Hydrological modelling of green urban drainage systems : Advancing the understanding and management of uncertainties in data, model structure and objective functions

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DOCTORA L T H E S I S

Ico Br

oekhuizen Hydr

olo

gical modelling of g

reen urban drainage systems

Department of Civil, Environmental and Natural Resources Engineering Division of Architecture and Water

ISSN 1402-1544

ISBN 978-91-7790-758-9 (print) ISBN 978-91-7790-759-6 (pdf) Luleå University of Technology 2021

Hydrological modelling of

green urban drainage systems

Advancing the understanding and management of

uncertainties in data, model structure and

objective functions

Ico Broekhuizen

Urban Water Engineering

134917 LTU_Broekhuizen.indd Alla sidor

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Hydrological modelling of

green urban drainage systems

Advancing the understanding and management of

uncertainties in data, model structure and

objective functions

Ico Broekhuizen Luleå, 2021

Urban Water Engineering Division of Architecture and Water

Department of Civil, Environmental and Natural Resources Engineering Luleå University of Technology

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ISSN: 1402-1544

ISBN: 978-91-7790-758-9 (print) ISBN: 978-91-7790-759-6 (electronic) Luleå 2021

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Preface

This doctoral dissertation presents the results of my work during the past five years in the Urban Water Engineering research group at Luleå University of Technology. The work was carried out as part of the research cluster Stormwater & Sewers, a collaboration between the Urban Water Engineering research group at LTU, the municipalities of Luleå, Skellefteå, Östersund and Boden, the municipal organizations Vakin, MittSverige Vatten & Avfall and VA Syd, and the Swedish Water and Wastewater Association. The work was financed by Formas (grant numbers 2015-121 and 2015-778) and by Vinnova as part of the DRIZZLE Centre for Stormwater management (grant number 2016-05176) and GreenNano (grant number 2018-00441).

First and foremost I would like to express my great gratitude to Günther and Maria for all their supervision, support, feedback, encouragement and the fruitful discussions during the past five years, and to Anna-Maria for her help in getting started on my PhD studies during my first half year of working at LTU. In addition, I had the pleasure of working together with several other experienced researchers on some of the papers, and I would like to thank Tone, Jiri, Santiago and Jean-Luc for their valuable contributions to the respective studies and papers. I would also like to thank Maria Roldin for her help with Mike SHE and Kelsey and Fredrik for their help with the abstract of the dissertation. Field measurements formed an important input to the modelling work in this disseration, and I would therefore like to send a big thank you to my colleagues from the Urban Water Engineering group for their help in the various field sites. In particular, I want to expres my gratitude to the people that initiated and maintained the measurement campaigns before me: to Helen, Karolina and Kerstin for their work on the pilot catchment in Porsön; to Hendrik for his extensive work on the test site in Solbacken; to Ralf for his work on both those sites; and to Anna, Joel and Peter for their work on the green roof in Umeå. The support and information from Luleå kommun and Akademiska Hus for the Porsön catchment, from Skellefteå kommun for the Solbacken site, and from Vakin for the green roof in Umeå are all gratefully acknowledged. My gratitude also goes out to the Fluid Mechanics research group at LTU for using their lab and Henrik Lycksam for his help with my work there. I want to thank Snežana for her help in the Porsön catchment and the fluid mechanics lab.

During my work on this dissertation I made extensive use of free and open source software, and I would like to thank all authors of and contributors to Python, Jupyter, Matplotlib, Numpy, Pandas, Pathos, SciPy, Seaborn, SPOTpy, Swmmtoolbox, Phydrus, and PyDREAM.

Finally I would like to thank all those who helped me to relax as well: my friends and family for being there, my colleagues for being fun to work with, and my teammates/opponents from Luleå Foreign Hockey Legion and StiL Fencing for all the fun I had training and practicing!

Ico Broekhuizen Luleå, March 2021

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Abstract

The use of green urban drainage systems such as green roofs, swales and pervious areas has, in recent years, become a popular option to reduce flood risk and water quality problems in a more sustainable way than with traditional pipe-based drainage systems. Computer models are valuable tools for the analysis and design of such systems. While uncertainties associated with these models have been investigated for pipe-based systems, their adaptation and application to green urban drainage systems requires re-examination of these uncertainties, as additional hydrological processes become relevant and new opportunities for model calibration arise. The overall aim of this dissertation is to contribute to improved understanding and reduction of uncertainties in the mathematical modelling of green urban drainage systems. Specific topics adressed are field measurements, data processing, data selection, model structures and objective functions. Weighing-bucket precipitation sensors were found to be accurate to within ±1% of accumulated precipitation. A new signal processing method was able to convert accumulated precipitation to noise-free 1-minute rainfall rates that reproduced total rainfall volumes with only minor errors. An area-velocity flow sensor was tested and its measurement uncertainty quantified in laboratory experiments for flow rates up to 9 L s-1_{. Flow rate uncertainty increased with increasing pipe}

slopes. In the presence of an upstream obstacle the uncertainty was two to three times larger, although this could be avoided if water levels in the pipe were increased.

Three different urban drainage models for green areas were compared using long-term simulations of synthetic catchments with different soil types and depths. In all models, surface runoff formed a significant component of the annual water balance for some soil profiles, while the models reacted differently to changes in soil type and depth. Inter-model variation was large compared to the variation between different soil profiles.

Four different models were tested for the simulation of runoff from two full-scale green roofs. More complex models showed better performance in reproducing observed runoff. The magnitude and sources of uncertainty in model predictions varied between the models. For all models, calibration periods with high inter-event variability in terms of rainfall retention provided more information in the calibration process.

The use of soil water content (SWC) observations in addition to flow measurements was investigated for the calibration of a detailed model of an urban swale. SWC observations were found to be useful for better identifying of certain model parameters, improving the model predictions, and for setting the initial SWC in simulations.

Calibration data selection was investigated using a model of a small green urban catchment. Model performance varied significantly when calibrated using different sets of events. Two-stage calibration strategies (using small rainfall events to calibrate impervious area parameters, before calibrating green area parameters using larger events) showed good performance, especially for runoff volume and peak flow. The benefits of the two-stage calibration were greater for a model with a lower spatial resolution.

For the same catchment an objective function was tested that explicitly allows for timing errors, rather than comparing simulations and observations for the same time step. Model predictions generated this way were equally reliable, but more precise and therefore of more practical value. Finally, drawing upon the practical experience from working with different models and drainage systems, the applicability of the techniques used in this dissertation to existing urban drainage models were overviewed.

Overall, this dissertation contributes to a better understanding of uncertainties in hydrological models for green urban drainage systems and provides methods for reducing these uncertainties, thereby improving the models' usefulness in practical and scientific applications.

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Sammanfattning

Gröna dagvattensystem såsom svackdiken, gröna tak och gröna ytor har blivit ett populärt alternativ för att minska risken för översvämning och förbättra vattenkvalitet på ett mer hållbart sätt än med ledningsbaserade lösningar. Matematiska modeller är värdefulla verktyg för analys och dimensionering av dagvattensystem. Osäkerheterna förknippade med modellerna är sedan tidigare kända för ledningsbaserade lösningar, men deras tillämpning på gröna dagvattensystem kräver nya undersökningar, eftersom ytterligare hydrologiska processer blir relevanta och nya möjligheter för modellkalibrering finns. Huvudsyftet med denna avhandling är att bidra till en förbättrad förståelse samt minskning av osäkerheter i matematiska modeller av gröna dagvattensystem. Avhandlingens delstudier fokuserar på fältmätningar, databearbetning, dataurval, modellers matematiska struktur, och målfunktioner i kalibreringen.

Vägande nederbördsmätare bekräftades vara tillräckligt noggrann (inom ±1% felmarginal) för att mäta ackumulerad nederbörd. En nyutvecklad metod kan konvertera ackumulerad nederbörd till brusfria 1-minutsvärden, utan skillnad för den totala uppmätta nederbördsmängden.

En area/hastighet flödessensor testades i labbet och mätosäkerheten kvantifierades för flöden upp till 9 L s-1_{. Mätosäkerheten blev större när lutningen på ledningen ökades. När ett uppströms}

hinder störde flödet blev mätosäkerheten två till tre gånger större, men denna effekt kunde undvikas om vattennivån i ledningen höjdes.

Tre olika dagvattenmodeller för gröna områden jämfördes genom långtidssimuleringar av syntetiska avrinningsområden med olika jordtyper och markdjup. Ytavrinning var en viktig del av vattenbalansen hos vissa jordtyper i alla tre modeller, och modellerna reagerade olika vid ändringar i jordtyp och markdjup. Variationer mellan modellerna var stora jämfört med skillnaderna mellan olika jordprofiler.

Fyra olika modeller testades för simulering av avrinning från två fullskaliga gröna tak. Mer komplexa modeller gav bättre simuleringar av avrinningen. Storleken på och källor av osäkerhet i modellens resultat varierade mellan modellerna. För alla modeller visade det sig att kalibreringsperioder, med stor variation i andelen avrinning mellan olika regntillfällen, gav mer information om lämpliga parametervärden.

Som komplement till flödesmätningar undersöktes jordfuktighetsmätningar för kalibrering av en detaljerad modell för ett svackdike. Jordfuktighet var värdefullt för att förbättra identifierbarheten av lämpliga värden för vissa modellparametrar samt tillförlitligheten av simuleringarna, och för att bestämma initiala förhållanden i modellkörningar.

Urval av kalibreringsdata undersöktes för att modellera avrinning från ett mindre urbant avrinningsområde. Modellens prestanda påverkades kraftigt beroende på vilka kalibreringstillfällen valdes ur. Två-stegskalibrering (där först mindre regntillfällen används för att kalibrera parametrar för hårdgjorda ytor, och sen större regntillfällen för gröna ytor) visade bra prestanda, i synnerhet för avrinningsvolym och maxflöde. Dessa effekter var större när en lägre modellupplösning användes.

För samma avrinningsområde testades en målfunktion som tar explicit hänsyn till temporala fel, istället för att jämföra simulerat och observerat flöde vid samma tidspunkt. Flödesprognoser utifrån målfunktionen var lika pålitliga, men mer precisa och därför mer värdefullt i praktiken. Till slut så användes praktisk erfarenhet av flera modeller och studier för att sammanfatta vilka modelleringsmetoder kan tillämpas i kombination med vilka modeller och hur detta kan förbättras.

Sammanfattningsvis ger denna avhandlingen bättre förståelse och metoder för hantering av osäkerheter i modeller av gröna dagvattensystem, som därmed blir mer värdefulla i vetenskapliga och praktiska sammanhang.

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List of papers

Paper I Paper II Paper III Paper IV Paper V Paper VI

Broekhuizen, I., Muthanna, T.M., Leonhardt, G., Viklander, M. (2019). Urban drainage models for green areas: Structural differences and their effects on simulated runoff. Journal of Hydrology X, 5, 100044. doi.org/10.1016/j.hydroa.2019.100044

Broekhuizen, I., Rujner, H., Leonhardt, G., Roldin, M., Viklander, M. Improving hydrological modelling of urban drainage swales through use of soil water content observations. Submitted to Urban Water Journal. Broekhuizen, I., Leonhardt, G., Marsalek, J., Viklander, M. (2020). Event selection and two-stage approach for calibrating models of green urban drainage systems. Hydrology and Earth System Sciences, 24, 869-885. doi.org/10.5194/hess-24-869-2020

Broekhuizen, I., Leonhardt, G., Viklander, M. Reducing uncertainties in urban drainage models by explicitly accounting for timing errors in objective functions. Resubmitted following minor revisions to Urban Water Journal.

Broekhuizen, I., Sandoval, S., Gao, H., Mendez-Rios, F., Leonhardt, G., Bertrand-Krajewski, J.L., Viklander, M. Performance comparison of green roof hydrological models for full-scale field sites. Submitted to Journal of Hydrology X.

Broekhuizen, I., Leonhardt, G., Viklander, M. (2020) Adapting weighing‐ bucket rainfall observations to urban applications. Presented at ICUD 2020 Young Researcher Webinar Series.

Other publications

Broekhuizen, I., Muthanna, T.M., Leonhardt, G., Viklander, M. (2019). Data for: Urban drainage models for green areas: structural differences and their effects on simulated runoff, [Data set]. Mendeley Data, V1, doi.org/10.17632/bw27b93ccp.1

PyHMA (v. 1.1). [Software]. Zenodo. Broekhuizen, I. (2020).

doi.org/10.5281/zenodo.3923792

Broekhuizen, I., Leonhardt, G., & Viklander, M. (2020). Rainfall-runoff data from an urban catchment in Luleå, Sweden. (Version v1.0.0) [Data set]. Zenodo. doi.org/10.5281/zenodo.3931582

Broekhuizen, I., Leonhardt, G., Viklander, M. (2020). Supporting data for "Reducing uncertainties in urban drainage models by explicitly accounting for timing errors in objective functions" (Version v1.0.0) [Data set]. Zenodo. doi.org/10.5281/zenodo.3925024

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Assessment of contribution to the papers

Paper Development

of idea Research study design Data collection Data processing and analysis Data interpretation Publication process Manuscript preparation for submission Responding to reviewers I Shared responsibility Shared responsibility Responsible Shared responsibility Shared responsibility Shared responsibility Shared responsibility II Shared _{responsibility} Responsible Responsible Responsible Responsible Shared _{responsibility} NA III Shared _{responsibility} Shared _{responsibility} Responsible Responsible Shared _{responsibility} Shared _{responsibility} Shared _{responsibility} IV Responsible Shared _{responsibility} Responsible Responsible Responsible Shared _{responsibility} Responsible V Shared responsibility Shared responsibility Shared responsibility Responsible Shared responsibility Shared responsibility NA VI Responsible Responsible Responsible Responsible Responsible Responsible NA Responsible – developed, consulted (where needed) and implemented a plan for completion of the task.

Shared responsibility – made essential contributions towards the task completion in collaboration with other members in the research team

Contributed – worked on some aspects of the task completion

No contribution – for valid reason, has not contributed to completing the task (e.g. joining the research project after the task completion)

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1. Introduction

Urban areas around the world require systems for managing stormwater to avoid damages to people, properties and the environment. Traditionally accomplished using pipe-based drainage systems, recent decades have seen a shift towards more natural and green solutions. Green urban drainage systems aim to locally retain, infiltrate and evaporate stormwater, thereby mitigating some of the problems associated with pipe-based drainage systems in terms of both water quantity (limited capacity, moving flooding problems downstream, alteration of the natural water balance) and water quality (unmitigated discharge of pollutants into receiving waters) (e.g. Fletcher et al., 2013; Eckart et al., 2017). Additional benefits of green infrastructure may include lower costs (e.g. by reducing the need for excavation) and improving the living climate of urban areas (e.g. Ashley et al., 2018).

Resource-efficient planning and maintenance of drainage systems requires estimates of the drainage systems performance, which are usually made using mathematical models (e.g. Elliott and Trowsdale, 2007; Salvadore et al., 2015). These models can be used to investigate whether drainage systems will provide sufficient capacity for expected future rainfalls or to accommodate potential changes in the drainage system’s design. For any model, it is unavoidable that the results contain some uncertainties. Reasons for this include (among others) that measurements describing the system behaviour (e.g. precipitation or outflow) will contain errors while some aspects cannot be measured at all, that models use relatively simple mathematical equations to describe complex physical systems, and that models can be calibrated for specific study sites in different ways (e.g. Deletic et al., 2012). To contribute to the practical application of models, these uncertainties need to be understood and where possible, reduced.

Various urban drainage models have been developed in the past decades, focused initially on impermeable surfaces and pipe-based networks. More recently, models have been extended or developed for green urban drainage systems, such as green roofs, swales and green areas (e.g. Elliott and Trowsdale, 2007). This shift from simulating mainly fast runoff and collection processes towards slower in-soil processes (Fletcher et al., 2013; Salvadore et al., 2015) means that previous research findings regarding uncertainties in urban drainage modelling may no longer apply and new investigations are necessary. In addition, it needs to be investigated whether the greener nature of urban drainage systems opens up new possibilities in the modelling process.

1.1. Aim & objectives

The overall aim of this doctoral dissertation is to contribute to understanding and reducing uncertainties in the mathematical modelling of green urban drainage systems. The specific objectives of this dissertation address different sources of uncertainty in urban drainage modelling:

1. To evaluate and improve the applicability and measurement uncertainty of (a) precipitation and (b) flow sensors used for urban drainage modelling studies.

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2. To provide insight into the effects of (a) different model structures and (b) different model resolutions on urban drainage modelling studies.

3. To investigate improvements to the selection of calibration data for urban drainage models, considering (a) potential additional sources of information for model calibration and (b) different ways of utilising existing flow data.

4. To propose and evaluate calibration objective functions that (a) combine different types of data in different ways and (b) explicitly consider timing errors.

The objectives are examined over different scales, ranging from single sensor installations via single facilities (swales and green roofs) to a small urban catchment.

1.2. Structure of the doctoral dissertation

This dissertation presents the results from five papers in scientific journals (two already published, one resubmitted following minor revisions, two submitted) and one conference contribution (presented) that are summarized in the main text and provided in full at the end of the dissertation, as well as some original results not published in the papers. The relationships between the papers and the source(s) of uncertainty in the hydrological modelling of green urban drainage systems that they address are visualised in Figure 1.1.

Figure 1.1: Overview of the papers (and sections of the dissertation presenting new results) and which sources of uncertainty in modelling they address. Dashed lines indicate that a source of uncertainty is discussed in a paper, despite not being the primary aim. The numbering of the sources of uncertainty (1-10) corresponds to the sections in Chapter 2 where the scientific state-of-the-art is described.

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1.2 Structure of the doctoral dissertation 3

First, chapter 2 describes the scientific state-of-the-art regarding uncertainties that may be encountered in urban drainage modelling studies. Chapter 3 presents the methods used in the dissertation with Chapter 4 presenting in full those results that are not reported elsewhere and the main results from the six papers. Finally, Chapter 5 discusses the findings of this dissertation and the conclusions are summarised in Chapter 6. The scientific journal articles and the conference paper are provided as the final part of the dissertation.

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2. Background

To avoid damage to property and injury to people, stormwater needs to be removed from urban areas. The common approach during the last decades has been to use underground pipe networks to collect and remove the water. Downsides of this approach are that it can lead to high flow rates and move flooding problems, rather than solve them, and that it can have negative effects on the quality of the receiving water – since pollutants from building and road surfaces are transported without treatment (e.g. Burns et al., 2012; Fletcher et al., 2013).

One approach to resolving these issues is the use of green infrastructure for stormwater management. Facilities such as drainage swales, grass areas and green roofs allow water to infiltrate into the soil and delay the conveyance of excess water (see Hopkins et al., 2020 for recent experimental data), thus contributing to reducing flooding while also allowing for some removal of pollutants. Additional recognised benefits of green urban drainage infrastructure include reducing the urban heat island effect, contributing to biodiversity, and improving air quality and health in urban environments (Gill et al., 2007; Ashley et al., 2018).

The computer models that are commonly used to analyse and predict the performance of urban drainage systems (and how they will be affected by changes or new developments) need to be updated to facilitate green drainage infrastructure. In traditional urban drainage models, runoff from impervious surfaces and processes in the collection network are the driving factors behind system behaviour. As green drainage infrastructure becomes more common, models need to describe additional processes: infiltration into the soil, variations in infiltration capacity, evapotranspiration, and percolation to deeper soil layers. The additional processes and associated longer time scales (Salvadore et al., 2015) mean that previous research findings from impervious-focused models may no longer apply, while they may also create new possibilities to improve modelling practice.

One important aspect to consider when using computer models is the

inherent uncertainties that arise from i.a. measurement uncertainties, imperfect representations of real-life systems, and different calibration approaches (e.g. Butts et al., 2004; Wagener and Gupta, 2005; Deletic et al., 2012). Understanding and estimating the magnitudes of uncertainties is critical if models are to be used in an effective way and to improve our understanding of the urban drainage systems we try to model (e.g. Pappenberger and Beven, 2006; Reichert, 2012; Juston et al., 2013). The aim of this chapter is therefore to describe the scientific state-of-the-art regarding the uncertainties that may be encountered in a modelling process (§§2.1-2.10) before summarising relevant literature on hydrological modelling of swales and green roofs, two specific types of green infrastructure addressed in this dissertation (§§2.11-2.12).

2.1. Precipitation measurements

Precipitation data is the most important input for urban drainage models and many researchers have investigated the uncertainties of the associated measurements.

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Precipitation measurements are usually made using gauging stations on the ground. A common source of error for all types of gauge is that up to 23% of the rainfall may be missed (McMillan et al., 2012; Pollock et al., 2018), with wind-related undercatch reported at 4-5% for liquid precipitation (Duchon and Essenberg, 2001) and almost 40% for snow (Boudala et al., 2017). The performance of individual gauges depends strongly on the type and model: rainfall estimates from co-located gauges can differ by more than 20% (Lanza and Stagi, 2009; Liu et al., 2013).

Different types of errors are associated with different types of precipitation sensors. Tipping bucket sensors require a funnel which can lead to wetting losses of 0.14 mm (Yang et al., 1999). Up to 8.4% of the precipitation may be missed because it takes some time for the bucket to tip from one side to the other (Liao et al., 2020). For weighing bucket gauges the main error sources are diurnal variations in the measured weight, evapotranspiration, and conversion of the noisy continuous signal to useable values of (accumulated) rainfall at the required time step (Pan et al., 2016; Smith et al., 2019; Ross et al., 2020). This issue has not been researched extensively, especially for the small time steps that are required for modelling rainfall-runoff in small urban drainage systems. A benefit of weighing bucket gauges is that they preserve the accumulated precipitation so that their performance can be tested in situ by adding known weights (e.g. Duchon, 2002), but results of such evaluations are rarely reported.

One important aspect specific to urban hydrological studies is the high spatial and temporal resolution that is required (Schilling, 1991; Berne et al., 2004; Ochoa-Rodriguez et al., 2015). The spatial variation becomes larger for heavier rainfall events and assuming uniform rainfall over catchments can lead to deviations in rainfall estimation

of up to 125% for a 125 km2_{urban area (Maier et al., 2020).}

In practice, it is not always feasible to operate the required dense gauge network, so alternative approaches have been investigated. The most common are the use of rainfall radars and commercial microwave links. National meteorological institutes often provide radar rainfall data for their territories that can be used for urban hydrological applications (e.g. Rico-Ramirez et al., 2015; Thorndahl et al., 2017). Radar rainfall data can be merged with gauge data to improve its accuracy (see Ochoa‐Rodriguez et al., 2019 for a review). Cell-phone towers communicate with each other through microwave links, whose signal strength can be measured and the attenuation related to the amount of water (i.e. rainfall) between the two towers, thereby providing rainfall estimates between each pair of communicating towers (e.g. Leijnse et al., 2007; Overeem et al., 2013). The associated measurement uncertainties were described by e.g. Zinevich et al. (2010) and Rios Gaona et al. (2015) while Pastorek et al. (2019) specifically investigated the effects of different configurations of microwave links on runoff simulations.

2.2. Catchment delineation and discretisation

Before a model of a specific study site can be created, data needs to be collected that allows the identification of the catchment area and to (if necessary) divide the whole catchment into smaller subcatchments or to setup a computational model grid. Automated approaches to (sub)catchment delineation using Geographical Information

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2.3 Mathematical model structure 7

Systems (GIS) exist, but errors in total catchment areas of up to 25% have been reported so field investigations may be required (Jankowfsky et al., 2013). However, it has also been shown that using additional geographic information to produce a more detailed model setup can improve model performance (Krebs et al., 2014), up to some point where additional data no longer improves the results (Petrucci and Bonhomme, 2014); it also requires that information about e.g. the location of drainage inlets is sufficiently detailed (Pina et al., 2016). It has been reported that low-resolution setups with subcatchments aggregated from high-resolution setups tend to lead to lower peak flow rates (Tscheikner-Gratl et al., 2016; Chang et al., 2019), although this may be reversed for small rainfall events (Hou et al., 2018). High-resolution models are also facilitated by ongoing developments in methods for collecting data on urban catchments (e.g. Tokarczyk et al., 2015; Leitão et al., 2016) and the development of automated model setup tools (e.g. Dongquan et al., 2009; Warsta et al., 2017). The increase in computational time caused by the larger number of computational elements may be reduced by automatically merging stormwater control measures or subcatchments with homogenous properties (e.g. Elliott et al., 2009; Niemi et al., 2019).

While some models (e.g. SWMM (§3.4.1), Mike URBAN (§3.4.2)) allow user-defined subcatchments of mixed sizes and shapes, other models (e.g. Mike SHE (§3.4.3)) use a (regular) computational grid where each grid cell is a certain size. The grid size and the resolution of data used to populate the model parameters (e.g. elevation) in each cell have been shown to affect the results of modelling studies for natural catchments (Vázquez et al., 2002; Vázquez and Feyen, 2007): smaller grid sizes may be desirable because they allow for a more detailed representation of the variation of physical characteristics and model parameters (e.g. elevation), however model runtimes will typically be longer than for larger grid sizes. Such detailed models have so far seen little application in urban drainage modelling (see Zölch et al., 2017 for an example) and so little research has been done on these grid size effects, with the exception of surface flood modelling (e.g. Fewtrell et al., 2011; Rafieeinasab et al., 2015; Cao et al., 2020). Nonetheless, the size of green features of urban drainage systems such as swales often necessitates a fine model resolution to accurately represent their geometry (e.g. Rujner et al., 2018b).

2.3. Mathematical model structure

The previous section already touched upon some differences between different models that can be used for urban drainage studies. Different models differ not only in terms of spatial resolution, but also in how they conceptualise water fluxes (on surfaces, in the soil, and in pipes) and in what equations are used to describe these. For both natural catchments (e.g. Kaleris and Langousis, 2016; Koch et al., 2016) and urbanized catchments (Nayeb Yazdi et al., 2019) it has been shown that different models can produce similar outflow rates while results for other components of the mass balance diverge. Model structures for flow over impervious surfaces and in storm sewer pipes are relatively simple and well-established, but this is not the case for slower in-soil processes. Including these processes is important since permeable areas can (in wet conditions) contribute runoff (Davidsen et al., 2018) with up to 60% of the precipitation (Skaugen et al., 2020) while simulated evapotranspiration has been shown to reach 18% of rainfall

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even in Nordic climate (Hailegeorgis and Alfredsen, 2018). The effects of including groundwater levels when estimating mitigation of combined sewer overflows (CSO) by using stormwater infiltration measures were investigated by Roldin et al. (2012), who found that ignoring groundwater constraints led to a CSO reduction of 68% while including groundwater constraints led to a reduction of only 24%.

Model structures for urban drainage models have not received so much attention in urban drainage modelling so far (although Duan et al. (2011) compared some classical infiltration models for lawn soils), but it should not be assumed that current model structures are sufficient in all cases. For example, Sandoval and Bertrand-Krajewski (2019) reported that different (types of) rainfall events resulted in different calibrated parameter values. Fry and Maxwell (2018) showed that a lumped SWMM setup may overestimate the effects of implementing green infrastructure compared to a distributed model setup. For example, studies examining LID submodules in SWMM have come across counterintuitive results for biofilters (Fassman-Beck and Saleh, 2018), many insensitive and potentially superfluous parameters in green roof models (Leimgruber et al., 2018a) and non-transferability of parameters between green roofs of identical structure (Johannessen et al., 2019). In stormwater quality modelling, buildup-washoff models gave good results in some studies (e.g. Muschalla et al., 2008), but several studies have also questioned their validity (Bonhomme and Petrucci, 2017; Sandoval et al., 2018). As complexity in models increases, the model runtime tends to increase as well, which can become prohibitive when many thousands of model runs are made during calibration (§2.8). Several authors have proposed faster models for e.g. optimizing green infrastructure placement in catchments (e.g. Haghighatafshar et al., 2019) or for simulating infiltration in urban drainage systems (Sage et al., 2020). Another avenue of research is the use of emulators, surrogate models or meta-models, where a limited number of full runs is used to establish a simple, fast function that can estimate the model output for other similar sets of parameter values, so that this function may be used to estimate model parameters at lower computational cost (e.g. Carbajal et al., 2017; Machac et al., 2018; Moreno-Rodenas et al., 2020; Nagel et al., 2020).

2.4. Flow measurements

Once a model has been setup, it is often necessary to calibrate the model so that its results resemble those of the real system, most commonly flow rates measured in the (storm or combined) sewer leaving the area. Uncertainties in these measurements affect the outcome of the calibration. Storm sewer flow rates are commonly measured using area-velocity (AV) sensors. Manufacturers of AV sensors typically specify an accuracy or ±2% for flow velocity and less than that for flow depth, but errors in flow rate frequently exceed 10% with errors as high as 63% reported in laboratory testing (Heiner and Vermeyen, 2012). Estimates of uncertainty for in-sewer measurements have been reported e.g. as ±75% for low flows to ±20% for high flows (Vezzaro et al., 2013). Aguilar et al. (2016) used laboratory experiments to estimate the in-situ uncertainty for one sensor as 13-107% for and for another at as 34-256%. However, these studies used large testing

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2.5 Other types of calibration data 9

the measurements in smaller pipes and lower flow rates that can occur in urban drainage studies. Methods to check or calibrate flow sensors for a specific site include the tracer-dilution method (Lepot et al., 2014), mechanical or acoustic velocity sensors (Oberg and Mueller, 2007) or computational fluid dynamics (CFD; Bonakdari and Zinatizadeh, 2011).

Other types of flow measurement are also used in urban applications. For low flow rates (e.g. from a single green roof or biofilter) tipping buckets can be used as a flow gauge, in which case similar considerations as outlined in §2.1 apply. Weirs and flumes can be an alternative if there is enough space to install them and have recently received attention for their potential in the measurements of small flows from LID devices (Piro et al., 2019). Requiring only a measurement of water level means that contact with the water can be avoided, but the conversion of this level to a flow rate introduces additional uncertainties (Dabrowski and Polak, 2012). It may also be possible to use data from pumping stations to estimate sewer flow rates (Fencl et al., 2019).

2.5. Other types of calibration data

Although flow data is the most commonly used for model calibration, any system state or output for which both measurements and corresponding model state/output are available can be used. The use of additional types of data can be useful since it might provide additional information (for example on certain model parameters) that is not available from outflow measurements alone (Refsgaard, 1997; Feyen et al., 2000; Madsen, 2003; Pokhrel and Gupta, 2011). This issue has not received much attention for urban drainage studies. Thorndahl et al. (2008) showed how different combinations of two flow rate measurements and one CSO overflow duration measurement affected the model results. Montserrat et al. (2017) showed that using the duration of CSOs as calibration objective gives similar results to using a measurement of the CSO volume.

For green urban drainage facilities (e.g. swales) the use of soil water content (SWC) measurements could be an attractive option and this has been done for natural catchments (e.g. Christiaens and Feyen, 2002; Mertens et al., 2004) and urbanising catchments (Easton et al., 2007), but it has not been used to any great extent for urban hydrological studies except for green roof modelling (e.g. Poë et al., 2015; Jahanfar et al., 2018; Brunetti et al., 2020). SWC measurements are particularly attractive in detailed models where it is easy to link the location of measurement points to a single computational element in the model. Results from natural catchments indicate that SWC measurements can reduce biases in SWC predictions without negatively affecting runoff predictions (Koren et al., 2008; Shahrban et al., 2018) or even make calibration possible for a model where outflow alone proved insufficient (Wooldridge et al., 2003). One potential advantage is that SWC observations can help improve the identifiability of certain model parameters (Wooldridge et al., 2003; Thorstensen et al., 2015). Although some studies have used SWC measurements for calibration (e.g. Xiao et al. (2007) for hourly observations of a residential plot), only Brunetti et al. (2020) specifically demonstrated the added value of SWC measurements but only for modelling a lab scale green roof

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module. The question of what benefits might be gained from using SWC observations in the calibration of detailed models of actual urban drainage facilities is still open.

2.6. Calibration event selection

Calibration is ideally performed using data (flow and/or other sources) over a long period of time, as longer datasets with more events are expected to result in calibrated models that are more generally applicable than models calibrated to single events (e.g. Gamerith et al., 2011). Computational requirements may make this impossible, requiring the selection of a shorter time period or set of rainfall-runoff events instead. Different ways of making this selection (e.g. based only on rainfall characteristics, or also considering runoff characteristics) have not been investigated extensively. Tscheikner-Gratl et al. (2016) showed that some events did not lead to a successful model calibration, and that other events lead to calibrated models that were only able to predict up to 60% of the other events. For calibration of CSOs Kleidorfer et al. (2009b) showed that fewer events were needed for successful calibration when selecting long-duration rainfall events instead of high peak intensity rainfall events. Leimgruber et al (2018b) developed a method for selecting rainfall events (based on a multi-objective approach to maximize CSO volume and minimize the length of the simulation period) to use in calibrating a model for predicting CSOs.

Studies of natural catchments have previously reported good results from dividing the calibration into two stages (e.g. Fenicia et al., 2007; Gelleszun et al., 2017), but such strategies have not yet been investigated for urban catchments. For urban areas containing considerable permeable surfaces, the differences in rainfall events could be used to identify which rainfall events are useful for calibrating certain model parameters: since small rainfall events would generate runoff only from impervious areas (e.g. Boyd et al., 1993; Ebrahimian et al., 2018), only model parameters relating to these areas could be calibrated first, before using larger events with more runoff to calibrate green areas. The separation of runoff from impervious areas and green areas further raises the question if the effects of a two-stage calibration strategy would be the same for both high-resolution model setups (where each subcatchment or grid cell is either 100% impervious or 100% green, see §2.2) and for low-resolution setups (with subcatchments containing both types of area).

2.7. Objective functions

Different objective functions (that indicate how well simulated flow rates match observed flow rates) are available (e.g. Bennett et al., 2013; Hauduc et al., 2015) and can lead to different results, yet not much research has been done so far on this subject in urban drainage applications. Barco et al. (2008) showed that using an objective function weighing flow volume and peak flow errors lead to similar results as an objective function that combined flow volume, peak flow, and instantaneous flow rates throughout the event. Zhang and Li (2015) showed that different objective functions were useful for estimating the values of different SWMM parameters and therefore recommended the use of a weighted multi-criteria objective function. Thorndahl et al. (2008) investigated

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2.8 Calibration algorithm 11

different weights assigned to two observation points with sewer flow rates and one with combined sewer overflow duration.

Where objective functions provide empirical performance measures, likelihood functions have a formal mathematical background: a probability distribution is constructed based on the simulated value (and additional parameters describing e.g. the spread of the distribution), so that the likelihood of the observed value as a random sample from that distribution can be calculated. This formal mathematical background makes likelihood functions suitable for use in Bayesian inference (§2.8), if a likelihood function can be defined that matches the observed errors between the simulations and observations. Research has been done on likelihood functions in cases where errors show bias, magnitude increasing with flow rate (i.e. heteroscedasticity) and/or autocorrelation (e.g. Schoups and Vrugt, 2010; Ammann et al., 2019; Moreno-Rodenas et al., 2020), where periods of zero flow are present such as in stormwater drains (Oliveira et al., 2018), and where observations are binary such as in CSO structures (Wani et al., 2017). It has been noted that in urban hydrology it can be challenging to deal with autocorrelation of errors (Métadier and Bertrand-Krajewski, 2012) and non-normality of errors (Dotto et al., 2011, 2013); alternative descriptions of rainfall (Del Giudice et al., 2016) and of the error structure (Del Giudice et al., 2013, 2015) have been proposed to improve this situation. In some cases simulated hydrographs may match the shape of the observed hydrograph well, but with a small shift in time. Most common objective and likelihood functions compare the simulated and observed points for the same time point, and will therefore give a relatively low score to such a simulation, which may not be desirable (depending on the study aims, timing errors may be acceptable) and can influence the calibration process. This was shown by e.g. Barco et al. (2008), who found that adding instantaneous flow rates (in addition to peak flow and volume metrics) did not improve the results of their model calibration, since there were no calibration parameters that affected the timing of the hydrograph to a sufficient extent. Objective functions that focus more on the shape of the hydrograph (similar to what a hydrologist might do) could be an alternative. Two proposals for such functions that have been made are the Hydrograph Matching Algorithm (Ewen, 2011) and the Series Distance concept (Ehret and Zehe, 2011; Seibert et al., 2016). Both of these draw connecting rays between observed and simulated hydrographs, where the length of the rays increases as the model fit is poorer. The effect of using such approaches in the calibration process has however not yet been investigated. It could be especially relevant for urban hydrology, since the small time scales involved mean that relatively small timing errors (e.g. from data logger clock drift, storms reaching the gauge and parts of the catchment at different times, or model deficiencies) will be large relative to the duration of runoff during and following a rainfall event.

2.8. Calibration algorithm

Once an objective or likelihood function is selected, automatic calibration algorithms are usually used to calibrate the model. These can be divided into two groups: optimisation algorithms that try to find the set of parameter values that gives the best objective function

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value, and algorithms that try to estimate how likely different sets of parameter values are (i.e. providing information on how uncertain the estimates are) and that allow for making probabilistic predictions.

Different optimisation algorithms have been proposed over the years that attempt to find the best performing parameter set in a trial and error process where results for earlier parameter sets are used to iteratively refine the search area (e.g. Barco et al., 2008). Some algorithms such as Non-dominated Sorting Genetic Algorithm (NSGA) can be used to perform a multi-objective calibration, i.e. a calibration that attempts to identify the points where it is not possible to improve one of the objective functions without worsening another (e.g. Krebs et al., 2013). Despite the extensive use of optimisation algorithms, there is little guidance as to which algorithm to use for different cases (Houska et al., 2015). Common for all algorithms is that it cannot be assured that they actually find the global optimum rather than a somewhat suboptimal point or a local optimum (see Lee and Kang (2016) and Perin et al. (2020) for examples from urban hydrology).

Approaches like Bayesian inference and the Generalized Likelihood Uncertainty Estimation (GLUE) are able to provide uncertain estimates (probability densities) of how likely different sets of parameter values are and can therefore also be used to generate uncertain predictions of model outputs such as flow. GLUE is an empirically based approach that runs the model for many parameter sets and accepts all the sets for which

the objective or likelihood function1_{exceeds a certain threshold value (Beven and Binley,}

1992). The parameter samples are used to visualise the distributions of parameter values. Advantages of this method are that implementation and parameter sampling are relatively easy and that no information on the simulation-observation error structure is required (e.g. Dotto et al., 2012). The main downside is that the acceptance threshold is arbitrary and the method lacks a formal mathematical basis (e.g. Mantovan and Todini, 2006; Stedinger et al., 2008; Dotto et al., 2012). On the other hand, Bayesian inference does have a formal mathematical basis in Bayes’ rule for conditional probabilities, and as a result it can be proven that parameter probabilities are accurate for the model and data set used. One downside of Bayesian inference is that it may be challenging to find a formal likelihood function which accounts for issues like autocorrelation, bias and heteroscedasticity (§2.7). Using a likelihood function, Bayesian algorithms then usually use an iterative approach to generate parameter samples in such a way that proportionally more samples are taken in regions of high likelihood, so that the samples will be accurate representations of the actual probability of parameter values. Many different algorithms are available and have been used in (urban) hydrological modelling, including classical approaches like Metropolis (Kuczera and Parent, 1998) and more recent developments like DREAM (Vrugt, 2016) or MULTINEST (e.g. Brunetti et al., 2020).

1_{Note that in the literature on GLUE (e.g. Beven and Binley, 1992) the term ‘likelihood function’}

is applied also to mathematically informal measures (e.g. Nash-Sutcliffe). Papers II and IV of this dissertation follow this terminology, but in the dissertation text ‘objective function’ is used when referring to informal measures and ‘likelihood function’ is used only for formal measures.

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2.10 Physical interpretation of parameter values 13

The pros and cons of the informal GLUE method and formal Bayesian methods have been discussed extensively in the literature. It has also been shown that, in practice, both methods can give similar results (Vrugt et al., 2009; Jin et al., 2010; Dotto et al., 2012). It has also been noted that GLUE can be seen as a version of Approximate Bayesian Computation (Nott et al., 2012; Sadegh and Vrugt, 2013; Kavetski et al., 2018), a technique that can be used for Bayesian inference when it is difficult to formulate or sample from a formal likelihood function.

2.9. Parametric and predictive uncertainty

A model calibration using GLUE or a formal Bayesian approach (see §2.8) results in two main outputs: a sample from the posterior parameter distribution and a sample from the model posterior output, i.e. the model outputs corresponding to the parameter sample (for an example of both these methods in an urban hydrological application, see Dotto et al. (2012)). The model outputs form an ensemble of e.g. outflow from the studied system. Both of these distributions can be visualised or summarised using e.g. histograms

or kernel density estimates (more common for parameters) or using percentiles (e.g. 5th

and 95th_{for the central 90% interval) or averages (more common for outflow predictions,}

since these are easier to visualise as a time series). Summary statistics for model predictions have been proposed to describe the uncertainty and accuracy of the predictions (e.g. Jin et al., 2010; Dotto et al., 2012; Evin et al., 2014; McInerney et al., 2017; Ammann et al., 2019). Parametric uncertainty is the degree to which it is possible to identify a narrow interval in which the calibrated value of a parameter falls (e.g. Thyer et al., 2009) while predictive uncertainty refers both to the uncertainty of the model predictions (i.e. the spread of the prediction ensemble) and how accurate they are. This latter aspect can be measured either by the percentage of observations falling within e.g. the 90% central interval (e.g. Jin et al., 2010; Dotto et al., 2012; Vezzaro et al., 2013) or by using the predictive distribution for each observation time point to assess where the observed value would fall on this distribution, and if this (over all observation points) matches the expected statistical distribution (e.g. Evin et al., 2014; McInerney et al., 2017; Ammann et al., 2019).

2.10. Physical interpretation of parameter values

Since model parameters are often the only factor that is adjusted during calibration, the estimated values (whether single values from optimisation or probability distributions from GLUE or a Bayesian calibration) may be affected by errors in other model components. For example, systematic errors in rainfall data may be compensated for by changes in model parameters representing the (impervious) area of a catchment (Kleidorfer et al., 2009a; Dotto et al., 2014). In these cases, it may be more specific to include e.g. a rainfall multiplier as a calibration parameter (Kavetski et al., 2006; Vrugt et al., 2008; McMillan et al., 2011; Sun and Bertrand‐Krajewski, 2013; Datta and Bolisetti, 2016; Fuentes-Andino et al., 2017). Del Giudice et al. (2016) proposed describing the rainfall as a stochastic process in order to infer the true rainfall input during calibration, which can avoid bias in other parameters. Similar effects also exist for errors in calibration flow data (Dotto et al., 2014).

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Some model parameters describe physical aspects of the system (e.g. area) and therefore their values have a direct physical interpretation. When such parameters are calibrated it should be noted that they may no longer reflect just the physical catchment characteristics but could also be compensating for other aspects of model performance. Barco et al. (2008) for example noticed that calibrated imperviousness was larger than expected from land-cover data, and Johannessen et al. (2019) reported that parameters of a green roof model calibrated for one site did not give good performance for roofs with the same construction but in a different location. Although model performance may in the end be unaffected, care should be taken with the physical interpretation of such parameters. It may also be possible to estimate some parameters directly from maps and site visits rather than calibrating them (Krebs et al., 2014; Petrucci and Bonhomme, 2014; Warsta et al., 2017). Kokkonen et al. (2019) showed that some existing land cover data sets can provide an equal model performance to field mapping, but not all datasets are equally suitable. Soil hydraulic properties such as infiltration capacity are another example of a type of data that may be calibrated, measured in the field, or estimated based on soil maps or easily observable properties, but care should be taken that urban soils may be compacted and show different behaviour than natural soils (Gregory et al., 2006; Pitt et al., 2008; Schifman and Shuster, 2019).

2.11. Hydrological modelling of urban drainage swales

Drainage swales are commonly used in urban areas and their representation in models has been studied with dedicated models for single events (e.g. Munoz-Carpena et al., 1999; Deletic and Fletcher, 2006) and for annual time scales (García-Serrana et al., 2018a). The performance of swales for removal of pollutants has been investigated in several studies (see Gavric et al., 2019; Yu et al., 2019 for reviews). Urban drainage models such as Mike URBAN and SWMM include functionality to represent LIDs (Rossman and Huber, 2016a; DHI, 2019) and the green nature of swales also makes them suitable to study with detailed hydrologic models originally developed for natural catchments such as Mike SHE (Helmers and Eisenhauer, 2006; Rujner et al., 2018b). An advantage of such models can be that they allow for a detailed representation of site topography. Helmers and Eisenhauer (2006) found that overland flow was affected significantly by uneven topography (see also García-Serrana et al., 2018b) and to a lesser degree by spatial variation of surface roughness and soil hydraulic properties. Rujner et al. (2018b) found that high-resolution topographic information allowed to accurately reproduce the location of ponding in a swale. Despite the previous work on modelling swales, some avenues have not yet been explored. For example, soil water content (SWC) observations (§2.5) are possible in vegetated swales and could therefore provide useful information in the calibration process (see Christiaens and Feyen, 2002 for an example in a natural catchment). Kanso et al. (2019) presented a 2D-model for road-side filter strips (i.e. for the slope perpendicular to the road), which achieved good performance for SWC sensors further from the road, but worse performance for sensors placed closer to the road. Kanso et al. (2019) did however not consider the combination of SWC and outflow for model calibration or using multiple SWC sensors along the length of the swale to obtain spatially distributed data, which could be useful in regard to the reported high spatial variability

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2.13 Knowledge gaps and links to dissertation objectives 15

of soil properties in swales (Helmers and Eisenhauer, 2006; Ahmed et al., 2015; Rujner et al., 2018a).

2.12. Hydrological modelling of green roofs

Green roofs are one of the drainage facilities that have received the most attention in urban drainage modelling research, with the goal of understanding their functioning and estimating the effects their implementation could have on the catchment scale (e.g. Versini et al., 2015; Palla et al., 2018). Models that have been used for green roofs range from empirical equations (e.g. Villarreal and Bengtsson, 2005; Carson et al., 2013; Fassman-Beck et al., 2013) via simple conceptual models (e.g. Kasmin et al., 2010; Carbone et al., 2014; Locatelli et al., 2014; Vesuviano et al., 2014; Skala et al., 2019) to more complex conceptual models (e.g. She and Pang, 2010; Rossman and Huber, 2016a; Herrera et al., 2018) and mechanistic models using Richards equation (e.g. Avellaneda et al., 2014; Brunetti et al., 2016; Skala et al., 2020). The SWMM green roof module has been used extensively (e.g. Peng and Stovin, 2017), but some authors have found problems with it, such as the insensitivity of certain model parameters (Leimgruber et al., 2018a) and the fact that parameters calibrated for one site did not transfer successfully to other sites with identical roof constructions, suggesting that climatic conditions influence the physical model parameters (Johannessen et al., 2019).

Although many different green roof models are available, only a few studies have compared different models (Palla et al., 2012; Soulis et al., 2017; Brunetti et al., 2020; Xie et al., 2020), but these comparisons have some limitations. Firstly, they often use lab- or pilot-scale roofs (except for Palla et al. 2012), which means that some scale effects may be unaccounted for (Hakimdavar et al., 2014); reliable estimations of green roof effects at catchment scale require that models work for full-scale green roofs. Another common limitation is that often only one roof is studied, which raises the question of to what extent the results are generalisable. Therefore there is a need for a comparison of multiple green roof models across multiple full-scale field roofs, ideally in different climatic conditions, to allow for more general conclusions on the applicability of different models.

2.13. Knowledge gaps and links to dissertation objectives

The knowledge gaps that have been identified in the previous sections can be summarized and linked to the dissertation objectives (§1.1) as follows:

 Weighing bucket precipitation sensors have infrequently been tested in situ and the processing of the continuous signal from such sensors into noise-free values of precipitation intensity has not been investigated fully, especially for the small time steps associated with urban drainage modelling studies (objective 1a).

 Sensors for flow rates in storm drains have mainly been tested for large channels and high flow rates, so additional tests are needed for smaller channels and lower flow rates as are often encountered in urban drainage settings (objective 1b).  The implications of different model structures for green areas have received

limited attention, and model structures for green roofs have rarely been compared for multiple full-scale roofs (objective 2a).

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 Soil water content observations as an additional source of information in the calibration of detailed models of urban drainage facilities have received little attention (objective 3a), except for in green roof modelling.

 Using different characteristics of rainfall-runoff events for selecting calibration events from a longer record have not been investigated extensively for urban drainage modelling (objective 3b).

 It may be possible to use different events to calibrate different model parameters, i.e. using small events to calibrate runoff from impervious areas and larger events to calibrate runoff from green areas (objective 3b). The suitability of such an approach should be considered both for high-resolution model setups that fully separate impervious and green areas and for low-resolution setups that combine both area types in a single catchment (objective 2b).

 Different ways of combining multiple types of data (e.g. outflow and soil water content) have not been compared extensively for urban drainage modelling (objective 4a).

 Explicit consideration of timing errors in objective functions for urban drainage model calibration has not been investigated (objective 4b).

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17

3. Methods

3.1. Field sites

3.1.1. Risvollan, Trondheim

The Risvollan urban hydrological station (Thorolfsson and Brandt, 1996; Trondheim, Norway; Thorolfsson et al., 2003) provided a long-term series of observed precipitation and temperature used in Paper I. Precipitation totals were measured for every 5 minutes, using a heated 0.1 mm tipping bucket. Potential evapotranspiration was estimated by first calculating rates according to the Penman-Monteith equation (Allen et al., 1998) for a nearby meteorological station (MET Norway, 2018). Since these rates only covered part of the precipitation record, they were used to calibrate the Hargreaves equation for temperature data from the Risvollan station (Hargreaves and Samani, 1982; Almorox and Grieser, 2015).

3.1.2. Porsön, Luleå

The Porsön test catchment (Figure 3.1) covers an area of 10.2 ha in Luleå, Sweden, consisting of a residential area and a part of the university campus. 12% of the surface of the catchment is impermeable and connected directly to a separated storm sewer; 25% is impermeable and drains to adjacent green areas, and the remaining 63% is green area. Roadside swales are connected to the storm sewer network at their lowest point. Precipitation was monitored at 1-minute intervals with a weighing bucket gauge (§3.2.1) that was installed 500 m away from the closest catchment boundary and 1000 m from the furthest. Sewer flow was measured at the outflow point from the catchment with an area-velocity sensor (§3.2.2). Measurements were available for individual events in 2013-2015 and nearly continuously from 2016.

Figure 3.1: Aerial overview of the Porsön study catchment (border in red) including the main storm sewers (blue arrow).

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3.1.3. Solbacken, Skellefteå

The pilot site in Solbacken (Figure 3.2) is part of a commercial area near Skellefteå,

Sweden. The site includes a large gravel swale (approx. 2,500 m2_{) that receives runoff}

from an adjacent asphalt car park (approx. 5,000 m2_{). The upstream end of the swale lies}

approx. 27 metres away from and approx. 3 metres lower than the edge of the park. At the downstream end, this is approx. 33 metres and approx. 5 metres respectively. Outflow from the swale was measured using a long-throated V-shaped flume and a pressure transducer (§3.2.2). In addition, seven volumetric soil water content (SWC) sensors (CS616; Campbell Scientific, 2016) were installed along the bottom of the swale. Rainfall was measured both in the centroid of the swale (using a 0.1 mm tipping bucket) and at a separate location 800 metres away using a weighing bucket (§3.2.1). Data is available since 2014, although a loss of power and damaged equipment resulted in some gaps in the data.

Figure 3.2: Left: Aerial view of the pilot swale in Skellefteå. Right: schematic view of the swale and measurement locations.

3.1.4. Ön, Umeå

One of the buildings at the Ön wastewater treatment plant in Umeå, Sweden, was fitted with a green roof during construction in 2014. Runoff from part of the roof (2,469 m² of green roof and 169 m² of flat impervious roof) was measured from late 2017 to November 2020. A 1 L tipping bucket (HyQuest, 2016) was used for flow rates up to 25

L min-1_{and an area-velocity sensor (§3.2.2) for higher flow rates. The roof consists of a}

number of sloped sections (15° to 38°) with dimensions as indicated in Figure 3.3 and substrate depth varying from 42 to 80 mm (60 mm average). In the narrower section of the roof, a drain was installed at either end of the bottom of the section. In the wider sections, drains were installed at ¼ and ¾ of the total width. A 25 mm drainage layer underneath the substrate removes excess water. Rainfall was measured on-site by the treatment plant operator, using a 0.2 mm tipping bucket.

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3.2 Instruments 19

Figure 3.3: Geometry of the green roof in Umeå with dimensions in m. In the model Mike SHE only the indicated part of the roof was simulated.

3.1.5. Convention Centre, Lyon

Part of the roof of the Lyon Convention Centre (France) was equipped with a green roof

during construction in 1995. The flat green roof is 280 m2_{and consists of a 50 mm}

drainage layer and 40 to 140 mm of substrate. Rainfall was measured using a tipping bucket gauge installed on the roof and runoff from the single drain in the roof was measured using an electromagnetic flow meter. Measurements were carried out during a period from September 2012 to August 2013.

3.2. Instruments

3.2.1. Precipitation sensors

In Porsön and Solbacken precipitation was measured using a T200B weighing-bucket rain gauge (Geonor AS, 2015) equipped with a single Alter-type wind shield. Liquid or

solid precipitation falls through a 200 cm2_{opening into a bucket suspended from three}

chains. The bucket has to be emptied regularly, and, during winter, an anti-freeze mixture is added to melt solid precipitation. A thin layer of mineral oil is added to prevent evaporation. One of the chains is fitted with a vibrating-wire load cell. The frequency of the vibrating wire is converted to the accumulated precipitation in the bucket using:

𝑃 𝐴 𝑓 𝑓 𝐵 𝑓 𝑓 3. 1

Where PA is accumulated precipitation in the bucket (cm), f is the observed frequency

(Hz), f0 the frequency when PA = 0, and A (cm Hz-1) and B (cm Hz-2)

manufacturer-provided calibration constants (Geonor AS, 2015). The good field performance of this sensor was confirmed by previous studies (Duchon, 2002; Lanza et al., 2010). Practical advantages of weighing bucket gauges compared to tipping bucket gauges are that they do not have a funnel which might get clogged, that there are no tipping losses, and that they can measure solid precipitation without the need for heating.

The accuracy of the cumulative precipitation measurement was tested several times (in both Porsön and Solbacken) by adding a series of known weights (corresponding to known amounts of precipitation) into the bucket. In May 2016 (for Porsön) the weights were each 1 L of de-ionised water prepared in the laboratory. In June 2016 (Porsön), a

15.4 39.4 9.0 3.9 5.03.4 5.7 3.9 5.0 3.5 5.6 4.0 5.0 3.7 8.1 5.1 Drain North SHE sim. area

Hydrological modelling of green urban drainage systems : Advancing the understanding and management of uncertainties in data, model structure and objective functions

DOCTORA L T H E S I S

Ico Br

oekhuizen Hydr

olo

gical modelling of g

reen urban drainage systems

Hydrological modelling of

green urban drainage systems

Advancing the understanding and management of

uncertainties in data, model structure and

objective functions

Ico Broekhuizen

Urban Water Engineering

Hydrological modelling of

green urban drainage systems

Advancing the understanding and management of

uncertainties in data, model structure and

objective functions

Preface

Abstract

Sammanfattning

Table of Contents

List of papers

1. Introduction

2. Background

3. Methods