# EmiStatR: A Simplified and Scalable Urban Water Quality Model for Simulation of Combined Sewer Overflows

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Conceptual Model

- Dry weather flow (DWF): EmiStatR assumes a constant DWF resulting from specific water consumption per population equivalent (PE) and a specific discharge of infiltration inflow per hectare of contributing impervious area to combined sewage flow (CSF).
- Pollution of DWF: This is the specific load contribution per PE and day of COD and NH${}_{4}$. No pollutant contribution of infiltration inflow is taken into account.
- Rain weather flow (RWF): This is the total run-off of rainfall on the impervious catchment area contributing to CSF. The RWF is discharged in a specific flow time (${t}_{\mathit{fS}}$) to the sewer outlet or CSO structures downstream from the catchment; that is, the flow time in the sub-catchment (${t}_{\mathit{fS}}$) is a parameter of calibration.
- Pollution of RWF: Constant surface run-off concentrations of COD and NH${}_{4}$ are assumed. EmiStatR further assumes the complete mixing of pollutants in simultaneously flowing volume components and CSO chamber (CSOC) structures.
- CSF and pollution: These are the sum of the DWF and RWF for the CSF and the consequent pollution load.
- CSO volume and pollution: These are the volume diverted towards the receiving water body that is produced when the overflow or spill weir level in the CSOC is exceeded and the pollution measured as COD and NH${}_{4}$ loads.

#### 2.2. Governing Equations

#### 2.2.1. Dry Weather Flow

- $i$ is the ith term of the time series (−),
- $\mathit{pe}$ are the PEs of the connected CSO structure at time i (PE),
- $\mathrm{PE}$ is the units for PEs (unit per capita loading), and
- $\mathit{qs}$ is the individual water consumption at time i (residential) $(\mathrm{L}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1})$.

- ${A}_{\mathit{imp}}$ is the impervious area of the catchment (ha), and
- ${q}_{f}$ is the specific infiltration water inflow at time i $(\mathrm{L}\xb7{\mathrm{s}}^{-1}\xb7{\mathrm{ha}}^{-1})$.

#### 2.2.2. DWF Pollutants

- ${C}_{\mathit{COD},S}$ is the COD sewage pollution per capita (PE) load per day (g·PE
^{−1}·day^{−1}), and - ${C}_{\mathit{NH}\mathit{4},S}$ is the NH
_{4}sewage pollution per capita (PE) load per day (g·PE^{−1}·day^{−1}).

#### 2.2.3. Rain Run-Off Volume and Rain Weather Flow

- ${P}_{\mathit{1}}$ is the rainfall depth per time step ($\Delta t$) at time i$\left(\mathrm{mm}\right)$,
- ${A}_{\mathit{imp}}$ is the impervious area of the catchment (ha),
- ${A}_{\mathit{total}}$ is the total area of the catchment (ha),
- ${C}_{imp}$ is the run-off coefficient for impervious areas (−), and
- ${C}_{per}$ is the run-off coefficient for pervious areas (−).

#### 2.2.4. Combined Sewage Flow

- $\u03f5$ is the precision term equal to ${10}^{-5}$ (–).

#### 2.2.5. CSO Volume

- ${Q}_{d}$ is the throttled outflow to the WwTP $(\mathrm{L}\xb7{\mathrm{s}}^{-1})$;
- ${C}_{d}$ is the orifice coefficient of discharge (−);
- ${A}_{d}$ is the orifice area ($\pi \xb7{D}_{d}^{2}/4$) $\left({\mathrm{m}}^{2}\right)$;
- g is the gravitational acceleration, 9.81 m$\xb7{\mathrm{s}}^{-2}$; and
- $Lev$ is the water level in the CSOC (m).

^{−1}), defined by the user:

- ${o}_{\mathit{cfyn}}$ is the status variable for the CSOC filling up or spilling out (1—filling up; 0—spilling out) $(-)$,
- ${V}_{d}$ is the volume of throttled outflow to the WwTP at time i $\left({\mathrm{m}}^{3}\right)$, and
- ${Q}_{d}$ is the throttled outflow to the WwTP at time i $(\mathrm{L}\xb7{\mathrm{s}}^{-1})$.

- V is the volume of the CSOC $\left({\mathrm{m}}^{3}\right)$.

#### 2.2.6. CSO Pollutants

- ${B}_{\mathit{COD},\mathit{Sv}}$ is the COD load in the spill volume (g),
- ${\mathit{COD}}_{r}$ is the rainwater pollution∔COD concentration $(\mathrm{mg}\xb7{\mathrm{L}}^{-1})$,
- ${B}_{\mathit{NH}\mathit{4},\mathit{Sv}}$ is the NH
_{4}load in the spill volume (g), and - $\mathit{NH}{\mathit{4}}_{r}$ is the rainwater pollution—NH${}_{4}$ concentration $(\mathrm{mg}\xb7{\mathrm{L}}^{-1})$.

^{−1}), which is defined as the ratio of ${B}_{\mathit{COD},\mathit{Sv}}$ and ${V}_{\mathit{Sv}}$. Similarly, ${C}_{\mathit{NH}\mathit{4},\mathit{Sv}}$ (mg·L

^{−1}) is the ratio of ${B}_{\mathit{NH}\mathit{4},\mathit{Sv}}$ and ${V}_{\mathit{Sv}}$.

#### 2.3. Model Implementation in R

#### 2.3.1. Input Data Definition

- Wastewater production data, that is, water consumption in PE and characterisation of the pollution load of wastewater in terms of COD and NH${}_{4}$ concentrations in PE.
- Run-off and specific pollutant load contribution per PE and day (COD and NH${}_{4}$ concentrations) of infiltration water.
- Precipitation data, that is, time series of rainfall and rainfall run-off pollution in terms of concentrations of COD and NH${}_{4}$.

- Identification, that is, ID and name of structure.
- Catchment data, that is, name of the municipality, name and number of the catchment, land use (residential, commercial, and industrial), total area of the catchment, impervious area, and PEs connected to the sewer system.
- CSO structure data, that is, data regarding the throttled outflow diverted to the WwTP and the total storage volume of the CSOC.

#### 2.3.2. Implementation of a Scalable Approach

- Start up M “worker” processes, and do any initialisation needed for the workers.
- Send any data required for each task to the workers.
- Split the task into M roughly equally sized chunks, and send the chunks (including the R code needed) to the workers.
- Wait for all workers to complete their tasks, and collect results.
- Repeat steps 1 to 4 for any further tasks.
- Stop and close the worker processes.

## 3. Case Study

#### 3.1. Study Area

#### 3.2. Model Calibration

- ${O}_{i}$ is the ith observation,
- ${S}_{i}$ is the ith simulation,
- $\overline{O}$ is the mean of the observations, and
- N is the number of observations (and simulations).

#### Calibration Results of the Water Quantity Model

#### 3.3. Validation of Model Predictions

^{®}[62]. This model was used to simulate surface run-off and discharge characteristics in local sewer systems and the behaviour of CSO structures in the Goesdorf sub-catchment and future sewer systems linked to weather periods. Besides the catchment data and structural data of sewer sections planned and in operation, the simulations were based on local rain data for local calibration and on regional long-term rain data to simulate the long-term performance of the system. In the framework of a coarse calibration and validation process, it was proved that the model reproduced discharge characteristics in local sewer systems of selected villages sufficiently. The resulting parameterisation to model surface run-off characteristics from impervious areas in the villages, such as initial losses, was applied to further catchments showing similar characteristics [62]. The calibrated model of the catchment and drainage network of the case study, implemented in InfoWorks CS and upgraded to InfoWorks ICM 7.5, was used to validate the performance of EmiStatR. We followed a similar procedure as presented by Meirlaen et al. [28] for developing a mechanistic surrogate model from a CMM.

#### 3.4. Scalability and Performance

## 4. Discussion

#### 4.1. Conceptual and Mathematical Model

#### 4.2. Model Implementation

#### 4.3. Model Calibration and Validation

#### 4.4. Scalability

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

COD | Chemical oxygen demand |

CSO | Combined sewer overflow |

CSOC | Combined sewer overflow chamber |

DOAJ | Directory of open access journals |

MDPI | Multidisciplinary Digital Publishing Institute |

NH${}_{4}$ | Ammonium |

PE | Population equivalent |

${A}_{d}$ | Orifice area (m${}^{2}$) |

${C}_{d}$ | Orifice coefficient of discharge (–) |

${C}_{imp}$ | Run-off coefficient for impervious areas (–) |

${C}_{per}$ | Run-off coefficient for pervious areas (–) |

${D}_{d}$ | Orifice diameter (m) |

$Lev$ | Water level in the CSOC (m) |

$Le{v}_{ini}$ | Initial water level in the CSOC (m) |

V | Volume of the CSOC structure (m${}^{3}$) |

$\u03f5$ | Precision term (10${}^{-5}$) (–) |

${A}_{imp}$ | Impervious area of the catchment (ha) |

${A}_{total}$ | Total area of the catchment (ha) |

${B}_{COD,Sv}$ | Load of COD in spill volume (g) |

${B}_{NH4,Sv}$ | Load of NH 4 in spill volume (g) |

$CO{D}_{f}$ | COD infiltration water pollution per capita (PE) load per day (g · PE${}^{-1}$ · day${}^{-1}$) |

$CO{D}_{r}$ | Rainwater pollution - COD concentration (mg · L${}^{-1}$) |

${C}_{COD,Sv}$ | Concentration of COD in spill volume (mg · L${}^{-1}$) |

${C}_{COD,S}$ | COD sewage pollution per capita (PE) load per day (g · PE${}^{-1}$ · day${}^{-1}$) |

${C}_{COD}$ | Mean dry weather COD concentration (mg · L${}^{-1}$) |

${C}_{NH4,Sv}$ | Concentration of NH 4 in spill volume (mg · L${}^{-1}$) |

${C}_{NH4,S}$ | NH${}_{4}$ sewage pollution per capita (PE) load per day (g · PE${}^{-1}$ · day${}^{-1}$) |

${C}_{NH4}$ | Mean dry weather NH 4 concentration (mg · L${}^{-1}$) |

$NH{4}_{f}$ | NH${}_{4}$ infiltration water pollution per capita (PE) load per day (g · PE${}^{-1}$ · day${}^{-1}$) |

$NH{4}_{r}$ | Rainwater pollution - NH 4 concentration (mg · L${}^{-1}$) |

${P}_{1}$ | Rainfall depth time series (mm) |

${Q}_{d,max}$ | Maximum throttled outflow to the WwTP (L · s${}^{-1}$) |

${Q}_{{d}_{i}}$ | Throttled outflow to the WwTP at time i (L · s${}^{-1}$) |

${Q}_{d}$ | Throttled outflow to the WwTP (L · s${}^{-1}$) |

${Q}_{f}$ | Infiltration flow (L · s${}^{-1}$) |

${Q}_{s24}$ | DWF (L · s${}^{-1}$) |

${Q}_{t24}i$ | Total DWF (L · s${}^{-1}$) |

${V}_{Chamber}$ | CSOC filling-up volume (m${}^{3}$) |

${V}_{Sv}$ | Spill volume (m${}^{3}$) |

${V}_{{d}_{i}}$ | Volume of throttled outflow to the WwTP at time i (m${}^{3}$) |

${V}_{dw}$ | Dry weather volume (amount of dry weather water in CSF) (m${}^{3}$) |

${V}_{r}$ | Rainwater volume (amount of rainwater in CSF) (m${}^{3}$) |

$c{s}_{mr}$ | Combined sewage mixing ratio (–) |

i | ith term of the time series (–) |

${o}_{cfy{n}_{i}}$ | Status variable for CSOC filling at time i (yes or no) (–) |

$p{e}_{i}$ | PEs of connected CSO structure (PE) |

$pe$ | PEs of connected CSO structure at time i (PE) |

${q}_{f}$ | Infiltration water inflow (L · s${}^{-1}$ · ha${}^{-1}$) (specific infiltration discharge) |

${q}_{{f}_{i}}$ | Infiltration water inflow at time i (L · s${}^{-1}$ · ha${}^{-1}$) (specific infiltration discharge) |

$qs$ | Individual water consumption (residential) (L · PE${}^{-1}$ · day${}^{-1}$) |

${t}_{fS}$ | Flow time or delay in the sub-catchment or structure (time steps) |

g | Gravity acceleration (m · s${}^{-2}$) |

$PE$ | Units for PEs (unit per capita loading) |

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**Figure 1.**Main components of the EmiStatR model: (1) Dry weather flow (DWF) including infiltration flow (IF), (2) pollution of DWF, (3) rain weather flow (RWF), (4) pollution of RWF, (5) combined sewage flow (CSF) and pollution, and (6) combined sewer overflow (CSO) and pollution. CSOC—CSO chamber (background adapted from Sanitary District [46]).

**Figure 2.**Workflow for EmiStatR and the parallelised approach. Parallelisation is set in the input() class, slot(x, “cores”). Level 1: Parallel computing is done inside EmiStatR. Level 2: Parallel computing is done outside of EmiStatR, e.g., Monte Carlo simulation or optimisation.

**Figure 3.**The Haute-Sûre sub-catchment. Combined sewer overflow (CSO) structures are located in Goesdorf (GOE), Kaundorf (KAU), and Nocher-Route (NOR).

**Figure 4.**Rainfall and combined sewer overflow chamber (CSOC) volume at Goesdorf. (

**a**) Time series of May to June 2011 calibrated with DREAM; (

**b**) June to July 2011 simulated time series for validation with observations and the CMM.

**Figure 5.**Rainfall (

**top**), CSO volume (

**second**), chemical oxygen demand (COD) load (

**third**), and NH${}_{4}$ load (

**bottom**). January to December 2010 time series (Esch-sur-Sûre rain gauge) for validation of EmiStatR using output of a complex mechanistic model (CMM). Simulation at 10 min resolution at Goesdorf; results aggregated to 120 min.

General Input | Units | CSO Input | Units |
---|---|---|---|

1. Wastewater | 1. Identification | ||

Water consumption, $\mathit{qs}$ | $\mathrm{L}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$^{a} | ID of the structure | – |

Water consumption, factors ^{b} | – | Name of the structure | – |

Pollution COD ^{c}, ${C}_{\mathit{COD},S}$ | $\mathrm{g}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$ | ||

Pollution NH_{4} ^{d}, ${C}_{\mathit{NH}\mathit{4},S}$ | $\mathrm{g}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$ | 2. Catchment data | |

Name of the municipality | – | ||

2. Infiltration water | Name of the catchment | – | |

Inflow, ${q}_{f}$ | L· s${}^{-1}$ · ha${}^{-1}$ | Number of the catchment | – |

Pollution COD, COD_{f} | $\mathrm{g}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$ | Land use | – |

Pollution NH${}_{4}$, $\mathit{NH}{\mathit{4}}_{f}$ | $\mathrm{g}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$ | Total area, ${A}_{\mathit{total}}$ | ha |

Impervious area, ${A}_{\mathit{imp}}$ | ha | ||

3. Rainwater | Run-off coefficient for impervious area, ${C}_{imp}$ | – | |

Precipitation time series, ${P}_{\mathit{1}}$ | mm | Run-off coefficient for pervious area, ${C}_{per}$ | – |

Pollution COD, ${\mathit{COD}}_{r}$ | $\mathrm{mg}\xb7{\mathrm{L}}^{-1}$ | Flow time structure, ${t}_{\mathit{fS}}$ | time step |

Pollution NH${}_{4}$, $\mathit{NH}{\mathit{4}}_{r}$ | $\mathrm{mg}\xb7{\mathrm{L}}^{-1}$ | Population equivalents, ${\mathit{pe}}_{i}$ | PE |

Population equivalents, factors ^{b} | – | ||

3. CSO structure data | |||

Volume, V | m${}^{3}$ | ||

Curve level–volume, $lev2vol$ | m, m${}^{3}$ | ||

Initial water level, $Le{v}_{ini}$ | m | ||

Maximum throttled outflow, ${Q}_{d,max}$ | L· s${}^{-1}$ | ||

Orifice diameter, ${D}_{d}$ | m | ||

Orifice coefficient of discharge, ${C}_{d}$ | – |

^{a}Population equivalent (PE).

^{b}Factors for daily, weekly, and monthly patterns.

^{c}Chemical oxygen demand (COD).

^{d}Ammonium (NH

_{4}).

Input | Units | Reference Value | Literature Source | Range (This Study) |
---|---|---|---|---|

Wastewater | ||||

Water consumption, $\mathit{qs}$ | $\mathrm{L}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$^{a} | 150 ^{b} | [50] | [130, 170] |

Pollution COD ^{c}, ${C}_{\mathit{COD},S}$ | $\mathrm{g}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$ | 120 | [51] | [90, 150] |

Pollution TKN ^{d} | $\mathrm{g}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$ | 11 | [51] | [7, 15] |

Pollution NH${}_{4}$ ^{e} | $\mathrm{g}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$ | 4.7 | This study | [1, 8] |

Infiltration water | ||||

Inflow, ${q}_{f}$ | L· s${}^{-1}$ · ha${}^{-1}$ | 0.05 | [52] | [0, 2] |

Catchment data | ||||

Run-off coefficient for impervious area, ${C}_{imp}$ | – | See [53] | [53] | [0.20, 095] |

Run-off coefficient for pervious area, ${C}_{per}$ | – | See [53] | [53] | [0.05, 0.50] |

Flow time structure, ${t}_{\mathit{fS}}$ | time step | 2 | This study | [0, 12] |

CSO structure data | ||||

Initial water level, $Le{v}_{ini}$ | m | ${L}_{max}$^{f}/2 | This study | [0, ${L}_{max}$] |

Orifice coefficient of discharge, ${C}_{d}$ | – | 1.25 | This study | [0.01, 2] |

^{a}PE: Population equivalent units;

^{b}mean value for European countries;

^{c}COD: Chemical oxygen demand;

^{d}TKN: Total Kjeldahl nitrogen;

^{e}NH${}_{4}$: Ammonium;

^{f}${L}_{max}$: Maximum water level in the combined sewer overflow chamber (CSOC).

**Table 3.**Calibration and validation results of the hydraulic model in EmiStatR as calibrated with the DREAM algorithm (Goesdorf 2011, 10 min time step).

Parameter | Units | Range of Sampling | Calibrated Value |
---|---|---|---|

Water consumption, $qs$ | $\mathrm{L}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$ | [130, 170] | 152 |

Infiltration flow, ${q}_{f}$ | L·s${}^{-1}\xb7$ha${}^{-1}$ | [0, 0.2] | 0.116 |

Time flow, ${t}_{fS}$ | time step | [0, 12] | 1 |

Run-off coefficient for impervious area, ${C}_{imp}$ | – | [0.20, 0.95] | 0.28 |

Run-off coefficient for pervious area, ${C}_{per}$ | – | [0.05, 0.50] | 0.07 |

Orifice coefficient of discharge, ${C}_{d}$ | – | [0, 2] | 0.67 |

Initial water level, $le{v}_{ini}$ | m | [0.1, 3.5] | 0.57 |

**Table 4.**Comparison results for the complex mechanistic model (CMM) and EmiStatR (Esch-sur-Sure rain gauge 2 h averages over 1 year period).

Combined Sewer Overflow (CSO) Summary Results | CMM | EmiStatR 1.2.1.0 |
---|---|---|

Period, p (day) | 365 | 365 |

Duration of CSO spill volume, ${d}_{Sv}$ (h) | 90 | 100 |

Frequency of CSO spill volume, ${f}_{Sv}$ (events) | 19 | 16 |

Total CSO spill volume, ${V}_{Sv}$ (m${}^{3}$) | 373 | 222 |

Average CSO, ${Q}_{Sv}$ (L/s) | 1.15 | 0.62 |

95th percentile of CSO spill volume, ${V}_{Sv,95}$ (m${}^{3}$) | 27.74 | 15.26 |

Maximum CSO spill volume, ${V}_{Sv,max}$ (m${}^{3}$) | 33.06 | 21.62 |

COD total load (BCOD), ${B}_{COD,Sv}$ (kg) | 5.875 | 4.610 |

Average BCOD, ${B}_{COD,Sv,av}$ (kg) | 0.131 | 0.092 |

95th percentile of BCOD, ${B}_{COD,Sv,95}$ (kg) | 0.320 | 0.252 |

Maximum BCOD, ${B}_{COD,Sv,max}$ (kg) | 0.450 | 0.360 |

NH${}_{4}$ total load (BNH4), ${B}_{NH4,Sv}$ (kg) | 0.224 | 0.208 |

Average BNH4, ${B}_{NH4,Sv,av}$ (kg) | 0.005 | 0.004 |

95th percentile of BNH4, ${B}_{NH4,Sv,95}$ (kg) | 0.012 | 0.011 |

Maximum BNH4, ${B}_{NH4,Sv,95}$ (kg) | 0.020 | 0.020 |

Run time (min) | 30 | 1.09 |

General Input | Units | Value |
---|---|---|

Wastewater | ||

Water consumption, $\mathit{qs}$ | $\mathrm{L}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$^{a} | 150 |

Daily factors for water consumption, | ||

ATV-A134 curve | – | – |

Pollution COD ^{b}, ${C}_{\mathit{COD},S}$ | $\mathrm{g}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$ | 120 |

Pollution NH${}_{4}$ ^{c}, ${C}_{\mathit{NH}\mathit{4},S}$ | $\mathrm{g}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$ | 4.7 |

Infiltration water | ||

Inflow, ${q}_{f}$ | L· s${}^{-1}$ · ha${}^{-1}$ | 0.05 |

Pollution COD, COD_{f} | $\mathrm{g}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$ | 0 |

Pollution NH${}_{4}$, $\mathit{NH}{\mathit{4}}_{f}$ | $\mathrm{g}\xb7{\mathrm{PE}}^{-1}\xb7{\mathrm{day}}^{-1}$ | 0 |

Rainwater | ||

Precipitation time series, ${P}_{\mathit{1}}$ | mm | – |

Pollution COD, ${\mathit{COD}}_{r}$ | $\mathrm{mg}\xb7{\mathrm{L}}^{-1}$ | 0 |

Pollution NH${}_{4}$, $\mathit{NH}{\mathit{4}}_{r}$ | $\mathrm{mg}\xb7{\mathrm{L}}^{-1}$ | 0 |

^{a}PE: population equivalent;

^{b}COD: chemical oxygen demand;

^{c}NH${}_{4}$: ammonium.

**Table 6.**General input data of the combined sewer overflow (CSO) structures of the EmiStatR scalability test, after calibration for structure 1. Structures 2 and 3 were not calibrated; therefore, reference values were defined.

CSO Input | Sub-Catchment | ||
---|---|---|---|

Identification | |||

ID of the structure | 1 | 2 | 3 |

Name of the structure | FBH Goesdorf | FBN Kaundorf | FBH Nocher-Route |

Sub-catchment data | |||

Name of the municipality | Goesdorf | Kaundorf | Nocher-Route |

Name of the catchment | Haute-Sûre | Haute-Sûre | Haute-Sûre |

Number of the catchment | 1 | 1 | 1 |

Land use ^{a} | R/I | R/I | R/I |

Total area, ${A}_{ges}$ (ha) | 30 | 22 | 18.6 |

Impervious area, ${A}_{imp}$ (ha) | 5 | 11 | 4.3 |

Run-off coefficient for impervious area, ${C}_{imp}$ | 0.28 | 0.30 | 0.30 |

Run-off coefficient for pervious area, ${C}_{per}$ | 0.07 | 0.10 | 0.10 |

Flow time structure, ${t}_{fS}$ (min) | 1 | 2 | 2 |

Population equivalents, $pe$ (PE) | 611 | 358 | 326 |

Structure data | |||

Volume, V (m${}^{3}$) | 190 | 180 | 157 |

Curve level–volume, $lev2vol$ | Goesdorf | Kaundorf | Nocher-Route |

Initial water level, $Le{v}_{ini}$ | 0.57 | 1.8 | 1.8 |

Maximum throttled outflow, ${Q}_{d,max}$ | 5 | 9 | 4 |

Orifice diameter, ${D}_{d}$ | 0.015 | 0.015 | 0.015 |

Orifice coefficient of discharge, ${C}_{d}$ | 0.67 | 0.67 | 0.67 |

**Table 7.**Runtime in minutes and “speed-up” factor as a function of number of cores used in simulations.

32 Simulations | 320 Simulations | 3200 Simulations | ||||
---|---|---|---|---|---|---|

Cores | Time | SF^{a} | Time | SF | Time | SF |

1 | 3.4 | 1.0 | 33.9 | 1.0 | 334.9 | 1.0 |

2 | 1.9 | 1.8 | 18.1 | 1.9 | 176.6 | 1.9 |

4 | 0.9 | 3.7 | 8.9 | 3.8 | 87.8 | 3.8 |

8 | 0.6 | 5.7 | 4.8 | 7.0 | 46.0 | 7.3 |

16 | 0.4 | 9.1 | 2.6 | 13.0 | 25.3 | 13.3 |

32 | 0.3 | 12.2 | 1.5 | 22.0 | 14.2 | 23.6 |

^{a}Speed-up factor (SF), computed as the ratio between the time for one core and the time for the ith core.

© 2018 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/).

## Share and Cite

**MDPI and ACS Style**

Torres-Matallana, J.A.; Leopold, U.; Klepiszewski, K.; Heuvelink, G.B.M.
EmiStatR: A Simplified and Scalable Urban Water Quality Model for Simulation of Combined Sewer Overflows. *Water* **2018**, *10*, 782.
https://doi.org/10.3390/w10060782

**AMA Style**

Torres-Matallana JA, Leopold U, Klepiszewski K, Heuvelink GBM.
EmiStatR: A Simplified and Scalable Urban Water Quality Model for Simulation of Combined Sewer Overflows. *Water*. 2018; 10(6):782.
https://doi.org/10.3390/w10060782

**Chicago/Turabian Style**

Torres-Matallana, Jairo Arturo, Ulrich Leopold, Kai Klepiszewski, and Gerard B. M. Heuvelink.
2018. "EmiStatR: A Simplified and Scalable Urban Water Quality Model for Simulation of Combined Sewer Overflows" *Water* 10, no. 6: 782.
https://doi.org/10.3390/w10060782