IndexIITPP 3.2.2.3.2.2. TimeTime to the of Pollutograph TPP The time to the peak of the pollutograph index TPP, may be used to predict the time that elapses
The time to the peak of the pollutograph index TPP, may be used to predict the time that elapses from the beginning of the episode until the maximum value of turbidity is achieved. It is defined from from the beginning of the episode until the maximum value of turbidity is achieved. It is defined from dimensionless factors [26]: dimensionless factors [26]: .02 TPH .13 TOTAL (5) = 0.13 0.02 TPP TPH PTOTAL TOTAL ANNUAL ITPP = (5) PTOTAL C hydrograph where TPH is the time to the peak ofTthe that was ANNU AL measured in S1, San Félix, and Ensanche sub-catchments and Tc is the time of concentration of the sub-catchment. Those values were
wherenotTPH is theintime to the peakand ofCordon the hydrograph that was(see measured S1, San works Félix, and registered the Saint-Mihiel Blue sub-catchments Table 4). in In previous Ensanche sub-catchments and T is the time of concentration of the sub-catchment. Those values c [26], it was analyzed the most suitable equation to obtain the time to concentration, Tc, in urban subwere catchments not registered in the Saint-Mihiel and Cordon Blue sub-catchments (see Table 4). In previous with flow through sewer networks. The most suitable equation seems to be the Témez works [26], it was modified analyzedfor theurban most areas suitable to obtain the timeEquation to concentration, [33] equation [34].equation Further information about (5) and theTc , in of its terms presented in [26]. urbanexplanation sub-catchments withisflow through sewer networks. The most suitable equation seems to be the Figure 7 shows the linear between the time information to the peak ofabout the pollutograph index, Témez [33] equation modified forrelationship urban areas [34]. Further Equation (5) and the and the time to the peak of pollutograph. A linear regression that relates the time to the peak of the explanation of its terms is presented in [26]. pollutograph index and the time to the peak, expressed in minutes, was obtained for S1 and San Félix sub-catchments as:
TPP = 401.47
TPP
− 256.35
In the Ensanche sub-catchment, the following linear regression was obtained:
(6)
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Figure 7 shows the linear relationship between the time to the peak of the pollutograph index, and the time to the peak of pollutograph. A linear regression that relates the time to the peak of the pollutograph index and the time to the peak, expressed in minutes, was obtained for S1 and San Félix sub-catchments as: TPP = 401.47ITPP − 256.35 (6) In the Ensanche sub-catchment, the following linear regression was obtained: TPP = 268.60ITPP − 228.96
(7)
For the adjustment of Equation (7), two points that had a value of time to peak less than ten Sustainability 2018, 10, x FOR REVIEW 10 of 17 minutes were omitted for thePEER adjustment. Sustainability 2018, 10,S1 x FOR PEER REVIEW SAN FÉLIX
ENSANCHE
10 of 17
Linear regression
180.0 160.0
S1 AND SAN SANFELIX FÉLIX TPP = 401.47ITTP - 256.35 R² = 0.95 S1 AND SAN FELIX TPP = 401.47ITTP - 256.35 R² = 0.95
S1
140.0 180.0
TPP (min) TPP (min)
120.0 160.0 100.0 140.0 80.0 120.0
ENSANCHE
Linear regression
60.0 100.0 40.0 80.0 20.0 60.0 0.0 40.0 0.7 20.0
0.8
0.8
0.9
0.9
1.0
1.0
ITTP
ENSANCHE TPP = 268.6ITTP - 228.96 R² = 0.89 ENSANCHE 1.1 TPP1.1 1.2 = 268.6I1.2 TTP - 228.96 R² = 0.89
0.0 0.7 0.8 Linear 0.8 adjustment 0.9 0.9 1.0 1.0 1.1 index Figure 7. Linear adjustment of TPP prediction index ITPP. 1.1ITPP . Figure 7. of TPPwith with prediction
1.2
1.2
ITTP
In the same way as previous section, Equations (6) and (7) may be dimensionless dividing both
In the same wayequation as previous section, Equations (6)pollutograph. andprediction (7) may belognormal dimensionless dividing both Figure 7. Linear of TPP with index ITPP. sides of each by a variable of adjustment time to peak of The distribution is sides of each equation a variable peak of pollutograph. Thesub-catchments. lognormal distribution is adjusted for theby variables TPP of andtime TPHtofor S1 and San-Félix grouped An In the same way asisprevious section, Equationssub-catchment. (6) and (7) mayFigures be dimensionless dividing both independent adjustment obtained for the 8 and 9 present theindependent fit adjusted for the variables TPP and TPH for S1 Ensanche and San-Félix grouped sub-catchments. An each a variable distribution. of time to peak of pollutograph. The lognormal distribution ofsides TPP of and TPHequation values toby a lognormal Lognormal parameters such as location, scale, p- is adjustment is obtained the Ensanche 8 and 9 present the fit of TPP and adjusted for significance, thefor variables andsub-catchment. TPH for S1 statistic and Figures San-Félix value for 0.05 andTPP the Anderson–Darling are also grouped presentedsub-catchments. [32]. The figures An TPH values to a the lognormal distribution. Lognormal parameters such as location, independent adjustment is obtained for theintervals. Ensanche Figures 8 andscale, 9 present the fitfor 0.05 include fitted line and the 95% confidence Insub-catchment. summary, the 90th percentile of TPPp-value could of TPP and TPH values to a lognormal distribution. Lognormal parameters such as location, scale, p- fitted significance, and the Anderson–Darling statistic are also presented [32]. The figures include be used as the variable for dimensionless specifically for each sub-catchment. These operations would the value for 0.05 significance, and the Anderson–Darling statistic are also presented [32]. The figures not change the results obtained in Equations (6) and (7) of TPP. line and the 95% confidence intervals. In summary, the 90th percentile of TPP could be used as the include the fitted line and the 95% confidence intervals. In summary, the 90th percentile of TPP could variable for dimensionless for each sub-catchment. These operations would not change the 99 specifically be used as the variable for dimensionless specifically for each sub-catchment. These operations would results obtained in Equations (6) andin(7) of TPP.(6) and (7) of TPP. not change the results obtained Equations 95
9099 7095 60 90 50 4080 30 70 2060 50 10 40 530
Variable TPH (MIN) TPP (MIN)
Percent
Percent
80
20 1 10 5
Location Scale Data A-D P-value Variable 4.747 0.4320 21 0.391 0.349 TPH (MIN) 4.687 0.2043 21 0.535 0.151 TPP (MIN) 100
1000
Location Scale Data A-D P-value TPH, TPP (min) 4.747 0.4320 4.687 0.2043
21 0.391 21 0.535
0.349 0.151
Figure 8. Probability plot for variables TPH and TPP fit to a lognormal distribution for the S1 and San1 100 1000 Félix sub-catchments. TPH, TPP (min)
Figure 8. Probability plotvariables for variables TPHand and TPP to atolognormal distribution for the S1 for and the San-S1 and Figure 8. Probability plot for TPH TPPfitfit a lognormal distribution Félix sub-catchments. San-Félix sub-catchments.
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99 95 90
Percent
80 70 60 50 40 30
Variable TPH (MIN) TPP (MIN)
20 10
Location Scale Data A-D P-value 2.839 0.6380 10 0.344 0.409 2.534 0.8023 10 0.186 0.874
5
1
1
10
100
TPH, TPP (min)
Figure 9. Probability plot for variables TPH and TPP. Fit to a lognormal distribution for the Ensanche sub-catchment.
3.3. Definition of Pollutographs Pollutographs from from Prediction Prediction Indices Indices 3.3. Definition of Once the the TPP TPP and and the the CCMAXtb MAXtb have necessary Once havebeen beencalculated, calculated, to to complete complete the the pollutograph pollutograph it it is is necessary to know the ascent and descent curve and the time to descent of pollutograph, TDP. According to to know the ascent and descent curve and the time to descent of pollutograph, TDP. According to García et et al. al. [26], [26], the the line line of of ascent ascent may may be be adjusted adjusted with with the the following following exponential exponential equation: equation: García = xab= C = Ca = ab 0
"
MAXtb C MAXtb C0
1 Na
#n
(8) (8)
thenumber number intervals 5 min in which the ascent is divided; n indicates the where NNaisisthe where of of intervals of 5ofmin in which the ascent time istime divided; n indicates the interval a interval (0 ≤ n ≤ N a) in units of five minutes; and Ca and C0 are the turbidity values at each interval n (0 ≤ n ≤ Na ) in units of five minutes; and Ca and C0 are the turbidity values at each interval n and at andbeginning at the beginning of the pollutograph, respectively (measured in The NTU). Theofvalue C0 is assumed the of the pollutograph, respectively (measured in NTU). value C0 isofassumed as the as the dry weather value at the beginning of the episode. dry weather value at the beginning of the episode. The time time to to the the descent descent of of pollutograph pollutograph TDP, TDP, is is defined defined as as the the time time interval interval between between the the instant instant The of the the maximum maximum concentration concentration and and the the time time when when the the concentration concentration reaches reaches dry dry weather weather values. values. The The of time to the descent of the pollutograph value has been adjusted for each sub-catchment showing time to the descent of the pollutograph value has been adjusted for each sub-catchment showinga relationship with pollutograph time to the peak. TheThe adjustment of TDP for the subalinear linear relationship with pollutograph time to the peak. adjustment of TDP forEnsanche the Ensanche catchment is given by: by: sub-catchment is given ENSANCHE TDP==10 10TPP (9) (9) ENSANCHE → → TDP TPP −−5 5 where where TPP TPP and and TDP TDP are are expressed expressed in in minutes minutesin inthis thisequation. equation. In the same way as in previous sections, Equation (9) could be dimensionless by considering the 90th percentile of of TPP, TPP, not not introducing introducing modifications modifications in in the the results. results. The descent line of the pollutographs may be adjusted to pollutographs may be adjusted to aa logarithmic logarithmic function function as: as: TStb MAXtb CTStb −−CMAXtb ln(n − −N + 1 + (10) Cd = a=ln(ln x ) + b+= = ln ln (10) a + 1) + CMAXtb MAXtb − ln( Nd − Na ++11) where Nd is the number of intervals of five minutes in which the descent time is divided; n indicates where Nd is the number of intervals of five minutes in which the descent time is divided; n indicates the interval (Na ≤ n ≤ Nd) in units of five minutes; and Cd and CTStb are the turbidity values at each n the interval (Na ≤ n ≤ Nd ) in units of five minutes; and Cd and CTStb are the turbidity values at each interval and at the end of the event, corresponding to TDP time, respectively (measured in NTU)., n interval and at the end of the event, corresponding to TDP time, respectively (measured in NTU)., When n = Na, ln(n − Na + 1) = 0, and Ca = Cd = CMAXtb, ensuring continuity of Equation (10). When n = Na , ln(n − Na + 1) = 0, and Ca = Cd = CMAXtb , ensuring continuity of Equation (10). Figures 10–13 show the measured and calculated pollutographs that correspond with episodes Figures 10–13 show the measured and calculated pollutographs that correspond with episodes 02, 02, 06, 07 and 09 of Ensanche sub-catchment [6]. Pollutographs are compared for the three alternatives 06, 07 and 09 of Ensanche sub-catchment [6]. Pollutographs are compared for the three alternatives of adjustment proposed for this sub-catchment: Alternative (1) general adjustment for the CMAXtb; Alternative (2) linear regression for CMAXtb obtained only with the Ensanche sub-catchment data;
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of adjustment proposed for this sub-catchment: Alternative (1) general adjustment for the CMAXtb ; Alternative (2) linear regression for CMAXtb obtained only with the Ensanche sub-catchment data; Sustainability 2018, 10, x FOR PEER REVIEW 12 of 17 Alternative (3) 2018, predictor index changing the power factors to the values of 0.43 and 0.85, and linear Sustainability 10, x FOR PEER REVIEW 12 of 17 regression obtained only with the Ensanche sub-catchment data (Section 3.2.1). In this way the previous Alternative (3) predictor index changing the power factors to the values of 0.43 and 0.85, and linear Alternative predictor index changing the power factors (11): to the values of 0.43 and 0.85, and linear Equation (5) in(3) the case ofonly Alternative 3 becomes regression obtained with the Ensanche Equation sub-catchment data (Section 3.2.1.). In this way the regression obtained only with the Ensanche sub-catchment data (Section 3.2.1.). In this way the previous Equation (5) in the case of Alternative 3 becomes Equation (11): 0.43Equation previous Equation (5) in the case ofAlternative 3 becomes (11): P TOTAL
ICMAX =
TOTAL P ANNU AL CMAX =TOTAL TOTAL
=
CMAX
800 700
500 400
DWR DWR .
.
shape shape
EN_2 Alternative 2 EN_2 Alternative 2
400 300 300 200 200 100
700 600 500 400 400 300 300 200 200 100 100
0
Measured pollutograph Proposed pollutograph Measured pollutograph Dry weather turbidity Proposed pollutograph Dry weather turbidity
600 500
0
0
0
Date (day/month/year hour:minutes) Date (day/month/year hour:minutes) 800 800 700
Measured pollutograph Measured pollutograph Proposed pollutograph Proposed pollutograph Dry weather turbidity Dry weather turbidity
700 600
Turbidity (NTU) Turbidity (NTU)
Date (day/month/year hour:day) Date (day/month/year hour:day)
EN_2 Alternative 3 EN_2 Alternative 3
600 500 500 400 400 300 300 200 200 100 100
0
0
Date (day/month/year hour:minutes) Date (day/month/year hour:minutes)
Figure 10. Comparison of measured the measured pollutographwith withthe thethree three alternatives alternatives proposed, forfor thethe Figure 10. Comparison of of the proposed, Figure 10. Comparison the measuredpollutograph pollutograph with the three alternatives proposed, for the event of Ensanche 02 21/10/2008 [6]. eventevent of Ensanche 02 21/10/2008 of Ensanche 02 21/10/2008 [6]. [6].
400.00 350.00
Turbidity (NTU)
Turbidity (NTU)
350.00 300.00 300.00 250.00 250.00 200.00
EN_6 Alternative 1 EN_6 Alternative 1 Measured pollutograph Measured pollutograph Proposed pollutograph Proposed pollutograph Dry weather turbidity Dry weather turbidity
200.00 150.00 150.00 100.00 100.0050.00 50.00 0.00 0.00
Date (day/month/year hour:minutes) Date (day/month/year hour:minutes) 400 400
Turbidity (NTU) Turbidity (NTU)
350 300 250 200 150 100
350 300 250
400
EN_6 Alternative 2 EN_6 Alternative 2
Measured pollutograph Measured pollutograph Proposed pollutograph Dry weather turbidity Proposed pollutograph Dry weather turbidity
400 350
Turbidity (NTU) Turbidity (NTU)
400.00
350 300 300 250
(11)
(11) (11)
800 700
Turbidity (NTU) Turbidity (NTU)
Turbidity (NTU) Turbidity (NTU)
600 500
(DWR)0.85 Fshape
800
Measured pollutograph Proposed pollutograph Measured pollutograph Dry weather turbidity Proposed pollutograph Dry weather turbidity
700 600
.
TOTALANNUAL TOTALANNUAL
EN_2 Alternative 1 EN_2 Alternative 1
800
100
S.
250 200 200 150 150 100 100 50 50
Date (day/month/year hour:minutes) Date (day/month/year hour:minutes) EN_6 Alternative 3 EN_6 Alternative 3 Measured pollutograph Proposed pollutograph Measured pollutograph Dry weather turbidity Proposed pollutograph Dry weather turbidity
200 150 100 50
50
Date (day/month/year hour:minutes) Date (day/month/year hour:minutes)
Figure 11. Comparison of the measured pollutograph with the three alternatives proposed, for the Figure 11. Comparison of the measured pollutograph with the three alternatives proposed, for the
of Ensanche 06 [6]. pollutograph with the three alternatives proposed, for the Figureevent 11. Comparison of10/05/2009 the measured event of Ensanche 06 10/05/2009 [6]. event of Ensanche 06 10/05/2009 [6].
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700 700 600 600 500 500 400 400 300 300 200 200 100 100 0 0
13 of 17 13 of 17
EN_7 Alternative 1 EN_7 Alternative 1 Measured pollutograph Measured pollutograph Proposed pollutograph Proposed Dry weatherpollutograph turbidity Dry weather turbidity
Turbidity (NTU) Turbidity (NTU)
Date (day/month/year hour:minutes) Date (day/month/year hour:minutes) 700 700 600 600 500 500 400 400 300 300 200 200 100 100 0 0
Turbidity (NTU) Turbidity (NTU)
Turbidity (NTU) Turbidity (NTU)
Sustainability 2018, 10, x FOR PEER REVIEW Sustainability 2018, 10, x FOR PEER REVIEW EN_7 Alternative 2 EN_7 Alternative 2
700 700 600 600 500 500 400 400 300 300 200 200 100 100 0 0
Measured pollutograph Proposed pollutograph Measured pollutograph Dry weatherpollutograph turbidity Proposed Dry weather turbidity
Date (day/month/year hour:minutes) Date (day/month/year hour:minutes) EN_7 Alternative 3 EN_7 Alternative 3 Measured pollutograph Measured pollutograph Proposed pollutograph Proposed Dry weatherpollutograph turbidity Dry weather turbidity
Date (day/month/year hour:minutes) Date (day/month/year hour:minutes)
Figure 12. Comparison of the measured pollutograph with the three alternatives proposed, for the Figure Figure 12. 12. Comparison Comparison of of the the measured measured pollutograph pollutograph with with the the three three alternatives alternatives proposed, proposed, for for the the event of Ensanche 07 23/05/2009 [6]. event of Ensanche 07 23/05/2009 [6]. event of Ensanche 07 23/05/2009 [6].
700 600 600 500 500 400 400 300
EN_9 Alternative 1 EN_9 Alternative 1 Measured pollutograph Measured pollutograph Proposed pollutograph Proposed Dry weatherpollutograph turbidity Dry weather turbidity
300 200 200 100 100 0 0
Turbidity (NTU) Turbidity (NTU)
Date (day/month/year hour:minute) Date (day/month/year hour:minute) 800 800 700 700 600 600 500 500 400 400 300 300 200 200 100 100 0 0
800 800 700
Turbidity (NTU) Turbidity (NTU)
Turbidity (NTU) Turbidity (NTU)
800 800 700
700 600 600 500 500 400 400 300
EN_9 Alternative 2 EN_9 Alternative 2 Measured pollutograph Measured pollutograph Proposed pollutograph Proposed Dry weatherpollutograph turbidity Dry weather turbidity
300 200 200 100 100 0 0
Date (day/month/year hour:minutes) Date (day/month/year hour:minutes) EN_9 Alternative 3 EN_9 Alternative 3 Measured pollutograph Measured pollutograph Proposed pollutograph Proposed Dry weatherpollutograph turbidity Dry weather turbidity
Date (day/month/year hour:minutes) Date (day/month/year hour:minutes)
Figure 13. Comparison of the measured pollutograph with the three alternatives proposed, for the Figure 13. 13. Comparison Comparison of of the the measured measured pollutograph pollutograph with with the the three three alternatives alternatives proposed, proposed, for for the the Figure event of Ensanche 09 26/06/2009 [6]. event of Ensanche 09 26/06/2009 [6]. event of Ensanche 09 26/06/2009 [6].
Considering the results observed on Figures 10–13, a good agreement between the measured Considering the results observed on Figures 10–13, a good agreement between the measured and calculated pollutographs is obtained in the 10–13, basis of the accuracy index (AI) proposed for and the Considering the results observed on Figures a good agreement between the measured and calculated pollutographs is obtained in the basis of the accuracy index (AI) proposed for the Ccalculated MAXtb. The pollutographs AI is the root mean square deviation (RMSD) between the samples and estimated values is obtained in the basis of the accuracy index (AI) proposed for the CMAXtb . CMAXtb. The AI is the root mean square deviation (RMSD) between the samples and estimated values with theisproposed model, all normalized with the between average of concentration of turbidity of The AI the root mean square deviation (RMSD) themaximum samples and estimated values with the with the proposed model, all normalized with the average of maximum concentration of turbidity of all events measured. Results can with be observed in Table 7, where,concentration in the case of of theturbidity Alternative 2, the AI proposed model, all normalized the average of maximum of all events all events measured. Results can be observed in Table 7, where, in the case of the Alternative 2, the AI index achieves values for in the Ensanche sub-catchment, is considered measured. Results can of be 9.17% observed Table 7, where, in the case ofwhich the Alternative 2, the in AI good index index achieves values of 9.17% for the Ensanche sub-catchment, which is considered in good agreement with of values until 20%Ensanche considered acceptable inwhich termsisofconsidered quality forinthe CMAXtb definition. achieves values 9.17% for the sub-catchment, good agreement with agreement with values until 20% considered acceptable in terms of quality for the CMAXtb definition. Theuntil best20% results were obtained considering 3. Differences values considered acceptable in termsAlternative of quality for the CMAXtb observed definition.in the time to the The best results were obtained considering Alternative 3. Differences observed in the time to the peak The of pollutograph between the measured andAlternative the proposed pollutographs are lower than five best results were obtained considering 3. Differences observed in the time to peak of pollutograph between the measured and the proposed pollutographs are lower than five minutes, is, the calculation time of the samples used in Ensanche. Someare of lower the events the peak that of pollutograph between thestep measured and the proposed pollutographs than minutes, that is, the calculation time step of the samples used in Ensanche. Some of the events measured in Ensanche sub-catchment present duration, being difficult the adjustment with five minutes, that is, the calculation time step aofshort the samples used in Ensanche. Some of the events measured in Ensanche sub-catchment present a short duration, being difficult the adjustment with the proposed predictor indices. The Ensanche sub-catchment is a very small sub-catchment with a the proposed predictor indices. The Ensanche sub-catchment is a very small sub-catchment with a surface area of around 20 ha upstream in the monitoring point, and with a time of concentration of surface area of around 20 ha upstream in the monitoring point, and with a time of concentration of
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measured in Ensanche sub-catchment present a short duration, being difficult the adjustment with the proposed predictor indices. The Ensanche sub-catchment is a very small sub-catchment with a surface area of around 20 ha upstream in the monitoring point, and with a time of concentration of around 15 min. The present methodology was previously adjusted for sub-catchments with relatively larger areas than Ensanche. The accuracy index, AI, proposed represents the sample standard deviation of the differences between predicted values and observed values. The AI index is normalized with the average of maximum concentration of turbidity of all events measured, C MAX , and calculated from Equation (12). Values obtained with Equation (12) are presented in Table 7 for the five sub-catchments studied and in function of regressions presented in Table 6. q RMSD = AI (%) = C MAX
1 n
∑in (C MAX_measured_i − C MAX_calculated_i )
2
C MAX
(12)
where AI is the uncertainty index in the percentage of the averaged value of maximum concentration of turbidity measured during the events, C MAX , (NTU); C MAX_measured_i and C MAX_calculated_i are the values of maximum turbidity concentration of each event measured and calculated, respectively, (NTU); and n is the number of measured events. The Nash–Sutcliffe model efficiency coefficient (NSE) is also calculated and presented in Table 7. This is an index of the goodness of fit measure used in hydrologic and water quality modeling [35–37]. The index is presented in Equation (13). The index presents quite good results for the sub-catchments S1, San Félix. and Ensanche, while low values of this coefficient are obtained for the sub-catchments Saint-Mihiel and Cordon-Bleu that address to have additional field measurements for a better evaluation: − CMAX_calculated_i )2 ∑n (C NSE(%) = 1 − i MAX_measured_i (13) 2 ∑in C MAX_measured_i − C MAX Table 7. Uncertainty Indexes, AI and NSE (%). Sub-Catchment
CMAX (NTU)
RMSD (NTU)
AI (%)
NSE (%)
S1 San-Félix Saint-Mihiel Cordon-Bleu Ensanche
643.4 701.2 473.5 350.8 546.2
16.35 24.09 61.07 57.73 50.11
2.54 3.44 12.90 16.46 9.17
93.84 91.86 45.81 91.60 13.44
4. Conclusions A methodology to adjust pollutographs and its characteristics has been analyzed in this study. Its accuracy was also considered in previous works from data measured in two sub-catchments in the south-east of Spain [26]. In this work, it has been evaluated in other different sub-catchments, such as Saint-Mihiel and Cordon-Bleu sub-catchments, from data collected by Hannouche [30], and the Ensanche sub-catchment with data from Del Río [6]. A total of ninety-three events are considered in the present work, of which seventy-four are novel, and the rest where considered for previous adjustment of the proposed stochastic model in García et al. [26]. The tested statistical model presents two key predictor indices: the time to peak of pollutograph, ITPP , and the maximum turbidity concentration, ICMAX . Quite good agreement has been found for both indices for all the different evaluated sub-catchments, in terms of coefficient of determination, R2 , shown in Sections 3.2.1 and 3.2.2. between measured samples and the linear regressions proposed for the ITTP and ICMAX indices.
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In the Ensanche sub-catchment, due to the available data, it was possible to apply the methodology to calculate the pollutograph. The comparison between measured data and proposed pollutograph was presented with acceptable agreement, in terms of an accuracy index based on the root mean square deviation between samples and predictions, taking into account the important differences between the compared sub-catchments. This work represents the initial steps to achieve a general stochastic model that allows to define the pollutograph for any sub-catchment. The model is evaluated in different sub-catchments to those where it was first proposed. More measurements are needed in different sub-catchments that allow to improve the methodology with the objective of obtaining prediction indices that help in the understanding and prediction of pollution due to runoff from storm water. Author Contributions: J.T.G., P.E.-L., A.V.-R., J.M.C., and L.G.C. processed field information, undertook the statistical treatment, and established the methodology to achieve the pollutographs. All authors contributed equally to the manuscript revision. Funding: External funding was received from Empresa Municipal de Aguas y Saneamiento de Murcia, S.A. through the project: “Estudio de flujos de contaminación transportados por un sistema de saneamiento y drenaje unitario en tiempo de lluvia para la ciudad de Murcia” ref-C-74/2016. Acknowledgments: The authors are grateful for the financial support received from Empresa Municipal de Aguas y Saneamiento de Murcia, S.A. through the project: “Estudio de flujos de contaminación transportados por un sistema de saneamiento y drenaje unitario en tiempo de lluvia para la ciudad de Murcia” ref-C-74/2016. Conflicts of Interest: The authors declare no conflict of interest.
Notation A CMAXtb CMAX DWP DWR EMC ICMAX Imax Imax5, Imax10, Imax60 Imean ITTP L M(V) Na , Nd PTOTAL PTOTAL_ANNUAL Qmax Qmean Qmaxdw S Tc TDP TPH TPP TSS
Catchment area (ha) Maximum concentration for turbidity (NTU) Maximum concentration of a pollutant (NTU) Dry weather period (days) Proportion of consecutive dry weather days previous to the event in the last month Event mean concentration of a pollutant Pollution prediction index associated to the maximum concentration of turbidity (-) Maximum rainfall intensity (mm/h) Maximum 5, 10, 60 min rainfall intensity (mm/h), respectively Mean rainfall intensity (mm/h) Pollution prediction index associated to the time to the peak of the pollutograph (-) Catchment flow length (km) Quantity of pollution in function of percentage of runoff volume (kg) Number of intervals of five minutes in which the pollutograph is divided, applied to ascent and descent part respectively (-) Total event rainfall (mm) Total precipitation expected in a year (mm) Maximum event inflow (m3 /s) Mean event inflow (m3 /s) Maximum dry weather inflow (m3 /s) Mean slope of the catchment (m/m) Time of concentration of urban catchment (h) Descent time of the pollutograph (h) Peak time of hydrograph (h) Time to the peak of pollutograph (h) Total suspended solids (mg/L)
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