# A Method for Modeling Urban Water Infrastructures Combining Geo-Referenced Data

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## Abstract

**:**

## 1. Introduction

## 2. State-of-the-Art

#### 2.1. Spatial Disaggregation of Water Demand

#### 2.2. Generation of Water Distribution Systems

#### 2.3. Resilience of Water Distribution Systems

## 3. Framework

## 4. Data and Methods

#### 4.1. Data

_{Total,blue}= 0.33 · Q

_{Total,yellow}= 31.4 Mio.m

^{3}/y.

#### 4.2. Disaggregation of Water Demand

#### 4.3. Identification of the Possible Water Network

#### 4.4. Water Distribution System Design Optimization Problem

#### 4.5. Optimization Instance

## 5. Results and Discussion

#### Limitations

## 6. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MDPI | Multidisciplinary Digital Publishing Institute |

DOAJ | Directory of open access journals |

TLA | Three letter acronym |

LD | Linear dichroism |

LCZ | Local Climate Zones |

WDS | water distribution system |

## References

- Louis, H. Sullivan. The tall office building artistically considered. West. Archit.
**1922**, 1922, 3–11. [Google Scholar] - Rams, D.; Klatt, J. Weniger, Aber Besser: Skizze für Phonokombination TP 1 = Less but Better: Drawing for Phono Combination TP 1; Jo Klatt Design und Design Verlag: Hamburg, Germany, 1995. [Google Scholar]
- Pelz, P.F.; Groche, P.; Pfetsch, M.E.; Schäffner, M. Mastering Uncertainty in Mechanical Engineering; Springer Tracts in Mechanical Engineering; Springer International Publishing: Berlin/Heidelberg, Germany, 2021. [Google Scholar]
- Bao, K.; Padsala, R.; Thrän, D.; Schröter, B. Urban Water Demand Simulation in Residential and Non-Residential Buildings Based on a CityGML Data Model. ISPRS Int. J. Geo-Inf.
**2020**, 9, 642. [Google Scholar] [CrossRef] - Sitzenfrei, R.; Fach, S.; Kleidorfer, M.; Urich, C.; Rauch, W. Dynamic virtual infrastructure benchmarking: DynaVIBe. Water Supply
**2010**, 10, 600–609. [Google Scholar] [CrossRef] - Shin, S.; Lee, S.; Judi, D.; Parvania, M.; Goharian, E.; McPherson, T.; Burian, S. A Systematic Review of Quantitative Resilience Measures for Water Infrastructure Systems. Water
**2018**, 10, 164. [Google Scholar] [CrossRef] [Green Version] - Pesantez, J.E.; Berglund, E.Z.; Kaza, N. Smart meters data for modeling and forecasting water demand at the user-level. Environ. Model. Softw.
**2020**, 125, 104633. [Google Scholar] [CrossRef] - Zubaidi, S.; Al-Bugharbee, H.; Ortega-Martorell, S.; Gharghan, S.; Olier, I.; Hashim, K.; Al-Bdairi, N.; Kot, P. A Novel Methodology for Prediction Urban Water Demand by Wavelet Denoising and Adaptive Neuro-Fuzzy Inference System Approach. Water
**2020**, 12, 1628. [Google Scholar] [CrossRef] - Zubaidi, S.L.; Ortega-Martorell, S.; Al-Bugharbee, H.; Olier, I.; Hashim, K.S.; Gharghan, S.K.; Kot, P.; Al-Khaddar, R. Urban Water Demand Prediction for a City That Suffers from Climate Change and Population Growth: Gauteng Province Case Study. Water
**2020**, 12, 1885. [Google Scholar] [CrossRef] - Viola, F.; Caracciolo, D.; Deidda, R. Modelling the mutual interactions between hydrology, society and water supply systems. Hydrol. Sci. J.
**2021**, 66, 1265–1274. [Google Scholar] [CrossRef] - Demuzere, M.; Hankey, S.; Mills, G.; Zhang, W.; Lu, T.; Bechtel, B. Combining expert and crowd-sourced training data to map urban form and functions for the continental US. Sci. Data
**2020**, 7, 264. [Google Scholar] [CrossRef] - Pastor-Jabaloyes, L.; Arregui, F.; Cobacho, R. Water End Use Disaggregation Based on Soft Computing Techniques. Water
**2018**, 10, 46. [Google Scholar] [CrossRef] [Green Version] - Stewart, I.D.; Oke, T.R. Local Climate Zones for Urban Temperature Studies. Bull. Am. Meteorol. Soc.
**2012**, 93, 1879–1900. [Google Scholar] [CrossRef] - Demuzere, M.; Bechtel, B.; Middel, A.; Mills, G. Mapping Europe into local climate zones. PLoS ONE
**2019**, 14, e0214474. [Google Scholar] [CrossRef] [Green Version] - Taubenböck, H.; Debray, H.; Qiu, C.; Schmitt, M.; Wang, Y.; Zhu, X.X. Seven city types representing morphologic configurations of cities across the globe. Cities
**2020**, 105, 102814. [Google Scholar] [CrossRef] - Hu, J.; Wang, Y.; Taubenböck, H.; Zhu, X.X. Land consumption in cities: A comparative study across the globe. Cities
**2021**, 113, 103163. [Google Scholar] [CrossRef] - Mair, M.; Zischg, J.; Rauch, W.; Sitzenfrei, R. Where to Find Water Pipes and Sewers?—On the Correlation of Infrastructure Networks in the Urban Environment. Water
**2017**, 9, 146. [Google Scholar] [CrossRef] [Green Version] - DIN-Normausschuss Bauwesen. DIN 1998-Placement of Service Conduits in Public Circulation Areas—Guideline for Planning; German Standardisation Agency: Berlin, Germany, 2018. [Google Scholar]
- Planet Dump. 2015. Available online: https://planet.openstreetmap.org/ (accessed on 18 June 2021).
- Google. Satellite Images of Cologne. Available online: https://www.google.de/maps/@50.93517027036617,6.9501295729336405z (accessed on 14 June 2021).
- Jarvis, A.; Reuter, H.I.; Nelson, A.; Guevara, E. Hole-Filled Seamless SRTM Data V4; CIAT: Rome, Italy, 2008. [Google Scholar]
- Sitzenfrei, R.; Möderl, M.; Rauch, W. Automatic generation of water distribution systems based on GIS data. Environ. Model. Softw. Environ. Data News
**2013**, 47, 138–147. [Google Scholar] [CrossRef] [Green Version] - Müller, T.M.; Leise, P.; Lorenz, I.S.; Altherr, L.C.; Pelz, P.F. Optimization and validation of pumping system design and operation for water supply in high-rise buildings. Optim. Eng.
**2021**, 22, 643–686. [Google Scholar] [CrossRef] - Lorenz, I.S.; Pelz, P. Optimal Resilience Enhancement of Water Distribution Systems. Water
**2020**, 12, 2602. [Google Scholar] [CrossRef] - Schänzle, C.; Altherr, L.C.; Ederer, T.; Lorenz, U.; Pelz, P.F. As Good As It Can Be-Ventilation System Design By A Combined Scaling And Discrete Optimization Method. In Proceedings of the International Conference on Fan Noise, Fan Technology and Numerical Methods (Fan 2015), Lyon, France, 15–17 April 2015. [Google Scholar]
- Pelz, P.F.; Lorenz, U.; Ludwig, G. Besser geht’s nicht. TOR plant das energetisch optimale Fluidsystem. Chem. More
**2014**, 6, 2–9. [Google Scholar] - Ugarelli, R.; Venkatesh, G.; Brattebø, H.; Di Federico, V.; Sægrov, S. Asset Management for Urban Wastewater Pipeline Networks. J. Infrastruct. Syst.
**2010**, 16, 112–121. [Google Scholar] [CrossRef] - Altherr, L.C.; Brötz, N.; Dietrich, I.; Gally, T.; Geßner, F.; Kloberdanz, H.; Leise, P.; Pelz, P.F.; Schlemmer, P.D.; Schmitt, A. Resilience in Mechanical Engineering—A Concept for Controlling Uncertainty during Design, Production and Usage Phase of Load-Carrying Structures. Appl. Mech. Mater.
**2018**, 885, 187–198. [Google Scholar] [CrossRef] [Green Version] - Yazdani, A.; Otoo, R.A.; Jeffrey, P. Resilience enhancing expansion strategies for water distribution systems: A network theory approach. Environ. Model. Softw.
**2011**, 26, 1574–1582. [Google Scholar] [CrossRef] - Herrera, M.; Abraham, E.; Stoianov, I. A Graph-Theoretic Framework for Assessing the Resilience of Sectorised Water Distribution Networks. Water Resour. Manag.
**2016**, 30, 1685–1699. [Google Scholar] [CrossRef] [Green Version] - Lorenz, I.S.; Altherr, L.C.; Pelz, P.F. Resilience Enhancement of Critical Infrastructure—Graph Theoretical Resilience Analysis of the Water Distribution System in the German City of Darmstadt. In 14th WCEAM Proceedings; Crespo Márquez, A., Komljenovic, D., Amadi-Echendu, J., Eds.; Lecture Notes in Mechanical Engineering; Springer International Publishing: Cham, Switzerland, 2021; pp. 137–149. [Google Scholar] [CrossRef]
- Altherr, L.C.; Joggerst, L.; Leise, P.; Pfetsch, M.E.; Schmitt, A.; Wendt, J. On Obligations in the Development Process of Resilient Systems with Algorithmic Design Methods. Appl. Mech. Mater.
**2018**, 885, 240–252. [Google Scholar] [CrossRef] [Green Version] - Todini, E. Looped water distribution networks design using a resilience index based heuristic approach. Urban Water
**2000**, 2, 115–122. [Google Scholar] [CrossRef] - Hollnagel, E. Epilogue: RAG—The resilience analysis grid. In Resilience Engineering in Practice. A Guidebook; Hollnagel, E., Pariès, J., Woods, D.D., Wreathall, J., Eds.; Ashgate Publishing, Ltd.: Farnham, UK, 2011; pp. 275–296. [Google Scholar]
- Hollnagel, E. Prologue: The scope of resilience engineering. In Resilience Engineering in Practice. A Guidebook; Hollnagel, E., Pariès, J., Woods, D.D., Wreathall, J., Eds.; Ashgate Publishing, Ltd.: Farnham, UK, 2011. [Google Scholar]
- Hollnagel, E. FRAM, The Functional Resonance Analysis Method. Modelling Complex Socio-Technical Systems; CRC Press: Boca Raton, FL, USA, 2012. [Google Scholar]
- Bruneau, M.; Chang, S.E.; Eguchi, R.T.; Lee, G.C.; O’Rourke, T.D.; Reinhorn, A.M.; Shinozuka, M.; Tierney, K.; Wallace, W.A.; von Winterfeldt, D. A Framework to Quantitatively Assess and Enhance the Seismic Resilience of Communities. Earthq. Spectra
**2003**, 19, 733–752. [Google Scholar] [CrossRef] [Green Version] - Hashimoto, T.; Stedinger, J.R.; Loucks, D.P. Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation. Water Resour. Res.
**1982**, 18, 14–20. [Google Scholar] [CrossRef] [Green Version] - Qiu, C.; Schmitt, M.; Zhu, X.X. Fusing Multi-Seasonal Sentinel-2 Images with Residual Convolutional Neural Networks for Local Climate Zone-Derived Urban Land Cover Classification. In Proceedings of the IGARSS 2019—2019 IEEE International Geoscience and Remote Sensing Symposium, Yokohama, Japan, 28 July–2 August 2019; IEEE: Piscataway, NJ, USA, 2019; Volume 72019, pp. 5037–5040. [Google Scholar] [CrossRef] [Green Version]
- QGIS Association. 2021. Available online: https://www.qgis.org/en/site/index.html (accessed on 12 June 2021).
- Hart, W.E. Pyomo-Optimization Modeling in Python, 2nd ed.; Springer Optimization and Its Applications; Springer: Cham, Switzerland, 2017; Volume 67. [Google Scholar]
- Hagberg, A.A.; Schult, D.A.; Swart, P.J. Exploring Network Structure, Dynamics, and Function using NetworkX. In Proceedings of the 7th Python in Science Conference, Pasadena, CA, USA, 19–24 August 2008; Varoquaux, G., Vaught, T., Millman, J., Eds.; pp. 11–15. [Google Scholar]
- Varoquaux, G.; Vaught, T.; Millman, J. (Eds.) In Proceedings of the 7th Python in Science Conference, SciPy, Pasadena, CA, USA, 19–24 August 2008. Available online: https://hal.inria.fr/hal-00502586/en (accessed on 19 August 2021).
- DIN Deutsches Institut für Normung e.V. DIN 1988–Technische Regeln für Trinkwasser-Installationen – Teil 200: Installation Typ A (geschlossenes System)–Planung, Bauteile, Apparate, Werkstoffe; Technische Regel des DVGW German Standardisation Agency: Berlin, Germany, 2012. [Google Scholar]
- Chee, R.; Lansey, K.; Chee, E. Estimation of Water Pipe Installation Construction Costs. J. Pipeline Syst. Eng. Pract.
**2018**, 9. [Google Scholar] [CrossRef] - Nussbaum, T.; Thalmann, S. Dimensionierung von Fernwärmenetzen: Minimale Rohrdurchmesser Reduzieren Kosten und Netzverluste; VDI Verlag GmbH: Düsseldorf, Germany, 2017; Available online: www.ingenieur.de (accessed on 14 June 2021).
- Lorenz, I.S.; Pouls, K.; Pelz, P.F. Comparability of Water Infrastructure Resilience of Different Urban Structures. In ICUME; Springer: Cham, Switzerland, 2020. [Google Scholar]
- Meirelles, G.; Brentan, B.; Izquierdo, J.; Ramos, H.; Luvizotto, E. Trunk Network Rehabilitation for Resilience Improvement and Energy Recovery in Water Distribution Networks. Water
**2018**, 10, 693. [Google Scholar] [CrossRef] [Green Version] - Tatem, A.J. WorldPop, open data for spatial demography. Sci. Data
**2017**, 4, 170004. [Google Scholar] [CrossRef]

**Figure 2.**(

**a**) Satellite image (Google Earth, 2021) and (

**b**) local climate zones of Cologne, Germany [15]. The yellow polygon marks the administrative boundary, and the blue one, the inner city, which is investigated in this paper. (

**c**) Streets from OpenStreetMap with the possible network topology are represented by blue edges. (

**d**) The possible network topology with sizes of the nodes (yellow points) represent the water demand disaggregated to the graph.

**Figure 3.**Cost composition of the total pipe installation cost per meter in dependence on the diameter.

**Figure 4.**Cost-optimal WDS (blue) with different line widths to represent the change in pipe diameter and maximum possible network topology (grey).

**Figure 5.**Quasi-stationary behavior of the generated WDS. (

**a**) Volume flow in the pipes, (

**b**) pressure at demand nodes.

**Table 1.**Local climate zones adapted from [13]. * The value for the local climate zone class 10 (heavy industry) is calculated by doubling the highest value occurring in the other classes (i.e., 12.5 m/A for class 1).

LCZ | Description | Built-Up Surface Fraction in % | Height in m | Average Surface Fraction in % | Average Height in m | Av. Volume per Area in m |
---|---|---|---|---|---|---|

1 | Compact high-rise | 40–60 | >25 | 50 | 25 | 12.5 |

2 | Compact midrise | 40–70 | 10–25 | 55 | 17.5 | 9.625 |

3 | Compact low-rise | 20–40 | 3–10 | 30 | 6.5 | 1.95 |

4 | Open high-rise | 20–40 | >25 | 30 | 25 | 7.5 |

5 | Open midrise | 20–40 | 10–25 | 30 | 17.5 | 5.25 |

6 | Open low-rise | 60–90 | 3–10 | 75 | 6.5 | 4.875 |

7 | Lightweight low-rise | 30–50 | 2–4 | 40 | 3 | 1.2 |

8 | Large low-rise | 10–20 | 3–10 | 15 | 6.5 | 0.975 |

9 | Sparsely built | 20–30 | 3–10 | 25 | 6.5 | 1.625 |

10 | Heavy industry | 20–30 | 5–15 | - | - | 25 * |

Set | Subset of | Description |
---|---|---|

$\mathcal{N}$ | Set of nodes. | |

${\mathcal{A}}_{n}$ | $\mathcal{N}$ | Set of adjacent nodes $\forall n\in \mathcal{N}$. |

$\mathcal{C}$ | $\mathcal{N}$ | Set of consumer nodes. |

$\mathcal{R}$ | $\mathcal{N}$ | Set of reservoir nodes. |

${\mathcal{R}}_{0}$ | $\mathcal{R}$ | Root reservoir node to constrain one connected network. |

$\mathcal{E}$ | $\mathcal{N}\times \mathcal{N}$ | Set of directed edges with start- and end-node ($i,\phantom{\rule{0.166667em}{0ex}}j$). |

$\mathcal{D}$ | Set of available pipe diameters. |

Variable | Domain | Description |
---|---|---|

${q}_{i,j}$ | ${\mathbb{R}}_{0}^{+}$ | Volume flow rate for each directed pipe. $(i,j)$. |

${s}_{n}$ | ${\mathbb{R}}_{0}^{+}$ | Source volume flow $\forall n\in \mathcal{R}$. |

${p}_{n}$ | ${\mathbb{R}}_{0}^{+}$ | Pressure at each node $\forall n\in \mathcal{N}$. |

$\Delta {p}_{i,j}$ | ${\mathbb{R}}_{0}^{+}$ | Pressure loss $\forall i,j\in \mathcal{E}$. |

$\Delta {p}_{i,j}^{\mathrm{pump}}$ | ${\mathbb{R}}_{0}^{+}$ | Pressure increase due to pumps $\forall i,j\in \mathcal{E}$. |

${d}_{i,j,d}$ | $\{0,1\}$ | Decision variable for choosing the edges on which to place pipes and their diameters. $\forall i,j\in \mathcal{E}$, $\forall d\in \mathcal{D}$ |

${c}_{i,j,r}$ | $\{0,1\}$ | Decision variable for choosing a path between all reservoirs to guarantee one connected network $\forall i,j\in \mathcal{E}$, $\forall r\in \mathcal{R}$. |

${b}_{i,j}$ | $\{0,1\}$ | Decision variable for choosing the pump locations $\forall i,j\in \mathcal{E}$. |

Parameter | Domain | Description |
---|---|---|

Scalar parameters | ||

${Q}^{\mathrm{max}}$ | ${\mathbb{R}}_{0}^{+}$ | Maximum volume flow rate |

${P}^{C,\mathrm{min}}$ | ${\mathbb{R}}_{0}^{+}$ | Minimum pressure at consumer nodes. |

$\Delta {P}^{\mathrm{pump},\mathrm{min}}$ | ${\mathbb{R}}_{0}^{+}$ | Minimum pressure increase for pumps. |

${P}^{\mathrm{max}}$ | ${\mathbb{R}}_{0}^{+}$ | Maximum pressure for big-M expression. |

${P}^{\mathrm{stat},\mathrm{max}}$ | ${\mathbb{R}}_{0}^{+}$ | Maximum static pressure to protect pipes. |

${U}^{\mathrm{mean}}$ | ${\mathbb{R}}_{0}^{+}$ | Mean velocity for pressure loss calculation. |

G | ${\mathbb{R}}_{0}^{+}$ | Gravitational constant. |

$\varrho $ | ${\mathbb{R}}_{0}^{+}$ | Density of water. |

${l}^{\mathrm{min}}$ | ${\mathbb{R}}_{0}^{+}$ | Minimum average link density [29]. |

$<O{>}^{\mathrm{min}}$ | ${\mathbb{R}}_{0}^{+}$ | Minimum average node degree [29]. |

${R}^{\mathrm{m},\mathrm{min}}$ | ${\mathbb{R}}_{0}^{+}$ | Minimum meshed-ness coefficient [29]. |

Indexed Parameters | ||

${Q}_{r}^{\mathrm{res},\mathrm{max}}$ | ${\mathbb{R}}_{0}^{+}$ | Maximum volume flow $\forall r\in \mathcal{R}$. |

${Q}_{n}^{\mathrm{demand}}$ | ${\mathbb{R}}_{0}^{+}$ | Water demand $\forall n\in \mathcal{N}$. |

${Q}_{d}^{\mathrm{max}}$ | ${\mathbb{R}}_{0}^{+}$ | Maximum volume flow to limit maximum velocity $\forall d\in \mathcal{D}$. |

${P}_{r}^{\mathrm{res}}$ | ${\mathbb{R}}_{0}^{+}$ | Static pressure $\forall r\in \mathcal{R}$. |

${H}_{n}$ | ${\mathbb{R}}_{0}^{+}$ | Elevation $\forall n\in \mathcal{N}$. |

${L}_{i,j}$ | ${\mathbb{R}}_{0}^{+}$ | Pipe length $\forall (i,j)\in \mathcal{E}$. |

${D}_{d}$ | ${\mathbb{R}}_{0}^{+}$ | Pipe diameter $\forall d\in \mathcal{D}$. |

${r}_{i,j}$ | ${\mathbb{R}}_{0}^{+}$ | Pressure loss coefficient $\forall (i,j)\in \mathcal{E}$. |

${C}_{d}^{\mathrm{pipe}}$ | ${\mathbb{R}}_{0}^{+}$ | Installation cost for pipes $\forall d\in \mathcal{D}$. |

Parameter | Instance | Description |
---|---|---|

Scalar parameters | Value | |

${Q}^{\mathrm{max}}$ | 2.71 m^{3} s^{−1} | Maximum volume flow rate |

${P}^{C,\mathrm{min}}$ | 4 bar | Minimum pressure at consumer nodes. |

$\Delta {P}^{\mathrm{pump},\mathrm{min}}$ | 1 bar | Minimum pressure increase for pumps. |

${P}^{\mathrm{max}}$ | 14.18 bar | Maximum pressure for big-M expression. |

${P}^{\mathrm{stat},\mathrm{max}}$ | 8 bar | Maximum static pressure to protect pipes. |

${U}^{\mathrm{mean}}$ | $1\mathrm{m}{\mathrm{s}}^{-1}$ | Mean velocity for pressure loss calculation. |

G | 9.81 m s^{−2} | Gravitational constant. |

$\varrho $ | 1000 kg m^{−3} | Density of water. |

${l}^{\mathrm{min}}$ | 0.0008 | Minimum average link density [29]. |

$<O{>}^{\mathrm{min}}$ | 2 | Minimum average node degree [29]. |

${R}^{\mathrm{m},\mathrm{min}}$ | 0.04 | Minimum meshed-ness coefficient [29]. |

Indexed Parameters | Range | |

${Q}_{r}^{\mathrm{res},\mathrm{max}}$ | $[0.189,1.12]\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{3}{\mathrm{s}}^{-1}$ | Maximum volume flow $\forall r\in \mathcal{R}$. |

${Q}_{n}^{\mathrm{demand}}$ | $[0,0.046]\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{3}{\mathrm{s}}^{-1}$ | Water demand $\forall n\in \mathcal{N}$. |

${Q}_{d}^{\mathrm{max}}$ | $[0.157,1.414]\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{3}{\mathrm{s}}^{-1}$ | Maximum volume flow to limit maximum velocity $\forall d\in \mathcal{D}$. |

${P}_{r}^{\mathrm{res}}$ | $[0,0]\phantom{\rule{0.166667em}{0ex}}bar$ | Static pressure $\forall r\in \mathcal{R}$. |

${H}_{n}$ | $[41,63]\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$ | Elevation $\forall n\in \mathcal{N}$. |

${L}_{i,j}$ | $[143,5086]\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$ | Pipe length $\forall (i,j)\in \mathcal{E}$. |

${D}_{d}$ | $[0.2,0.6]\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$ | Pipe diameter $\forall d\in \mathcal{D}$. |

${r}_{i,j}$ | $[5.26,769]$ | Pressure loss coefficient $\forall (i,j)\in \mathcal{E}$. |

${C}_{d}^{\mathrm{pipe}}$ | $[219,634]\phantom{\rule{0.166667em}{0ex}}$€$/m$ | Installation cost for pipes $\forall d\in \mathcal{D}$. |

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## Share and Cite

**MDPI and ACS Style**

Rehm, I.-S.; Friesen, J.; Pouls, K.; Busch, C.; Taubenböck, H.; Pelz, P.F.
A Method for Modeling Urban Water Infrastructures Combining Geo-Referenced Data. *Water* **2021**, *13*, 2299.
https://doi.org/10.3390/w13162299

**AMA Style**

Rehm I-S, Friesen J, Pouls K, Busch C, Taubenböck H, Pelz PF.
A Method for Modeling Urban Water Infrastructures Combining Geo-Referenced Data. *Water*. 2021; 13(16):2299.
https://doi.org/10.3390/w13162299

**Chicago/Turabian Style**

Rehm, Imke-Sophie, John Friesen, Kevin Pouls, Christoph Busch, Hannes Taubenböck, and Peter F. Pelz.
2021. "A Method for Modeling Urban Water Infrastructures Combining Geo-Referenced Data" *Water* 13, no. 16: 2299.
https://doi.org/10.3390/w13162299