Urban Runoff Characteristics in Combined Sewer Overflows (Csos): Analysis of Storm Events in Southeastern Spain

water

Article Urban Runoff Characteristics in Combined Sewer Overﬂows (CSOs): Analysis of Storm Events in Southeastern Spain

Juan Tomás García 1,*, Pablo Espín-Leal 1, Antonio Vigueras-Rodriguez 1, Luis G. Castillo 1, José M. Carrillo 1, Pedro D. Martínez-Solano 2 and Simón Nevado-Santos 2 1 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] (L.G.C.); [email protected] (J.M.C.) 2 Empresa Municipal de Aguas y Saneamiento de Murcia, S.A., Plaza Circular 9, 30008 Murcia, Spain; [email protected] (P.D.M.-S.); [email protected] (S.N.-S.) * Correspondence: [email protected]; Tel.: +34-968-327-026; Fax: +34-968-325-435

Academic Editor: Arjen Y. Hoekstra Received: 23 February 2017; Accepted: 23 April 2017; Published: 26 April 2017

Abstract: Storm water overflows have an important impact on the environment in many European countries. Nowadays, a better knowledge of combined sewer overflows (CSOs) pollution is required for implementing measures to reduce these emissions. In this work, pollution flows mobilized during rainy events have been monitored and modeled in two urban catchments located in the city of Murcia (southeast Spain). For each analyzed event, rainfall volume, in-sewer turbidity and water flow depth have been continuously measured. Therefore, sets of pollutographs and hydrographs have been obtained for each event analyzed. Characteristic variables have been defined and obtained for each event such as the maximum concentration of turbidity, the total event rainfall, the previous dry weather period, the time to the peak of the hydrograph and to the peak of the pollutograph, among others. Relations between variables have been adjusted through a statistical model. The adjusted parameters are used to generate pollutographs that are compared with those measured in field. The present work provides tools to assist in the knowledge of pollution transported through sewer network during stormy events, suggesting the creation of design pollutographs which may facilitate the evaluation of measures to reduce urban runoff pollution.

Keywords: combined sewer overﬂow (CSO); sewer system; turbidity; pollution prediction indexes; pollutographs

1. Introduction The reduction of pollution emissions from combined sewer overflows (CSOs) is currently a prime issue. Actually, European Directives aim to quantify and reduce them to protect the environment and human health, and to provide water leisure activities and water abstraction for agriculture [1]. Although a lack of knowledge of the quantity and the quality of these overflows is recognized and policies have yet to be achieved in most countries, important efforts are being done (e.g., [2–5]). Risk based approaches are usually implemented taking into account the type of collecting systems and the intensity of the rain events or flooding. Spill frequency, or volume percentage retained, are habitually selected [4,6]. Other approach is the receiving water quality criteria, based on Urban Pollution Management procedures (UPM) standards [5]. It requires being aware of ecological state of receiving water and effects induced by the pollution. Field measurement campaigns of the urban sub-catchment are recommended as a previous step to implement an approach [3,7,8] so that pollution mobilized during rain events can be evaluated.

Water 2017, 9, 303; doi:10.3390/w9050303 www.mdpi.com/journal/water Water 2017, 9, 303 2 of 16

Continuous water-quality monitoring sensors are being increasingly implemented in sewers. In order to replace traditional sampling, turbidimeters can be used to estimate total suspended solids (TSS) and chemical oxygen demand (COD) concentration in sewers, by linear regression of on-site turbidity with site-specific measurements [7–13]. The relationship between pollutant load of TSS and runoff, by statistical approaches, constitutes a field of research to identify pollution associated to CSOs [7,14–20]. In this way, measured hydrographs and pollutographs analysis are used to relate the peak of the pollutant concentration of the flow, and the mass and flow cumulative volume curves M(V), which, for instance, allow determining whether the first flush effect exists for a particular catchment [7,14–17]. Suarez and Puertas [17] fitted the maximum suspended solids concentration (CMAXSS) by means of probability distributions. With regard to rainy events, several researchers [7,18–20] performed regression analysis between TSS and hydrological and hydraulic variables (Table1). These statistical models gave rise to adjusted pollution parameters, which can be used for forecasting transported pollution characteristics along storm events, providing useful information to establish effective policies of combined sewer overflow control. As these studies are usually catchment specific, an important aim would be to define standard coefficients for a wide range of catchment conditions [18].

Table 1. Variables and adjusted parameters of TSS pollution load.

Variables and Adjusted Parameters Gupta and Saul [18] LeBoutillier et al. [19] Gromaire et al. [20] Del Rio [7]

Imax (mm/h) X X X Drain (h) X X X DWP (day) X X X Hydrology RD (mm) X X X Imax5 (mm/h) X Tc (h) X Variables A (ha) X 3 Qmax (m /s) XX 3 Qmean (m /s) X 3 Hydraulic Qmaxdw (m /s) X TPH (h) X TPP (h) X

TSSTE (kg/event) X TSS (kg/event) XX Adjusted parameters ff CMAXSS (mg/L) X CSMSS (kg/ha) X

Notes: Imax = maximum rainfall intensity; Drain = rainfall duration; DWP = dry weather period; RD = rain depth; Imax5 = maximum five-minute rainfall intensity; Tc = time of concentration of the catchment; A = catchment area; Qmax = maximum event inflow; Qmean = mean event inflow; Qmaxdw = maximum dry weather inflow; TPH = time to the peak of the hydrograph; TPP = time to the peak of the pollutograph; TSSTE = cumulative suspended solids per event; TSSff = total pollutant load in the first flush; CMAXSS = maximum suspended solids concentration; and CSMSS = specific mobilized volume of suspended solids.

For a proper design of sustainable sewer systems, hydraulic and quality modeling tools are utilized [8,19,21]. Hydraulic models, such as USEPA Storm Water Management Model (SWMM) [22], predict the runoff flow rate and volume from observed rainfall intensities with accuracy. However, for quality models, the uncertainty is an order of magnitude greater than that for the hydraulic submodels [23]. That makes their calibration and use complex. In this work, statistical models are proposed to predict the event maximum turbidity concentration (CMAXtb), the time to the peak of the pollutograph (TPP), and the time to the descent of pollutograph (TDP). The statistical models are based upon analysis of data collected from rainfall events during period from June 2014 to April 2016 at two urban catchments in the city of Murcia (southeast Spain). Both catchments were monitored with continuous measurements from rain gauges, in-sewer turbidimeters and water gauges. Several input parameters of the statistical models were considered to assess their significance, and the most significant parameters were selected. Predicted pollutograph parameters are calculated and modeled. The proposed pollutographs are compared with the measured Water 2017, 9, 303 3 of 17

Both catchments were monitored with continuous measurements from rain gauges, in-sewer turbidimeters and water gauges. Several input parameters of the statistical models were considered Waterto assess2017, 9 , 303their significance, and the most significant parameters were selected. Predicted3 of 16 pollutograph parameters are calculated and modeled. The proposed pollutographs are compared with the measured ones showing a significant agreement. A calibrated hydraulic model of the city of ones showing a signiﬁcant agreement. A calibrated hydraulic model of the city of Murcia has been Murcia has been generated in the USEPA Storm Water Management Model (SWMM). The numerical generated in the USEPA Storm Water Management Model (SWMM). The numerical model is used to model is used to analyze the catchment hydraulic response to each rainfall event. analyze the catchment hydraulic response to each rainfall event. The present work provides tools to assist in the knowledge of pollution transported through The present work provides tools to assist in the knowledge of pollution transported through sewer network during stormy events, suggesting the creation of design pollutographs which may sewer network during stormy events, suggesting the creation of design pollutographs which may facilitate the evaluation of measures to reduce urban runoff pollution. facilitate the evaluation of measures to reduce urban runoff pollution.

2. Experimental Methods

2.1. Description of the Experimental Catchment Areas Murcia is a southeastern Spanish city with an equivalentequivalent population of 525,027. It is situated in a valleyvalley atat thethe confluence confluence of of the the Guadalent Guadalentínín and and Segura Segura rivers rivers (Figure (Figure1). The1). The study study site includessite includes two urbantwo urban catchments, catchments, called called San Fé lixSan and Félix S1. Bothand S1. catchments Both catchments are residential are residential areas, their imperviousareas, their areasimpervious being 21%areas and being 47%, 21% respectively and 47%, (Table respective2). The sewerly (Table system 2). isThe combined sewer system incorporating is combined storm water.incorporating Due to thestorm flat topographicwater. Due to conditions, the flat topo theregraphic are several conditions, sewer pump there stations.are several Both sewer catchments pump flowstations. into Both “Murcia catchments Este” Wastewater flow into Treatment “Murcia Este” Plant whoseWastewater maximum Treatment capacity Plant during whose dry maximum weather is 3 maxdw 3 Qcapacitymaxdw = during 10.000 mdry/h. weather At the is outlet Q pipe = 10.000 of each m /h. catchment, At the outlet monitoring pipe of each equipments catchment, were monitoring placed in Qualityequipments Control were Stations placed (inQCS Quality) (Figure Control1). Stations (QCS) (Figure 1).

Figure 1. Location of the study site.

The catchment slope was estimatedTable 2.fromCatchments a Digital description. Elevation Model with a 2 m × 2 m grid, using ArcGIS 10.3 software. The catchment flow length was obtained from the sewer network geodatabase of the Empresa Municipal de AguasCatchment y Saneamiento de Murcia San Félix S.A. (Emuasa). S1 Area of catchment (km2), A 14.89 47.53 Population density (inh/km2) 14,250 2685 Ratio of imperviousness (m2/m2) 0.47 0.21 Mean slope (m/m), S 0.0043 0.0013 Catchment ﬂow length (km), L 10.75 17.00 Length combined sewerage (km) 513.15 616.84

The catchment slope was estimated from a Digital Elevation Model with a 2 m × 2 m grid, using ArcGIS 10.3 software. The catchment ﬂow length was obtained from the sewer network geodatabase of the Empresa Municipal de Aguas y Saneamiento de Murcia S.A. (Emuasa). Water 2017, 9, 303 4 of 17

Table 2. Catchments description.

Catchment San Félix S1 Area of catchment (km2), A 14.89 47.53 Water 2017, 9, 303 Population density (inh/km2) 14,250 2685 4 of 16 Ratio of imperviousness (m2/m2) 0.47 0.21 Mean slope (m/m), S 0.0043 0.0013 2.2. Monitoring EquipmentCatchment flow length (km), L 10.75 17.00 The city of MurciaLength is equipped combined sewerage with 39 (km) tipping-bucket 513.15 rain gauges 616.84 that cover the different catchments.2.2. Monitoring Their measurements Equipment range is between 0 and 7 mm/min, with an accuracy of 0.2 mm. Data are continuously sent and plotted through a SCADA system. The city of Murcia is equipped with 39 tipping-bucket rain gauges that cover the different Monitoring equipments were placed at the outlet sewer pipe of the analysed catchments, close catchments. Their measurements range is between 0 and 7 mm/min, with an accuracy of 0.2 mm. to an importantData are continuously overﬂow point sent and (Figure plotted1). through They consisted a SCADA system. of a water gauge to continuously monitor the ﬂow. TheMonitoring water equipments level was were measured placed at with the outlet an ultrasonicsewer pipe of sensor the analysed Endress catchments, + Hauser close FMR50. The wastewaterto an important circulating overflow in sewerspoint (Figure is continuously 1). They consisted pumped of a water by means gauge of to acontinuously 1 L/s peristaltic monitor pump to a 20 L sedimentationthe flow. The water tank, level through was measured a suction with 25 mm-diameter an ultrasonic sensor pipe insertedEndress + in Hauser the sewer FMR50. and The protected wastewater circulating in sewers is continuously pumped by means of a 1 L/s peristaltic pump to a by a screen of stainless steel to trap sediments (Figure2). Wastewater passes through a 20 L tank, in 20 L sedimentation tank, through a suction 25 mm-diameter pipe inserted in the sewer and protected which theby probesa screen areof stainless located. steel The to probestrap sediments measure (Figure turbidity, 2). Wastewater conductivity passes through and temperature. a 20 L tank, in Data are recordedwhich within the aprobes 20 s timeare located. interval. The Theprobes turbidity measure dataturbidity, are obtainedconductivity with and an temperature. infra-red Data nephelometric are turbidimeterrecorded Endress within + a Hauser20 s time CUSinterval. 42 measuringThe turbidity at data a wavelength are obtained ofwith 880 an nm infra-red according nephelometric to the standard NF ENturbidimeter 27027, associated Endress to+ Hauser a data CUS logger. 42 measuring A backwash at a wavelength proccess with of 880 clear nm wateraccording is automatizedto the each hourstandard to avoid NF disturbingEN 27027, associated measurements. to a data Turbidimeters logger. A backwash are calibrated proccess with clear formazine water is solution. automatized each hour to avoid disturbing measurements. Turbidimeters are calibrated with A technique for the removal of these outliers has been implemented. formazine solution. A technique for the removal of these outliers has been implemented.

Figure 2. (a) Scheme of Quality Control Station devices; and (b) Image of QCS. Figure 2. (a) Scheme of Quality Control Station devices; and (b) Image of QCS. The rating curve for each monitoring station was developed in previous studies. There is a Thecontrol rating section-free curve for overfall each monitoring in the Quality station Control was Station developed of San Felix. in previous A water level studies. measurement There is is a control used in the Quality Control Station of S1. Velocity sensors were used in a straight conduit of 1.8 m section-free overfall in the Quality Control Station of San Felix. A water level measurement is used in diameter and around 1000 m length, where uniform conditions were confirmed. the Quality Control Station of S1. Velocity sensors were used in a straight conduit of 1.8 m diameter and around2.3. Hydraulic 1000 m Model length, where uniform conditions were conﬁrmed.

2.3. Hydraulic Model The US Environmental Protection Agency’s Storm Water Management Model (USEPA) is a numerical model that allows simulating the hydrological and hydraulic behavior of an urban drainage system. A calibrated SWMM hydraulic model of the city of Murcia has been used. It serves to study the catchment response to any rainfall event (Figure3). The characteristics of the model are shown in Table3. The total length of the network included in the model is around 234.5 km. The Horton equation was used for infiltration modeling. Values adopted are in accordance with soil characteristics and with those proposed in the literature [21,22]. The maximum infiltration, f 0, is around 20 mm/h, while the minimum infiltration, fc, is 1 mm/h. The decay coefficient, k, has been estimated at 4.14 h−1. The Manning’s roughness coefficients for pervious and impervious areas were Water 2017, 9, 303 5 of 16 Water 2017, 9, 303 5 of 17

The US Environmental Protection Agency’s Storm Water Management Model (USEPA) is a used as calibrationnumerical model parameters that allows of thesimulating model. the Initialhydrological values and were hydraulic selected behavior from of an the urban literature [21,22]: 0.02–0.045 fordrainage pervious system. areas A calibrated and 0.01–0.015SWMM hydraulic for imperviousmodel of the city areas. of Murcia The has Manning been used.roughness It serves coefﬁcient for conduitsto variesstudy the from catchment 0.011 response to 0.013 to any depending rainfall event on (Figure the pipe 3). The material. characteristics of the model are shown in Table 3. The total length of the network included in the model is around 234.5 km.

Figure 3. View of the hydraulic model of Murcia in USEPA Storm Water Management Model Figure 3. View(SWMM). of the hydraulic model of Murcia in USEPA Storm Water Management Model (SWMM).

Table 3. Description of the hydraulic model of Murcia. Table 3. Description of the hydraulic model of Murcia. Description Element Number Pluviographs 39 DescriptionHydrology Element Number Subcatchments 4553 PluviographsNodes 6073 39 Hydrology SubcatchmentsOutfalls 58 4553 Hydraulics Tanks 70 LinksNodes 6304 6073 PumpOutfalls stations 100 58 Hydraulics Tanks 70 The Horton equation was used for infiltrationLinks modeling. Values adopted 6304 are in accordance with soil characteristics and with those proposed Pumpin the literature stations [21,22]. The maximum 100 infiltration, f0, is around 20 mm/h, while the minimum infiltration, fc, is 1 mm/h. The decay coefficient, k, has been estimated at 4.14 h−1. The Manning’s roughness coefficients for pervious and impervious areas were The comparisonused as calibration of the parameters measured of the and model. simulated Initial values ﬂow were depth selected is shownfrom the inliterature Figure [21,22]:4. In wet weather, two different0.02–0.045 events for are pervious presented. areas and Some 0.01–0.015 differences for impervious are areas. found The in Manning S1 Catchment, roughness coefficient whereas a quite good for conduits varies from 0.011 to 0.013 depending on the pipe material. agreement is observedThe comparison in San of the Felix measured Catchment. and simulated Those flow differences, depth is shown which in Figure are 4. In below wet weather, 10%, are caused by pumpWater stations. 2017two, 9 ,different 303 events are presented. Some differences are found in S1 Catchment, whereas a quite 6 of 17 good agreement is observed in San Felix Catchment. Those differences, which are below 10%, are caused Wetby pump weather stations. event 04/04/2016 (QCS S1) Wet weather event 09/05/2016 (QCS San Felix) 1.2 1.2 NIVELMeasured EN CAMPO 1 NIVELMeasured EN CAMPO 1 NIVELCalculated MODELO NIVELCalculated MODELO 0.8 0.8 0.6 0.6 0.4 0.4 Flow depth (m) Flow depth0.2 (m) 0.2 0 0 0:00:00 12:00:00 0:00:00 12:00:00 0:00:00 12:00:00 12:00:00 0:00:00 12:00:00 0:00:00 12:00:00 Time (hh:mm) Time (hh:mm)

FigureFigure 4. Flow 4. Flow depth depth measured measured and and calculated calculated by the hy hydraulicdraulic model model during during wet wet weather weather at Quality at Quality Control Stations S1 and San Felix. Control Stations S1 and San Felix.

From the hydraulic model, the time of concentration, Tc, is obtained for each catchment. The Fromconcentration the hydraulic time, Tc, may model, be decomposed the time of into concentration, two terms: overlandTc, is runoff obtained time, forTE, and each in-sewer catchment. The concentrationrun time, TR [3]: time, Tc, may be decomposed into two terms: overland runoff time, TE, and in-sewer run time, TR [3]: = + Tc TE TR (1) Tc = TE + TR (1) A common expression to calculate Tc in non-urban catchments is presented by Temez [24]: L0.76 T = 0.3 (2) c _ rural S 0.19 where L is the longest overland flow length (km), and S the mean catchment slope (-). Values calculated from the hydraulic model and presented in Table 4 adjust to the Temez equation modified for urban areas [25]:

Tc _ rural T = (3) c 1+ 3 μ()2 − μ

where Tc is the concentration time modified for urban catchments that takes into account the in-sewer run time, and μ is the fraction of the area that is impervious. The time of concentration of the catchment was obtained introducing a uniform precipitation in each sub-catchment with a duration higher enough to assure that all the surface contributes to the outfall. The values of the modified concentration time, Tc, calculated by the hydraulic model and by Equation (3) are presented in the following table:

Table 4. Comparison of the modified concentration time.

Concentration Time, Tc (min) Catchment Hydraulic Model Equation (3) S1 193.75 200 San Felix 87.14 80

3. Results and Discussion

3.1. Variables Definition from Wet Weather Measured Events The data registered from monitoring rainfall events corresponds to the period from June 2014 to April 2016 at both urban catchments. During this period, 10 storm events were measured in the S1 QCS and 9 in the San Felix QCS. Measured values are presented in Tables 5 and 6 for San Felix and S1, respectively. All rainfalls exceed the total amount of 2 mm, which is the minimum value to assure runoff.

Water 2017, 9, 303 6 of 16

A common expression to calculate Tc in non-urban catchments is presented by Temez [24]:

L0.76 T = 0.3 (2) c_rural S0.19 where L is the longest overland flow length (km), and S the mean catchment slope (-). Values calculated from the hydraulic model and presented in Table4 adjust to the Temez equation modified for urban areas [25]: Tc_rural Tc = p (3) 1 + 3 µ(2 − µ) where Tc is the concentration time modified for urban catchments that takes into account the in-sewer run time, and µ is the fraction of the area that is impervious. The time of concentration of the catchment was obtained introducing a uniform precipitation in each sub-catchment with a duration higher enough to assure that all the surface contributes to the outfall. The values of the modified concentration time, Tc, calculated by the hydraulic model and by Equation (3) are presented in the following table:

Table 4. Comparison of the modiﬁed concentration time.

Concentration Time, Tc (min) Catchment Hydraulic Model Equation (3) S1 193.75 200 San Felix 87.14 80

3. Results and Discussion

3.1. Variables Deﬁnition from Wet Weather Measured Events The data registered from monitoring rainfall events corresponds to the period from June 2014 to April 2016 at both urban catchments. During this period, 10 storm events were measured in the S1 QCS and 9 in the San Felix QCS. Measured values are presented in Tables5 and6 for San Felix and S1, respectively. All rainfalls exceed the total amount of 2 mm, which is the minimum value to assure runoff.

Table 5. Variables of rainfall events at San Felix Catchment.

San Felix Catchment Event code SF_1 SF_2 SF_3 SF_4 SF_5 SF_6 SF_7 SF_8 SF_9 Year 2014 2014 2015 2015 2015 2015 2015 2016 2016 Date (dd-m) 17 June 14 December 22 March 11 June 5 September 27 September 15 January 9 May 4 June PTOTAL (mm) 7.34 30.71 2.47 10.13 56.47 7.53 11.57 6.80 2.27 Imean (mm/h) 4.63 1.23 0.99 1.40 2.26 2.44 2.28 1.01 2.27 Imax10 (mm/h) 19.67 8.86 2.76 5.32 18.76 5.28 4.71 4.84 6.04 DWP (days) 15 10 1 22 19 17 17 18 22 Qmax (L/s) 2710 2930 1580 2530 3170 2590 2650 2260 1680 Qmean (L/s) 945.00 1396.53 746.67 1217.95 1726.96 1073.25 1173.92 989.42 680.19 Qmax/Qmeandw 10.04 10.85 5.85 9.37 11.74 9.59 9.81 8.37 6.22 TPH (min) 35 60 105 80 95 130 205 180 90 EV (m3) 32,493 155,853 25,536 64,308 195,837 38,637 60,222 46,305 22,038 3 EVdw (m ) 10,467 31,638 11,028 17,046 30,993 9846 15,729 13,149 10,335 3 EVww (m ) 22,026 12,4215 14,508 47,262 164,844 28,791 44,493 33,156 11,703 Eww/EVdw 0.68 0.80 0.57 0.73 0.84 0.75 0.74 0.72 0.53 CMAXtb (NTU) 626 851 481 770 994 765 830 498 593 EMCtb (NTU) 251 279 286 319 270 308 440 301 318 TPP (min) 64.81 99.88 111.89 110.18 132.82 128.67 165.61 156.51 64.81 Water 2017, 9, 303 7 of 16

Table 6. Variables of rainfall events at S1 Catchment.

S1 Catchment Event code S1_1 S1_2 S1_3 S1_4 S1_5 S1_6 S1_7 S1_8 S1_9 S1_10 Year 2014 2014 2014 2015 2015 2015 2015 2016 2016 2016 Date (dd-m) 24 June 22 September 14 December 20 May 11 June 27 September 15 January 30 January 21 March 4 April PTOTAL (mm) 12.06 3.29 30.37 3.03 8.69 8.18 11.16 14.19 27.48 13.46 Imean (mm/h) 1.90 0.67 1.22 1.35 1.16 2.80 2.09 3.70 0.99 0.71 Imax10 (mm/h) 4.24 2.55 7.62 3.86 4.24 5.87 5.33 8.25 4.39 7.05 DWP (days) 7 5 10 24 22 17 17 15 13 12 Qmax (L/s) 2360 1520 2480 1560 2350 2430 2440 1970 2150 2580 Qmean (L/s) 1567.34 960.00 1617.77 790.00 1393.44 1580.00 1690.00 1190.00 1700.87 1390.00 Qmax/Qmeandw 5.06 3.10 5.22 2.55 4.49 5.10 5.45 3.84 7.81 4.48 TPH (min) 130.0 175.2 110.0 150.0 150.0 109.8 205.2 145.2 155.0 135.0 EV (m3) 74,292 32,349 184,911 32,628 75,246 50,091 65,745 63,048 210,663 99,084 3 EVdw (m ) 12,975 10,242 36,918 14,592 18,495 10,884 12,891 14,661 39,162 21,297 3 EVww (m ) 61,317 22,107 147,993 18,036 56,751 39,207 52,854 48,387 171,501 77,787 Eww/EVdw 0.83 0.68 0.80 0.55 0.75 0.78 0.80 0.77 0.81 0.79 CMAX (mg/L) 588 522 788 822 767 652 698 728 564 496 EMCtb (NTU/L) 174 257 171 299 226 229 292 239 147 237 TPP (min) 96.03 107.12 100.37 103.06 105.33 90.19 120.65 110.65 119.82 104.76 Water 2017, 9, 303 8 of 16 Water 2017, 9, 303 9 of 17

SeveralSeveral variables variables have have been been calculated calculated from from the themonitored monitored data dataand are and also are collected also collected in Tables in 5Tables and 6,5 andsuch6, assuch the total as the rainfall total rainfallvolume volume PTOTAL, thePTOTAL maximum, the maximum rainfall inte rainfallnsity intensityduring ten during minutes ten Iminutesmax10, the Imeanmax10, intensity the mean Imean intensity, and theImean number, and the of antecedent number of dry antecedent days DWP dry. daysThereDWP are also. There others are parametersalso others parameterssuch as the suchmaximum as the runoff maximum flow runoff rate Q ﬂowmax, the rate meanQmax runoff, the mean flow runoffrate Q ﬂowmean, the rate timeQmean to , hydrographthe time to hydrographpeak TPH, peakthe totalTPH runoff, the total volume runoff EV volume, the partEV ,of the the part runoff of the volume runoff volumethat would that correspondwould correspond to dry weather to dry weather EVdw, theEV differencedw, the difference between both between EVww both, the maximumEVww, the maximumturbidity registered turbidity duringregistered the during episode the C episodeMAXtb, theCMAXtb mean, the event mean turbidity event turbidity value EMC valuetb,EMC andtb the, and time the timeto the to thepeak peak of pollutographof pollutograph TPPTPP. . TheseThese variables variables have have been been calcul calculatedated for for all all rainfalls, rainfalls, which which are are hereinafter hereinafter used used to to study study the the correlationcorrelation among among them them to to adjust adjust statistical statistical models models that that allow allow predicting predicting several several variables variables at at any any rainfallrainfall event, event, e.g., the event maximum turbidity concentration CMAXtb, ,and and the the time time to to the the peak peak of of pollutographpollutograph TPP.. TheThe hydrographs hydrographs and and turbidity-pollutographs of of some some of of the the measured measured rainfall rainfall events events are are presentedpresented in Figure5 5.. The The pollutograph pollutograph peak peak does does not not always always precede precede the the hydrograph hydrograph one, one, as canas can be beobserved observed in Tablein Table5 and 5 and Figure Figure5 for 5 Sanfor San Felix Felix Catchment. Catchment. TheThe calibrated hydraulic modelmodel inin SWMMSWMM hashas been been used used to to obtain obtain the the hydrographs hydrographs presented presented in inFigure Figure5. 5.

S1_1 Rainfall (mm) Turbidity (NTU) Hydrograph (L/S) San Felix_1 Rainfall (mm) Turbidity (NTU) Hydrograph (L/S) 3000 0 3000 0 0.2 0.2 2500 2500 0.4 0.4 0.6 0.6 2000 Q (L/s) 2000 Q (L/s) 0.8 0.8 1500 1 1500 1 1.2 1.2 1000 1000 Rainfall (mm) 1.4 1.4 Rainfall (mm) 1.6 1.6 500 500

1.8 Turbidity , (NTU) 1.8 Turbidity, (NTU) 0 2 0 2 2:09 4:33 6:57 9:21 11:45 14:09 16:33 17:16 18:28 19:40 20:52 22:04 23:16 0:28 1:40 2:52 Time (hh:mm) Time (hh:mm)

S1_3 Rainfall (mm) Turbidity (NTU) Hydrograph (L/S) San Felix_3 Rainfall (mm) Turbidity (NTU) Hydrograph (L/S) 3000 0 2000 0 0.2 0.2 2500 0.4 0.4 1500 0.6 0.6 Q (L/s) Q (L/s) 2000 0.8 , 0.8 1500 1 1000 1 1.2 1.2 1000 Rainfall(mm) 1.4 1.4 Rainfall (mm) 500 1.6 500 1.6 Turbidity (NTU) Turbidity , (NTU) 1.8 1.8 0 2 0 2 11:45 23:45 11:45 11:45 14:09 16:33 18:57 21:21 Time (hh:mm) Time (hh:mm) S1_5 Rainfall (mm) Turbidity (NTU) Hydrograph (L/S) San_Felix 5 Rainfall (mm) Turbidity (NTU) Hydrograph (L/S)

2500 0 3500 0 0.2 0.2 3000 2000 0.4 0.4 0.6 Q (L/s) 2500 0.6 ,

Q (L/s) 1500 0.8 2000 0.8 , 1 1 1000 1.2 1500 1.2 Rainfall (mm) 1.4 Rainfall (mm) 1000 1.4 500 1.6 1.6 Turbidity (NTU) 500 1.8 1.8

Turbidity (NTU) 0 2 0 2 7:12 9:36 12:00 14:24 16:48 19:12 21:36 0:00 21:21 2:09 6:57 11:45 16:33 21:21 2:09 Time (hh:mm) Time (hh:mm) Figure 5. Cont.

Water 2017, 9, 303 9 of 16 Water 2017, 9, 303 10 of 17

San Felix_6 Rainfall (mm) Turbidity (NTU) Hydrograph (L/S) S1_6 Rainfall (mm) Turbidity (NTU) Hydrograph (L/S) 3000 0 3000 0 0.2 0.2 2500 2500 0.4 0.4 0.6 2000 0.6 Q (L/s)

Q (L/s) 2000 0.8 0.8 , 1500 1 1500 1 1.2 1.2 1000 1000 1.4 Rainfall (mm) 1.4 Rainfall (mm) Rainfall 1.6 1.6 500 500 1.8 1.8 Turbidity (NTU) Turbidity , (NTU) 0 2 0 2 19:26 20:38 21:50 23:02 0:14 1:26 2:38 3:50 5:02 19:26 20:38 21:50 23:02 0:14 1:26 2:38 3:50 5:02 Time (hh:mm) Time (hh:mm) San Felix_7 S1_8 Rainfall (mm) Turbidity (NTU) Hydrograph (L/S) Rainfall (mm) Turbidity (NTU) Hydrograph (L/S) 2500 0 3000 0 0.2 0.2 2500 2000 0.4 0.4 0.6 0.6 2000 Q (L/s) Q (L/s) 1500 0.8 0.8 , 1 1500 1 1000 1.2 1.2 1000

1.4 1.4 (mm) Rainfall Rainfalln (mm) Rainfalln 1.6 500 1.6 500 1.8 1.8 Turbidity (NTU) Turbidity (NTU) (NTU) , Turbidity 0 2 0 2 1:26 3:50 6:14 8:38 11:02 13:26 15:50 5:02 7:26 9:50 12:14 14:38 17:02 19:26 21:50 Time (hh:mm) Time (hh:mm)

FigureFigure 5. 5.Rainfall, Rainfall, hydrographs hydrographs and and turbidity-pollutographturbidity-pollutograph of of events: events: S1_1; S1_1; S1_3; S1_3; S1_5; S1_5; S1_6; S1_6; S1_8; S1_8; SanSan Felix_1; Felix_1; San_Felix_3; San_Felix_3; San San Felix_5; Felix_5; San San Felix_6;Felix_6; andand San Felix_7.

3.2.3.2. Predictor Predictor Variables Variables Correlations Correlations With the objective of adjusting a statistical model, the correlation between predictor variables With the objective of adjusting a statistical model, the correlation between predictor variables has been traced. The chosen predictor variables are DWP, Qmax, TPH, PTOTAL, Imax10, CMAXtb, and TPP. has been traced. The chosen predictor variables are DWP, Q , TPH, P , I , C , and TPP. The correlation matrix is presented in Tables 7 and 8 for S1max and San FelixTOTAL catchments,max10 MAXtb respectively. The correlation matrix is presented in Tables7 and8 for S1 and San Felix catchments, respectively. The Pearson’s correlation coefficient has been applied to the sample of each pair of variables. From The Pearson’s correlation coefﬁcient has been applied to the sample of each pair of variables. From the matrices, correlation between the time to pollutograph peak, TPP, and the time to hydrograph thepeak, matrices, TPH, correlationis observed betweenwith values the of time R2 = to0.79 pollutograph and 0.94 for peak,S1 andTPP San, andFelix, the respectively. time to hydrograph The dry peak, TPH, is observed with values of R2 = 0.79 and 0.94 for S1 and San Felix, respectively. The dry period preceding the episode, DWP, and the maximum concentration of turbidity, CMAXtb, show good periodrelation, preceding especially the in episode, the S1 CatchmentDWP, and thewith maximum R2 = 0.68. There concentration is also certain of turbidity, relationshipCMAXtb between, show the good 2 relation,maximum especially concentration in the S1 of Catchment turbidity, C withMAXtb,R with= 0.68. the total There precipitation is also certain and relationship the maximum between flow in the maximumthe San Felix concentration Catchment. of turbidity, CMAXtb, with the total precipitation and the maximum ﬂow in the San Felix Catchment. Table 7. Correlation matrix for variables of rainfall events at S1 Catchment. Table 7. Correlation matrix for variables of rainfall events at S1 Catchment. DWP Qmax TPH PTOTAL Imax10 CMAXtb TPP DWP 1.00 −0.01 0.09 −0.29 0.02 0.68 0.07 DWP Qmax TPH PTOTAL Imax10 CMAXtb TPP Qmax 1.00 −0.35 0.24 0.55 0.02 −0.31 DWP 1.00 −0.01 0.09 −0.29 0.02 0.68 0.07 TPH 1.00 −0.32 −0.43 −0.10 0.79 Qmax 1.00 −0.35 0.24 0.55 0.02 −0.31 TPH PTOTAL 1.00 − 1.000.32 0.50−0.43 0.01− 0.100.24 0.79 PTOTALImax10 Symmetrical 1.00 1.00 0.50 0.21 0.01 −0.06 0.24 Imax10CMAXtb Symmetrical 1.001.00 0.21 −0.08− 0.06 CMAXtbTPP 1.00 1.00 −0.08 TPP 1.00

Table 8. Correlation matrix for variables of rainfall events at San Felix Catchment. Table 8. Correlation matrix for variables of rainfall events at San Felix Catchment. DWP Qmax TPH PTOTAL Imax10 CMAXtb TPP

DWPDWP 1.00 Qmax0.28 TPH0.12 P 0.10TOTAL 0.13Imax10 0.32CMAXtb 0.19 TPP Qmax 1.00 −0.12 0.74 0.61 0.84 0.06 DWP 1.00 0.28 0.12 0.10 0.13 0.32 0.19 Qmax TPH 1.00 −1.000.12 −0.18 0.74 −0.61 0.61 −0.08 0.84 0.94 0.06 TPH PTOTAL 1.00 −1.000.18 0.59−0.61 0.80− 0.080.11 0.94 PTOTALImax10 Symmetrical 1.00 1.00 0.59 0.48 0.80 −0.52 0.11 Imax10CMAXtb Symmetrical 1.001.00 0.48 0.16 −0.52 CMAXtbTPP 1.001.00 0.16 TPP 1.00

Water 2017, 9, 303 10 of 16 Water 2017, 9, 303 11 of 17

3.3. Pollution Pollution Prediction Prediction Indexes. Statistical Statistical Model Model From the the previous previous section, section, the the correlation correlation between between predictor predictor variables variables individually individually analyzed analyzed is consideredis considered not not significant signiﬁcant enough enough to be to used be used as a prediction as a prediction tool of tool the of pollution the pollution in a rainfall in a rainfall event. Forevent. this For reason, this reason, multivariate multivariate indexes indexes are proposed are proposed.. The aim The is aim to predict, is to predict, on the on one the hand, one hand, the maximumthe maximum concentration concentration of turbidity of turbidity during during each each event, event, CCMAXtbMAXtb, and,, and, on on the the other other hand, hand, the the time time elapsed from the beginning beginning of the the event event un untiltil the the maximum maximum peak peak of of the the pollutograph, pollutograph, TPPTPP.. To To achieve achieve this,this, two indexes of prediction are adjusted:adjusted: the timetime toto peakpeak ofof thethe pollutographpollutograph index,index, IITPPTPP,, and and the the maximum concentration index, ICMAX. .

3.3.1. Time to the Peak of Pollutograph Index, I 3.3.1. Time to the Peak of Pollutograph Index, ITPP The index time to the peak peak of of the the pollutograph pollutograph will will be be used used to to predict predict the the time time that that elapses elapses from from thethe beginning beginning of of the the episode episode until until the the maximum maximum value of turbidity in the event is reached, reached, TPP.. It It can can be defined defined with dimensionless factors: 0.13 0.02 TPH 0.13 P 0.02 I =  TOTAL  (4) TPP TPH  PTOTAL I =  TC  PTOTAL_ANNUAL (4) TPP      TC   PTOTAL_ ANNUAL  where PTOTAL_ANNUAL is the total precipitation expected in a year, adopting 350 mm for this region. In whereEquation PTOTAL_ANNUAL (4), the time is the to the total peak precipitation of the hydrograph, expected TPHin a ,year, is considered. adopting Its350 significant mm for this relation region. with In EquationTPP is shown (4), the in thetime correlation to the peak matrices of the hydrograph, (Tables7 and TPH8). , is considered. Its significant relation with TPP isThe shown first in term the correlation of Equation matrices (4), TPH/T (Tablesc, reflects7 and 8). the time of the catchment to respond as a functionThe first of: term (i) of how Equation the rain (4), isTPH/T distributedc, reflects proportionally the time of the tocatchmentTPH; and to respond (ii) the shapeas a function of the of:catchment (i) how the inversely rain is distributed proportional proportionally to Tc. The secondto TPH; term,and (ii)P TOTALthe shape/PTOTAL_ANNUAL of the catchment, magnitude inversely of proportionalthe rainfall, isto also Tc. proportional The second to term, the time PTOTAL to the/PTOTAL_ANNUAL peak of the, magnitude pollutograph. of the In this rainfall, Equation, is also the proportionalterm PTOTAL/P toTOTAL_ANNUAL the time to thehas peak lower of the influence pollutograph. on the In index this Equation, than TPH/T thec .term However, PTOTAL/P itsTOTAL_ANNUAL inclusion 2 2 hasimproves lower theinfluence adjustment on the from indexR than= 0.87 TPH/T to Rc. =However, 0.96. Figure its inclusion6 shows the improves linear relationship the adjustment between from Rthe2 = pollutograph0.87 to R2 = 0.96. time Figure to the 6 peak shows index, the linear defined relationship in previous between equation, the andpollutograph the time totime the to peak the peakof pollutograph. index, defined in previous equation, and the time to the peak of pollutograph.

180 TPP = 419.78.I -273.76 160 TPP R² = 0.96 140

120

TPP (min)TPP 100 ItppITTP S1 80 ItppITTP San Félix 60 0.80 0.85 0.90 0.95 1.00 1.05 1.10 ITPP

Figure 6. Linear adjustment of TPP with prediction index ITPP. Figure 6. Linear adjustment of TPP with prediction index ITPP. In Figure 6, a linear regression that relates the time index to the peak of the pollutograph and the timeIn Figure to the6 peak,, a linear expressed regression in minutes, that relates can the be timeobtained index as: to the peak of the pollutograph and the time to the peak, expressed in minutes, can be obtained as: = − TPP 419.78ITPP 273.76 (5) TPP = 419.78ITPP − 273.76 (5)

3.3.2. Maximum Maximum Concentration Concentration Index, IICMAX

The maximum concentration index IICMAX arisesarises with with the the objective objective of of estimating estimating the maximum concentration of turbidity, CCMAXtbMAXtb, ,from from predictor predictor variables variables quantified quantiﬁed in in rainfall rainfall events. events. Together Together with with the ITPP, they allow estimating both the magnitude of the pollutograph and the location in time of the higher turbidity. The equation for ICMAX is defined as

Water 2017, 9, 303 11 of 16

the ITPP, they allow estimating both the magnitude of the pollutograph and the location in time of the higher turbidity. The equation for ICMAX is deﬁned as

0.3 PTOTAL 0.3 ICMAX = S (DWR) Fshape (6) PTOTAL_ANNUAL Water 2017, 9, 303 12 of 17 where DWR is the proportion of consecutive dry weather days previous to the event in the last month.

Equation (6) is dimensionless and can be divided into0.3 three main terms. The first term is related  P  0.3 to the power of the event, whereI an=  increaseTOTAL in theS  total()DWR rainfallF causes a greater sediment(6) wash. CMAX  P  shape Assuming the rest of parameters fixed, aTOTAL higher_ ANNUAL maximum concentration will occur in the catchment with a higherwhere DWR average is theslope. proportion The of second consecutive term dry reflects weather that days during previous the to time the event without in the precipitation last month. there is sedimentationEquation (6) and is dimensionless accumulation and ofcan deposits be divided along into three the network main terms. that The can first be term washed is related away to during storm events.the power Finally, of the theevent, third where term an isincrease a shape in factorthe total of rainfall the catchment. causes a greater It is a sediment catchment wash. geometric parameterAssuming defined the accordingrest of parameters to fixed, a higher maximum concentration will occur in the catchment with a higher average slope. The second term reflects that10A during the time without precipitation there F = (7) is sedimentation and accumulation of depositsshape along theL2 network that can be washed away during storm events. Finally, the third term is a shape factor of the catchment. It is a catchment geometric 2 where Aparameteris the area defined of the according catchment to (km ) and L is the catchment flow length (km). Table9 summarizes the shape factor obtained in both catchments analyzed. = 10A Fshape 2 (7) Table 9. CatchmentsL shape factors. where A is the area of the catchment (km2) and L is the catchment flow length (km). 2 CatchmentTable 9 summarizes Slope (m/m) the shape Catchment factor obtained Flow in Length, both catchmentsL (km) analyzed.S (km ) Fshape S1 0.0013 17.00 47.53 1.645 Table 9. Catchments shape factors. San Félix 0.0043 10.75 14.89 1.288 Catchment Slope (m/m) Catchment Flow Length, L (km) S (km2) Fshape S1 0.0013 17.00 47.53 1.645 Figure7 presentsSan the Félix values 0.0043 of ICMAX , calculated 10.75 by Equation (6) 14.89for each 1.288 rainfall event, and the maximum of measured turbidity in each event, CMAXtb. Most values fit around a line except four cases: Figure 7 presents the values of ICMAX, calculated by Equation (6) for each rainfall event, and the (i) S1_4:maximum It is of an measured episode turbidity with veryin each low event, precipitation CMAXtb. Most values (3 mm). fit around Thus, a line although except four thecases: previous dry(i) period S1_4: It is an very episode extensive with very (24low precipitation days), the (3 prediction mm). Thus, although index yields the previous lower dry values period of the maximumis very concentration. extensive (24 days), the prediction index yields lower values of the maximum (ii) S1_9 andconcentration. S1_10: The measured maximum concentration values are below the trend followed by(ii) the S1_9 other and data. S1_10: The The possible measured reason maximum of thisconcen phenomenontration values seemsare below to the be relatedtrend followed with theby energy the other data. The possible reason of this phenomenon seems to be related with the energy of of both events. The rains on these two days are characterized by an average intensity of low both events. The rains on these two days are characterized by an average intensity of low precipitationprecipitation (less (less than than 1 mm/h), 1 mm/h), soso thatthat the the catchment catchment and and the network the network were slowly were slowlywashed.washed. (iii) SF_8:(iii) ItSF_8: is similar It is similar to episode to episode S1_4. S1_4. The The precipitation is isvery very low low (2.3 (2.3mm). mm).

Those reasons justify discarding the four cases. The relationship between CMAXtb and ICMAX fit to Those reasons justify discarding the four cases. The relationship between CMAXtb and ICMAX ﬁt to a line with a correlation coefficient of R2 = 0.91. a line with a correlation coefﬁcient of R2 = 0.91.

IcmaxICMAX S1 IcmaxICMAX San Félix Excluded S1 Excluded San Félix 1200 1000 800

(NTU) 600

MAXtb 400 C C = 5377.2I + 353.84 200 MAXtb CMAX R² = 0.91 0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 ICMAX

Figure 7. Linear adjustment of CMAXtb with the prediction index ICMAX. Figure 7. Linear adjustment of CMAXtb with the prediction index ICMAX.

Water 2017, 9, 303 12 of 16 Water 2017, 9, 303 13 of 17

TheThe ﬁttedfitted line line of of the the adjustment adjustment between between the the maximum maximum concentration concentration index, index,ICMAX ICMAX,, andand thethe maximummaximum concentration concentration of of turbidity, turbidity,C CMAXtbMAXtb, is given by a linear regression = + CMAXtb 5377.2ICMAX 353.84 (8) CMAXtb = 5377.2ICMAX + 353.84 (8) Table 1 summarizes the parameters presented in the literature to predict pollution. This Table1 summarizes the parameters presented in the literature to predict pollution. This manuscript proposes a new model to estimate CMAXtb. Moreover, proposed methodology also allows manuscript proposes a new model to estimate C . Moreover, proposed methodology also allows estimating TPP from hydraulic and hydrologicalMAXtb parameters. estimating TPP from hydraulic and hydrological parameters. 3.4. Development of Pollutographs from Prediction Indexes 3.4. Development of Pollutographs from Prediction Indexes Pollutograph is the representation of the concentration of a certain pollutant over time. The Pollutograph is the representation of the concentration of a certain pollutant over time. analysis of the ensemble formed by the hydrograph, the rainfall and the pollutograph of a given event The analysis of the ensemble formed by the hydrograph, the rainfall and the pollutograph of a given can provide very important information about the mass mobilization of contaminants in an episode. event can provide very important information about the mass mobilization of contaminants in For this reason, the knowledge of this graph is essential for the tasks of pollution management. Figure an episode. For this reason, the knowledge of this graph is essential for the tasks of pollution 8 presents a standard pollutograph. management. Figure8 presents a standard pollutograph.

Pollutograph Dry weather pollutograph 1000 TPP TDP 800 CMAXtb 600

400 Turbidity(NTU) 200

Dry weather concentration 0 22:40 23:52 1:04 2:16 Time (hh:mm)

FigureFigure 8. 8.Main Main parameters parameters of of a a design design pollutograph. pollutograph.

TheThe line line of of ascent ascent can can be be adjusted adjusted to to the the following following exponential exponential equation equation 1 n " 1 #n C C NNaa C = =abx =x C=  MAXtbMAXtb  (9) aCa ab 0C0   (9)  C0    C0    where Na is the number of intervals of 5 min in which the ascent time is divided; n indicates the interval a (0where≤ n ≤ NN ais) inthe units number of ﬁve of minutes; intervals and of 5C aminand inC 0whichare the the turbidity ascent valuestime is atdivided; each interval n indicatesn and the at a a 0 theinterval beginning (0 ≤ n of ≤ theN ) pollutograph,in units of five respectively minutes; and (measured C and C in are NTU). the turbidity The value values of C0 is at assumed each interval as the n dryand weather at the beginning value at theof the beginning pollutograph, of the episode.respectively (measured in NTU). The value of C0 is assumed as theOnce dry CweatherMAXtb and valueTPP at havethe beginning been calculated of the episode. from prediction indexes, the time to the descent of pollutograph,Once CMAXtb TDPand ,TPP can have be deﬁned been calculated as the time from interval prediction between indexes, the instantthe time of to the the maximum descent of concentrationpollutograph, and TDP the, timecan whenbe defined the concentration as the time reaches interval dry between weather values.the instant Thetime of the to the maximum descent ofconcentration pollutograph and value the has time been when adjusted the forconcentratio each of then catchmentsreaches dry showing weather a values. linear relationship The time to with the pollutographdescent of pollutograph time to the peak. value The has adjustment been adjusted of TDP forfor each each catchmentof the catchments is given byshowing a linear relationship with pollutograph time to the peak. The adjustment of TDP for each catchment is given by S1 → TDP = 3.5TPP − 125 S1 → TDP = 3.5TPP − 125 (10) San Felix → TDP = 4.24TPP − 40 (10) San Felix → TDP = 4.24TPP − 40 where TPP and TDP, in this equation, are expressed in minutes. where TPP and TDP, in this equation, are expressed in minutes. Differences between measured and calculated TDP at the studied events present average relative Differences between measured and calculated TDP at the studied events present average relative errors below 13% for the S1 catchment and 14% for the San Félix catchment. errors below 13% for the S1 catchment and 14% for the San Félix catchment. The descent line of the pollutographs can be adjusted to a logarithmic function:

Water 2017, 9, 303 13 of 16

Water 2017, 9, 303 14 of 17 The descent line of the pollutographs can be adjusted to a logarithmic function: −  CTStb CMAXtb  C = aln()x + b = CTStb − CMAXtb ln()n − N +1 + C (11) Cd =d a ln(x) + b =  ()− + ln(n − Na a+ 1) + CMAXtbMAXtb (11) lnln(NNd −d NNa +a 1)1  where Ndd is the number of intervals of five ﬁve minutesminutes in which the descent time is divided; n indicates the interval (Na ≤ nn ≤≤ NNd)d in) in units units of of five ﬁve minutes; minutes; and and CCd dandand CCTStbTStb areare the the turbidity turbidity values values at ateach each n nintervalinterval and and at at the the end end of of the the event, event, corresponding corresponding to to TDPTDP time,time, respectively respectively (measured (measured in in NTU). NTU). Equation (11), when n = Na,, ln( ln(nn −− NNa a+ +1) 1) = =0, 0,and and CaC =a C=d C=d C=MAXtbCMAXtb, assures, assures continuity. continuity. Figure9 9 shows shows somesome ofof thethe measuredmeasured pollutographs.pollutographs. TheyThey areare comparedcompared withwith thethe pollutographspollutographs obtained by Equations (9)–(11). Results show a good agreement between measured and calculatedcalculated pollutographs; therefore, therefore, the the proposed proposed methodology methodology is suitable is suitable for estimating for estimating pollutographs pollutographs from fromindexes. indexes.

S1_1 Measured pollutograph Adjusted pollutograph Dry weather turbidity SF_1 Measured pollutograph Adjusted pollutograph Dry weather turbidity 700 800

600 700 600 500 500 400 400 300 300

Turbidity (NTU) Turbidity 200 (NTU) Turbidity 200

100 100

0 0 2:24 4:48 7:12 9:36 12:00 14:24 16:48 19:12 16:48 18:00 19:12 20:24 21:36 22:48 0:00 1:12 2:24 3:36 4:48

S1_3 Measured pollutograph Time Adjusted(hh:mm) pollutograph Dry weather turbidity SF_4 Measured pollutograph Time Adjusted(hh:mm) pollutograph Dry weather turbidity 900 900 800 800 700 700 600 600 500 500 400 400 300 300 Turbidity (NTU) Turbidity (NTU) 200 200 100 100 0 0 9:36 14:24 19:12 0:00 4:48 9:36 14:24 19:12 0:00 7:12 9:36 12:00 14:24 16:48 19:12 21:36 0:00 Time (hh:mm) Time (hh:mm)

S1_5 Measured pollutograph Adjusted pollutograph Dry weather turbidity SF_5 Measured pollutograph Adjusted pollutograph Dry weather turbidity 900 1200 800 1000 700 600 800 500 600 400 300 400 Turbidity (NTU) Turbidity (NTU) Turbidity 200 200 100 0 0 7:12 9:36 12:00 14:24 16:48 19:12 21:36 0:00 19:12 0:00 4:48 9:36 14:24 19:12 0:00 4:48 9:36 Time (hh:mm) Time (hh:mm)

S1_8 Measured pollutograph Adjusted pollutograph Dry weather turbidity SF_9 Measured pollutograph Adjusted pollutograph Dry weather turbidity 800 700

700 600 600 500 500 400 400 300 300 Turbidity (NTU) Turbidity Turbidity (NTU) Turbidity 200 200

100 100

0 0 0:00 2:24 4:48 7:12 9:36 12:00 14:24 16:48 15:36 16:48 18:00 19:12 20:24 21:36 22:48 0:00 1:12 2:24 Time (hh:mm) Time (hh:mm)

FigureFigure 9. Comparison 9. Comparison between between measured measured pollutographs pollutographs and calculated and calculated ones through ones through the suggested the suggested methodology. methodology.

Several multi-peaked hydrographs have been registered, however none of them led to a multi- peak pollutograph (see case S1_3 and San Felix _5 in Figure 5). Actually, the flushing produced by the first hydrograph peak leads to the removal of a second peak in the pollutograph. Present

Water 2017, 9, 303 14 of 16

Several multi-peaked hydrographs have been registered, however none of them led to a multi-peak pollutograph (see case S1_3 and San Felix _5 in Figure5). Actually, the ﬂushing produced by the ﬁrst hydrograph peak leads to the removal of a second peak in the pollutograph. Present methodology also covers multi-peak hydrographs with unique pollutograph peak, according to observed events.

4. Conclusions Time-continuous measurements of rainfall, in-sewer turbidity and water flow depth have been registered for almost two years. From the measurements, quality and hydraulic rainfall-event variables have been defined (Tables5 and6). In this paper, turbidity has been chosen as a pollutant indicator as other authors have pointed out it can be used in order to estimate different water quality parameters, e.g., TSS or COD, through on-site linear regressions. The correlation between variables has been studied (Tables7 and8). High correlations have been found between some of the analyzed variables, such as between the time to the peak of hydrograph, TPH, and the time to peak of pollutograph, TPP. To improve those correlations, two prediction indexes have been suggested: the pollutograph time to the peak index, ITPP, presented in Equation (4), and the maximum concentration index, ICMAX, shown in Equation (6). From the above prediction indexes, a statistical model has been proposed. This model allows estimating the time to peak of the pollutographs, TPP, presented in Equation (5), and the maximum values of turbidity, CMAXtb, as seen in Equation (8). The statistic model proposed has a high correlation for catchments S1 and San Felix in the city of Murcia. This model constitutes a useful tool for providing knowledge about pollutants transport in the combined sewer overflow in the city of Murcia. In fact, it can help, as an advisory tool, to support the design of CSO tanks or to forecast pollution risks for use within a CSO management strategy. An application of the proposed model is the definition of pollutographs. In Figure8, a standard pollutograph is shown. Pollutograph is modeled through the former index variables together with the pollutographs time to descent, TDP, proposed in Equation (10). Ascent and descent curves are proposed in Equations (9) and (11). Pollutographs estimated through this methodology agree reasonably well with the measured ones during the registered events (Figure9). In this way, from a rainfall forecast, PTOTAL, and other variables such as the dry weather period, DWP, and the time to peak of the hydrograph, pollutographs can be simulated for multiple prognosis scenarios. Thus, the methodology provides information of the pollution during wet weather in combined sewer systems. Although this study is specific for these catchments, it may be used as a starting point for other catchments to establish effective policies for combined sewer overflow control. Moreover, the authors consider that extending the pollutographs to other catchments could lead to standardize the coefficients so that a “design pollutograph” can be defined and used as a reference for other studies.

Acknowledgments: The authors are grateful for the financial support received from Empresa Municipal de Aguas y Saneamiento de Murcia, S.A. through 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. Author Contributions: Pedro D. Martinez-Solano and Simón Nevado-Santos built and calibrated the hydraulic model, supervised and calibrated the field instrumentation and arranged information from rainfall events. Juan Tomás García, Pablo Espín-Leal, Antonio Vigueras-Rodríguez, Luis G. Castillo and José M. Carrillo processed field information, undertook the statistical treatment and established the methodology to achieve the pollutographs. All authors contributed equally to the manuscript revision. Conflicts of Interest: The authors declare no conflict of interest. Water 2017, 9, 303 15 of 16

Notation

A Catchment area (ha) CMAXSS Maximum concentration for suspended solids (mg/L) CMAXtb Maximum concentration for turbidity (NTU) CSMSS Specific mobilized volume of suspended solids (kg/ha) Ca,Cd,C0,CTStb Turbidity at the ascent, descent, beginning and end part of pollutographs, respectively (NTU) Drain Rainfall duration (h) Drunoff (h) Runoff duration (h) DWP Dry weather period (days) DWR Proportion of consecutive dry weather days previous to the event in the last month EMC Mean event concentration (mg/L) EMCtb Mean event concentration of turbidity (NTU) EV Event runoff volume (m3) ICMAX Pollution prediction index associated to the maximum concentration of turbidity (-) Imax Maximum rainfall intensity (mm/h) Imax10 Maximum 10 minutes rainfall intensity (mm/h) Imean Mean rainfall intensity (mm/h) ITTP Pollution prediction index associated to the time to the peak of pollutograph (-) L Catchment flow length (km) Number of intervals of five minutes in which the pollutograph is divided, applied to ascent Na,N d and descent part respectively (-) PTOTAL Total event rainfall (mm) PTOTAL_ANNUAL Total precipitation expected in a year, adopting 350 mm for this region 3 Qmax Maximum event inflow (m /s) 3 Qmean Mean event inflow (m /s) 3 Qmaxdw Maximum dry weather inflow (m /s) QCS Quality Control Station, place where monitoring instrumentation is located RD Rain depth (mm) S Mean slope of the catchment (m/m) Tc Time of concentration of urban catchment (h) Tc_rural Time of concentration of rural catchment (h) TDP Descent time of the pollutograph (h) TPH Peak time of hydrograph (h) TPP Time to the peak of pollutograph (h) TSS Total suspended solids (mg/L) TSSTE Cumulative suspended solids per event (kg/event) TSSff Total pollutant load in the first flush (kg/event) M(V) Cumulative load and runoff ratios M Ratio of impervious area with total area (-)

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