water

Article Empirical Sewer Water Quality Model for Generating Influent Data for WWTP Modelling

Jeroen Langeveld 1,2,* , Petra Van Daal 2,3, Remy Schilperoort 1, Ingmar Nopens 4 , Tony Flameling 5 and Stefan Weijers 5

1 Partners4UrbanWater, Javastraat 104a, Nijmegen 6524 MJ, The Netherlands; [email protected] 2 Section Sanitary Engineering, Department of Water Management, Delft University of Technology, P.O. Box 5048, Delft 2628 CD, The Netherlands; [email protected] 3 Witteveen+Bos, P.O. Box 233, Deventer 7400 AE, The Netherlands 4 BIOMATH, Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Coupure Links 653, Gent 9000, Belgium; [email protected] 5 Waterschap De Dommel, P.O. Box 10.001, Boxtel 5280 DA, The Netherlands; tfl[email protected] (T.F.); [email protected] (S.W.) * Correspondence: [email protected]; Tel.: + 31-6-1897-6283

Received: 30 March 2017; Accepted: 30 June 2017; Published: 5 July 2017

Abstract: Wastewater treatment plants (WWTP) typically have a service life of several decades. During this service life, external factors, such as changes in the effluent standards or the loading of the WWTP may change, requiring WWTP performance to be optimized. WWTP modelling is widely accepted as a means to assess and optimize WWTP performance. One of the challenges for WWTP modelling remains the prediction of water quality at the inlet of a WWTP. Recent applications of water quality sensors have resulted in long time series of WWTP influent quality, containing valuable information on the response of influent quality to e.g., storm events. This allows the development of empirical models to predict influent quality. This paper proposes a new approach for water quality modelling, which uses the measured hydraulic dynamics of the WWTP influent to derive the influent water quality. The model can also be based on simulated influent hydraulics as input. Possible applications of the model are filling gaps in time series used as input for WWTP models or to assess the impact of measures such as real time control (RTC) on the performance of wastewater systems.

Keywords: sewer system; empirical model; influent generator; influent modelling; gap filling

1. Introduction Modelling of wastewater treatment plants (WWTPs) using activated sludge models (ASM) has become a standard in both industry and academia for a range of objectives, amongst others WWTP design [1,2], operation [3], and control [4,5]. Especially the latter objective, developing control strategies and assessing the performance of control strategies requires high frequency influent data [6]. In a comprehensive review, [7] discussed the available approaches for generating influent data. The approaches range from (1) data driven methods based on creating databases with monitoring and experimental data and derived models using the data; (2) very simple models based on harmonic functions; and (3) phenomenological models [8,9]. The data driven methods comprise two different approaches. The first method [10] uses pollutant release patterns derived from literature to generate dynamic influent data aggregating the punctual emissions from the database. The second method [11] interpolates available influent data at e.g., a daily timescale to e.g., hourly dynamics.

Water 2017, 9, 491; doi:10.3390/w9070491 www.mdpi.com/journal/water Water 2017, 9, 491 2 of 18

The simple models based on harmonic functions are very well suited for the analyses of dry weather flow (DWF) situations, but less so for wet weather flow (WWF) situations [7]. The phenomenological models are the most detailed influent models, that can give a phenomenological representation of dynamics of WWTP influent, including diurnal patterns, weekend, seasonal, and holiday variations as well as rain events [7,8]. Despite being labelled as ‘promising’ [7], todays phenomenological models cannot adequately reproduce the dynamics in WWTP influent during wet weather due to a relatively poor representation of the build-up and wash off of urban pollutants. This is also true for the most recently published influent generator by [12], who use a mix of statistical and conceptual modelling techniques for synthetic generation of influent time series. The limitations associated with the use of influent generators are not surprising given the state of the art knowledge on the physical-chemical, biological and transport processes occurring in sewer systems [13–17]. Sediment transport especially is not very well understood and not very successfully reproduced in deterministic sewer models. This is partly due to the fact that it is currently not possible to get enough data on the initial sewer sediment conditions throughout an entire sewer network. It is interesting to note that the developers of influent generators, showing many similarities with simplified or parsimonious sewer models [18,19], are facing the same issues as sewer modelers in the past, i.e., how to incorporate the contribution of in-sewer stocks during storm events to the outflow of sewers via either combined sewer overflow (CSO) or WWTP influent. In order to overcome the limitations of deterministic sewer models, regression models have been proposed, which are validated against monitoring data. A recent successful example of this approach is given by [20], who developed an empirical model for storm water total suspended solids (TSS), event mean concentrations with rainfall depth, and antecedent dry weather period as input variables. These empirical relations, that are valid at a CSO or storm sewer outfall (SSO), however, are not suitable for the prediction of WWTP influent quality, as these models do not predict the influent quality during DWF. For WWTP influent modelling, the empirical model described by [21], relates the influent concentration to the daily flows. A weak point of this approach is the impossibility to account for the dynamics during storm events. This is a major drawback, as storm events typically do not last a full day. Recent applications of water quality sensors have resulted in the availability of long time series of WWTP influent quantity and quality [22,23]. These time series contain a lot of information on the response of influent quality to storm events and the contribution of in-sewer stocks to WWTP influent [24]. In this study, time series analysis is used to understand the dynamics of WWF related variations in WWTP influent quality and to relate the variation in influent quality to influent hydraulics. This allowed the development of an empirical model based on understanding of the underlying physical processes. The paper is organized as follows: first, the available data set of WWTP Eindhoven is described. Second, the model development and calibration method are presented. Next, the calibration results, model results and the transferability of the concept are presented, discussed, and finally, some foreseen applications of the model are introduced.

2. Materials and Methods

2.1. System Description: The Dommel River IUWS The Dommel river is relatively small and sensitive to loadings from CSOs and WWTP effluent. The river flows through the city of Eindhoven (the Netherlands) from the Belgian border (south) into the River Meuse (north). The Dommel receives discharges from the 750,000 people equivalent (PE) WWTP of Eindhoven and from over 200 CSOs in 10 municipalities. In summer time, the base flow in the river just downstream of the WWTP comprises 50% of WWTP effluent, increasing to 90% during small storm events. The Dommel River does not yet meet the requirements of the European Water 2017, 9, 491 3 of 18 Water 2017, 9, 491 3 of 18

Unionoxygen Water (DO) Framework depletion, Directiveammonia (WFD)peaks [and25]. seasonal The water average quality nutrient issues to concentration be addressed arelevels dissolved [26,27]. oxygenEarlier (DO)research depletion, within ammoniathe KALLISTO peaks project and seasonal [18,25] averagedemonstrated nutrient that concentration the WWTP effluent levels [26 is,27 the]. Earliermain source research for within the toxic the KALLISTOammonia peaks project in [the18,25 Dommel] demonstrated river and that that the the WWTP ammonium effluent peaks is the in main the sourceWWTP for effluent the toxic can ammonia be significantly peaks in reduced the Dommel by applied river and integrated that the ammoniumreal time control peaks (RTC). in the WWTPIn [28], effluentthe use of can RTC be significantlyby activating reducedin-sewer bystorage applied volume integrated to reduce real and time delay control the hydraulic (RTC). In [peak28], theloading use ofof RTCthe byWWTP activating during in-sewer storm storageevents volumehas been to shown reduce andto be delay an effective the hydraulic measure. peak Reference loading of the[29] WWTPintroduced during a new storm RTC events concept: has been the smart shown buffer, to be anwh effectiveich minimizes measure. the Referencepeak load [ 29to] the introduced biology at a newWWTP RTC Eindhoven concept: the by smart applying buffer, the which aforementioned minimizes the RTC peak combined load to thewith biology using atonly WWTP one Eindhovenof the three byprimary applying clarifiers the aforementioned (PC) during dry RTC weather combined (DWF) with and using using only the one other of thetwo three PCs only primary during clarifiers storm (PC)events. during dry weather (DWF) and using the other two PCs only during storm events. TheThe 1010 municipalitiesmunicipalities contributingcontributing to to thethe WWTPWWTP influentinfluentare are divideddivided overover threethree catchmentcatchmentareas areas thatthat are are very very different different in in size size and and character, character, each each having having a separatea separate inflow inflow to theto the WWTP WWTP (see (see Figure Figure1). Wastewater1). Wastewater from from Eindhoven Eindhoven Stad Stad (ES, municipality(ES, municipality of Eindhoven) of Eindhoven) accounts accounts for approximately for approximately 50% 3 (in50% practice (in practice ranging ranging between between 14,000 14,000 and and 17,000 17,000 m /h) m3/h) of of the the hydraulic hydraulic capacity capacity and and is is discharged discharged directlydirectly toto thethe WWTP.WWTP. The The other other nine nine (much (much smaller) smaller) municipalities municipalities are are each each connected connected to toone oneof ofthe the twotwo wastewaterwastewater transporttransport mains, one one to to the the north north (N (Nuenen/Sonuenen/Son or or NS, NS, 7 km 7 km in inlength) length) and and one one to the to 3 thesouth south (Riool (Riool Zuid Zuid or RZ, or RZ, 32 32km km in inlength), length), accounting accounting for for respectively respectively 7% 7% (3000 (3000 m3 m/h)/h) and and 43% 43% (in 3 (inpractice practice ranging ranging from from 14,000 14,000 to to15,000 15,000 m3 m/h)/h) of the of thehydraulic hydraulic capacity. capacity. An Anelaborate elaborate description description of the of thestudied studied wastewater wastewater system system can can be befound found in [23]. in [23 ].

Closing section catchment area: ps Son river Nuenen/Son ps Nederwetten Eindhoven Stad Riool-Zuid ps Gerwen ps Nuenen

wwtp cs rwzi Eindhoven ps Eeneind ps Wintelre ps Mierlo

sludge Veldhoven Geldrop proc. inst. ps Aalst ps Knegsel cs de Meren Aalst ps Heeze ps Waalre ps Steensel cs Valkenswaard ps Eersel ps Sterksel ps Duizel Valkenswaard ps Riethoven ps Leende

Bergeijk ps Westerhoven wwtp Eindhoven ps Weebosch free flow conduits ps Borkel pressure mains pumping stations control stations Luijksgestel sludge proc. inst. N 0 3 6 9 km

FigureFigure 1.1.Wastewater Wastewater system systemof of Eindhoven Eindhoven( Left(Left)) and and its its receiving receiving streams streams and and schematic schematic lay lay out out of of thethe wastewater wastewater system; system; ( Right(Right)) Figure Figure reproduced reproduced with with permission permission from from [ 23[23].].

2.2. Monitoring Network and Data Validation 2.2. Monitoring Network and Data Validation At each of the three inflows into the WWTP (locations ‘A’ in Figure 1 at the right) on-line At each of the three inflows into the WWTP (locations ‘A’ in Figure1 at the right) on-line spectroscopy sensors (UV-VIS) have been installed that measure equivalent concentration values of spectroscopy sensors (UV-VIS) have been installed that measure equivalent concentration values of wastewater quality parameters: total suspended solids (TSS), chemical oxygen demand (COD), and wastewater quality parameters: total suspended solids (TSS), chemical oxygen demand (COD), and filtered COD (CODf), i.e., the dissolved fraction of COD, at an interval of 2 min. In addition, flow is filtered COD (CODf), i.e., the dissolved fraction of COD, at an interval of 2 min. In addition, flow is recorded every minute at these locations and ammonium (NH4, using Hach Lange Amtax sensors) at recorded every minute at these locations and ammonium (NH4, using Hach Lange Amtax sensors) the Eindhoven Stad and Riool Zuid catchments. In this study, monitoring data for the year 2012 was at the Eindhoven Stad and Riool Zuid catchments. In this study, monitoring data for the year 2012 used. was used. The monitoring data were validated manually, focusing on obtaining reliable data for calibration The monitoring data were validated manually, focusing on obtaining reliable data for calibration of of wet weather flow processes. Figure 2 shows an example of data and their evaluation. After wet weather flow processes. Figure2 shows an example of data and their evaluation. After validation, validation, only 38.5% of the data was considered to have an acceptable quality during the condition required. This percentage of data perceived ‘good enough’ after validation may seem relatively low.

Water 2017, 9, 491 4 of 18

Water 2017, 9, 491 4 of 18 only 38.5% of the data was considered to have an acceptable quality during the condition required. ThisDuring percentage earlier research of data projects perceived (2007–2008) ‘good enough’ at WWTP after Eindhoven validation on may UV-VIS seem sensors, relatively the low. percentage During ofearlier ‘good research enough’ projects data after (2007–2008) data validation at WWTP ranged Eindhoven between on UV-VIS 50% and sensors, 75%, thedespite percentage very intensive of ‘good maintenanceenough’ data afterand datasurveillance validation [23] ranged and betweenwithout 50%restrictions and 75%, on despite the influent very intensive conditions. maintenance WWTP influentand surveillance has shown [23 ]to and be withouta very difficult restrictions medium on the for influent water conditions. quality monitoring. WWTP influent The dataset has shown after validationto be a very comprises difficult mediumapproximately for water 30 storm quality events monitoring. with good The data dataset for each after calibration validation performed. comprises Inapproximately the model calibration, 30 storm events these with events, good including data for eachthe antecedent calibration performed.dry day and In several the model following calibration, dry days,these events,were used. including In Figure the antecedent2, and all other dry dayFigures, and severalthe data following used for calibration dry days, were is represented used. In Figure by the2, darkand all grey other bullets, Figures, data the not data used used for calibration for calibration with islight represented grey bullet bys.the An darkassessment grey bullets, of routine data 24 not h waterused for quality calibration samples with of WWTP light grey influent bullets. showed An assessment that the DWF of routine does not 24 hshow water a noticeable quality samples seasonal of WWTPpattern. influent showed that the DWF does not show a noticeable seasonal pattern.

Figure 2. Example of quality evaluation of monitoring data.

2.3. Data Analysis In earlier work [16], [16], a part of this datadata setset was used to studystudy thethe dynamicsdynamics of wastewater composition. ThisThis resulted resulted in wellin well described described typical typical diurnal diurnal patterns patterns during DWFduring and DWF typical and dynamics typical dynamicsduring WWF during (Figure WWF3). (Figure 3).

Figure 3. Wet weather flow (WWF) dynamics during the stages of a storm event on 12 June 2008 in Figure 3. Wet weather flowflow (WWF) dynamics during the stages of a storm event on 12 June 2008 in Eindhoven Stad catchment. Eindhoven Stad catchment.

WaterWater2017 2017, 9, ,9 491, 491 55 of of 18 18

For WWF, it has been observed that the concentration levels of the wastewater show a typical patternFor WWF,during it a has storm been event: observed a short that period the concentration called ‘onset’ levels of the of storm the wastewater event, with show an aincreased typical patternconcentration during level a storm for event:particulate a short matter period but called not ‘onset’for dissolved of the stormmatter, event, a longer with anperiod increased called concentration‘dilution’, where level dilution for particulate of both matter dissolved but not and for dissolvedparticulate matter, matter a longertakes place, period and called ‘recovery’, ‘dilution’, a whereperiod dilution where dissolved of both dissolved and particulate and particulate matter slowly matter return takes to place, DWF and levels. ‘recovery’, a period where dissolved and particulate matter slowly return to DWF levels. 2.4. Model Development 2.4. Model Development The general idea behind the model development is that the measured hydraulic influent data, i.e., Theflow general and water idea level behind in the the influent model pumping development station, is that can the be used measured to make hydraulic a distinction influent between data, i.e.,the flowfour andpatterns: water DWF, level onset in the of influent WWF, pumpingdilution du station,ring WWF can beand used recovery to make after a distinction WWF. Each between of these thepatterns four patterns: is denoted DWF, as a onsetsystem of state, WWF, during dilution which during a certain WWF relation and recovery between after flow WWF. and Eachconcentration of these patternslevel applies. is denoted This allows as a system the incorporation state, during of which the contribution a certain relation of in-sewer between stocks flow on and top concentration of the mixing levelprocess applies. between This allowswastewater the incorporation and stormwater. of the The contribution latter is ofa common in-sewer stocksfeature on of top influent of the mixingmodels processapplied between to simulate wastewater both dry and and stormwater. wet periods, The while latter explicitly is a common accounting feature of for influent the contribution models applied of in- tosewer simulate stocks both circumventing dry and wet the periods, relatively while limi explicitlyted knowledge accounting associated for the in contributionsewer processes. of in-sewer stocksThe circumventing water quality the average relatively dry limited weather knowledge diurnal pattern associated is the in core sewer of processes.the model. As long as the systemThe state water is quality‘DWF’, average the average dry weatherdry weather diurnal diurnal pattern pattern is the based core of on the monitoring model. As data long is as used, the systemtogether state with is the ‘DWF’, measured the average flow data. dry weatherThe aver diurnalage dry pattern weather based diurnal on monitoringpattern has databeen isderived used, togetherfrom flow with monitoring the measured data flowby averaging data. The the average monitori dryng weather data of diurnal 10 dry patterndays over has 5 been min derivedintervals from with flowthe same monitoring timestamp. data by averaging the monitoring data of 10 dry days over 5 min intervals with the same timestamp.During wet weather, the model superimposes a number of processes on the DWF pattern for waterDuring quality wet to weather,mimic onset, the modeldilution, superimposes and recovery. a numberThe type of of processes parameter on (NH the4 DWF or COD) pattern and forthe watertype of quality event to(small, mimic medium onset,dilution, or large) anddetermine recovery. wh Theich of type these of processes parameter is (NH to be4 orapplied. COD) The and type the typeof event of event is used (small, as characteristic medium or large) of a storm determine event, which as it was of these found processes that the isrelation to be applied.between The flow type and ofconcentration event is used levels as characteristic differs very of amuch storm event,between as itsmall, was foundmedium, that theand relation large storm between events. flow andThe concentrationmeasured hydraulics, levels differs in this very case much the betweenflow and small, water medium, level in the and influent large storm pumping events. station, The measured are used hydraulics,to determine in thiswhich case ofthe the flow described and water processes level inshould the influent be activated pumping in the station, mode arel, using used the to determine scheme of whichFigure of 4. the described processes should be activated in the model, using the scheme of Figure4.

yes

DWF, process 1

no

yes

DWF, process 1

no

yes ∩ small event, process 6 dilution and restoration

no

yes ∩ medium event, process 2 dilution, process 3 dilution during onset, process 5 first flush during onset (for COD only) and process 4 recovery

no

yes large event, process 2 dilution, process 3 dilution during onset, process 5 first flush during onset (for COD only) and process 4 recovery

Figure 4. Selection of water quality processes to be superimposed on process 1 during dry weather Figure 4. Selection of water quality processes to be superimposed on process 1 during dry weather (DWF), using information on hydraulics. The abbreviation Th in the figure is short for threshold. (DWF), using information on hydraulics. The abbreviation Th in the figure is short for threshold.

Water 2017, 9, 491 6 of 18

As indicated in Figure4, two conditions have to be met to change from DWF to WWF. The first is that the upper limit for dry weather conditions (QDWF, set at the 95th percentile of the flow values collected during dry weather at a specific timestamp) has to be exceeded, the second that the volume should exceed a certain threshold (set at 5000 m3). The second condition is added to exclude apparent events in the data caused by interference of the pump operation due to for example to maintenance. The value of 5000 m3, equivalent to the volume of 2 h of DWF, shown to be sufficient to filter flow values exceeding QDWF due to operational issues during DWF. A small storm event is defined as an event for which the water level in the influent chamber does not rise above the DWF threshold value (set at 11.30 m AD) and the flow exceeds the 95 percentile DWF value with less than a threshold set at 4000 m3/h These events are very small storm events, where the inflow is less than 0.2 mm/h or 2 m3/ha). Medium events are defined as events where the water level in the influent chamber does not exceed the DWF threshold value, but the flow exceeds the 95 percentile DWF value with more than the threshold. These events are typically relatively small, low intensity storm events, where the inflow is less than the available pumping capacity (which is equal to an interceptor capacity of 0.7 mm/h or 7 m3/ha). Large storm events are defined as events during which not only flow increases, but also the water level in the influent pumping station increases above the DWF threshold value. This occurs only if the sewer system starts filling during bigger storm events exceeding the pumping capacity of the WWTP. The processes applied in the model are: Process 1 the basic process for all parameters, is the DWF pattern for water quality. It is derived from high-frequency monitoring data collected during multiple dry weather days, by averaging over the same time stamps. Process 2 mimics dilution and is based on the ratio between the actual flow (Qactual) and the upper limit for the flow during DWF at that time of the day at the location of the WWTP inlet works (QDWF). The wastewater concentration is calculated using Formula (1):

CWWF(t) = CDWF(t) (a1 QDWF(t)/Qactual(t) − a1 + 1) (1)

With CWWF = calculated concentration during wet weather, and CDWF = the concentration during DWF conditions at that time of the day. The dilution factor a1 (-) is introduced to allow adjustment to the dilution rate if necessary. A value of 1 for factor a1 indicates that the dilution is exactly inverse to the increase in flow. A value of a1 smaller than 1 would impose an increase in pollutant loads during the event, which could be necessary to account for pollutant contributions originating from in-sewer stocks. A value of a1 larger than 1 would impose a decrease in pollutant loads during the event, which could be expected for a compound where in-sewer stocks are zero and a part of the pollutants would be discharged via a CSO. For low dilution ratios, i.e., QDWF(t)/Qactual(t) being close to 1, the factor a1 has a limited influence, for higher dilution ratios, the factor a1 contributes to a larger extent. Process 3 accounts for dilution during the onset of storm events. Process 3 is described by a parabolic function, valid for the period between the start of the storm event and the moment of the maximum dilution. The length of this period, the duration of the onset a3, is determined during model calibration. This process is necessary to account for the delayed dilution observed in the monitoring data, see Figure5. During the first part of the event on 28 July 2012, the influent flow increased 3 rapidly to the maximum flow rate of 14,000 m /h, while the NH4 concentration gradually reduced to a minimum of 5 mg NH4/l. Using Formula (1) during the onset of the storm event, would result in an overestimation of the dilution. Instead, Formula (3) applies during the onset of the storm event:

2 2 CWWF(t) = CDWF(t) × (dilution depth/a2 ) × (t − tend onset) - dilution depth + 1 (2) where a2 = duration of onset and dilution depth = the minimal ratio CDWF(t)/CWWF(t) during the onset of the storm event. Figure5 shows how the parameters in the parabolic function of Formula (2) are defined. Water 2017, 9, 491 7 of 18 Water 2017, 9, 491 7 of 18

Figure 5.5.Parameters Parameters of parabolicof parabolic function function that describesthat describes the delayed the delayed dilution ofdilution the quality of the parameters quality comparedparameters to compared the flow. to the flow.

Process 4 reproduces restoration, which describes the gradual return of concentration values to Process 4 reproduces restoration, which describes the gradual return of concentration values to DWF values after the storm event. Based on the analysis of the available data set, restoration can be DWF values after the storm event. Based on the analysis of the available data set, restoration can be assumed to be a linear process at rate a3 (mg/(L·s)) until the concentration returns to the DWF value. assumed to be a linear process at rate a (mg/(L·s)) until the concentration returns to the DWF value. During the restoration phase, the concentration3 is calculated by: During the restoration phase, the concentration is calculated by: CWWF(t + 1) = CWWF(t) (1 + a3) dt. (3) C (t + 1) = C (t) (1 + a ) dt. (3) Process 5 describes a first flushWWF in concentrationWWF levels of 3particulate material (see Figure 3), it is thus not valid for soluble substances. This initial peak increases the concentrations during the first Process 5 describes a first flush in concentration levels of particulate material (see Figure3), it stage of storm events, before dilution becomes the dominant process. Process 5 is modeled as a is thus not valid for soluble substances. This initial peak increases the concentrations during the triangle that causes an instant increase of the COD concentration of a4 mg/l at the onset of the event, first stage of storm events, before dilution becomes the dominant process. Process 5 is modeled as a decreasing with a fixed rate a5 (mg/(L·s)). triangle that causes an instant increase of the COD concentration of a4 mg/l at the onset of the event, Process 6 regards dilution and restoration for small events. Process 6 describes the concentration decreasing with a fixed rate a5 (mg/(L·s)). profile as a fixed-shape triangle, where dilution takes place at a fixed rate a6 (mg/(L·s)) during x h and Process 6 regards dilution and restoration for small events. Process 6 describes the concentration recovery at the same rate a6 (mg/L/s) during the next x h. In the case of Eindhoven Stad and Riool profile as a fixed-shape triangle, where dilution takes place at a fixed rate a6 (mg/(L·s)) during x h and Zuid a duration of 13 h proved to be a good estimate of the duration of process 6. recovery at the same rate a6 (mg/L/s) during the next x h. In the case of Eindhoven Stad and Riool Zuid a duration of 13 h proved to be a good estimate of the duration of process 6. 2.5. Model Calibration 2.5. ModelIn this Calibration study the differential evolution adaptive metropolis (DREAM) algorithm is the method [30,31]In applied this study to calibrate the differential the parameters evolution of the adaptive empirical metropolis model to (DREAM)find the minimal algorithm difference is the methodbetween [ 30the,31 empirical] applied model to calibrate output the and parameters the monito of thering empirical data. The model effectiveness to find the of minimal DREAM difference in water betweenrelated model the empirical calibration model has outputbeen demonstrat and the monitoringed in many data. previous The effectiveness studies, e.g., of[32–34]. DREAM in water relatedTable model 1 shows calibration the model has beenparameters, demonstrated units and in the many searching previous range studies, for the e.g., calibration [32–34]. procedure. The thresholdTable1 shows values the modelfor selecting parameters, the type units of andeven thet were searching derived range during for the data calibration analysis procedure.before the Thecalibration threshold of the values model for parameters selecting the and type were of eventconsequently were derived not included during in data theanalysis model calibration. before the calibrationFuture users of of the the model model parameters on other catchments and were consequentlymay include notthese included parameters in the as modelpart of calibration. the model Futurecalibration. users For of reasons the model of clarity, on other these catchments parameters may are include listed here: these parameters as part of the model calibration.VTh: threshold For reasons value of for clarity, making these distinction parameters between are listed real here: storm events and irregularities in the DWF due to operational issues. In this study set at equivalent of 2 h of DWF. VTh: threshold value for making distinction between real storm events and irregularities in the DWFQ dueTh: threshold to operational value issues. to distinguish In this study medium set at equivalentfrom small ofstorm 2 h of events. DWF. Set in this study at an equivalent of 0.2 mm/h of runoff. QTh: threshold value to distinguish medium from small storm events. Set in this study at an equivalenthTh: threshold of 0.2 mm/h value of to runoff. distinguish large from medium storm events. Set in this study at 0.30 m above the setpoint of the frequency controlled pumps. hTh: threshold value to distinguish large from medium storm events. Set in this study at 0.30 m abovex: theduration setpoint of ofdilution the frequency and restoration controlled for pumps.small events: Set in this study at 13 h. x: duration of dilution and restoration for small events: Set in this study at 13 h.

Water 2017, 9, 491 8 of 18

Table 1. Model parameters, units, and search range. COD = chemical oxygen demand.

Model Parameter Abbreviation Unit Search Range Parameter

dilution factor a1 - 0–2 NH4, COD dilution delay factor a2 minutes 0–600 NH4, COD recovery factor a3 mg/(L·s) 0–0.01 NH4, COD Water 2017, 9, 491 8 of 18 peak first flush concentration a4 mg/l 0–2000 COD · recovery factor firstTable flush 1. Model parameters, a 5units, and search mg/(Lrange. CODs) = chemical oxygen 0–10 demand. COD recovery factor small events a6 mg/(L·s) 0–0.01 NH4, COD Model Parameter Abbreviation Unit Search Range Parameter dilution factor a1 - 0–2 NH4, COD The calibration isdilution performed delay factor using 5000 iterations a2 inminutes DREAM for0–600 the CODNH model4, COD and 2500 for the recovery factor a3 mg/(L·s) 0–0.01 NH4, COD NH4 model, as itpeak was first found flush concentration from test runs that a4 the cumulativemg/l density0–2000 functionsCOD of the parameters do not change (withinrecovery the factor parameter first flush stability) a5 after amg/(L·s) few thousand 0–10 iterations. COD The last 50% of the iterations are usedrecovery for further factor small analysis: events the optimal a6 parametermg/(L·s) set0–0.01 and modelNH output4, COD are derived, and the model is runThe with calibration all these is performed parameter using sets 5000 to iterations determine in DREAM the 95% for the confidence COD model intervals and 2500 for the NH4 and COD concentrations.the NH4 model, as it was found from test runs that the cumulative density functions of the parameters do not change (within the parameter stability) after a few thousand iterations. The last 50% of the 3. Resultsiterations and Discussion are used for further analysis: the optimal parameter set and model output are derived, and the model is run with all these parameter sets to determine the 95% confidence intervals for the NH4 This sectionand COD presents concentrations. an overview of the model results, a discussion of their quality and the transferability of the model concept. The model was first developed, tested and calibrated on data of 3. Results and Discussion Eindhoven Stad only and the data from the subcatchment Riool Zuid were used to be able to discuss the transferabilityThis ofsection the concept.presents an overview of the model results, a discussion of their quality and the transferability of the model concept. The model was first developed, tested and calibrated on data of Eindhoven Stad only and the data from the subcatchment Riool Zuid were used to be able to discuss 3.1. Calibration Results the transferability of the concept. The DREAM algorithm was applied with a total of 5000 iterations for the COD model and 2500 3.1. Calibration Results for the NH4 model. The algorithm uses 2 × n Markov Chains, with n being the number of model The DREAM algorithm was applied with a total of 5000 iterations for the COD model and 2500 parameters being evaluated. This resulted in 312 iterations for the COD model and 208 iterations for for the NH4 model. The algorithm uses 2 × n Markov Chains, with n being the number of model the NH4 model.parameters Figure being6 shows evaluated. the This variation resulted in in model312 iterations parameter for the COD values model during and 208 the iterations calibration for process for the modelthe NH for4 model. NH4 forFigure catchment 6 shows the Eindhoven variation in Stad model for parameter the first values Markov during Chain the calibration of each iteration. process for the model for NH4 for catchment Eindhoven Stad for the first Markov Chain of each Parameters concerning medium and large storm events are denoted in Figure6 as subscripts M and iteration. Parameters concerning medium and large storm events are denoted in Figure 6 as L respectively. The value of each of the model parameters is relatively stable during the calibration subscripts M and L respectively. The value of each of the model parameters is relatively stable during process, showingthe calibration that theprocess, number showing of that iterations the number was of sufficient iterations was to converge.sufficient to converge.

Figure 6. Parameter values during model calibration. For each iteration, only the first Markov Chain Figure 6. Parameter values during model calibration. For each iteration, only the first Markov Chain of of the parameter set is shown. the parameter set is shown. The correlation between the model parameters was found to be limited from Figure 7, showing a high identifiability of the model parameters. The correlation between the model parameters was found to be limited from Figure7, showing a high identifiability of the model parameters. Water 2017, 9, 491 9 of 18 Water 2017, 9, 491 9 of 18

Figure 7. PosteriorPosterior distribution distribution of of model parameters a 1 toto a 6 for the NH4 model for catchment Eindhoven Stad based on the secondsecond 50% of thethe iterations.iterations. The histograms represent the posterior distribution ofof individual individual model model parameters parameters and and the scatterthe scatter plots plots represent represent the relationships the relationships for various for variouscombinations combinations of parameters. of parameters.

The model parameter values are shown in Table 2 for the NH4 and COD model. For the NH4 The model parameter values are shown in Table2 for the NH 4 and COD model. For the NH4 model, there is no strong need to make a distinction between large and medium storms, as the model parameters are rather similar. For COD, however, the model parameters differ strongly for large and medium storm events. A A value value of 1 of the dilution factor would mean no contribution of in-sewer stocks and only perfect dilution, values below 1 woul wouldd indicate a contribution of in-sewer stocks. The values for the dilution factor for NH4 are just below 1, indicating that for NH4 the contribution of in values for the dilution factor for NH4 are just below 1, indicating that for NH4 the contribution of sewer stocks is relatively limited. For the COD, however, the values of a1 are quite low. A value for in sewer stocks is relatively limited. For the COD, however, the values of a1 are quite low. A value a1 of approximately 0.5 leads to CWWF = 0.57 × CDWF based on Formula (1) and the maximum ratio for a1 of approximately 0.5 leads to CWWF = 0.57 × CDWF based on Formula (1) and the maximum between Qactual and QDWF (15,000/2100 = 7.1). This means that at a flow of 15,000 m3/h, the concentration3 ratio between Qactual and QDWF (15,000/2100 = 7.1). This means that at a flow of 15,000 m /h, the in the WWTP influent is still 0.57 × CDWF. Consequently, the influent load at that moment will be concentration in the WWTP influent is still 0.57 × CDWF. Consequently, the influent load at that momentapproximately will be 4 approximately (7.1 × 0.57) times 4 (7.1 the× 0.57)DWF timesload. theThis DWF peak load. load This factor peak was load observed factor was regularly observed in regularlymonitoring in data monitoring for this datacatchment for this [23]. catchment [23].

Table 2. Model parameters values for NH4 and COD model for Eindhoven Stad Catchment. Subscript Table 2. Model parameters values for NH4 and COD model for Eindhoven Stad Catchment. Subscript M and L in model parameters denote medium and large storm events. M and L in model parameters denote medium and large storm events.

Model Parameter Abbreviation NH4 Model COD Model Model Parameter Abbreviation NH4 Model COD Model dilution factor, large storms a1,L 0.95 (-) 0.63 (-) dilutiondilution delay factor, factor, large large storms storms a1,L a2,L 0.95 123 (-)(min) 342 0.63 (min) (-) dilution delay factor, large storms a2,L 123 (min) 342 (min) dilution factor, medium storms a1,M 0.82 (-) 0.47 (-) dilution factor, medium storms a1,M 0.82 (-) 0.47 (-) dilution delay factor, medium storms a2,M 115 (min) 589 (min) dilution delay factor, medium storms a2,M 115 (min) 589 (min) recoveryrecovery factor factor a3 a3 0.00025 0.00025 (mg/(L (mg/(L·s))·s)) 0.00014 0.00014 (mg/(L (mg/(L·s))·s)) peakpeak firstfirst flushflush concentration concentration a4 a4 Not Not applicable applicable 48 48(mg (mg COD/(L COD/(L·s))·s)) recovery factor first flush a Not applicable 0.19 (mg COD/(L·s)) recovery factor first flush 5 a5 Not applicable 0.19 (mg COD/(L·s)) recovery factor small events a6 0.00059 (mg/(L·s)) 0.00017 (mg/(L·s)) recovery factor small events a6 0.00059 (mg/(L·s)) 0.00017 (mg/(L·s))

Water 2017, 9, 491 10 of 18 Water 2017, 9, 491 10 of 18 3.2. Model Results 3.2.3.2. Model Results Figure 8 shows the resulting predicted water quality and the measured water quality for NH4 in Figure 8 shows the resulting predicted water quality and the measured water quality for NH4 in the WWTPFigure 8influent shows thefor Eindhoven resulting predicted Stad. water quality and the measured water quality for NH 4 in thethe WWTPWWTP influentinfluent forfor EindhovenEindhoven Stad.Stad.

Figure 8. Model vs. monitoring data: NH4 concentration in the wastewater treatment plant (WWTP) influent.FigureFigure 8. ModelModel vs. vs. monitoring monitoring data: data: NH4 concentration NH4 concentration in the wastewater in the wastewater treatment treatment plant (WWTP) plant (WWTP)influent. influent. The results show that the dynamics in the model (solid black line) and the monitoring data (grey dots)The Theshow results an overall showshow thatgoodthat the agreement dynamics in inin terms the model of dynamics (solid black and line)values and du thering monitoring wet weather data during (grey thedots)dots) large showshow events anan overalloverall of 28 and goodgood 29 agreement agreementJuly. In the inin monitoring termsterms ofof dynamicsdynamics data, dilution andand values valuesstarts a duringdu littlering bit wetwet earlier weatherweather than duringduring in the model.thethe large During events the of of medium28 28 and and 29 29 event July. July. onIn In the31 the July,monitoring monitoring the mo deldata, data, fit dilution is dilution less satisfying. starts starts a little a During little bit bitearlier dry earlier weather than than in (25the in model. During the medium event on 31 July, the model fit is less satisfying. During dry weather (25 Julythe model. till 28 July), During the the daily medium variation event in the on 31measured July, the concentration model fit is less of satisfying.NH4 is represented During dry well weather by the July till 28 July), the daily variation in the measured concentration of NH4 is represented well by the model.(25 July The till 28 remaining July), the differences daily variation are indue the to measured the fact that concentration the DWF dynamics of NH4 is in represented the model well represent by the themodel.model. average TheThe remainingremainingDWF concentration differences differences levels are are due due and to to thethe the fact DWF fact that that varies the the DWF perDWF dynamicsday. dynamics The inroot thein meanthe model model squared represent represent error the the average DWF concentration levels and the DWF varies per day. The root mean squared error (RMSE)average for DWF the concentration NH4 model based levels on and the the data DWF used varies in the per calibration day. The root is 6.3 mean mg squaredNH4/l, or error nearly (RMSE) 16% (RMSE) for the NH4 model based on the data used in the calibration is 6.3 mg NH4/l, or nearly 16% relatedfor the NHto the4 model mean basedDWF onconcentration. the data used Figure in the 9 calibrationshows the isnormalized 6.3 mg NH cumulative4/l, or nearly density 16% related function to related to the mean DWF concentration. Figure 9 shows the normalized cumulative density function (CDF)the mean of the DWF model concentration. results and Figure the monitoring9 shows the data normalized for NH4 and cumulative COD. Both density the RMSE function and (CDF) the CDF of (CDF) of the model results and the monitoring data for NH4 and COD. Both the RMSE and the CDF arethe modelbased on results the entire and the dataset monitoring used for data modelling, for NH4 and which COD. includes Both the all RMSEstorm andevents the with CDF aresufficient based dataonare the based quality entire on datasetandthe entirethe used dry dataset fordays modelling, usedpreceding for whichmodelling, and includesfollo whichwing all theincludes storm storm events all event. storm with As sufficientevents expected, with data sufficientthe quality high concentrations,anddata thequality dry daysand which precedingthe dryoccur days during and preceding following DWF, areand the not stormfollo capturedwing event. the very As storm expected,well event. due theto As the high expected, daily concentrations, variation the high in DWFwhichconcentrations, concentrations. occur during which DWF, At occur lower are notduring co capturedncentration DWF, very are levels, wellnot captured duethe toagreement the very daily well between variation due to model in the DWF daily and concentrations. variationmonitoring in dataAtDWF lower is concentrations. reasonable. concentration At levels, lower the co agreementncentration between levels, the model agreement and monitoring between datamodel is reasonable.and monitoring data is reasonable.

Figure 9. CDFs of model results and measurements for NH4 and COD in WWTP influent for the Figure 9. CDFs of model results and measurements for NH4 and COD in WWTP influent for the Figure 9. CDFs of model results and measurements for NH4 and COD in WWTP influent for the Eindhoven Stad (ES) catchment. Eindhoven Stad (ES) catchment.

Water 2017, 9, 491 11 of 18 Water 2017, 9, 491 11 of 18

TheThe CODCOD modelmodel alsoalso incorporatesincorporates processprocess 55 describingdescribing thethe peakpeak firstfirst flushflush concentrationconcentration thatthat waswas observedobserved inin thethe monitoringmonitoring data,data, seesee FigureFigure3 .3. The The model model results results for for the the COD COD model model for for the the EindhovenEindhoven StadStad catchmentcatchment areare shownshown inin FigureFigure 1010.. AsAs expected,expected, thethe modelmodel fitfit isis notnot asas goodgood asas thethe modelmodel fit fit for for NH NH4, which4, which is partly is partly due todue the to difference the difference in the quality in the ofquality the monitoring of the monitoring data, illustrated data, byillustrated the outliers by the in theoutliers monitoring in the monitoring data shown data in Figure shown 10 in and Figure partly 10 dueand topartly the factdue that to the modelling fact that suspendedmodelling suspended solids is much solids more is much difficult more than difficult modelling than modelling of solutes. ofThe solutes. RMSE The for RMSE the COD for the model COD basedmodel on based monitoring on monitoring data used data in used the calibration in the calibration is 109 mg is 109 COD/l, mg COD/l, equivalent equivalent with 18% with of 18% the meanof the DWFmean concentration. DWF concentration. This RMSE This RMSE for COD for is COD in relative is in relative terms comparableterms comparable to the RMSEto the RMSE for NH for4. NH4.

Figure 10. Model vs. monitoring data: CODtotal in the WWTP influent for Eindhoven Stad. The small Figure 10. Model vs. monitoring data: CODtotal in the WWTP influent for Eindhoven Stad. The small peaks in influent concentration (typically referred to as ‘first flush’) at the beginning of storm events peaks in influent concentration (typically referred to as ‘first flush’) at the beginning of storm events on on 4 June, 6 June and 8 June are adequately represented by the model. 4 June, 6 June and 8 June are adequately represented by the model.

The influent model has been developed to be used to deliver input for WWTP models that is reliableThe enough influent to model assess hasWWTP been performance developed toand be to used assess to deliverthe impact input of measures, for WWTP such models as real that time is reliablecontrol (RTC) enough in towastewater assess WWTP systems. performance An earlier andversion to assess of this the influent impact model of measures, presented such has already as real timebeen controlused for (RTC) this purpose in wastewater in the KALLISTO systems. An project earlier at versionwater board of this De influent Dommel model [26,28]. presented The current has alreadyversion beenis applied used forin the this assessment purpose in of the the KALLISTO performance project of the at water smart board buffer De concept Dommel at [WWTP26,28]. The current version is applied in the assessment of the performance of the smart buffer concept at Eindhoven [29]. The values for the RMSE for NH4 just meet the quality requirements for WWTP WWTPinfluent Eindhoven data derived [29 by]. The[35], values while forfor theCOD RMSE they foreasily NH meet4 just these meet requirements. the quality requirements This shows that for WWTPthe influent influent model data is derived sufficiently by [35 good], while for the for described COD they modelling easily meet purposes. these requirements. This shows that the influent model is sufficiently good for the described modelling purposes. 3.3. Transferability of the Concept 3.3. Transferability of the Concept The structure of the influent model was developed for the catchment Eindhoven Stad (ES) only. The structure of the influent model was developed for the catchment Eindhoven Stad (ES) only. The data from the catchment Riool Zuid (RZ) were used to verify the concept, using the same routines The data from the catchment Riool Zuid (RZ) were used to verify the concept, using the same routines for calibration. With respect to the transferability, it has to be noted that the subcatchments ES and for calibration. With respect to the transferability, it has to be noted that the subcatchments ES and RZ RZ are independent catchments, allowing the transferability of the concept to be tested. are independent catchments, allowing the transferability of the concept to be tested. The model parameters are shown in Table 3. For catchment RZ, the model parameters for The model parameters are shown in Table3. For catchment RZ, the model parameters for medium medium and large storms are very similar for both the NH4 and COD model, showing that this and large storms are very similar for both the NH and COD model, showing that this distinction distinction between large and medium events is4 not necessary for this catchment. The model between large and medium events is not necessary for this catchment. The model parameter values for parameter values for the dilution factor a1 for the RZ catchment show a strong similarity with the the dilution factor a1 for the RZ catchment show a strong similarity with the model parameters for the model parameters for the ES catchment. For NH4, the dilution during the storm event, calculated by ES catchment. For NH , the dilution during the storm event, calculated by Formula (1), remains nearly Formula (1), remains 4nearly reciprocal to the increase in influent flow during the storm event. This reciprocal to the increase in influent flow during the storm event. This indicates that during the storm indicates that during the storm event, nearly all nitrogen in the WWTP influent stems from the event, nearly all nitrogen in the WWTP influent stems from the wastewater, with only very limited wastewater, with only very limited contributions from the rainfall runoff and the in-sewer stocks. contributions from the rainfall runoff and the in-sewer stocks.

Water 2017, 9, 491 12 of 18 Water 2017, 9, 491 12 of 18

Table 3. Model parameters values for NH4 and COD model for Riool Zuid Catchment. Subscript M

and L in model parameters denote medium and large storm events. Table 3. Model parameters values for NH4 and COD model for Riool Zuid Catchment. Subscript M and LModelin model Paramete parametersr denoteAbbreviation medium and large storm NH events.4 Model COD Model dilution factor, large storms a1,L 0.96 (-) 0.49 (-) dilution delayModel factor, Parameter large storms Abbreviation a2,L 373NH 4(min)Model COD 590 Model (min)

dilutiondilution factor, factor, medium large storms storms a1,M a 1,L 0.980.96 (-) (-) 0.49 0.49 (-) (-) dilutiondilution delay delay factor, largemedium storms a2,L 373 (min) 590 (min) a2,M 427 (min) 548 (min) dilution factor,storms medium storms a1,M 0.98 (-) 0.49 (-) dilution delay factor, medium storms a2,M 427 (min) 548 (min) recovery factor a3 0.00033 (mg/(L·s)) 0.00034 (mg/(L·s)) recovery factor a3 0.00033 (mg/(L·s)) 0.00034 (mg/(L·s)) peakpeak first first flush flush concentration concentration a4 a4 NotNot applicable applicable 60 60 (mg (mg COD/(L COD/(L·s))·s)) recoveryrecovery factor factor first first flush flush a5 a5 NotNot applicable applicable 0.06 0.06 (mg (mg COD/(L COD/(L·s))·s)) recovery factor small events a 0.00027 (mg/(L·s)) 0.00002 (mg/(L·s)) recovery factor small events a6 6 0.00027 (mg/(L·s)) 0.00002 (mg/(L·s))

For the COD, the dilution factor of a 1 ofof 0.49 0.49 results results in in COD COD concentration concentration levels during the high flowflow period of storm events of between 250 and 300300 mgmg COD/LCOD/L and, and, as as a a consequence, consequence, high influent influent peak loads.loads. ThisThis additional additional load load arriving arriving via thevia influentthe influent at the WWTPat the WWTP during aduring storm eventa storm originates event originatesmainly from mainly the in-sewer from the stocks in-sewer [15], givenstocks the [15], fairly given low the COD fairly concentration low COD concentration in Dutch stormwater in Dutch of stormwater61 mg COD/L of 61 [36 mg]. COD/L [36]. The overalloverall model model performance performance for thefor RZthe catchment, RZ catchment, expressed expressed in terms in of RMSE,terms isof comparable RMSE, is comparablewith the performance with the forperformance the ES catchment. for the ES The catchment. RMSE amounts The RMSE to 8.9 mgamounts NH4/L, to equivalent8.9 mg NH with4/L, equivalent22% of the meanwith 22% DWF of valuethe mean for the DWF NH value4 model for andthe toNH 1264 model mg COD/L, and to 126 equivalent mg COD/L, with equivalent 25% of the withmean 25% DWF of the value mean for DWF the COD value model. for the As COD for model. Eindhoven As for Stad, Eindhoven the cumulative Stad, the density cumulative function density for functionmodel results for model and monitoring results and data monitoring show reasonable data show agreement reasonable for agreement both NH4 forand both COD, NH see4 and Figure COD, 11, seewith Figure once again11, with the once biggest again differences the biggest being difference in thes higher being in (DWF) the higher concentration (DWF) concentration ranges. ranges.

Figure 11. CDFsCDFs ofofmodel model results results and and measurements measurements for for NH NH4 and4 and COD COD in WWTP in WWTP influent influent for the for Riool the RioolZuid (RZ)Zuid catchment.(RZ) catchment.

As there was no need to change the model structure, it was concluded that the model is in principle transferable to other catchments, provid provideded that the dynamics during WWF show similar patterns as described in Figure 33.. LiteratureLiterature confirmsconfirms thesethese patternspatterns toto bebe fairlyfairly generalgeneral [[37,38],37,38], A A number of distinct phases in the influentinfluent pollutograph are defineddefined duringduring stormstorm events:events: Phase 1) increase increase of of flow flow rate rate and and subsequently subsequently an an increase increase of theof the load load arriving arriving at theat the WWTP WWTP due due to the to ‘push’the ‘push’ of wastewater of wastewater with DWFwith concentrationDWF concentration levels. Thislevels. phase This is morephase distinct is more the distinct more wastewater the more wastewateris stored downstream is stored downstream in either large in interceptoreither large sewers interceptor or rising sewers mains. or rising mains. Phase 2) increased increased concentration concentration of of suspended suspended solidssolids asas erodederoded sewersewer sedimentssediments start to arrive at the WWTP. These sediments are usually transported transported with with a a velocity velocity lower lower than than the the fluid fluid velocity velocity [14]. [14 ]. Phase 3) arrival arrival of of diluted diluted wastewater wastewater at at the the WWTP. WWTP. Phase 4) return to DWF equilibrium. Equilibrium for dissolved compounds will be reached as soon as all remaining storm runoff has been transported (pumped) towards the WWTP. Reaching

Water 2017, 9, 491 13 of 18

Phase 4) return to DWF equilibrium. Equilibrium for dissolved compounds will be reached as soon as all remaining storm runoff has been transported (pumped) towards the WWTP. Reaching equilibrium for suspended solids may last longer since it takes time before all depressions within the sewer system are filled again with sediment. Phases 1 and 2 are both part of the onset of the storm event, phase 3 is similar to the dilution stage, while phase 4 relates closely to the stage of recovery after the storm events. Despite the need of further research on the transferability, the similarities in system dynamics strongly indicate a wider applicability of the model then just for Eindhoven Stad and Riool Zuid. The consistency in the dilution factors for NH4 and COD for Eindhoven Stad and Riool Zuid (with dilution factors for NH4 just a little smaller than 1, indicating a small contribution of in-sewer stocks and dilution factors for COD around 0.5, indicating a large contribution of in-sewer stocks) demonstrate that the empirical model is able to capture the contribution of in-sewer stocks during the dilution phase of the event adequately. This is an important benefit of the model compared with influent generators reviewed by [7]. The differences in model parameters related to the first flush and recovery after the event seem to be linked to the differences in lay out of the sewer system. Future research is necessary to further elaborate on the relation between parameter values and physical characteristics of the catchment. The amount of in-sewer storage relative to the pumping capacity of the WWTP will likely be related to the length of the recovery period, as these characteristics determine the emptying time of the sewer system, which will be related to the length of the recovery. The differences in performance, although relatively small, can be attributed to the different characteristics of the RZ catchment and possibly also to the limited quality of the sensor data. This is illustrated by Figures 12 and 13. In Figure 12, the results for NH4 are shown for the RZ catchment for the week after 16 July and in Figure 13 for the first two weeks of December 2012. During the events of 17 July and 21 July, the monitoring data show two distinct dilution phases during the events. One dilution phase occurs at the beginning of the storm event and one at the end. This phenomenon does not occur during the storm events of 2 and 4 December, but to a lesser extent on 10 December. The Riool Zuid catchment (the light grey catchments in Figure1, left) has a very different structure compared with ‘Eindhoven Stad’ (the dark colored central catchment in Figure1, left). While the ES catchment is a gravity system draining to one central point, the RZ catchment is 32 km long with a number of subcatchments of various sizes at different distances. It is assumed that the double dip is caused by a difference in transport times for two main areas in this catchment, which causes the concentrations to drop for a second time during a storm event. The double dilution dip is of course driven by rainfall and as a result, the spatial variation in the rainfall is the main explanatory factor for the differences per event. In the model, this effect could be mimicked by dividing the Riool Zuid catchment into two catchment basins, with a cut at pumping station Aalst, see Figure1 (left), and to add the transport time in the transport sewer to one of the basins. However, as the error made in the model results is relatively small due to the low influent flows, this adjustment was not considered necessary at this moment. The base line of the model consists of the mean DWF concentration. Data analysis of available 24 h composite samples of the WWTP influent showed that there was no seasonal trend for NH4 and COD. Despite the absence of a seasonal trend, the mean DWF concentration varied during the monitoring period. Due to a lack of sampling data, it could not be determined whether changes in this DWF concentration level were due to real changes or due to e.g., a temporary drift of the sensor. Differences in the main DWF concentration levels were observed for NH4, e.g., compare the concentration levels on 16 July in Figure 12 (around 40 mg/L) and 1 December in Figure 13 (around 55 mg/L). This difference is even bigger for COD, see Figure 14. The mean DWF, derived from monitoring data, is nearly 500 mg COD/L, while the monitoring data on 2 June are nearly 700 mg COD/L. In this study, the model has been calibrated using the mean DWF derived from all available monitoring data during DWF. Water 2017, 9, 491 14 of 18 WaterWater 2017 2017, ,9 9, ,491 491 1414 of of 18 18

4 FigureFigureFigure 12. 12. 12.Model Model Model vs. vs. vs. monitoring monitoring monitoringdata: data: data: NH NH444 concentration concentrationconcentration in in the the WWTP WWTP influent influent influent catchment catchment catchment Riool-Zuid Riool-Zuid Riool-Zuid betweenbetweenbetween 16 1616 July JulyJuly and andand 23 2323 July. July.July. ‘Double’ ‘Double’‘Double’dilution dilutiondilution dips dipsdips occuroccur atat 1717 JulyJuly around around noon noon andand 1818 18 JulyJuly July aroundaround around midnightmidnightmidnight and andand on onon 21 2121 July JulyJuly at atat 2:00 2:002:00 a.m. a.m.a.m.and andand 12:00 12:0012:00 a.m. a.m.a.m.

4 FigureFigureFigure 13. 13. 13.Model Model Model vs. vs. vs. monitoring monitoring monitoringdata: data: data: NH NH444 concentration concentrationconcentration in in the the WWTP WWTP influent influent influent catchment catchment catchment Riool-Zuid Riool-Zuid Riool-Zuid betweenbetweenbetween 1 1December1 DecemberDecember and andand 15 1515 December. December.December.

FigureFigureFigure 14. 14.14.Model ModelModel vs. vs.vs. monitoring monitoringmonitoring data: data:data: COD CODCOD concentration concentratconcentrationion inin WWTP WWTPWWTP influent influentinfluent catchmentcatchment Riool-Zuid.Riool-Zuid. Riool-Zuid.

Water 2017, 9, 491 15 of 18

Finally, the results shown in this paper are based on NH4 and COD only, where NH4 is representative for solutes predominantly derived from wastewater and COD for parameters for which the in-sewer stocks, i.e., sediment and biofilm, contribute significantly to the pollutant load in the influent during storm events [24]. For WWTP modelling other parameters, such as phosphorous, also need to be taken into account. Total phosphorous is known to exert similar behavior as the COD and consequently, the COD model may be used to recalculate the total phosphorous concentration. Ortho-phosphate, on the other hand, is dissolved and behaves in the sewer like NH4 [37] and consequently, the NH4 model may be used.

3.4. Applications: Influent Generation, Surveillance of Monitoring Equipment and Gap Filling The influent model as described in this paper generates influent water quality dynamics using measured influent hydraulics as input. This application was used in [29] to evaluate the performance of integrated RTC for urban wastewater system Eindhoven. Another application of the influent model is described in [28], where (an earlier version of) the influent model was implemented in the WEST software [28] to generate influent water quality dynamics based on the simulated influent water quantity by the sewer sub model. In this application, a representative DWF curve based on monitoring data was used [28]. It would also have been possible to use harmonic functions for DWF and to use the influent model to complement the time series with WWF dynamics. In other words, the influent model can be applied on measured or simulated hydraulics and may also be applied in combination with the harmonic functions described in the introduction. Moreover, as the empirical influent model is developed to adequately mimic WWF dynamics, it might be included in the phenomenological influent pollutant disturbance scenario generator [9], which is the latest version of the phenomenological model developed by [8], replacing the relatively weak sewer model module of this model. The influent model can also be used for surveillance of monitoring equipment at the inlet of the WWTP. e.g., earlier research has shown that the hydraulic monitoring data at WWTP Eindhoven is very reliable with over 99% good data [23]. Running the influent model continuously on measured hydraulic data and comparing raw monitoring data of the influent water quality with the simulated influent water quality data would allow easy detection of anomalies in the monitoring data. This could be used to alarm operators to check the monitoring equipment. Early detection of problems with sensors will possibly result in a higher yield of good quality data. A final application of the influent model discussed in this paper is gap filling in time series [39]. Figure 15 shows an example of the application of gap filling. The dots show the measured NH4 concentration in the influent of WWTP Eindhoven. The dark grey dots are data that could be used e.g., for assessing the performance of the influent model, the light grey dots show data that are rejected during the validation. The black line shows the simulated concentrations by the influent model. By applying gap filling a continuous time series is generated, the final time series is composed of the dark grey dots and where these are missing data are filled in using the influent model results. For some of the potential applications of the model, such as gap filling or data validation, it is advisable to regularly check the absolute value of the sensor data during DWF to ascertain whether changes in the DWF concentration level are due to real changes or due to a sensor drift. In case these are due to e.g., seasonal variation in the influent concentration levels during DWF, this should be accounted for when applying the influent model. The routine 24-h samples typically available for WWTP influent may be used to check for a seasonal pattern. Water 2017, 9, 491 16 of 18 Water 2017, 9, 491 16 of 18

FigureFigure 15. GapGap filling filling with with the theinfluent influent model. model. Example Example for NH4 forin WWTP NH4 in influent WWTP catchment influent catchmentEindhoven. Eindhoven.

4.4. Conclusions andand OutlookOutlook ModellingModelling ofof influentinfluent qualityquality isis anan increasinglyincreasingly importantimportant tooltool toto enableenable WWTPWWTP modelsmodels toto optimizeoptimize thethe performanceperformance ofof WWTPsWWTPs duringduring wetwet weather.weather. TheThe mainmain issueissue inin modellingmodelling wastewaterwastewater qualityquality duringduring stormstorm eventsevents isis toto accountaccount forfor in-sewerin-sewer stocks,stocks, whichwhich havehave aa varyingvarying contributioncontribution toto thethe wastewaterwastewater quality.quality. NeitherNeither traditionaltraditional sewersewer waterwater qualityquality modelsmodels nornor thethe availableavailable influentinfluent generatorsgenerators areare capablecapable ofof adequatelyadequately addressingaddressing thisthis issue.issue. TheThe proposedproposed empiricalempirical modelmodel isis basedbased onon aa detaileddetailed studystudy ofof thethe observedobserved waterwater qualityquality andand predictspredicts itit byby combiningcombining aa numbernumber ofof actualactual processesprocesses suchsuch asas DWF, DWF, dilution, dilution, restoration, restoration, and and first first flush. flush. Overall, Overall, the the model model shows shows that that it isit ableis able to reasonablyto reasonably predict predict NH NH4 concentration,4 concentration, which which is is a a solute solute substance, substance, as as well well as as toto reasonablyreasonably predictpredict CODCOD concentration,concentration, whichwhich isis toto aa largelarge extentextent associatedassociated withwith particles.particles. TheThe modelmodel structurestructure waswas demonstrateddemonstrated toto bebe transferabletransferable toto aa catchmentcatchment withwith differentdifferent characteristics.characteristics. EindhovenEindhoven Stad Stad is is a largea large catchment catchment with with the the WWTP WWTP located located near near the center, the center, Riool Riool Zuid comprisesZuid comprises of a long of a interceptor long interceptor sewer, sewer, which which drains drains the wastewater the wastewater from seven from municipalitiesseven municipalities with a rangewith a of range catchment of catchment sizes. Due sizes. to spatialDue to variationspatial variation of the rainfall of the andrainfall variation and variation in travel in times, travel ‘double times, dilution’‘double dilution’ dips may dips occur may in theoccur influent in the coming influent from coming Riool from Zuid. Riool Despite Zuid. these Despite different these dynamics different anddynamics characteristics, and characteristics, there was no there need was to adjust no need the modelto adjust structure the model of the structure empirical of influent the empirical model. Futureinfluent research model. inFuture catchments research in sewerin catchments systems in with sewer less systems in-sewer with storage lessvolume in-sewer is storage needed volume to further is exploreneeded theto further transferability explore ofthe the transferability model concept. of the model concept. TheThe modelmodel conceptconcept isis used used in in ongoing ongoing research research to to test test the the performance performance of of RTC RTC of of smart smart buffers buffers at WWTPat WWTP Eindhoven Eindhoven [28 [28].]. The The model model concept concept could could also also be be used used to to fill fill gaps gaps in in time time series series forfor influentinfluent waterwater qualityquality andand bebe usedused forfor advancedadvanced datadata validationvalidation toto detectdetect outliersoutliers andand driftdrift ofof waterwater qualityquality sensors,sensors, asas thesethese sensorssensors areare stillstill veryvery vulnerablevulnerable andand datadata qualityquality controlcontrol remainsremains a a difficult difficult issue. issue.

Acknowledgments:Acknowledgments: TheThe project project is funded is byfunded KRW-innovation by KRW-inno subsidyvation from AgentschapNLsubsidy from (www.agentschapnl. AgentschapNL nl(www.agentschapnl.nl).). The Dutch Foundation The for Dutch Applied Foundation Water Research for Applie (STOWA)d Water is Research engaged (STOWA) in the project is engaged to communicate in the project and publish the research results. to communicate and publish the research results. Author Contributions: Jeroen Langeveld and Remy Schilperoort developed the influent model, Petra Van Daal improvedAuthor Contributions: the model structure Jeroen Langeveld and performed and Remy the model Schilperoort calibration, developed while Tony the influent Flameling model, and Petra Stefan Van Weijers Daal wereimproved involved the model in the developmentstructure and ofperformed the model the and model provision calibration, of data. while Ingmar Tony Nopens Flameling contributed and Stefan to theWeijers gap filling.were involved Jeroen Langeveld in the development wrote the paper.of the model and provision of data. Ingmar Nopens contributed to the gap Conflictsfilling. Jeroen of Interest: LangeveldThe wrote authors the declare paper. no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.

Water 2017, 9, 491 17 of 18

References

1. Benedetti, L.; De Baets, B.; Nopens, I.; Vanrolleghem, P.A. Multi-criteria analysis of wastewater treatment plant design and control scenarios under uncertainty. Environ. Model. Softw. 2010, 25, 616–621. [CrossRef] 2. Rieger, L.; Gillot, S.; Langergraber, G.; Ohtsuki, T.; Shaw, A.; Takács, I.; Winkler, S. Guidelines for Using Activated Sludge Models. In IWA Scientific and Technical Report No. 22; IWA Publishing: London, UK, 2012. 3. Rodriguez-Roda, I.; Sànchez-Marrè, M.; Comas, J.; Baeza, J.; Colprim, J.; Lafuente, J.; Cortes, U.; Poch, M. A hybrid supervisory system to support WWTP operation: Implementation and validation. Water Sci. Technol. 2002, 45, 289–297. [PubMed] 4. Flores-Alsina, X.; Rodríguez-Roda, I.; Sin, G.; Gernaey, K. Multi-criteria evaluation of wastewater treatment plant control strategies under uncertainty. Water Res. 2008, 42, 4485–4497. [CrossRef][PubMed] 5. Nopens, I.; Benedetti, L.; Jeppsson, U.; Pons, M.N.; Alex, J.; Copp, J.B.; Gernaey, K.V.; Rosen, C.; Steyer, J.P.; Vanrolleghem, P.A. Benchmark simulation model No 2: Finalisation of plant layout and default control strategy. Water Sci. Technol. 2010, 62, 1967–1974. [CrossRef][PubMed] 6. Maruejouls, T.; Lessard, P.; Wipliez, B.; Pelletier, G.; Vanrolleghem, P.A. A phenomenological retention tank model using settling velocity distributions. Water Res. 2012, 46, 6857–6867. [CrossRef][PubMed] 7. Martin, C.; Vanrolleghem, P.A. Analysing, completing, and generating influent data for WWTP modelling: A critical review. Environ. Model. Softw. 2014, 60, 188–201. [CrossRef] 8. Gernaey, K.V.; Flores-Alsina, X.; Rosen, C.; Benedetti, L.; Jeppsson, U. Dynamic influent pollutant disturbance scenario generation using a phenomenological modelling approach. Environ. Model. Softw. 2011, 26, 1255–1267. [CrossRef] 9. Flores-Alsina, X.; Saagi, R.; Lindblom, E.; Thirsing, C.; Thornberg, D.; Gernaey, K.V.; Jeppsson, U. Calibration and validation of a phenomenological influent pollutant disturbance scenario generator using full-scale data. Water Res. 2014, 51, 172–185. [CrossRef][PubMed] 10. De Keyser, W.; Gevaert, V.; Verdonck, F.; De Baets, B.; Benedetti, L. An emission time series generator for pollutant release modelling in urban areas. Environ. Model. Softw. 2010, 25, 554–561. [CrossRef] 11. Devisscher, M.; Ciacci, G.; Fé, L.; Benedetti, L.; Bixio, D.; Thoeye, C.; De Gueldre, G.; Marsili-Libelli, S.; Vanrolleghem, P.A. Estimating costs and benefits of advanced control for wastewater treatment plants—The MAgIC methodology. Water Sci. Technol. 2006, 53, 215–223. [CrossRef][PubMed] 12. Talebizadeh, M.; Belia, E.; Vanrolleghem, P.A. Influent generator for probabilistic modeling of nutrient removal wastewater treatment plants. Environ. Model. Softw. 2016, 77, 32–49. [CrossRef] 13. Bertrand-Krajewski, J.-L. Stormwater pollutant loads modelling: Epistemological aspects and case studies on the influence of field data sets on calibration and verification. Water Sci. Technol. 2007, 55, 1–17. [CrossRef] [PubMed] 14. Bertrand-Krajewski, J.-L.; Briat, P.; Scrivener, O. Sewer sediment production and transport modelling: A literature review. J. Hydraul. Res. 1993, 31, 435–460. [CrossRef] 15. Bertrand-Krajewski, J.-L.; Chebbo, G.; Saget, A. Distribution of pollutant mass vs volume in stormwater discharges and the first flush phenomenon. Water Res. 1998, 32, 2341–2356. [CrossRef] 16. Ashley, R.M.; Bertrand-Krajewski, J.L.; Hvitved-Jacobsen, T.; Verbanck, M. Solids in-Sewers; IWA Publishing: London, UK, 2004. 17. Ashley, R.M.; Hvitved-Jacobsen, T.; Bertrand-Krajewski, J.-L. Quo vadis sewer process modelling? Water Sci. Technol. 1999, 39, 9–22. [CrossRef] 18. Willems, P. Random number generator or sewer water quality model? Water Sci. Technol. 2006, 54, 387–394. [CrossRef][PubMed] 19. Willems, P. Parsimonious model for combined sewer overflow pollution. J. Environ. Eng. 2010, 136, 316–325. [CrossRef] 20. Dembélé, A.; Bertrand-Krajewski, J.-L.; Becouze, C.; Barillon, B. A new empirical model for stormwater TSS event mean concentrations (EMCs). Water Sci. Technol. 2011, 64, 1926–1934. [CrossRef][PubMed] 21. Rousseau, D.; Verdonck, F.; Moerman, O.; Carrette, R.; Thoeye, C.; Meirlaen, J.; Vanrolleghem, P.A. Development of a risk assessment based technique for design/retrofitting of WWTPs. Water Sci. Technol. 2001, 43, 287–294. [PubMed] 22. Gruber, G.; Winkler, S.; Pressl, A. Quantification of pollution loads from CSOs into surface water bodies by means of online techniques. Water Sci. Technol. 2004, 50, 73–80. [PubMed] Water 2017, 9, 491 18 of 18

23. Schilperoort, R.P.S. Monitoring as a Tool for the Assessment of Wastewater Quality Dynamics. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands, 2011. 24. Schilperoort, R.P.S.; Dirksen, J.; Langeveld, J.G.; Clemens, F.H.L.R. Assessing characteristic time and space scales of in-sewer processes by analysis of one year of continuous in-sewer monitoring data. Water Sci. Technol. 2012, 66, 1614–1620. [CrossRef][PubMed] 25. 2000/60/EC. Directive of the European Parliament and of the Council Establishing a Framework for Community Action in the Field of Water Policy (2000/60/EC). 23 October 2000. Available online: http: //eur-lex.europa.eu (accessed on 3 July 2017). 26. Weijers, S.R.; de Jonge, J.; van Zanten, O.; Benedetti, L.; Langeveld, J.; Menkveld, H.W.; van Nieuwenhuijzen, A.F. KALLISTO: Cost Effective and Integrated Optimization of the Urban Wastewater System Eindhoven. Water Pract. Technol. 2012, 7.[CrossRef] 27. Benedetti, L.; Langeveld, J.; van Nieuwenhuijzen, A.F.; de Jonge, J.; de Klein, J.J.M.; de Flameling, T.; Nopens, I.; van Zanten, O.; Weijers, S. Cost-effective solutions for water quality improvement in the Dommel River supported by sewer-WWTP-river integrated modelling. Water Sci. Technol. 2013, 68, 965–973. [CrossRef][PubMed] 28. Langeveld, J.G.; Benedetti, L.; de Klein, J.J.M.; Nopens, I.; Amerlinck, Y.; van Nieuwenhuijzen, A.; Flameling, T.; van Zanten, O.; Weijers, S. Impact-based integrated real-time control for improvement of the Dommel River water quality. Urban Water J. 2013, 10, 312–329. [CrossRef] 29. Daal-Rombouts, P.; van Benedetti, L.; de Jonge, J.; Weijers, S.; Langeveld, J. Performance evaluation of a smart buffer control at a wastewater treatment plant. Water Res. 2017. submit (under review). 30. Vrugt, J.A.; Ter Braak, C.J.F.; Clark, M.P.; Hyman, J.M.; Robinson, B.A. Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation. Water Resour. Res. 2008, 44, 1–15. [CrossRef] 31. Vrugt, J.A.; Ter Braak, C.J.F.; Gupta, H.V.; Robinson, B.A. Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling? Stoch. Environ. Res. Risk Assess. 2009, 23, 1011–1026. [CrossRef] 32. Keating, E.H.; Doherty, J.; Vrugt, J.A.; Kang, Q. Optimization and uncertainty assessment of strongly nonlinear groundwater models with high parameter dimensionality. Water Resour. Res. 2010, 46, 1–8. [CrossRef] 33. Leonhardt, G.; Sun, S.; Rauch, W.; Bertrand-Krajewski, J.-L. Comparison of two model based approaches for areal rainfall estimation in urban hydrology. J. Hydrol. 2014, 511, 880–890. [CrossRef] 34. Van Daal-Rombouts, P.; Sun, S.; Langeveld, J.; Bertrand-Krajewski, J.-L.; Clemens, F. Design and performance evaluation of a simplified dynamic model for combined sewer overflows in pumped sewer systems. J. Hydrol. 2016, 538, 609–624. [CrossRef] 35. Langeveld, J.G.; Clemens, F.H.L.R.; Van Der Graaf, J.H.J.M. Interactions within the wastewater system: Requirements for sewer processes modelling. Water Sci. Technol. 2003, 47, 101–108. [PubMed] 36. Boogaard, F.; Lemmen, G. STOWA Stormwater Database: The Facts about the Quality of Stormwater Runoff ; STOWA 2007-21; STOWA: Amersfoort, The Netherlands, 2007. (In Dutch) 37. Krebs, P.; Merkel, K.; Kühn, V. Dynamic Changes in Wastewater Composition during Rain Runoff. In Proceedings of the 8ICUSD, Sydney, Australia, 30 August–3 September 1999; pp. 920–927. 38. Bruns, J.; von Regenwasserbehandlung, D.K.; bei Mischwasserzufluss, A. Stuttgarter Berichte zur Siedlungswasserwirtschaft; Bd. 151. (Stuttgart, Univ. Diss., 1998); Oldenbourg: München, Germany, 1999. 39. De Mulder, C.; Flameling, T.; Langeveld, J.; Amerlinck, Y.; Weijers, S.; Nopens, I. Automating the Raw Data to Model Input Process Using Flexible Open Source Tools. In Proceedings of the Frontiers International Conference on Wastewater Treatment, Palermo, Italy, 21–24 May 2017.

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).